{
  "block": 43819675,
  "op": [
    "transfer",
    {
      "amount": "59.299 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6St7ZwLb74WhqNHEdaPwopUoNNuuTb8WTwXqPNvUyEw7MZcYtBHwiz2UpwiEPGqTaWLRGAvhq3g9V8k5DBxBCuVYRzwAaFbWGCEs1F43Zi",
      "to": "quant-finance"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2020-05-30T14:39:33",
  "trx_id": "ad402149ce85a0cc48295af9de8a918cccad76fe",
  "trx_in_block": 14,
  "virtual_op": 0
}

{
  "block": 38498218,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "0.000 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "0.000002 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-11-26T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 38296978,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.402 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-11-19T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 38095815,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.400 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-11-12T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 37894589,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.397 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-11-05T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 37693369,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.395 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-10-29T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 23
}

{
  "block": 37492168,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.393 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-10-22T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 37290974,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.391 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-10-15T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 37089796,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.388 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-10-08T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 36888603,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.386 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-10-01T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 36879674,
  "op": [
    "transfer",
    {
      "amount": "0.001 STEEM",
      "from": "drugwars",
      "memo": "DrugWars Reminder : The Purge is happening today at Midnight UTC. Few hours left before the goverment raid. Read more about the purge here : https://steemit.com/drugwars/@drugwars/drugwars-current-state-economics-purge-v6-and-v7-etc",
      "to": "complexcity"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-30T17:12:48",
  "trx_id": "fdc810a4ec0b9efe069ca93a7597ae1623e66d81",
  "trx_in_block": 23,
  "virtual_op": 0
}

{
  "block": 36687435,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.384 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-24T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 36686172,
  "op": [
    "transfer",
    {
      "amount": "0.001 STEEM",
      "from": "drugwars",
      "memo": "DrugWars - The Purge will happen the 30 September 2019 (at Midnight UTC). Only inactive players will be impacted. Read more about the purge here : https://steemit.com/drugwars/@drugwars/drugwars-current-state-economics-purge-v6-and-v7-etc",
      "to": "complexcity"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-23T23:37:00",
  "trx_id": "485e04ac3aa9a0582b68a5cd5d18107013deeb3d",
  "trx_in_block": 31,
  "virtual_op": 0
}

{
  "block": 36598561,
  "op": [
    "transfer",
    {
      "amount": "0.001 STEEM",
      "from": "dtube",
      "memo": "DTube Coin Round #1 is live! Visit https://token.d.tube for more information",
      "to": "complexcity"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-20T22:27:21",
  "trx_id": "f37e749987e972ae951bbf2ce676725421b20f06",
  "trx_in_block": 34,
  "virtual_op": 0
}

{
  "block": 36486256,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.381 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-17T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 2
}

{
  "block": 36285237,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.379 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-10T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 2
}

{
  "block": 36268230,
  "op": [
    "comment",
    {
      "author": "steemitboard",
      "body": "Congratulations @complexcity! You received a personal award!\n\n<table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@complexcity/birthday1.png</td><td>Happy Birthday! - You are on the Steem blockchain for 1 year!</td></tr></table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@complexcity) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=complexcity)_</sub>\n\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
      "json_metadata": "{\"image\":[\"https://steemitboard.com/img/notify.png\"]}",
      "parent_author": "complexcity",
      "parent_permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "permlink": "steemitboard-notify-complexcity-20190909t102523000z",
      "title": ""
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-09T10:25:24",
  "trx_id": "16e9a1b6f285ecaffc361a6afde3c1ba70e87ab3",
  "trx_in_block": 2,
  "virtual_op": 0
}

{
  "block": 36171929,
  "op": [
    "transfer",
    {
      "amount": "10.753 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc6U2ZEuU392YRsZUkPF2tZ2w41ECFwx7YfznpCfH1DaV6GUa2GTLh3QiUJr1N1Z",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-06T01:51:27",
  "trx_id": "daae6b203196c1915991a90e409ec673649097ef",
  "trx_in_block": 18,
  "virtual_op": 0
}

{
  "block": 36104024,
  "op": [
    "transfer",
    {
      "amount": "0.001 STEEM",
      "from": "dtube",
      "memo": "Final call to claim your DTube account! It takes only 5 minutes. Go now to https://d.tube",
      "to": "complexcity"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-03T16:55:33",
  "trx_id": "e91d2d61b21460ccb927b0bb28055d303803cdfc",
  "trx_in_block": 6,
  "virtual_op": 0
}

{
  "block": 36084749,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.377 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-09-03T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 35904619,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "5.375 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "10655.553887 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-27T00:40:15",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 2
}

{
  "block": 35799712,
  "op": [
    "transfer",
    {
      "amount": "24.445 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc55nFcCdz1ZskvhcNbi34frb1Zxkq7sdJdc4BtonCTLxkdBQw6DCrrjjargww3M",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-23T09:06:42",
  "trx_id": "a18bed37df7344aa89838d204989d362ad2901f0",
  "trx_in_block": 9,
  "virtual_op": 0
}

{
  "block": 35703337,
  "op": [
    "withdraw_vesting",
    {
      "account": "complexcity",
      "vesting_shares": "138522.200533 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-20T00:40:15",
  "trx_id": "929bbb3b60b8f04fbd01a4d4346eafb463d9936c",
  "trx_in_block": 15,
  "virtual_op": 0
}

{
  "block": 35703332,
  "op": [
    "withdraw_vesting",
    {
      "account": "complexcity",
      "vesting_shares": "0.000000 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-20T00:40:00",
  "trx_id": "1b41a57d95494325d87249b4f886b940dbc344c5",
  "trx_in_block": 23,
  "virtual_op": 0
}

{
  "block": 35663876,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "24.445 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "48483.553699 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-18T15:43:48",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 4
}

{
  "block": 35473936,
  "op": [
    "transfer",
    {
      "amount": "24.434 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc2aN1Ad3W9hBqzzVvGU5oFdFLnGbGfVzx7GEimwy8Y1GK7Ecj3josjocBYxLQKJ",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-12T01:10:18",
  "trx_id": "26f93dba0deb77da22455292547703b0095b8a7f",
  "trx_in_block": 5,
  "virtual_op": 0
}

{
  "block": 35462627,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "24.434 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "48483.553699 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-11T15:43:48",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 2
}

{
  "block": 35348375,
  "op": [
    "transfer",
    {
      "amount": "24.424 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc4ju3Tz8XnZvjuTvMqMN8hccBbZpfB29tiZUNNR9hPmYsLKyUVKz9SQd5AepHLX",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-07T16:18:36",
  "trx_id": "4326afc966755aacb1b48cbbdbec2ccbfdc2613b",
  "trx_in_block": 31,
  "virtual_op": 0
}

{
  "block": 35262276,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "24.424 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "48483.553699 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-08-04T15:43:48",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 9
}

{
  "block": 35072019,
  "op": [
    "transfer",
    {
      "amount": "24.413 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc5jfr9ipSwQK93HFzB7UxWdDxv61dHGLtQF16JG8pRBFZv4RLrBukTEHsutG1gf",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-29T00:52:42",
  "trx_id": "03afe045bf018a9f46e9090f2098f220d3652f3f",
  "trx_in_block": 21,
  "virtual_op": 0
}

{
  "block": 35061056,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "24.413 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "48483.553699 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-28T15:43:48",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 9
}

{
  "block": 34870712,
  "op": [
    "transfer",
    {
      "amount": "24.403 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc2Xbuo3s6YQDNEuihaUwJpn8aBMSfsTXc49zGa9wpiTK4ULfrk7etfNyNF7rezr",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-22T00:36:30",
  "trx_id": "261d5180f0e2f67ec27044bb6a3a4eb777b5c6e8",
  "trx_in_block": 9,
  "virtual_op": 0
}

{
  "block": 34860720,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "voter": "sacred-agent",
      "weight": 300
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T16:16:09",
  "trx_id": "f289188cea796902e2d0eb44e2223be5715c3489",
  "trx_in_block": 43,
  "virtual_op": 0
}

{
  "block": 34860543,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "voter": "rycharde",
      "weight": 320
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T16:07:18",
  "trx_id": "eb0a583ae9ba94368a2d1eb154b1934ed7059dd5",
  "trx_in_block": 17,
  "virtual_op": 0
}

{
  "block": 34860507,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "voter": "map10k",
      "weight": 44
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T16:05:30",
  "trx_id": "165bba3f7a18d3a2e4d9634cfeac49cab19d6f76",
  "trx_in_block": 29,
  "virtual_op": 0
}

{
  "block": 34860473,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "voter": "accelerator",
      "weight": 25
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T16:03:48",
  "trx_id": "f3dbc05286ea2db5aee725475ad9061ed2e2dc38",
  "trx_in_block": 18,
  "virtual_op": 0
}

{
  "block": 34860421,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Adaptation And Self-Organizing Systems</center> \n <hr> \n\n### [Co-Contagion Diffusion on Multilayer Networks](http://arxiv.org/abs/1903.06327v3) (1903.06327v3)\n<i>Ho-Chun Herbert Chang, Feng Fu</b>\n\n<h10>2019-03-15</h10>\n> This study examines the interface of three elements during co-contagion diffusion: the \\textbf{synergy} between contagions, the \\textbf{dormancy} rate of each individual contagion, and the \\textbf{multiplex network topology}. Dormancy is defined as a weaker form of \"immunity,\" where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.\n\n### [Critical Behavior at the Onset of Multichimera States in a  Coupled-Oscillator Array](http://arxiv.org/abs/1907.07285v1) (1907.07285v1)\n<i>Katsuya Kawase, Nariya Uchida</b>\n\n<h10>2019-07-16</h10>\n> We numerically investigate the onset of multi-chimera states in a linear array of coupled oscillators. As the phase delay ![](http://latex2png.com/output//latex_879bee8d9bc4848dee78650baeff05fd.png) is increased, they exhibit a continuous transition from the globally synchronized state to the multichimera state consisting of asynchronous and synchronous domains. Large-scale simulations show that the fraction of asynchronous sites ![](http://latex2png.com/output//latex_a0a7c05aba20a4e261bab2c48faa39ce.png) obeys the power law ![](http://latex2png.com/output//latex_565abe2d890b2677d43fe6ccc688a7b5.png), and that the spatio-temporal gaps between asynchronous sites show power-law distributions at the critical point. The critical exponents are distinct from those of the (1+1)-dimensional directed percolation and other absorbing-state phase transitions, indicating that this transition belongs to a new class of non-equilibrium critical phenomena. Crucial roles are played by traveling waves that rejuvenate asynchronous clusters by mediating non-local interactions between them.\n\n### [Hydrodynamic synchronization and collective dynamics of colloidal  particles driven along a circular path](http://arxiv.org/abs/1907.06813v1) (1907.06813v1)\n<i>Takumi Miyamoto, Masayuki Imai, Nariya Uchida</b>\n\n<h10>2019-07-16</h10>\n> We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of N particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For N = 2, the particles attract with each other and synchronize, forming a doublet that moves faster than a singlet. For N = 3 and 5, we find periodic rearrangement of doublets and a singlet. For N = 4 and 6, the system exhibits either a periodic oscillating state or a stable synchronized state depending on the initial conditions. These results reproduce main features of previous experimental findings. We quantitatively discuss the mechanisms governing the non-trivial collective dynamics.\n\n### [High-order couplings in geometric complex networks of neurons](http://arxiv.org/abs/1907.06765v1) (1907.06765v1)\n<i>A. Tlaie, I. Leyva, I. Sendiña</b>\n\n<h10>2019-07-15</h10>\n> We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the travelling wave phenomenon gets enhanced by these interactions, allowing the information to travel further in the system without generating pathological full synchronization states. This scheme could be a step towards a simple modelization of neuroglial networks.\n\n### [A Music-generating System Inspired by the Science of Complex Adaptive  Systems](http://arxiv.org/abs/1610.02475v2) (1610.02475v2)\n<i>Shawn Bell, Liane Gabora</b>\n\n<h10>2016-10-08</h10>\n> This paper presents NetWorks (NW), an interactive music generation system that uses a hierarchically clustered scale free network to generate music that ranges from orderly to chaotic. NW was inspired by the Honing Theory of creativity, according to which human-like creativity hinges on (1) the ability to self-organize and maintain dynamics at the 'edge of chaos' using something akin to 'psychological entropy', and (2) the capacity to shift between analytic and associative processing modes. At the 'edge of chaos', NW generates patterns that exhibit emergent complexity through coherent development at low, mid, and high levels of musical organization, and often suggests goal seeking behaviour. The architecture consists of four 16-node modules: one each for pitch, velocity, duration, and entry delay. The Core allows users to define how nodes are connected, and rules that determine when and how nodes respond to their inputs. The Mapping Layer allows users to map node output values to MIDI data that is routed to software instruments in a digital audio workstation. By shifting between bottom-up and top-down NW shifts between analytic and associative processing modes.\n\n# <center>Chaotic Dynamics</center> \n <hr> \n\n### [Estimating Lyapunov exponents in billiards](http://arxiv.org/abs/1904.05108v2) (1904.05108v2)\n<i>George Datseris, Lukas Hupe, Ragnar Fleischmann</b>\n\n<h10>2019-04-10</h10>\n> Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it.\n\n### [Effects of Stochastic Parametrization on Extreme Value Statistics](http://arxiv.org/abs/1903.05514v2) (1903.05514v2)\n<i>Guannan Hu, Tamás Bódai, Valerio Lucarini</b>\n\n<h10>2019-03-13</h10>\n> Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper we consider a modified version of the two-level Lorenz'96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks (2005) and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Wouters and Lucarini (2012, 2013). The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them.\n\n### [Dynamics of quasiperiodically driven spin systems](http://arxiv.org/abs/1907.07492v1) (1907.07492v1)\n<i>Sayak Ray, Subhasis Sinha, Diptiman Sen</b>\n\n<h10>2019-07-17</h10>\n> We study the stroboscopic dynamics of a spin-![](http://latex2png.com/output//latex_b1ad1296a99a7ee91c1c30beb874e181.png) object subjected to ![](http://latex2png.com/output//latex_f3083e142637eca4cd7d624a8dd68535.png)-function kicking in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed in the large spin limit, ![](http://latex2png.com/output//latex_2a602e70235d26e51b24569347e937f2.png). Upon evolving such a map for large kicking strength and time period, the phase space appears to be chaotic; interestingly, however, the geodesic distance increases linearly with the stroboscopic time implying that the Lyapunov exponent is zero. We derive the Sutherland invariant for the underlying ![](http://latex2png.com/output//latex_b38576c13b62680cb0f80d76299b920a.png) matrix governing the dynamics of classical spin variables and study the orbits for weak kicking strength. For the quantum dynamics, we observe that although the phase coherence of a state is retained throughout the time evolution, the fluctuations in the mean values of the spin operators exhibit fractality which is also present in the Floquet eigenstates. Interestingly, the presence of an interaction with another spin results in an ergodic dynamics leading to infinite temperature thermalization.\n\n### [Averaging Theory for Non-linear Oscillators](http://arxiv.org/abs/1506.07301v2) (1506.07301v2)\n<i>Aritra Sinha</b>\n\n<h10>2015-06-24</h10>\n> I have first discussed how averaging theory can be an effective tool in solving weakly non-linear oscillators. Then I have applied this technique for a Van der Pol oscillator and extended the stability criterion of a Van der Pol oscillator for any integer n(odd or even).\n\n### [Resonance--Assisted Tunneling in Deformed Optical Microdisks with a  Mixed Phase Space](http://arxiv.org/abs/1907.06900v1) (1907.06900v1)\n<i>Felix Fritzsch, Roland Ketzmerick, Arnd Bäcker</b>\n\n<h10>2019-07-16</h10>\n> The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance--assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.\n\n# <center>Cellular Automata And Lattice Gases</center> \n <hr> \n\n### [One-dimensional number-conserving cellular automata](http://arxiv.org/abs/1907.06063v1) (1907.06063v1)\n<i>Markus Redeker</b>\n\n<h10>2019-07-13</h10>\n> This paper contains two methods to construct one-dimensional number-conserving cellular automata in terms of particle flows. One method is a sequence of increasingly stronger restrictions on the particle flow, which always ends with the specification of a number-conserving rule. The other is based on minimal flow functions, from which all others can be constructed. These constructions also provide a classification for number-conserving rules and a way to specify rules as a supremum of minimal flows. Other questions, like that about the nature of non-deterministic number-conserving rules, are treated briefly at the end.\n\n### [Efficient methods to determine the reversibility of general 1D linear  cellular automata in polynomial complexity](http://arxiv.org/abs/1907.06012v1) (1907.06012v1)\n<i>Xinyu Du, Chao Wang, Tianze Wang, Zeyu Gao</b>\n\n<h10>2019-07-13</h10>\n> In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibility in a period. With existing methods, the time and space complexity of these two parts are still too expensive to be employed. So the process soon becomes totally incalculable with a slightly big size, which greatly limits its application. In this paper, we set out to solve these two problems using two efficient algorithms, which make it possible to solve reversible LCA of very large size. Furthermore, we provide an interesting perspective to conversely generate 1D LCA from a given period of reversibility. Due to our methods' efficiency, we can calculate the reversible LCA with large size, which has much potential to enhance security in cryptography system.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Universal One-Dimensional Cellular Automata Derived for Turing Machines  and its Dynamical Behaviour](http://arxiv.org/abs/1907.04211v1) (1907.04211v1)\n<i>Sergio J. Martinez, Ivan M. Mendoza, Genaro J. Martinez, Shigeru Ninagawa</b>\n\n<h10>2019-07-06</h10>\n> Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.\n\n### [Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model](http://arxiv.org/abs/1907.00636v1) (1907.00636v1)\n<i>Jan de Gier, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz</b>\n\n<h10>2019-07-01</h10>\n> Dynamical universality classes are distinguished by their dynamical exponent ![](http://latex2png.com/output//latex_bd61b29a408a64d11f1a55bca65fd0c4.png) and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known except for the special case ![](http://latex2png.com/output//latex_2fdb6000f3667b6e6887c72c14280977.png). Here the model corresponds to the TASEP (totally asymmetric simple exclusion process) that is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with ![](http://latex2png.com/output//latex_612eb39efa60bedf469ce3141e6664ff.png). In this paper, we show that the NaSch model also belongs to the KPZ class \\cite{KPZ} for general maximum velocities ![](http://latex2png.com/output//latex_d470cde12bfb573e851ddd17b54b2b41.png). Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. Performing large-scale Monte-Carlo simulations we show that the simulation results match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with dynamical lane changing rules.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-22",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 1|2019-07-22"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T16:01:12",
  "trx_id": "3f67858fc83bfec1c6618dea7a4a8ddd1f0b5b18",
  "trx_in_block": 19,
  "virtual_op": 0
}

{
  "block": 34860072,
  "op": [
    "fill_vesting_withdraw",
    {
      "deposited": "24.403 STEEM",
      "from_account": "complexcity",
      "to_account": "complexcity",
      "withdrawn": "48483.553699 VESTS"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-21T15:43:48",
  "trx_id": "0000000000000000000000000000000000000000",
  "trx_in_block": 4294967295,
  "virtual_op": 3
}

{
  "block": 34834643,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-21",
      "voter": "filipino",
      "weight": 1000
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-20T18:31:06",
  "trx_id": "59068f9806a3c15293ea5411392ffde2a2925295",
  "trx_in_block": 36,
  "virtual_op": 0
}

{
  "block": 34834114,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-21",
      "voter": "map10k",
      "weight": 44
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-20T18:04:39",
  "trx_id": "25a9f295f226584e0b886b617a0e928ed0759014",
  "trx_in_block": 20,
  "virtual_op": 0
}

{
  "block": 34834087,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-21",
      "voter": "accelerator",
      "weight": 25
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-20T18:03:18",
  "trx_id": "efcdfa182c0405a5183ef96af1e580f6deec4e11",
  "trx_in_block": 1,
  "virtual_op": 0
}

{
  "block": 34834025,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [On a nonlinear model of the localized vacuum hypothesis, for solving the  cosmological constant problem](http://arxiv.org/abs/1907.02781v3) (1907.02781v3)\n<i>Rishat Salimov</b>\n\n<h10>2019-07-05</h10>\n> A new model of oscillators was suggested, in which an oscillating particle in the minimum energy state has a nonzero velocity. A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been considered. It has been shown that, when taking into account relativistic effects, in the case of small rest masses of a particle an energy minimum at zero velocity is impossible for such a particle. It is showed that the behavior of a field in such a system is not stationary and is characterized by the presence of waves emitted and absorbed by the system in the minimum energy state. The system properties having being analyzed, a concept of the local vacuum was suggested; it was showed that the local vacuum hypothesis is useful in solving the cosmological constant problem.\n\n### [Bound state soliton gas dynamics underlying the noise-induced  modulational instability](http://arxiv.org/abs/1907.07914v1) (1907.07914v1)\n<i>Andrey Gelash, Dmitry Agafontsev, Vladimir Zakharov, Gennady El, Stephane Randoux, Pierre Suret</b>\n\n<h10>2019-07-18</h10>\n> We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in experiments and in simulations but have not been explained so far. In the framework of inverse scattering transform (IST), we propose a model of the asymptotic stage of the noise-induced MI based on ![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-soliton solutions (![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-SS) of the integrable focusing one-dimensional nonlinear Schr\\\"odinger equation (1D-NLSE). These ![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-SS are bound states of strongly interacting solitons having a specific distribution of the IST eigenvalues together with random phases. We use a special approach to construct ensembles of multi-soliton solutions with statistically large number of solitons ![](http://latex2png.com/output//latex_ac67e7daeda2c31886e105c9c908a56a.png). Our investigation demonstrates complete agreement in spectral (Fourier) and statistical properties between the long-term evolution of the condensate perturbed by noise and the constructed multi-soliton bound states. Our results can be generalised to a broad class of integrable turbulence problems in the cases when the wave field dynamics is strongly nonlinear and driven by solitons.\n\n### [Angular and radial correlation scaling in stochastic growth  morphodynamics: a unifying fractality framework](http://arxiv.org/abs/1803.03715v2) (1803.03715v2)\n<i>J. R. Nicolás-Carlock, J. M. Solano-Altamirano, J. L. Carrillo-Estrada</b>\n\n<h10>2018-03-09</h10>\n> Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of quantities such as the two-point density radial or angular correlations. However, persistent discrepancies found during the analysis of basic models, using these two quantification methods, demand important clarifications. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial-angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential, that, under the fractal dimension interpretation, resemble first- and second-order transitions, respectively. Remarkably, these and previous results can be unified under a single fractal dimensionality equation.\n\n### [High-order couplings in geometric complex networks of neurons](http://arxiv.org/abs/1907.06765v1) (1907.06765v1)\n<i>A. Tlaie, I. Leyva, I. Sendiña</b>\n\n<h10>2019-07-15</h10>\n> We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the travelling wave phenomenon gets enhanced by these interactions, allowing the information to travel further in the system without generating pathological full synchronization states. This scheme could be a step towards a simple modelization of neuroglial networks.\n\n### [Self-Localized Solitons of the Nonlinear Wave Blocking Problem](http://arxiv.org/abs/1907.03857v2) (1907.03857v2)\n<i>Cihan Bayindir</b>\n\n<h10>2019-07-08</h10>\n> In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\\\"odinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and the applicability of the proposed approach.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [Separation of variables bases for integrable  ![](http://latex2png.com/output//latex_4d5e7eeb393f3ec8cace4b17d024c92e.png) and Hubbard models](http://arxiv.org/abs/1907.08124v1) (1907.08124v1)\n<i>J. M. Maillet, G. Niccoli, L. Vignoli</b>\n\n<h10>2019-07-18</h10>\n> We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous ![](http://latex2png.com/output//latex_4d5e7eeb393f3ec8cace4b17d024c92e.png) supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with quasi-periodic twisted boundary conditions given by twist matrices having simple spectrum. The SoV bases are obtained by using the integrable structure of these quantum models,i.e. the associated commuting transfer matrices, following the general scheme introduced in [1]; namely, they are given by set of states generated by the multiple actions of the transfer matrices on generic co-vectors. The existence of such SoV bases implies that the corresponding transfer matrices have non degenerate spectrum and that they are diagonalizable with simple spectrum if the twist matrices defining the quasi-periodic boundary conditions have that property. Moreover, in these SoV bases the resolution of the transfer matrix eigenvalue problem leads to the resolution of the full spectral problem, i.e. both eigenvalues and eigenvectors. Indeed, to any eigenvalue is associated the unique (up to a trivial overall normalization) eigenvector whose wave-function in the SoV bases is factorized into products of the corresponding transfer matrix eigenvalue computed on the spectrum of the separate variables. As an application, we characterize completely the transfer matrix spectrum in our SoV framework for the fundamental ![](http://latex2png.com/output//latex_4d857c8651331fecf749dea59a3afdc9.png) supersymmetric integrable model associated to a special class of twist matrices. From these results we also prove the completeness of the Bethe Ansatz for that case. The complete solution of the spectral problem for fundamental inhomogeneous ![](http://latex2png.com/output//latex_4d5e7eeb393f3ec8cace4b17d024c92e.png) supersymmetric integrable models and for the inhomogeneous Hubbard model under the general twisted boundary conditions will be addressed in a future publication.\n\n### [A PDE Approach to the Combinatorics of the Full Map Enumeration Problem:  Exact Solutions and their Universal Character](http://arxiv.org/abs/1907.08026v1) (1907.08026v1)\n<i>Nicholas M. Ercolani, Patrick Waters</b>\n\n<h10>2019-07-18</h10>\n> Maps are polygonal cellular networks on Riemann surfaces. This paper completes a program of constructing closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. These closed form expressions have a universal character in the sense that they are independent of the explicit valence distribution of the tiling polygons. Nevertheless the valence distributions may be recovered from the closed form generating functions by a remarkable {\\it unwinding identity} in terms of the Appell polynomials generated by Bessel functions. Our treatment, based on random matrix theory and Riemann-Hilbert problems for orthogonal polynomials reveals the generating functions to be solutions of nonlinear conservation laws and their prolongations. This characterization enables one to gain insights that go beyond more traditional methods that are purely combinatorial. Universality results are connected to stability results for characteristic singularities of conservation laws that were studied by Caflisch, Ercolani, Hou and Landis as well as directly related to universality results for random matrix spectra as described by Deift, Kriecherbauer, McLaughlin, Venakides and Zhou.\n\n### [Bound state soliton gas dynamics underlying the noise-induced  modulational instability](http://arxiv.org/abs/1907.07914v1) (1907.07914v1)\n<i>Andrey Gelash, Dmitry Agafontsev, Vladimir Zakharov, Gennady El, Stephane Randoux, Pierre Suret</b>\n\n<h10>2019-07-18</h10>\n> We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in experiments and in simulations but have not been explained so far. In the framework of inverse scattering transform (IST), we propose a model of the asymptotic stage of the noise-induced MI based on ![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-soliton solutions (![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-SS) of the integrable focusing one-dimensional nonlinear Schr\\\"odinger equation (1D-NLSE). These ![](http://latex2png.com/output//latex_b9e69f0f03051ff98f89be64ae45918f.png)-SS are bound states of strongly interacting solitons having a specific distribution of the IST eigenvalues together with random phases. We use a special approach to construct ensembles of multi-soliton solutions with statistically large number of solitons ![](http://latex2png.com/output//latex_ac67e7daeda2c31886e105c9c908a56a.png). Our investigation demonstrates complete agreement in spectral (Fourier) and statistical properties between the long-term evolution of the condensate perturbed by noise and the constructed multi-soliton bound states. Our results can be generalised to a broad class of integrable turbulence problems in the cases when the wave field dynamics is strongly nonlinear and driven by solitons.\n\n### [Quantum spin chains from Onsager algebras and reflection ![](http://latex2png.com/output//latex_b1fd3f46fd8b093c8c19598c72475dbb.png)-matrices](http://arxiv.org/abs/1907.07881v1) (1907.07881v1)\n<i>Atsuo Kuniba, Vincent Pasquier</b>\n\n<h10>2019-07-18</h10>\n> We present a representation of the generalized ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png)-Onsager algebras ![](http://latex2png.com/output//latex_645507abd91378e810472f0a2c25636c.png), ![](http://latex2png.com/output//latex_edd3833bcc1306910ef00c4f52dd52e0.png), ![](http://latex2png.com/output//latex_1413b4792ac0fa1d70a09cb0f8602cf6.png), ![](http://latex2png.com/output//latex_de46e8a5d0287c3f8ccd104d3332101d.png) and ![](http://latex2png.com/output//latex_e40ffb01ef686648dc0153ba6dd05da8.png) in which the generators are expressed as local Hamiltonians of XXZ type spin chains with various boundary terms reflecting the Dynkin diagrams. Their symmetry is described by the reflection ![](http://latex2png.com/output//latex_b1fd3f46fd8b093c8c19598c72475dbb.png) matrices which are obtained recently by a ![](http://latex2png.com/output//latex_8252603f68bd2a6b7e714e5055bdac3d.png)-boson matrix product construction related to the 3D integrability and characterized by Onsager coideals of quantum affine algebras. The spectral decomposition of the ![](http://latex2png.com/output//latex_b1fd3f46fd8b093c8c19598c72475dbb.png) matrices with respect to the classical part of the Onsager algebra is described conjecturally. We also include a proof of a certain invariance property of boundary vectors in the ![](http://latex2png.com/output//latex_8252603f68bd2a6b7e714e5055bdac3d.png)-boson Fock space playing a key role in the matrix product construction.\n\n### [Collective Heavy Top Dynamics](http://arxiv.org/abs/1907.07819v1) (1907.07819v1)\n<i>Tomoki Ohsawa</b>\n\n<h10>2019-07-18</h10>\n> We construct a Poisson map ![](http://latex2png.com/output//latex_eb1c9bf542dbb83bc9643d6d0c4f2187.png) with respect to the canonical Poisson bracket on ![](http://latex2png.com/output//latex_0f0b1e314aa851324ccfccd2c55475e3.png) and the ![](http://latex2png.com/output//latex_5e16f6926feed8b60753422be0b86a44.png)-Lie--Poisson bracket on the dual ![](http://latex2png.com/output//latex_8cd64aa6d12a35ba4e843e59e5a89725.png) of the Lie algebra of the special Euclidean group ![](http://latex2png.com/output//latex_7cb6f5ad85d9079d8d030a95ae3a23ae.png). The essential part of this map is the momentum map associated with the cotangent lift of the natural right action of the semidirect product Lie group ![](http://latex2png.com/output//latex_b410b7e5d077eaf9e9e3ff3dbc0f0335.png) on ![](http://latex2png.com/output//latex_2ced4dca3817496f261bdd69a970336f.png). This Poisson map gives rise to a canonical Hamiltonian system on ![](http://latex2png.com/output//latex_14956593cc8ae204b5a61a76e58b03a1.png) whose solutions are mapped by ![](http://latex2png.com/output//latex_163c0e3fdedd7722f66d47df43de1ae2.png) to solutions of the heavy top equations. We show that the Casimirs of the heavy top dynamics and the additional conserved quantity of the Lagrange top correspond to the Noether conserved quantities associated with certain symmetries of the canonical Hamiltonian system. We also construct a Lie--Poisson integrator for the heavy top dynamics by combining the Poisson map ![](http://latex2png.com/output//latex_163c0e3fdedd7722f66d47df43de1ae2.png) with a simple symplectic integrator, and demonstrate that the integrator exhibits either exact or near conservation of the conserved quantities of the Kovalevskaya top.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-21",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-21"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-20T18:00:12",
  "trx_id": "22bed967e583e84e106686c09556d2e2049e8a83",
  "trx_in_block": 15,
  "virtual_op": 0
}

{
  "block": 34777145,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-19",
      "voter": "filipino",
      "weight": 1000
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-18T18:31:57",
  "trx_id": "f97397ea2995529b20bb8b31c65e90b721c122e7",
  "trx_in_block": 1,
  "virtual_op": 0
}

{
  "block": 34776577,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-19",
      "voter": "map10k",
      "weight": 46
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-18T18:03:33",
  "trx_id": "150b685d89c71819b360b091a460eb60354e1358",
  "trx_in_block": 16,
  "virtual_op": 0
}

{
  "block": 34776573,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-19",
      "voter": "bert0",
      "weight": 40
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-18T18:03:21",
  "trx_id": "f6ffa16d19404f90caee4fdb5ad41217c5e97b87",
  "trx_in_block": 10,
  "virtual_op": 0
}

{
  "block": 34776562,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-19",
      "voter": "accelerator",
      "weight": 25
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-18T18:02:48",
  "trx_id": "b48e285108fda07c684511674c5f1b50d8cd684d",
  "trx_in_block": 4,
  "virtual_op": 0
}

{
  "block": 34776512,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [Angular and radial correlation scaling in stochastic growth  morphodynamics: a unifying fractality framework](http://arxiv.org/abs/1803.03715v2) (1803.03715v2)\n<i>J. R. Nicolás-Carlock, J. M. Solano-Altamirano, J. L. Carrillo-Estrada</b>\n\n<h10>2018-03-09</h10>\n> Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of quantities such as the two-point density radial or angular correlations. However, persistent discrepancies found during the analysis of basic models, using these two quantification methods, demand important clarifications. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial-angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential, that, under the fractal dimension interpretation, resemble first- and second-order transitions, respectively. Remarkably, these and previous results can be unified under a single fractal dimensionality equation.\n\n### [High-order couplings in geometric complex networks of neurons](http://arxiv.org/abs/1907.06765v1) (1907.06765v1)\n<i>A. Tlaie, I. Leyva, I. Sendiña</b>\n\n<h10>2019-07-15</h10>\n> We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the travelling wave phenomenon gets enhanced by these interactions, allowing the information to travel further in the system without generating pathological full synchronization states. This scheme could be a step towards a simple modelization of neuroglial networks.\n\n### [Self-Localized Solitons of the Nonlinear Wave Blocking Problem](http://arxiv.org/abs/1907.03857v2) (1907.03857v2)\n<i>Cihan Bayindir</b>\n\n<h10>2019-07-08</h10>\n> In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\\\"odinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and the applicability of the proposed approach.\n\n### [Inverse scattering transform for two-level systems with nonzero  background](http://arxiv.org/abs/1907.06231v1) (1907.06231v1)\n<i>Gino Biondini, Ildar Gabitov, Gregor Kovacic, Sitai Li</b>\n\n<h10>2019-07-14</h10>\n> We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background states in general do not exist with a nonzero background field. We then use the formalism to compute explicitly the soliton solutions of this system. We discuss the initial population of atoms and show that the pure soliton solutions do not correspond to a pure state initially. We obtain a representation for the soliton solutions in determinant form, and explicitly write down the one-soliton solutions. We next derive periodic solutions and rational solutions from the one-soliton solutions. We then analyze the properties of these solutions, including discussion of the sharp-line and small-amplitude limits, and thereafter show that the two limits do not commute. Finally, we investigate the behavior of general solutions, showing that solutions are stable (i.e., the radiative parts of solutions decay) only when initially atoms in the ground state dominant, i.e., initial population inversion is negative.\n\n### [Spontaneous and engineered transformations of topological structures in  nonlinear media with gain and loss](http://arxiv.org/abs/1907.06180v1) (1907.06180v1)\n<i>B. A. Kochetov, O. G. Chelpanova, V. R. Tuz, A. I. Yakimenko</b>\n\n<h10>2019-07-14</h10>\n> In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen control carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [![](http://latex2png.com/output//latex_334b668160cbf5e0f4f9675ef2a85e8e.png) sigma models described through hypergeometric  orthogonal polynomials](http://arxiv.org/abs/1905.06351v2) (1905.06351v2)\n<i>N. Crampe, A. M. Grundland</b>\n\n<h10>2019-05-15</h10>\n> The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean ![](http://latex2png.com/output//latex_334b668160cbf5e0f4f9675ef2a85e8e.png) sigma model in two dimensions and the particular hypergeometric orthogonal polynomials called Krawtchouk polynomials. We show that any such projector solutions of the ![](http://latex2png.com/output//latex_334b668160cbf5e0f4f9675ef2a85e8e.png) model, defined on the Riemann sphere and having a finite action, can be explicitly parametrised in terms of these polynomials. We apply these results to the analysis of surfaces associated with ![](http://latex2png.com/output//latex_334b668160cbf5e0f4f9675ef2a85e8e.png) models defined using the generalised Weierstrass formula for immersion. We show that these surfaces are homeomorphic to spheres in the ![](http://latex2png.com/output//latex_2f589869aefa45f9970aba1115fd4007.png) algebra, and express several other geometrical characteristics in terms of the Krawtchouk polynomials. Finally, a connection between the ![](http://latex2png.com/output//latex_c15d0a9b9a4a892c1637570d499fe181.png) spin-s representation and the ![](http://latex2png.com/output//latex_334b668160cbf5e0f4f9675ef2a85e8e.png) model is explored in detail.\n\n### [An Index for Quantum Integrability](http://arxiv.org/abs/1907.07186v1) (1907.07186v1)\n<i>Shota Komatsu, Raghu Mahajan, Shu-Heng Shao</b>\n\n<h10>2019-07-16</h10>\n> The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index ![](http://latex2png.com/output//latex_27d55face22efddef1ccd7a5fd73d6ad.png) for each spin ![](http://latex2png.com/output//latex_2bf16ffdd8f00c6a451d8259ebcc64a4.png), with the property that ![](http://latex2png.com/output//latex_27d55face22efddef1ccd7a5fd73d6ad.png) is a lower bound on the number of quantum conserved currents of spin ![](http://latex2png.com/output//latex_2bf16ffdd8f00c6a451d8259ebcc64a4.png). In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the ![](http://latex2png.com/output//latex_d60a019c50627205b3fb926a556b9f66.png) model, the ![](http://latex2png.com/output//latex_15bd9ef3ae66ff8f168f11207184e383.png) model, and the flag sigma model ![](http://latex2png.com/output//latex_b0b0c0892cc162afcd3da8f0ad0d1377.png). For the ![](http://latex2png.com/output//latex_15bd9ef3ae66ff8f168f11207184e383.png) model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the ![](http://latex2png.com/output//latex_d60a019c50627205b3fb926a556b9f66.png) model for ![](http://latex2png.com/output//latex_fede5c65b08d274f9973c8958417b956.png) are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model ![](http://latex2png.com/output//latex_b0b0c0892cc162afcd3da8f0ad0d1377.png) for ![](http://latex2png.com/output//latex_fede5c65b08d274f9973c8958417b956.png) are all negative. Thus, it is unlikely that the flag sigma models are integrable.\n\n### [Benney-Lin and Kawahara equations: a detailed study through Lie  symmetries and Painlevé analysis](http://arxiv.org/abs/1907.06918v1) (1907.06918v1)\n<i>Andronikos Paliathanasis</b>\n\n<h10>2019-07-16</h10>\n> We perform a detailed study on the integrability of the Benney-Lin and KdV-Kawahara equations by using the Lie symmetry analysis and the singularity analysis. We find that the equations under our consideration admit integrable travelling-wave solutions. The singularity analysis is applied for the partial differential equations and the generic algebraic solution is presented.\n\n### [![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) gauge theory, free fermions on the torus and  Painlevé VI](http://arxiv.org/abs/1901.10497v2) (1901.10497v2)\n<i>Giulio Bonelli, Fabrizio Del Monte, Pavlo Gavrylenko, Alessandro Tanzini</b>\n\n<h10>2019-01-29</h10>\n> In this paper we study the extension of Painlev\\'e/gauge theory correspondence to circular quivers by focusing on the special case of ![](http://latex2png.com/output//latex_cbc8b64793550f050a6ba666b49627f9.png) ![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) theory. We show that the Nekrasov-Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of ![](http://latex2png.com/output//latex_26c0ff6806e4ce0f854a5f3e73a84417.png) flat connections on the one-punctured torus. This is achieved by reformulating the Riemann-Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the ![](http://latex2png.com/output//latex_cbc8b64793550f050a6ba666b49627f9.png) ![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) theory on self-dual ![](http://latex2png.com/output//latex_970679accb07e9aca06b71a2ec028a64.png)-background and, in the Seiberg-Witten limit, an elegant relation between the IR and UV gauge couplings.\n\n### [Algebra of Dunkl Laplace-Runge-Lenz vector](http://arxiv.org/abs/1907.06706v1) (1907.06706v1)\n<i>Misha Feigin, Tigran Hakobyan</b>\n\n<h10>2019-07-15</h10>\n> We introduce Dunkl version of Laplace-Runge-Lenz vector associated with a finite Coxeter group ![](http://latex2png.com/output//latex_18c0c1f38ea799215bdbb8acae5d3708.png) acting geometrically in ![](http://latex2png.com/output//latex_54fdaf06e02c91728b53723fdf6abd7e.png) with multiplicity function ![](http://latex2png.com/output//latex_e053a77cdf7898c5931d6fddef453b27.png). This vector commutes with Dunkl Laplacian with additional Coulomb potential ![](http://latex2png.com/output//latex_2d6617d2c01bf2f1078cedf4d959d5d4.png), and it generalises the usual Laplace-Runge-Lenz vector. We study resulting symmetry algebra ![](http://latex2png.com/output//latex_86c93f53d35e0f8a3011c9ba1103dd97.png) and show that it has Poincar\\'e-Birkhoff-Witt property. In the absence of Coulomb potential this symmetry algebra is a subalgebra of the rational Cherednik algebra ![](http://latex2png.com/output//latex_067bef88e14402c1e1142e99171b8471.png). We show that its central quotient is a quadratic algebra isomorphic to a central quotient of the corresponding Dunkl angular momenta algebra ![](http://latex2png.com/output//latex_76cfda7e17719ad750d3c45d182acdab.png). This gives interpretation of the algebra ![](http://latex2png.com/output//latex_76cfda7e17719ad750d3c45d182acdab.png) as the hidden symmetry algebra of Dunkl Laplacian. On the other hand by specialising ![](http://latex2png.com/output//latex_86c93f53d35e0f8a3011c9ba1103dd97.png) to ![](http://latex2png.com/output//latex_ebadc88bd62c641cc2c9cfd91e71bcf2.png) we recover a quotient of the universal enveloping algebra ![](http://latex2png.com/output//latex_969163a572fa4b21567b2bbfe037f9b6.png) as the hidden symmetry algebra of Coulomb problem in ![](http://latex2png.com/output//latex_558e3c25c04512ba9a222d13c10a5d72.png).\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-19",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-19"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-18T18:00:18",
  "trx_id": "4de11c278d1726952a76f6a323514bb6aeff6cdd",
  "trx_in_block": 12,
  "virtual_op": 0
}

{
  "block": 34747820,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-18",
      "voter": "map10k",
      "weight": 46
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-17T18:04:18",
  "trx_id": "50f1bc51433f7ca7f0c905930b62c856703e0e99",
  "trx_in_block": 49,
  "virtual_op": 0
}

{
  "block": 34747804,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-18",
      "voter": "anti-fraud",
      "weight": 900
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-17T18:03:30",
  "trx_id": "54ebea34b6f48a3866fe844f415cb1f5b498bb44",
  "trx_in_block": 25,
  "virtual_op": 0
}

{
  "block": 34747795,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-18",
      "voter": "accelerator",
      "weight": 25
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-17T18:03:03",
  "trx_id": "d3a39fb56ae7f773cc8c632e963f2a368752d85e",
  "trx_in_block": 40,
  "virtual_op": 0
}

{
  "block": 34747739,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [Angular and radial correlation scaling in stochastic growth  morphodynamics: a unifying fractality framework](http://arxiv.org/abs/1803.03715v2) (1803.03715v2)\n<i>J. R. Nicolás-Carlock, J. M. Solano-Altamirano, J. L. Carrillo-Estrada</b>\n\n<h10>2018-03-09</h10>\n> Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of quantities such as the two-point density radial or angular correlations. However, persistent discrepancies found during the analysis of basic models, using these two quantification methods, demand important clarifications. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial-angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential, that, under the fractal dimension interpretation, resemble first- and second-order transitions, respectively. Remarkably, these and previous results can be unified under a single fractal dimensionality equation.\n\n### [High-order couplings in geometric complex networks of neurons](http://arxiv.org/abs/1907.06765v1) (1907.06765v1)\n<i>A. Tlaie, I. Leyva, I. Sendiña</b>\n\n<h10>2019-07-15</h10>\n> We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the travelling wave phenomenon gets enhanced by these interactions, allowing the information to travel further in the system without generating pathological full synchronization states. This scheme could be a step towards a simple modelization of neuroglial networks.\n\n### [Self-Localized Solitons of the Nonlinear Wave Blocking Problem](http://arxiv.org/abs/1907.03857v2) (1907.03857v2)\n<i>Cihan Bayindir</b>\n\n<h10>2019-07-08</h10>\n> In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\\\"odinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and the applicability of the proposed approach.\n\n### [Inverse scattering transform for two-level systems with nonzero  background](http://arxiv.org/abs/1907.06231v1) (1907.06231v1)\n<i>Gino Biondini, Ildar Gabitov, Gregor Kovacic, Sitai Li</b>\n\n<h10>2019-07-14</h10>\n> We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background states in general do not exist with a nonzero background field. We then use the formalism to compute explicitly the soliton solutions of this system. We discuss the initial population of atoms and show that the pure soliton solutions do not correspond to a pure state initially. We obtain a representation for the soliton solutions in determinant form, and explicitly write down the one-soliton solutions. We next derive periodic solutions and rational solutions from the one-soliton solutions. We then analyze the properties of these solutions, including discussion of the sharp-line and small-amplitude limits, and thereafter show that the two limits do not commute. Finally, we investigate the behavior of general solutions, showing that solutions are stable (i.e., the radiative parts of solutions decay) only when initially atoms in the ground state dominant, i.e., initial population inversion is negative.\n\n### [Spontaneous and engineered transformations of topological structures in  nonlinear media with gain and loss](http://arxiv.org/abs/1907.06180v1) (1907.06180v1)\n<i>B. A. Kochetov, O. G. Chelpanova, V. R. Tuz, A. I. Yakimenko</b>\n\n<h10>2019-07-14</h10>\n> In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen control carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [Benney-Lin and Kawahara equations: a detailed study through Lie  symmetries and Painlevé analysis](http://arxiv.org/abs/1907.06918v1) (1907.06918v1)\n<i>Andronikos Paliathanasis</b>\n\n<h10>2019-07-16</h10>\n> We perform a detailed study on the integrability of the Benney-Lin and KdV-Kawahara equations by using the Lie symmetry analysis and the singularity analysis. We find that the equations under our consideration admit integrable travelling-wave solutions. The singularity analysis is applied for the partial differential equations and the generic algebraic solution is presented.\n\n### [![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) gauge theory, free fermions on the torus and  Painlevé VI](http://arxiv.org/abs/1901.10497v2) (1901.10497v2)\n<i>Giulio Bonelli, Fabrizio Del Monte, Pavlo Gavrylenko, Alessandro Tanzini</b>\n\n<h10>2019-01-29</h10>\n> In this paper we study the extension of Painlev\\'e/gauge theory correspondence to circular quivers by focusing on the special case of ![](http://latex2png.com/output//latex_cbc8b64793550f050a6ba666b49627f9.png) ![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) theory. We show that the Nekrasov-Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of ![](http://latex2png.com/output//latex_26c0ff6806e4ce0f854a5f3e73a84417.png) flat connections on the one-punctured torus. This is achieved by reformulating the Riemann-Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the ![](http://latex2png.com/output//latex_cbc8b64793550f050a6ba666b49627f9.png) ![](http://latex2png.com/output//latex_100f6a8ed50189c1819412414e6c26f4.png) theory on self-dual ![](http://latex2png.com/output//latex_970679accb07e9aca06b71a2ec028a64.png)-background and, in the Seiberg-Witten limit, an elegant relation between the IR and UV gauge couplings.\n\n### [Algebra of Dunkl Laplace-Runge-Lenz vector](http://arxiv.org/abs/1907.06706v1) (1907.06706v1)\n<i>Misha Feigin, Tigran Hakobyan</b>\n\n<h10>2019-07-15</h10>\n> We introduce Dunkl version of Laplace-Runge-Lenz vector associated with a finite Coxeter group ![](http://latex2png.com/output//latex_18c0c1f38ea799215bdbb8acae5d3708.png) acting geometrically in ![](http://latex2png.com/output//latex_54fdaf06e02c91728b53723fdf6abd7e.png) with multiplicity function ![](http://latex2png.com/output//latex_e053a77cdf7898c5931d6fddef453b27.png). This vector commutes with Dunkl Laplacian with additional Coulomb potential ![](http://latex2png.com/output//latex_2d6617d2c01bf2f1078cedf4d959d5d4.png), and it generalises the usual Laplace-Runge-Lenz vector. We study resulting symmetry algebra ![](http://latex2png.com/output//latex_86c93f53d35e0f8a3011c9ba1103dd97.png) and show that it has Poincar\\'e-Birkhoff-Witt property. In the absence of Coulomb potential this symmetry algebra is a subalgebra of the rational Cherednik algebra ![](http://latex2png.com/output//latex_067bef88e14402c1e1142e99171b8471.png). We show that its central quotient is a quadratic algebra isomorphic to a central quotient of the corresponding Dunkl angular momenta algebra ![](http://latex2png.com/output//latex_76cfda7e17719ad750d3c45d182acdab.png). This gives interpretation of the algebra ![](http://latex2png.com/output//latex_76cfda7e17719ad750d3c45d182acdab.png) as the hidden symmetry algebra of Dunkl Laplacian. On the other hand by specialising ![](http://latex2png.com/output//latex_86c93f53d35e0f8a3011c9ba1103dd97.png) to ![](http://latex2png.com/output//latex_ebadc88bd62c641cc2c9cfd91e71bcf2.png) we recover a quotient of the universal enveloping algebra ![](http://latex2png.com/output//latex_969163a572fa4b21567b2bbfe037f9b6.png) as the hidden symmetry algebra of Coulomb problem in ![](http://latex2png.com/output//latex_558e3c25c04512ba9a222d13c10a5d72.png).\n\n### [Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy](http://arxiv.org/abs/1907.06621v1) (1907.06621v1)\n<i>V. Prokofev, A. Zabrodin</b>\n\n<h10>2019-07-15</h10>\n> We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time ![](http://latex2png.com/output//latex_9a9b1cdd7de24d4417bfef5fdfdbebca.png). It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this correspondence to the level of hierarchies: the dynamics of poles with respect to the ![](http://latex2png.com/output//latex_bd42aa2845aca8c2a030ec647637009f.png)-th hierarchical time ![](http://latex2png.com/output//latex_5f1082f5731eec567e1226f8e3b7f4c4.png) (respectively, ![](http://latex2png.com/output//latex_7cee975df86172598476748a613cc3cf.png)) of the 2D Toda lattice hierarchy is shown to be governed by the Hamiltonian which is proportional to the ![](http://latex2png.com/output//latex_bd42aa2845aca8c2a030ec647637009f.png)-th Hamiltonian ![](http://latex2png.com/output//latex_1617d56fa1efb729f101da7761bd5398.png) (respectively, ![](http://latex2png.com/output//latex_6d96a28f2c822855ea2094f4d014a234.png)) of the Ruijsenaars-Schneider model, where ![](http://latex2png.com/output//latex_0ee8776a295f6d06670ea84906a0e45a.png) is the Lax matrix.\n\n### [Wave solutions of Gilson-Pickering equation](http://arxiv.org/abs/1907.06254v1) (1907.06254v1)\n<i>Karmina Kamal Ali, Resat Yilmazer, Samad Noeiaghdam</b>\n\n<h10>2019-07-14</h10>\n> In this work, we apply the (1/G')-expansion method to produce the novel soliton solution of the Gilson-Pickering equation. This method is fundamental on homogeneous balance procedure that gives the order of the estimating polynomial-type solution. Also it is based on the appreciate wave transform to reduce the governing equation. The solutions that we obtain are include of hyperbolic, complex and rational functions solutions. Finally, the results are graphically discussed.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-18",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-18"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-17T18:00:15",
  "trx_id": "1a53a884216c1b12b5748c17263268b43a528107",
  "trx_in_block": 1,
  "virtual_op": 0
}

{
  "block": 34719035,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-17",
      "voter": "map10k",
      "weight": 46
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T18:03:51",
  "trx_id": "a0812cb89cddff45bf4468b1aa6d67766d9a74a6",
  "trx_in_block": 45,
  "virtual_op": 0
}

{
  "block": 34719015,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-17",
      "voter": "accelerator",
      "weight": 28
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T18:02:51",
  "trx_id": "c373ac0c4f5f68c7928438ce6ee8137c35903ec4",
  "trx_in_block": 5,
  "virtual_op": 0
}

{
  "block": 34718962,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [Self-Localized Solitons of the Nonlinear Wave Blocking Problem](http://arxiv.org/abs/1907.03857v2) (1907.03857v2)\n<i>Cihan Bayindir</b>\n\n<h10>2019-07-08</h10>\n> In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\\\"odinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and the applicability of the proposed approach.\n\n### [Inverse scattering transform for two-level systems with nonzero  background](http://arxiv.org/abs/1907.06231v1) (1907.06231v1)\n<i>Gino Biondini, Ildar Gabitov, Gregor Kovacic, Sitai Li</b>\n\n<h10>2019-07-14</h10>\n> We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background states in general do not exist with a nonzero background field. We then use the formalism to compute explicitly the soliton solutions of this system. We discuss the initial population of atoms and show that the pure soliton solutions do not correspond to a pure state initially. We obtain a representation for the soliton solutions in determinant form, and explicitly write down the one-soliton solutions. We next derive periodic solutions and rational solutions from the one-soliton solutions. We then analyze the properties of these solutions, including discussion of the sharp-line and small-amplitude limits, and thereafter show that the two limits do not commute. Finally, we investigate the behavior of general solutions, showing that solutions are stable (i.e., the radiative parts of solutions decay) only when initially atoms in the ground state dominant, i.e., initial population inversion is negative.\n\n### [Spontaneous and engineered transformations of topological structures in  nonlinear media with gain and loss](http://arxiv.org/abs/1907.06180v1) (1907.06180v1)\n<i>B. A. Kochetov, O. G. Chelpanova, V. R. Tuz, A. I. Yakimenko</b>\n\n<h10>2019-07-14</h10>\n> In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen control carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.\n\n### [Nonlinear normal modes in the ![](http://latex2png.com/output//latex_553f31e4d6240d458384e018a30fd84f.png)-Fermi-Pasta-Ulam-Tsingou chain](http://arxiv.org/abs/1906.03981v2) (1906.03981v2)\n<i>Nathaniel J. Fuller, Surajit Sen</b>\n\n<h10>2019-05-30</h10>\n> Nonlinear normal mode solutions of the ![](http://latex2png.com/output//latex_a09ff5aa4faa8ac1a92a3e088b122835.png)-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths. Solutions for the N-body chain are found for purely nonlinear couplings. Three distinct solution types presented: a linear analogue, a chaotic amplitude mapping, and a localized nonlinear mode. The relaxation of perturbed modes are also explored using ![](http://latex2png.com/output//latex_bb45de4584d0d40730622b18c41ff2d4.png)-regularized least squares regression to estimate the free energy functional near the nonlinear normal mode solution. The perturbed modes are observed to decay sigmoidally towards a quasi-equilibrium state and a logarithmic relationship between the perturbation strength and mode lifetime is found.\n\n### [Travelling Waves in Monostable and Bistable Stochastic Partial  Differential Equations](http://arxiv.org/abs/1904.03037v3) (1904.03037v3)\n<i>Christian Kuehn</b>\n\n<h10>2019-04-05</h10>\n> In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular, this survey is intended for readers new to the topic but who have some knowledge in any sub-field of differential equations. The aim is to bridge different backgrounds and to identify the most important common principles and techniques currently applied to the analysis of stochastic travelling wave problems. Monostable and bistable reaction terms are found in prototypical dissipative travelling wave problems, which have already guided the deterministic theory. Hence,we expect that these terms are also crucial in the stochastic setting to understand effects and to develop techniques. The survey also provides an outlook, suggests some open problems, and points out connections to results in physics as well as to other active research directions in SPDEs.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy](http://arxiv.org/abs/1907.06621v1) (1907.06621v1)\n<i>V. Prokofev, A. Zabrodin</b>\n\n<h10>2019-07-15</h10>\n> We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time ![](http://latex2png.com/output//latex_9a9b1cdd7de24d4417bfef5fdfdbebca.png). It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this correspondence to the level of hierarchies: the dynamics of poles with respect to the ![](http://latex2png.com/output//latex_bd42aa2845aca8c2a030ec647637009f.png)-th hierarchical time ![](http://latex2png.com/output//latex_5f1082f5731eec567e1226f8e3b7f4c4.png) (respectively, ![](http://latex2png.com/output//latex_7cee975df86172598476748a613cc3cf.png)) of the 2D Toda lattice hierarchy is shown to be governed by the Hamiltonian which is proportional to the ![](http://latex2png.com/output//latex_bd42aa2845aca8c2a030ec647637009f.png)-th Hamiltonian ![](http://latex2png.com/output//latex_1617d56fa1efb729f101da7761bd5398.png) (respectively, ![](http://latex2png.com/output//latex_6d96a28f2c822855ea2094f4d014a234.png)) of the Ruijsenaars-Schneider model, where ![](http://latex2png.com/output//latex_0ee8776a295f6d06670ea84906a0e45a.png) is the Lax matrix.\n\n### [Wave solutions of Gilson-Pickering equation](http://arxiv.org/abs/1907.06254v1) (1907.06254v1)\n<i>Karmina Kamal Ali, Resat Yilmazer, Samad Noeiaghdam</b>\n\n<h10>2019-07-14</h10>\n> In this work, we apply the (1/G')-expansion method to produce the novel soliton solution of the Gilson-Pickering equation. This method is fundamental on homogeneous balance procedure that gives the order of the estimating polynomial-type solution. Also it is based on the appreciate wave transform to reduce the governing equation. The solutions that we obtain are include of hyperbolic, complex and rational functions solutions. Finally, the results are graphically discussed.\n\n### [Inverse scattering transform for two-level systems with nonzero  background](http://arxiv.org/abs/1907.06231v1) (1907.06231v1)\n<i>Gino Biondini, Ildar Gabitov, Gregor Kovacic, Sitai Li</b>\n\n<h10>2019-07-14</h10>\n> We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background states in general do not exist with a nonzero background field. We then use the formalism to compute explicitly the soliton solutions of this system. We discuss the initial population of atoms and show that the pure soliton solutions do not correspond to a pure state initially. We obtain a representation for the soliton solutions in determinant form, and explicitly write down the one-soliton solutions. We next derive periodic solutions and rational solutions from the one-soliton solutions. We then analyze the properties of these solutions, including discussion of the sharp-line and small-amplitude limits, and thereafter show that the two limits do not commute. Finally, we investigate the behavior of general solutions, showing that solutions are stable (i.e., the radiative parts of solutions decay) only when initially atoms in the ground state dominant, i.e., initial population inversion is negative.\n\n### [New integrable two-centre problem on sphere in Dirac magnetic field](http://arxiv.org/abs/1907.06174v1) (1907.06174v1)\n<i>A. P. Veselov, Y. Ye</b>\n\n<h10>2019-07-14</h10>\n> We present a new integrable version of the two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole. The new system can be written on the dual space of Lie algebra ![](http://latex2png.com/output//latex_cf019a516fc5475ccc0338d8a16b5636.png) and is integrable both in classical and quantum case.\n\n### [QES solutions of a two dimensional system with quadratic non-linearities](http://arxiv.org/abs/1907.05543v1) (1907.05543v1)\n<i>Bhabani Prasad Mandal, Brijesh Kumar Mourya, Aman Kumar Singh</b>\n\n<h10>2019-07-12</h10>\n> We consider a one parameter family of a PT symmetric two dimensional system with quadratic non-linearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this systems by constructing a non-Hermitian Hamiltonian of a particle with position dependent mass. We further construct a canonical transformation which maps this position dependent mass systems to a QES system. First few QES levels are calculated explicitly by using Bender-Dunne (BD) polynomial method.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-17",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-17"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T18:00:12",
  "trx_id": "08b0dd491b463f57c4e7a3898b1e6062e4fd36ff",
  "trx_in_block": 14,
  "virtual_op": 0
}

{
  "block": 34716730,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-17",
      "voter": "map10k",
      "weight": 46
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T16:08:30",
  "trx_id": "6cb9e7da08d9936b7b48e391463421a9f9d3f601",
  "trx_in_block": 10,
  "virtual_op": 0
}

{
  "block": 34716724,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-17",
      "voter": "serialfiller",
      "weight": 250
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T16:08:12",
  "trx_id": "8218e5050904ec54bb9430857411a10b51cea747",
  "trx_in_block": 5,
  "virtual_op": 0
}

{
  "block": 34716677,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-17",
      "voter": "accelerator",
      "weight": 28
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T16:05:51",
  "trx_id": "e5580042dbebcbab0f0fffc556f4aefde14825f3",
  "trx_in_block": 0,
  "virtual_op": 0
}

{
  "block": 34716583,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Adaptation And Self-Organizing Systems</center> \n <hr> \n\n### [Forced synchronization of an oscillator with a line of equilibria](http://arxiv.org/abs/1907.06595v1) (1907.06595v1)\n<i>Ivan A. Korneev, Andrei V. Slepnev, Vladimir V. Semenov, Tatiana Vadivasova</b>\n\n<h10>2019-07-15</h10>\n> The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: capture of the phase and frequency of oscillations and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown.\n\n### [Synchronization of periodic self-oscillators interacting via  memristor-based coupling](http://arxiv.org/abs/1807.00613v2) (1807.00613v2)\n<i>Ivan A. Korneev, Vladimir V. Semenov, Tatiana E. Vadivasova</b>\n\n<h10>2018-07-02</h10>\n> A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of quasi-harmonic reduction. It is shown that specifics of the memristor nonlinearity results in appearance of infinitely many equilibrium points, which form a line of equilibria in the phase space of the system under study. It is established that possibility to observe the effect of phase locking in the considered system depends both on parameter values and initial conditions. Consequently, boundaries of a synchronization area are determined by the initial conditions. It is demonstrated that addition of a small term into the memristor state equation gives rise to disappearance of the line of equilibria and eliminates the dependence of synchronization on the initial conditions.\n\n### [A dynamic over games drives selfish agents to win-win outcomes](http://arxiv.org/abs/1907.06338v1) (1907.06338v1)\n<i>Seth Frey, Curtis Atkisson</b>\n\n<h10>2019-07-15</h10>\n> Understanding the evolution of human social systems requires flexible formalisms for the emergence of institutions. Although game theory is normally used to model interactions individually, larger spaces of games can be helpful for modeling how interactions change. We introduce a framework for modeling \"institutional evolution,\" how individuals change the games they are placed in. We contrast this with the more familiar within-game \"behavioral evolution\". Starting from an initial game, agents trace trajectories through game space by repeatedly navigating to more preferable games until they converge on attractor games that are preferred to all others. Agents choose between games on the basis of their \"institutional preferences,\" which define between-game comparisons in terms of game-level features such as stability, fairness, and efficiency. Computing institutional change trajectories over the two-player space, we find that the attractors of self-interested economic agents over-represent fairness by 100% relative to baseline, even though those agents are indifferent to fairness. This seems to occur because fairness, as a game feature, co-occurs with the self-serving features these agents do prefer. We thus present institutional evolution as a mechanism for encouraging the spontaneous emergence of cooperation among inherently selfish agents. We then extend these findings beyond two players, and to two other types of evolutionary agent: the relative fitness maximizing agent of evolutionary game theory (who maximizes inequality), and the relative group fitness maximizing agent of multi-level/group selection theory (who minimizes inequality). This work provides a flexible, testable formalism for modeling the interdependencies of behavioral and institutional evolutionary processes.\n\n### [Tie-decay temporal networks in continuous time and eigenvector-based  centralities](http://arxiv.org/abs/1805.00193v2) (1805.00193v2)\n<i>Walid Ahmad, Mason A. Porter, Mariano Beguerisse-Díaz</b>\n\n<h10>2018-05-01</h10>\n> Network theory is a useful framework for studying interconnected systems of interacting agents. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions, which we model as discrete contacts, and ties, which represent strengths of relationships as functions of time. To illustrate our tie-decay network formulation, we adapt the well-known PageRank centrality score to the tie-decay framework in a mathematically tractable and computationally efficient way. We demonstrate our framework on a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.\n\n### [Fixation properties of rock-paper-scissors games in fluctuating  populations](http://arxiv.org/abs/1907.05184v2) (1907.05184v2)\n<i>Robert West, Mauro Mobilia</b>\n\n<h10>2019-07-11</h10>\n> Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different \"laws\" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the ![](http://latex2png.com/output//latex_561204284301b422c5bed9b3f64b096e.png) of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness \"levels the field\" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity.\n\n# <center>Chaotic Dynamics</center> \n <hr> \n\n### [Synchronization of periodic self-oscillators interacting via  memristor-based coupling](http://arxiv.org/abs/1807.00613v2) (1807.00613v2)\n<i>Ivan A. Korneev, Vladimir V. Semenov, Tatiana E. Vadivasova</b>\n\n<h10>2018-07-02</h10>\n> A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of quasi-harmonic reduction. It is shown that specifics of the memristor nonlinearity results in appearance of infinitely many equilibrium points, which form a line of equilibria in the phase space of the system under study. It is established that possibility to observe the effect of phase locking in the considered system depends both on parameter values and initial conditions. Consequently, boundaries of a synchronization area are determined by the initial conditions. It is demonstrated that addition of a small term into the memristor state equation gives rise to disappearance of the line of equilibria and eliminates the dependence of synchronization on the initial conditions.\n\n### [Nonlinear dynamics and energy transfer for two rotating dipoles in an  external field: A three-dimensional analysis](http://arxiv.org/abs/1907.06384v1) (1907.06384v1)\n<i>Rosario González-Férez, Manuel Iñarrea, J. Pablo Salas, Peter Schmelcher</b>\n\n<h10>2019-07-15</h10>\n> We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole-dipole interaction in an external homogeneous electric field. In the field-free stable head-tail configuration, an excess energy is provided to one of the dipoles, and we explore the resulting three-dimensional classical dynamics. This dynamics is characterized in terms of the kinetic energy transfer between the dipoles, their orientation along the electric field, as well as their chaotic behavior.   The field-free energy transfer mechanism shows an abrupt transition between equipartition and non-equipartition regimes, which   is independent of the initial direction of rotation due to the existence of an infinite set of equivalent manifolds. The field-dressed dynamics is highly complex and strongly depends on the electric field strength and on the initial conditions. In the strong field regime, the energy equipartition and chaotic behavior dominate the dynamics.\n\n### [Semiclassical evolution in phase space for a softly chaotic system](http://arxiv.org/abs/1907.06298v1) (1907.06298v1)\n<i>Gabriel M. Lando, Alfredo M. Ozorio de Almeida</b>\n\n<h10>2019-07-15</h10>\n> An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and become mainly chaotic as the kicking parameter is increased. Time-evolution is tracked using classical, quantum and semiclassical Wigner functions, obtained via the Herman-Kluk propagator. Quantitative comparisons are also included and carried out from probability marginals and autocorrelation functions. Sub-Planckian classical structure such as small stability islands and thin/folded classical filaments do impact semiclassical accuracy, but the approximation is seen to be accurate for multiple Ehrenfest times.\n\n### [Routes to long-term atmospheric predictability in reduced-order coupled  ocean-atmosphere systems -- Impact of the ocean basin boundary conditions](http://arxiv.org/abs/1901.06203v2) (1901.06203v2)\n<i>Stéphane Vannitsem, Roman Solé-Pomies, Lesley De Cruz</b>\n\n<h10>2019-01-18</h10>\n> The predictability of the atmosphere at short and long time scales, associated with the coupling to the ocean, is explored in a new version of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), based on a 2-layer quasi-geostrophic atmosphere and a 1-layer reduced-gravity quasi-geostrophic ocean. This version features a new ocean basin geometry with periodic boundary conditions in the zonal direction. The analysis presented in this paper considers a low-order version of the model with 40 dynamical variables.   First the increase of surface friction (and the associated heat flux) with the ocean can either induce chaos when the aspect ratio between the meridional and zonal directions of the domain of integration is small, or suppress chaos when it is large. This reflects the potentially counter-intuitive role that the ocean can play in the coupled dynamics.   Second, and perhaps more importantly, the emergence of long-term predictability within the atmosphere for specific values of the friction coefficient occurs through intermittent excursions in the vicinity of a (long-period) unstable periodic solution. Once close to this solution the system is predictable for long times, i.e. a few years. The intermittent transition close to this orbit is, however, erratic and probably hard to predict.   This new route to long-term predictability contrasts with the one found in the closed ocean-basin low-order version of MAOOAM, in which the chaotic solution is permanently wandering in the vicinity of an unstable periodic orbit for specific values of the friction coefficient. The model solution is thus at any time influenced by the unstable periodic orbit and inherits from its long-term predictability.\n\n### [Blinking chimeras in globally coupled rotators](http://arxiv.org/abs/1907.06201v1) (1907.06201v1)\n<i>Richard Janis Goldschmidt, Arkady Pikovsky, Antonio Politi</b>\n\n<h10>2019-07-14</h10>\n> In globally coupled ensembles of identical oscillators so-called chimera states can be observed. The chimera state is a symmetry-broken regime, where a subset of oscillators forms a cluster, a synchronized population, while the rest of the system remains a collection of non-synchronized, scattered units. We describe here a blinking chimera regime in an ensemble of seven globally coupled rotators (Kuramoto oscillators with inertia). It is characterized by a death-birth process, where a long-term stable cluster of four oscillators suddenly dissolves and is very quickly reborn with a new, reshuffled configuration. We identify three different kinds of rare blinking events and give a quantitative characterization by applying stability analysis to the long-lived chaotic state and to the short-lived regular regimes which arise when the cluster dissolves.\n\n# <center>Cellular Automata And Lattice Gases</center> \n <hr> \n\n### [One-dimensional number-conserving cellular automata](http://arxiv.org/abs/1907.06063v1) (1907.06063v1)\n<i>Markus Redeker</b>\n\n<h10>2019-07-13</h10>\n> This paper contains two methods to construct one-dimensional number-conserving cellular automata in terms of particle flows. One method is a sequence of increasingly stronger restrictions on the particle flow, which always ends with the specification of a number-conserving rule. The other is based on minimal flow functions, from which all others can be constructed. These constructions also provide a classification for number-conserving rules and a way to specify rules as a supremum of minimal flows. Other questions, like that about the nature of non-deterministic number-conserving rules, are treated briefly at the end.\n\n### [Efficient methods to determine the reversibility of general 1D linear  cellular automata in polynomial complexity](http://arxiv.org/abs/1907.06012v1) (1907.06012v1)\n<i>Xinyu Du, Chao Wang, Tianze Wang, Zeyu Gao</b>\n\n<h10>2019-07-13</h10>\n> In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibility in a period. With existing methods, the time and space complexity of these two parts are still too expensive to be employed. So the process soon becomes totally incalculable with a slightly big size, which greatly limits its application. In this paper, we set out to solve these two problems using two efficient algorithms, which make it possible to solve reversible LCA of very large size. Furthermore, we provide an interesting perspective to conversely generate 1D LCA from a given period of reversibility. Due to our methods' efficiency, we can calculate the reversible LCA with large size, which has much potential to enhance security in cryptography system.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Universal One-Dimensional Cellular Automata Derived for Turing Machines  and its Dynamical Behaviour](http://arxiv.org/abs/1907.04211v1) (1907.04211v1)\n<i>Sergio J. Martinez, Ivan M. Mendoza, Genaro J. Martinez, Shigeru Ninagawa</b>\n\n<h10>2019-07-06</h10>\n> Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.\n\n### [Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model](http://arxiv.org/abs/1907.00636v1) (1907.00636v1)\n<i>Jan de Gier, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz</b>\n\n<h10>2019-07-01</h10>\n> Dynamical universality classes are distinguished by their dynamical exponent ![](http://latex2png.com/output//latex_bd61b29a408a64d11f1a55bca65fd0c4.png) and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known except for the special case ![](http://latex2png.com/output//latex_2fdb6000f3667b6e6887c72c14280977.png). Here the model corresponds to the TASEP (totally asymmetric simple exclusion process) that is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with ![](http://latex2png.com/output//latex_612eb39efa60bedf469ce3141e6664ff.png). In this paper, we show that the NaSch model also belongs to the KPZ class \\cite{KPZ} for general maximum velocities ![](http://latex2png.com/output//latex_d470cde12bfb573e851ddd17b54b2b41.png). Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. Performing large-scale Monte-Carlo simulations we show that the simulation results match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with dynamical lane changing rules.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-17",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 1|2019-07-17"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T16:01:09",
  "trx_id": "9e8098738a45948f93c4a07de733cc586d23d9ce",
  "trx_in_block": 4,
  "virtual_op": 0
}

{
  "block": 34700732,
  "op": [
    "transfer",
    {
      "amount": "48.827 STEEM",
      "from": "complexcity",
      "memo": "#8qUYxaEhzhv1rE2w2CxYjwhWSuVzYHFMiZC3MsVG1y16w6JSH6WdvN9keNKCs7ZGKZTxUhCfPNGBx9NbsEqXNeVtc5oC88K6GsLAnHADAFpHmChfTL3mauxnyvTwrKJyXhruwjoPvq96pNTaq76QjV3",
      "to": "bittrex"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T02:47:21",
  "trx_id": "490fba5df0f568388c48899e081b640a721e84ee",
  "trx_in_block": 30,
  "virtual_op": 0
}

{
  "block": 34700671,
  "op": [
    "limit_order_create",
    {
      "amount_to_sell": "0.015 SBD",
      "expiration": "2019-08-12T02:40:46",
      "fill_or_kill": false,
      "min_to_receive": "0.051 STEEM",
      "orderid": 1563245050,
      "owner": "complexcity"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T02:44:18",
  "trx_id": "e8a87e18c4a7669904dcfba03e44624a21934496",
  "trx_in_block": 11,
  "virtual_op": 0
}

{
  "block": 34700671,
  "op": [
    "fill_order",
    {
      "current_orderid": 1563245050,
      "current_owner": "complexcity",
      "current_pays": "0.015 SBD",
      "open_orderid": 155240564,
      "open_owner": "fermion",
      "open_pays": "0.051 STEEM"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-16T02:44:18",
  "trx_id": "e8a87e18c4a7669904dcfba03e44624a21934496",
  "trx_in_block": 11,
  "virtual_op": 1
}

{
  "block": 34690367,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-16",
      "voter": "sergino",
      "weight": 500
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T18:08:24",
  "trx_id": "8cfa93aba3698d4ea5d77c41975cb3aebad584a1",
  "trx_in_block": 7,
  "virtual_op": 0
}

{
  "block": 34690203,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [Which wavenumbers determine the thermodynamic stability of soft matter  quasicrystals?](http://arxiv.org/abs/1907.05805v1) (1907.05805v1)\n<i>D. J. Ratliff, A. J. Archer, P. Subramanian, A. M. Rucklidge</b>\n\n<h10>2019-07-12</h10>\n> For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.\n\n### [MCF solitons and laser pulse self-compression at light bullet excitation  in the central core of MCF](http://arxiv.org/abs/1907.01275v2) (1907.01275v2)\n<i>Alexey A. Balakin, Alexander G. Litvak, Sergey A. Skobelev</b>\n\n<h10>2019-07-02</h10>\n> The propagation of laser pulses in multi-core fibers (MCF) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasi-soliton homogeneous solutions of the wave field in the considered MCF are found. The stability of the in-phase soliton distribution is shown analytically and numerically. At low energies, its wave field is distributed over all MCF cores and has a duration, which exceeds the duration of the NSE soliton with the same energy by many (five-six) times. On the contrary, almost all of the radiation at high energies is concentrated in the central core with a duration similar to the NSE soliton. The transition between the two types of distributions is very sharp and occurs at a critical energy, which is weakly dependent on the number of cores and on the coupling coefficient with the central core. The self-compression mechanism of laser pulses was proposed. It consists in injecting such MCF with a wave packet being similar to the found soliton and having an energy larger than the critical value. It is shown that the compression ratio weakly depends on the energy and the number of cores and is approximately equal to 6 times with an energy efficiency of almost 100\\%. The use of longer laser pulses allows one to increase the compression ratio up to 30-40 times with an energy efficiency of more than 50\\%. The obtained analytical estimates of the compression ratio and its efficiency are in good agreement with the results of numerical simulation.\n\n### [Pattern formation in the presence of memory](http://arxiv.org/abs/1907.05304v1) (1907.05304v1)\n<i>Reza Torabi, Jörn Davidsen</b>\n\n<h10>2019-07-11</h10>\n> We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to use reductive perturbation to investigate the formation and stability of patterns. Focusing in detail on the Hopf instability and short-term memory, we derive the corresponding complex Ginzburg-Landau equation that governs the amplitude of the critical mode and we establish the explicit dependence of its parameters on the memory properties. Numerical solution of this memory dependent complex Ginzburg-Landau equation as well as direct numerical simulation of the non-Markovian Brusselator model illustrate that memory changes the properties of the spatio-temporal patterns. Our results indicate that going beyond the Markovian approximation might be necessary to study the formation of spatio-temporal patterns even in systems with short-term memory. At the same time, our work opens up a new window into the control of these patterns using memory.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Coexisting Ordered States, Local Equilibrium-like Domains, and Broken  Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state](http://arxiv.org/abs/1812.06002v4) (1812.06002v4)\n<i>Atanu Chatterjee, Yash Yadati, Nicholas Mears, Germano Iannacchione</b>\n\n<h10>2018-12-14</h10>\n> A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-B{\\'e}nard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system's temperature manifold.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [QES solutions of a two dimensional system with quadratic non-linearities](http://arxiv.org/abs/1907.05543v1) (1907.05543v1)\n<i>Bhabani Prasad Mandal, Brijesh Kumar Mourya, Aman Kumar Singh</b>\n\n<h10>2019-07-12</h10>\n> We consider a one parameter family of a PT symmetric two dimensional system with quadratic non-linearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this systems by constructing a non-Hermitian Hamiltonian of a particle with position dependent mass. We further construct a canonical transformation which maps this position dependent mass systems to a QES system. First few QES levels are calculated explicitly by using Bender-Dunne (BD) polynomial method.\n\n### [On the thermodynamic limit of form factor expansions of dynamical  correlation functions in the massless regime of the XXZ spin ![](http://latex2png.com/output//latex_ad1b0cff5a6b0f5c79a89cdced1c2c58.png) chain](http://arxiv.org/abs/1706.09459v3) (1706.09459v3)\n<i>K. K. Kozlowski</b>\n\n<h10>2017-06-28</h10>\n> This work constructs a well-defined and operational form factor expansion in a model having a massless spectrum of excitations. More precisely, the dynamic two-point functions in the massless regime of the XXZ spin-1/2 chain are expressed in terms of properly regularised series of multiple integrals. These series are obtained by taking, in an appropriate way, the thermodynamic limit of the finite volume form factor expansions. The series are structured in way allowing one to identify directly the contributions to the correlator stemming from the conformal-type excitations on the Fermi surface and those issuing from the massive excitations (deep holes, particles and bound states). The obtained form factor series opens up the possibility of a systematic and exact study of asymptotic regimes of dynamical correlation functions in the massless regime of the XXZ spin ![](http://latex2png.com/output//latex_ad1b0cff5a6b0f5c79a89cdced1c2c58.png) chain. Furthermore, the assumptions on the microscopic structure of the model's Hilbert space that are necessary so as to write down the series appear to be compatible with any model -- not necessarily integrable -- belonging to the Luttinger liquid universality class. Thus, the present analysis provides also the phenomenological structure of form factor expansions in massless models belonging to this universality class.\n\n### [Continued fractions and Hankel determinants from hyperelliptic curves](http://arxiv.org/abs/1907.05204v1) (1907.05204v1)\n<i>Andrew N. W. Hone</b>\n\n<h10>2019-07-11</h10>\n> Following van der Poorten, we consider a family of nonlinear maps which are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus ![](http://latex2png.com/output//latex_cedb66854950d47d05ff624e4b43eb3a.png). Using the connection with the classical theory of J-fractions and orthogonal polynomials, we show that in the simplest case ![](http://latex2png.com/output//latex_56744cc0f7cc8859ae4e48b8185b2143.png) this provides a straightforward derivation of Hankel determinant formulae for the terms of a general Somos-4 sequence, which were found in a particular form by Chang, Hu and Xin, We extend these formulae to the higher genus case, and prove that generic Hankel determinants in genus two satisfy a Somos-8 relation. Moreover, for all ![](http://latex2png.com/output//latex_cedb66854950d47d05ff624e4b43eb3a.png) we show that the iteration for the continued fraction expansion is equivalent to a discrete Lax pair with a natural Poisson structure, and the associated nonlinear map is a discrete integrable system. This paper is dedicated to the memory of Jon Nimmo.\n\n### [Generalized primitive potentials](http://arxiv.org/abs/1907.05038v1) (1907.05038v1)\n<i>Dmitry Zakharov, Vladimir Zakharov</b>\n\n<h10>2019-07-11</h10>\n> In our previous work, we introduced a new class of bounded potentials of the one-dimensional Schr\\\"odinger operator on the real axis, and a corresponding family of solutions of the KdV hierarchy. These potentials, which we call primitive, are obtained as limits of rapidly decreasing reflectionless potentials, or multisoliton solutions of KdV. In this note, we introduce generalized primitive potentials, which are obtained as limits of all rapidly decreasing potentials of the Schr\\\"odinger operator. These potentials are constructed by solving a contour problem, and are determined by a pair of positive functions on a finite interval and a functional parameter on the real axis.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-16",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-16"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T18:00:12",
  "trx_id": "f4db08a47a3ebbe6874c8443721d23178e954669",
  "trx_in_block": 15,
  "virtual_op": 0
}

{
  "block": 34687939,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-16",
      "voter": "pc-tip",
      "weight": 300
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T16:06:36",
  "trx_id": "331021f756ce55d145c37421ac61336a3a174460",
  "trx_in_block": 13,
  "virtual_op": 0
}

{
  "block": 34687933,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-16",
      "voter": "map10k",
      "weight": 44
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T16:06:18",
  "trx_id": "b8c4c42c6b5b22e73e94054c63d01ef8b082dd01",
  "trx_in_block": 15,
  "virtual_op": 0
}

{
  "block": 34687933,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-16",
      "voter": "bert0",
      "weight": 40
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T16:06:18",
  "trx_id": "81f7ae3391d041ed33f58f8e9fcc4b57ac2519d2",
  "trx_in_block": 13,
  "virtual_op": 0
}

{
  "block": 34687927,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-16",
      "voter": "accelerator",
      "weight": 28
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T16:06:00",
  "trx_id": "9c0e4c93fcb08492a5f1499cf74e1f243bcaab4c",
  "trx_in_block": 20,
  "virtual_op": 0
}

{
  "block": 34687832,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Adaptation And Self-Organizing Systems</center> \n <hr> \n\n### [Fixation properties of rock-paper-scissors games in fluctuating  populations](http://arxiv.org/abs/1907.05184v2) (1907.05184v2)\n<i>Robert West, Mauro Mobilia</b>\n\n<h10>2019-07-11</h10>\n> Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different \"laws\" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the ![](http://latex2png.com/output//latex_561204284301b422c5bed9b3f64b096e.png) of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness \"levels the field\" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity.\n\n### [A Framework for the Construction of Generative Models for Mesoscale  Structure in Multilayer Networks](http://arxiv.org/abs/1608.06196v3) (1608.06196v3)\n<i>Marya Bazzi, Lucas G. S. Jeub, Alex Arenas, Sam D. Howison, Mason A. Porter</b>\n\n<h10>2016-08-22</h10>\n> Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. In this paper, we introduce a generative model for mesoscale structure in multilayer networks. Our model is very general, with the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. Our results provide a standardized set of null models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. We discuss the parameters and properties of our generative model, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks.\n\n### [Mobility restores the mechanism which supports cooperation in the  voluntary prisoner's dilemma game](http://arxiv.org/abs/1907.05482v1) (1907.05482v1)\n<i>Marcos Cardinot, Colm O'Riordan, Josephine Griffith, Attila Szolnoki</b>\n\n<h10>2019-07-11</h10>\n> It is generally believed that in a situation where individual and collective interests are in conflict, the availability of optional participation is a key mechanism to maintain cooperation. Surprisingly, this effect is sensitive to the use of microscopic dynamics and can easily be broken when agents make a fully rational decision during their strategy updates. In the framework of the celebrated prisoner's dilemma game, we show that this discrepancy can be fixed automatically if we leave the strict and frequently artifact condition of a fully occupied interaction graph, and allow agents to change not just their strategies but also their positions according to their success. In this way, a diluted graph where agents may move offers a natural and alternative way to handle artifacts arising from the application of specific and sometimes awkward microscopic rules.\n\n### [Analysis of Bivariate Jump-Diffusion Processes](http://arxiv.org/abs/1907.05371v1) (1907.05371v1)\n<i>Leonardo Rydin Gorjão, Jan Heysel, Klaus Lehnertz, M. Reza Rahimi Tabar</b>\n\n<h10>2019-07-11</h10>\n> We introduce the bivariate jump-diffusion process, comprising two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, non-parametric estimation procedure of higher-order Kramers--Moyal coefficients that allows one to reconstruct relevant aspects of the underlying jump-diffusion processes and recover the underlying parameters of a jump-diffusion process. The procedure is validated with numerically integrated data using synthetic bivariate continuous and discontinuous time series. We further evaluate the possibility of estimating the parameters of the jump-diffusion model via a data driven analyses of the higher-order Kramers--Moyal coefficients, and the limitations arising from the scarcity of points in the data or disproportionate parameters in the system.\n\n### [Dynamical modelling of cascading failures in the Turkish power grid](http://arxiv.org/abs/1907.05194v1) (1907.05194v1)\n<i>Benjamin Schäfer, G. Cigdem Yalcin</b>\n\n<h10>2019-07-11</h10>\n> A reliable supply of electricity is critical for our modern society and any large scale disturbances of the electrical system causes substantial costs. In 2015, one overloaded transmission line caused a cascading failure in the Turkish power grid, affecting about 75 million people. We focus on the dynamical and statistical properties of the Turkish power grid as a real-world system example that can be modelled based on complex networks structures and we propose for the first time a model that incorporates the dynamical properties of the Turkish power grid as a complex network topology by investigating these cascading failures. We find that the network damage depends on the load and generation distribution in the network with centralized generation being more susceptible to failures than a decentralized one. Furthermore, economic considerations on transmission line capacity are shown to conflict with stability.\n\n# <center>Chaotic Dynamics</center> \n <hr> \n\n### [Good and bad predictions: Assessing and improving the replication of  chaotic attractors by means of reservoir computing](http://arxiv.org/abs/1907.05639v1) (1907.05639v1)\n<i>Alexander Haluszczynski, Christoph Räth</b>\n\n<h10>2019-07-12</h10>\n> The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the reproduction of the long-term properties of a nonlinear system. Yet, a thorough statistical analysis of the forecast results is missing. Using the Lorenz and R\\\"ossler system we statistically analyze the quality of prediction for different parametrizations - both the exact short-term prediction as well as the reproduction of the long-term properties (the \"climate\") of the system as estimated by the correlation dimension and largest Lyapunov exponent. We find that both short and longterm predictions vary significantly among the realizations. Thus special care must be taken in selecting the good predictions as predictions which deliver better short-term prediction also tend to better resemble the long-term climate of the system. Instead of only using purely random Erd\\\"os-Renyi networks we also investigate the benefit of alternative network topologies such as small world or scale-free networks and show which effect they have on the prediction quality. Our results suggest that the overall performance with respect to the reproduction of the climate of both the Lorenz and R\\\"ossler system is worst for scale-free networks. For the Lorenz system there seems to be a slight benefit of using small world networks while for the R\\\"ossler system small world and Erd\\\"os -Renyi networks performed equivalently well. In general the observation is that reservoir computing works for all network topologies investigated here.\n\n### [Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow](http://arxiv.org/abs/1907.05860v1) (1907.05860v1)\n<i>Balachandra Suri, Ravi Kumar Pallantla, Michael F. Schatz, Roman O. Grigoriev</b>\n\n<h10>2019-07-11</h10>\n> Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions -- equilibria, periodic, and quasi-periodic orbits -- as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace.\n\n### [Statistical Measures and Selective Decay Principle for Generalized Euler  Dynamics](http://arxiv.org/abs/1907.05069v1) (1907.05069v1)\n<i>Giovanni Conti, Gualtiero Badin</b>\n\n<h10>2019-07-11</h10>\n> We investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or {\\alpha}-models. We aim to study the equilibrium mechanics, using initially a point-vortex approximation and then exploiting the full continuous equations, invoking the maximization of appropriate entropy functionals. The point-vortex approximation highlights an important difference between the 2D turbulence and local dynamics models. In the latter, it is in fact possible to derive a statistical measure only considering two conserved quantities as constraints for the maximization problem, the Hamiltonian and the angular impulse. This result does not hold for 2D turbulence. Both the continuous and the point vortex approximation allow for the derivation of mean field equations that act as constraints for the functional relation between the streamfunction and the active scalar of the model considered. Further, the analysis of the continuous equations suggests the existence of a selective decay principle for the whole family of models. To test these ideas we use numerical simulations of the partial differential equations of the {\\alpha}-models starting from different sets of initial conditions (i.c.s). For random i.c.s, all the solutions tend to a dipolar structure. The functional relation between the active scalar and the streamfunction shows an increase of nonlinearity with a decrease of the locality of the dynamics. We then test the evolution of the specific case of SQG for i.c.s in the form of a hyperbolic saddle, that is a candidate for the possible formation of singularity through a self-similar cascade though secondary instabilities. Results show the presence of a scale dependent selective decay associated to the breaking of the frontal structures emerging from the flow, suggesting a relation with the change of topology of the flow.\n\n### [Length-Divergent Thermal Conductivity in Long-Range Interacting  Fermi-Pasta-Ulam Chains](http://arxiv.org/abs/1906.11086v3) (1906.11086v3)\n<i>Jianjin Wang, Sergey V. Dmitriev, Daxing Xiong</b>\n\n<h10>2019-06-26</h10>\n> The power-law length (![](http://latex2png.com/output//latex_0ee8776a295f6d06670ea84906a0e45a.png)) divergence of thermal conductivity (![](http://latex2png.com/output//latex_39a1acc0a1fe620307fc63cb0815e3a7.png)) in one-dimensional (1D) systems, i.e., ![](http://latex2png.com/output//latex_b20866e36c2c81c0136fd88a226ed4ee.png), has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent ![](http://latex2png.com/output//latex_879bee8d9bc4848dee78650baeff05fd.png) are usually ranging from ![](http://latex2png.com/output//latex_90e13cc294761693602fb52e9bfa10a3.png) to ![](http://latex2png.com/output//latex_1dc26b2661fa7239c25eb86fa8572e08.png); however sometimes, the experimental observations can be higher, e.g., ![](http://latex2png.com/output//latex_39328b34a56faaf05d072b0ec10cb72b.png)-![](http://latex2png.com/output//latex_3868dd6a68cc6c62a53407e92b0150c9.png). This dispute has not yet been settled. Here we show the first convincing evidence that an exponent of ![](http://latex2png.com/output//latex_3e09866b5ba9179843d4b951ca50c1f1.png) that falls within experimental observations, can occur in a theoretical model of 1D long-range interacting Fermi-Pasta-Ulam chain. This, for the first time, theoretically supports the possibility of a higher divergent exponent and thus sheds new light on understanding of extremely high thermal conductivity in 1D materials at macroscopic scales.\n\n### [Dynamics of random pressure fields over bluff bodies: a dynamic mode  decomposition perspective](http://arxiv.org/abs/1904.02245v3) (1904.02245v3)\n<i>Xihaier Luo, Ahsan Kareem</b>\n\n<h10>2019-03-26</h10>\n> Aerodynamic pressure field over bluff bodies immersed in boundary layer flows is correlated both in space and time. Conventional approaches for the analysis of distributed aerodynamic pressures, e.g., the proper orthogonal decomposition (POD), can only offer relevant spatial patterns in a set of coherent structures. This study provides an operator-theoretic approach that describes dynamic pressure fields in a functional space rather than conventional phase space via the Koopman operator. Subsequently, spectral analysis of the Koopman operator provides a spatiotemporal characterization of the pressure field. An augmented dynamic mode decomposition (DMD) method is proposed to perform the spectral decomposition. The augmentation is achieved by the use of the Takens's embedding theorem, where time delay coordinates are considered. Consequently, the identified eigen-tuples (eigenvalues, eigenvectors, and time evolution) can capture not only dominant spatial structures but also identify each structure with a specific frequency and a corresponding temporal growth/decay. This study encompasses learning the evolution dynamics of the random aerodynamic pressure field over a scaled model of a finite height prism using limited wind tunnel data. The POD analysis of the experimental data was also carried out. To demonstrate the unique feature of the proposed approach, the DMD and POD based learning results including algorithm convergence, data sufficiency, and modal analysis are examined. The ensuing observations offer a glimpse of the complex dynamics of the surface pressure field over bluff bodies that lends insights to features previously masked by conventional analysis approaches.\n\n# <center>Cellular Automata And Lattice Gases</center> \n <hr> \n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Universal One-Dimensional Cellular Automata Derived for Turing Machines  and its Dynamical Behaviour](http://arxiv.org/abs/1907.04211v1) (1907.04211v1)\n<i>Sergio J. Martinez, Ivan M. Mendoza, Genaro J. Martinez, Shigeru Ninagawa</b>\n\n<h10>2019-07-06</h10>\n> Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.\n\n### [Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model](http://arxiv.org/abs/1907.00636v1) (1907.00636v1)\n<i>Jan de Gier, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz</b>\n\n<h10>2019-07-01</h10>\n> Dynamical universality classes are distinguished by their dynamical exponent ![](http://latex2png.com/output//latex_bd61b29a408a64d11f1a55bca65fd0c4.png) and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known except for the special case ![](http://latex2png.com/output//latex_2fdb6000f3667b6e6887c72c14280977.png). Here the model corresponds to the TASEP (totally asymmetric simple exclusion process) that is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with ![](http://latex2png.com/output//latex_612eb39efa60bedf469ce3141e6664ff.png). In this paper, we show that the NaSch model also belongs to the KPZ class \\cite{KPZ} for general maximum velocities ![](http://latex2png.com/output//latex_d470cde12bfb573e851ddd17b54b2b41.png). Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. Performing large-scale Monte-Carlo simulations we show that the simulation results match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with dynamical lane changing rules.\n\n### [Evaluation on asymptotic distribution of particle systems expressed by  probabilistic cellular automata](http://arxiv.org/abs/1907.01635v1) (1907.01635v1)\n<i>Kazushige Endo</b>\n\n<h10>2019-06-29</h10>\n> We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.\n\n### [Shift-Symmetric Configurations in Two-Dimensional Cellular Automata:  Irreversibility, Insolvability, and Enumeration](http://arxiv.org/abs/1703.09030v2) (1703.09030v2)\n<i>Peter Banda, John Caughman, Martin Cenek, Christof Teuscher</b>\n\n<h10>2017-03-27</h10>\n> The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration.   Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-16",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 1|2019-07-16"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T16:01:15",
  "trx_id": "65672097de4103ba36d93c1e3de0e39fa32a5607",
  "trx_in_block": 1,
  "virtual_op": 0
}

{
  "block": 34673889,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-15",
      "voter": "steemitboard",
      "weight": 100
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T04:23:27",
  "trx_id": "03b953d5782850c2bf1825be0d1a3f91dabbb06a",
  "trx_in_block": 4,
  "virtual_op": 0
}

{
  "block": 34673888,
  "op": [
    "comment",
    {
      "author": "steemitboard",
      "body": "Congratulations @complexcity! You have completed the following achievement on the Steem blockchain and have been rewarded with new badge(s) :\n\n<table><tr><td><img src=\"https://steemitimages.com/60x60/http://steemitboard.com/img/notifications/postallweek.png\"></td><td>You published a post every day of the week</td></tr>\n</table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@complexcity) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=complexcity)_</sub>\n<sub>_If you no longer want to receive notifications, reply to this comment with the word_ `STOP`</sub>\n\n\nTo support your work, I also upvoted your post!\n\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
      "json_metadata": "{\"image\":[\"https://steemitboard.com/img/notify.png\"]}",
      "parent_author": "complexcity",
      "parent_permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-15",
      "permlink": "steemitboard-notify-complexcity-20190715t042326000z",
      "title": ""
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-15T04:23:24",
  "trx_id": "782180e5baa98ba947142aed4fefb01bff462ba2",
  "trx_in_block": 42,
  "virtual_op": 0
}

{
  "block": 34661637,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-15",
      "voter": "map10k",
      "weight": 46
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-14T18:10:15",
  "trx_id": "cbab7d950c9f66fde137a905c168ec36ad4f2baf",
  "trx_in_block": 0,
  "virtual_op": 0
}

{
  "block": 34661575,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-15",
      "voter": "accelerator",
      "weight": 28
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-14T18:07:09",
  "trx_id": "4aedd5ec0d7fc924b30adf62fa02584dc6e86684",
  "trx_in_block": 10,
  "virtual_op": 0
}

{
  "block": 34661438,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Pattern Formation And Solitons</center> \n <hr> \n\n### [Pattern formation in the presence of memory](http://arxiv.org/abs/1907.05304v1) (1907.05304v1)\n<i>Reza Torabi, Jörn Davidsen</b>\n\n<h10>2019-07-11</h10>\n> We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to use reductive perturbation to investigate the formation and stability of patterns. Focusing in detail on the Hopf instability and short-term memory, we derive the corresponding complex Ginzburg-Landau equation that governs the amplitude of the critical mode and we establish the explicit dependence of its parameters on the memory properties. Numerical solution of this memory dependent complex Ginzburg-Landau equation as well as direct numerical simulation of the non-Markovian Brusselator model illustrate that memory changes the properties of the spatio-temporal patterns. Our results indicate that going beyond the Markovian approximation might be necessary to study the formation of spatio-temporal patterns even in systems with short-term memory. At the same time, our work opens up a new window into the control of these patterns using memory.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Coexisting Ordered States, Local Equilibrium-like Domains, and Broken  Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state](http://arxiv.org/abs/1812.06002v4) (1812.06002v4)\n<i>Atanu Chatterjee, Yash Yadati, Nicholas Mears, Germano Iannacchione</b>\n\n<h10>2018-12-14</h10>\n> A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-B{\\'e}nard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system's temperature manifold.\n\n### [Immiscible and miscible states in binary condensates in the ring  geometry](http://arxiv.org/abs/1905.04584v2) (1905.04584v2)\n<i>Zhaopin Chen, Yongyao Li, Nikolaos P. Proukakis, Boris A. Malomed</b>\n\n<h10>2019-05-11</h10>\n> We report detailed investigation of the existence and stability of mixed and demixed modes in binary atomic Bose-Einstein condensates with repulsive interactions in a ring-trap geometry. The stability of such states is examined through eigenvalue spectra for small perturbations, produced by the Bogoliubov-de Gennes equations, and directly verified by simulations based on the coupled Gross-Pitaevskii equations, varying inter- and intra-species scattering lengths so as to probe the entire range of miscibility-immiscibility transitions. In the limit of the one-dimensional (1D) ring, i.e., a very narrow one, stability of mixed states is studied analytically, including hidden-vorticity (HV) modes, i.e., those with opposite vorticities of the two components and zero total angular momentum. The consideration of demixed 1D states reveals, in addition to stable composite single-peak structures, double- and triple-peak ones, above a certain particle-number threshold. In the 2D annular geometry, stable demixed states exist both in radial and azimuthal configurations. We find that stable radially-demixed states can carry arbitrary vorticity and, counter-intuitively, the increase of the vorticity enhances stability of such states, while unstable ones evolve into randomly oscillating angular demixed modes. The consideration of HV states in the 2D geometry expands the stability range of radially-demixed states.\n\n### [Phonon and Shifton from a Real Modulated Scalar](http://arxiv.org/abs/1907.04069v1) (1907.04069v1)\n<i>Daniele Musso, Daniel Naegels</b>\n\n<h10>2019-07-09</h10>\n> We study a massive real scalar field that breaks translation symmetry dynamically. Higher-gradient terms favour modulated configurations and neither finite density nor temperature are needed. In the broken phase, the energy density depends on the spatial position and the linear fluctuations show phononic dispersion. We then study a related massless scalar model where the modulated vacua break also the field shift symmetry and give rise to an additional Nambu-Goldstone mode, the shifton. We discuss the independence of the shifton and the phonon and draw an analogy to rotons in superfluids. Proceeding from first-principles, we re-obtain and generalise some standard results for one-dimensional lattices. Eventually, we prove stability against geometric deformations extending existing analyses for elastic media to the higher-derivatives cases.\n\n# <center>Exactly Solvable And Integrable Systems</center> \n <hr> \n\n### [Continued fractions and Hankel determinants from hyperelliptic curves](http://arxiv.org/abs/1907.05204v1) (1907.05204v1)\n<i>Andrew N. W. Hone</b>\n\n<h10>2019-07-11</h10>\n> Following van der Poorten, we consider a family of nonlinear maps which are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus ![](http://latex2png.com/output//latex_cedb66854950d47d05ff624e4b43eb3a.png). Using the connection with the classical theory of J-fractions and orthogonal polynomials, we show that in the simplest case ![](http://latex2png.com/output//latex_56744cc0f7cc8859ae4e48b8185b2143.png) this provides a straightforward derivation of Hankel determinant formulae for the terms of a general Somos-4 sequence, which were found in a particular form by Chang, Hu and Xin, We extend these formulae to the higher genus case, and prove that generic Hankel determinants in genus two satisfy a Somos-8 relation. Moreover, for all ![](http://latex2png.com/output//latex_cedb66854950d47d05ff624e4b43eb3a.png) we show that the iteration for the continued fraction expansion is equivalent to a discrete Lax pair with a natural Poisson structure, and the associated nonlinear map is a discrete integrable system. This paper is dedicated to the memory of Jon Nimmo.\n\n### [Generalized primitive potentials](http://arxiv.org/abs/1907.05038v1) (1907.05038v1)\n<i>Dmitry Zakharov, Vladimir Zakharov</b>\n\n<h10>2019-07-11</h10>\n> In our previous work, we introduced a new class of bounded potentials of the one-dimensional Schr\\\"odinger operator on the real axis, and a corresponding family of solutions of the KdV hierarchy. These potentials, which we call primitive, are obtained as limits of rapidly decreasing reflectionless potentials, or multisoliton solutions of KdV. In this note, we introduce generalized primitive potentials, which are obtained as limits of all rapidly decreasing potentials of the Schr\\\"odinger operator. These potentials are constructed by solving a contour problem, and are determined by a pair of positive functions on a finite interval and a functional parameter on the real axis.\n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [![](http://latex2png.com/output//latex_1d3375894ecf6e5b9a29ff8866f7e7ad.png)-type Fermions and ![](http://latex2png.com/output//latex_1d3375894ecf6e5b9a29ff8866f7e7ad.png)-type KP hierarchy](http://arxiv.org/abs/1907.04226v1) (1907.04226v1)\n<i>Na Wang, Chuanzhong Li</b>\n\n<h10>2019-07-09</h10>\n> In this paper, we firstly construct ![](http://latex2png.com/output//latex_c14403f3d2f9c97a98478aa8a89cb12a.png)-type Fermions. According to these, we define ![](http://latex2png.com/output//latex_c14403f3d2f9c97a98478aa8a89cb12a.png)-type Boson-Fermion correspondence which is a generalization of the classical Boson-Fermion correspondence. We can obtain ![](http://latex2png.com/output//latex_c14403f3d2f9c97a98478aa8a89cb12a.png)-type symmetric functions ![](http://latex2png.com/output//latex_bc2ef7ea952dd02b2262c5f278d6760a.png) from the ![](http://latex2png.com/output//latex_c14403f3d2f9c97a98478aa8a89cb12a.png)-type Boson-Fermion correspondence, analogously to the way we get the Schur functions ![](http://latex2png.com/output//latex_1dc3f5908a47857117087cd43f96af77.png) from the classical Boson-Fermion correspondence (which is the same thing as the Jacobi-Trudi formula). Then as a generalization of KP hierarchy, we construct the ![](http://latex2png.com/output//latex_c14403f3d2f9c97a98478aa8a89cb12a.png)-type KP hierarchy and obtain its tau functions.\n\n### [Quantum torus symmetries of multicomponent modified KP hierarchy and  reductions](http://arxiv.org/abs/1907.04688v1) (1907.04688v1)\n<i>Chuanzhong Li, Jipeng Cheng</b>\n\n<h10>2019-07-09</h10>\n> In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the constrained multicomponent modified KP hierarchy and its Virasoro type additional symmetries.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-22019-07-15",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 2|2019-07-15"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-14T18:00:18",
  "trx_id": "bfc6821fd940d70406242c1d24b5d29f3cb074ba",
  "trx_in_block": 10,
  "virtual_op": 0
}

{
  "block": 34659200,
  "op": [
    "vote",
    {
      "author": "complexcity",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-15",
      "voter": "sergino",
      "weight": 500
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-14T16:08:21",
  "trx_id": "1f94ef14af4eff737caf348151a097e5eed3e98c",
  "trx_in_block": 16,
  "virtual_op": 0
}

{
  "block": 34659057,
  "op": [
    "comment",
    {
      "author": "complexcity",
      "body": "<center><b> Welcome To Nonlinear Sciences</b></center>\n\n# <center>Adaptation And Self-Organizing Systems</center> \n <hr> \n\n### [Analysis of Bivariate Jump-Diffusion Processes](http://arxiv.org/abs/1907.05371v1) (1907.05371v1)\n<i>Leonardo Rydin Gorjão, Jan Heysel, Klaus Lehnertz, M. Reza Rahimi Tabar</b>\n\n<h10>2019-07-11</h10>\n> We introduce the bivariate jump-diffusion process, comprising two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, non-parametric estimation procedure of higher-order Kramers--Moyal coefficients that allows one to reconstruct relevant aspects of the underlying jump-diffusion processes and recover the underlying parameters of a jump-diffusion process. The procedure is validated with numerically integrated data using synthetic bivariate continuous and discontinuous time series. We further evaluate the possibility of estimating the parameters of the jump-diffusion model via a data driven analyses of the higher-order Kramers--Moyal coefficients, and the limitations arising from the scarcity of points in the data or disproportionate parameters in the system.\n\n### [Dynamical modelling of cascading failures in the Turkish power grid](http://arxiv.org/abs/1907.05194v1) (1907.05194v1)\n<i>Benjamin Schäfer, G. Cigdem Yalcin</b>\n\n<h10>2019-07-11</h10>\n> A reliable supply of electricity is critical for our modern society and any large scale disturbances of the electrical system causes substantial costs. In 2015, one overloaded transmission line caused a cascading failure in the Turkish power grid, affecting about 75 million people. We focus on the dynamical and statistical properties of the Turkish power grid as a real-world system example that can be modelled based on complex networks structures and we propose for the first time a model that incorporates the dynamical properties of the Turkish power grid as a complex network topology by investigating these cascading failures. We find that the network damage depends on the load and generation distribution in the network with centralized generation being more susceptible to failures than a decentralized one. Furthermore, economic considerations on transmission line capacity are shown to conflict with stability.\n\n### [Fixation properties of rock-paper-scissors games in fluctuating  populations](http://arxiv.org/abs/1907.05184v1) (1907.05184v1)\n<i>Robert West, Mauro Mobilia</b>\n\n<h10>2019-07-11</h10>\n> Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different \"laws\" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the ![](http://latex2png.com/output//latex_561204284301b422c5bed9b3f64b096e.png) of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness \"levels the field\" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity.\n\n### [Coexisting Ordered States, Local Equilibrium-like Domains, and Broken  Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state](http://arxiv.org/abs/1812.06002v4) (1812.06002v4)\n<i>Atanu Chatterjee, Yash Yadati, Nicholas Mears, Germano Iannacchione</b>\n\n<h10>2018-12-14</h10>\n> A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-B{\\'e}nard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system's temperature manifold.\n\n### [The Beer Can Theory of Creativity](http://arxiv.org/abs/1309.7414v3) (1309.7414v3)\n<i>Liane Gabora</b>\n\n<h10>2013-09-28</h10>\n> This chapter explores the cognitive mechanisms underlying the emergence and evolution of cultural novelty. Section Two summarizes the rationale for viewing the process by which the fruits of the mind take shape as they spread from one individual to another as a form of evolution, and briefly discusses a computer model of this process. Section Three presents theoretical and empirical evidence that the sudden proliferation of human culture approximately two million years ago began with the capacity for creativity: that is, the ability to generate novelty strategically and contextually. The next two sections take a closer look at the creative process. Section Four examines the mechanisms underlying the fluid, associative thought that constitutes the inspirational component of creativity. Section Five explores how that initial flicker of inspiration crystallizes into a solid, workable idea as it gets mulled over in light of the various constraints and affordances of the world into which it will be born. Finally, Section Six wraps things up with a few speculative thoughts about the overall unfolding of this evolutionary process.\n\n# <center>Chaotic Dynamics</center> \n <hr> \n\n### [Statistical Measures and Selective Decay Principle for Generalized Euler  Dynamics](http://arxiv.org/abs/1907.05069v1) (1907.05069v1)\n<i>Giovanni Conti, Gualtiero Badin</b>\n\n<h10>2019-07-11</h10>\n> We investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or {\\alpha}-models. We aim to study the equilibrium mechanics, using initially a point-vortex approximation and then exploiting the full continuous equations, invoking the maximization of appropriate entropy functionals. The point-vortex approximation highlights an important difference between the 2D turbulence and local dynamics models. In the latter, it is in fact possible to derive a statistical measure only considering two conserved quantities as constraints for the maximization problem, the Hamiltonian and the angular impulse. This result does not hold for 2D turbulence. Both the continuous and the point vortex approximation allow for the derivation of mean field equations that act as constraints for the functional relation between the streamfunction and the active scalar of the model considered. Further, the analysis of the continuous equations suggests the existence of a selective decay principle for the whole family of models. To test these ideas we use numerical simulations of the partial differential equations of the {\\alpha}-models starting from different sets of initial conditions (i.c.s). For random i.c.s, all the solutions tend to a dipolar structure. The functional relation between the active scalar and the streamfunction shows an increase of nonlinearity with a decrease of the locality of the dynamics. We then test the evolution of the specific case of SQG for i.c.s in the form of a hyperbolic saddle, that is a candidate for the possible formation of singularity through a self-similar cascade though secondary instabilities. Results show the presence of a scale dependent selective decay associated to the breaking of the frontal structures emerging from the flow, suggesting a relation with the change of topology of the flow.\n\n### [Length-Divergent Thermal Conductivity in Long-Range Interacting  Fermi-Pasta-Ulam Chains](http://arxiv.org/abs/1906.11086v3) (1906.11086v3)\n<i>Jianjin Wang, Sergey V. Dmitriev, Daxing Xiong</b>\n\n<h10>2019-06-26</h10>\n> The power-law length (![](http://latex2png.com/output//latex_0ee8776a295f6d06670ea84906a0e45a.png)) divergence of thermal conductivity (![](http://latex2png.com/output//latex_39a1acc0a1fe620307fc63cb0815e3a7.png)) in one-dimensional (1D) systems, i.e., ![](http://latex2png.com/output//latex_b20866e36c2c81c0136fd88a226ed4ee.png), has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent ![](http://latex2png.com/output//latex_879bee8d9bc4848dee78650baeff05fd.png) are usually ranging from ![](http://latex2png.com/output//latex_90e13cc294761693602fb52e9bfa10a3.png) to ![](http://latex2png.com/output//latex_1dc26b2661fa7239c25eb86fa8572e08.png); however sometimes, the experimental observations can be higher, e.g., ![](http://latex2png.com/output//latex_39328b34a56faaf05d072b0ec10cb72b.png)-![](http://latex2png.com/output//latex_3868dd6a68cc6c62a53407e92b0150c9.png). This dispute has not yet been settled. Here we show the first convincing evidence that an exponent of ![](http://latex2png.com/output//latex_3e09866b5ba9179843d4b951ca50c1f1.png) that falls within experimental observations, can occur in a theoretical model of 1D long-range interacting Fermi-Pasta-Ulam chain. This, for the first time, theoretically supports the possibility of a higher divergent exponent and thus sheds new light on understanding of extremely high thermal conductivity in 1D materials at macroscopic scales.\n\n### [Dynamics of random pressure fields over bluff bodies: a dynamic mode  decomposition perspective](http://arxiv.org/abs/1904.02245v3) (1904.02245v3)\n<i>Xihaier Luo, Ahsan Kareem</b>\n\n<h10>2019-03-26</h10>\n> Aerodynamic pressure field over bluff bodies immersed in boundary layer flows is correlated both in space and time. Conventional approaches for the analysis of distributed aerodynamic pressures, e.g., the proper orthogonal decomposition (POD), can only offer relevant spatial patterns in a set of coherent structures. This study provides an operator-theoretic approach that describes dynamic pressure fields in a functional space rather than conventional phase space via the Koopman operator. Subsequently, spectral analysis of the Koopman operator provides a spatiotemporal characterization of the pressure field. An augmented dynamic mode decomposition (DMD) method is proposed to perform the spectral decomposition. The augmentation is achieved by the use of the Takens's embedding theorem, where time delay coordinates are considered. Consequently, the identified eigen-tuples (eigenvalues, eigenvectors, and time evolution) can capture not only dominant spatial structures but also identify each structure with a specific frequency and a corresponding temporal growth/decay. This study encompasses learning the evolution dynamics of the random aerodynamic pressure field over a scaled model of a finite height prism using limited wind tunnel data. The POD analysis of the experimental data was also carried out. To demonstrate the unique feature of the proposed approach, the DMD and POD based learning results including algorithm convergence, data sufficiency, and modal analysis are examined. The ensuing observations offer a glimpse of the complex dynamics of the surface pressure field over bluff bodies that lends insights to features previously masked by conventional analysis approaches.\n\n### [Many-body chaos near a thermal phase transition](http://arxiv.org/abs/1905.00904v3) (1905.00904v3)\n<i>Alexander Schuckert, Michael Knap</b>\n\n<h10>2019-05-02</h10>\n> We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.\n\n### [On optimal cover and its possible shape for fractals embedded into 2D  Euclidian space](http://arxiv.org/abs/1907.04578v1) (1907.04578v1)\n<i>Dmitry Zhabin</b>\n\n<h10>2019-07-10</h10>\n> In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition, the functional equation is resolved and possible shapes of optimal coverage are defined in correspondence with fractal dimension values.\n\n# <center>Cellular Automata And Lattice Gases</center> \n <hr> \n\n### [Double jump phase transition in a soliton cellular automaton](http://arxiv.org/abs/1706.05621v4) (1706.05621v4)\n<i>Lionel Levine, Hanbaek Lyu, John Pike</b>\n\n<h10>2017-06-18</h10>\n> In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) boxes are occupied independently with probability ![](http://latex2png.com/output//latex_54d64670d0b3c4acb87156b2b9135b2f.png), then the number of solitons is of order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for all ![](http://latex2png.com/output//latex_fcf34992423b3238c306f6d41c8f78d8.png), and the length of the longest soliton is of order ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_5bed66b158aec8fd350791ae06a2c454.png), order ![](http://latex2png.com/output//latex_3dd212720028b3748748f02be27fc35e.png) for ![](http://latex2png.com/output//latex_bf99a661823a6e747ce0d6382431b6d5.png), and order ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed ![](http://latex2png.com/output//latex_fa5c01670deb454b07cb181cc8e5d735.png), the top ![](http://latex2png.com/output//latex_8ace6052ac3b31a0068f97c7fdeb7cbd.png) soliton lengths have the same order as the longest for ![](http://latex2png.com/output//latex_8e11af97b25f56cb4c1274df08300c4a.png), whereas all but the longest have order at most ![](http://latex2png.com/output//latex_78232501826853eb49ca83739b5fe2ae.png) for ![](http://latex2png.com/output//latex_d0bdab79a806a6467b9e78249b3f74e8.png). As an application, we obtain scaling limits for the lengths of the ![](http://latex2png.com/output//latex_9cbd25abfe3eed1e51f51689c0c2c74e.png) longest increasing and decreasing subsequences in a random stack-sortable permutation of length ![](http://latex2png.com/output//latex_a78da909d65184636aa635647d3ad1fd.png) in terms of random walks and Brownian excursions.\n\n### [Universal One-Dimensional Cellular Automata Derived for Turing Machines  and its Dynamical Behaviour](http://arxiv.org/abs/1907.04211v1) (1907.04211v1)\n<i>Sergio J. Martinez, Ivan M. Mendoza, Genaro J. Martinez, Shigeru Ninagawa</b>\n\n<h10>2019-07-06</h10>\n> Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.\n\n### [Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model](http://arxiv.org/abs/1907.00636v1) (1907.00636v1)\n<i>Jan de Gier, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz</b>\n\n<h10>2019-07-01</h10>\n> Dynamical universality classes are distinguished by their dynamical exponent ![](http://latex2png.com/output//latex_bd61b29a408a64d11f1a55bca65fd0c4.png) and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known except for the special case ![](http://latex2png.com/output//latex_2fdb6000f3667b6e6887c72c14280977.png). Here the model corresponds to the TASEP (totally asymmetric simple exclusion process) that is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with ![](http://latex2png.com/output//latex_612eb39efa60bedf469ce3141e6664ff.png). In this paper, we show that the NaSch model also belongs to the KPZ class \\cite{KPZ} for general maximum velocities ![](http://latex2png.com/output//latex_d470cde12bfb573e851ddd17b54b2b41.png). Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. Performing large-scale Monte-Carlo simulations we show that the simulation results match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with dynamical lane changing rules.\n\n### [Evaluation on asymptotic distribution of particle systems expressed by  probabilistic cellular automata](http://arxiv.org/abs/1907.01635v1) (1907.01635v1)\n<i>Kazushige Endo</b>\n\n<h10>2019-06-29</h10>\n> We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.\n\n### [Shift-Symmetric Configurations in Two-Dimensional Cellular Automata:  Irreversibility, Insolvability, and Enumeration](http://arxiv.org/abs/1703.09030v2) (1703.09030v2)\n<i>Peter Banda, John Caughman, Martin Cenek, Christof Teuscher</b>\n\n<h10>2017-03-27</h10>\n> The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration.   Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.\n\n <br><hr> <center>Thank you for reading!<br> https://cdn.steemitimages.com/DQmbn3ovuKLM17k6aemZMrJj6iqKkYzXCYz5Qh1Fg7vPmRx/image.png <br> Don't forget to Follow and Resteem. @complexcity <br>Keeping everyone inform.</center>",
      "json_metadata": "{\"tags\": [\"complexsytems\"]}",
      "parent_author": "",
      "parent_permlink": "complexsytems",
      "permlink": "most-recent-arxiv-papers-in-nonlinear-sciences-12019-07-15",
      "title": "Most Recent Arxiv Papers In Nonlinear Sciences 1|2019-07-15"
    }
  ],
  "op_in_trx": 0,
  "timestamp": "2019-07-14T16:01:12",
  "trx_id": "644503d214c2af957a6e50b963f6146a648390bb",
  "trx_in_block": 2,
  "virtual_op": 0
}