Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Statistical Physics Pub Date : 2024-10-14 DOI:10.1007/s10955-024-03344-2
Luca Angelani, Alessandro De Gregorio, Roberto Garra, Francesco Iafrate
{"title":"Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations","authors":"Luca Angelani,&nbsp;Alessandro De Gregorio,&nbsp;Roberto Garra,&nbsp;Francesco Iafrate","doi":"10.1007/s10955-024-03344-2","DOIUrl":null,"url":null,"abstract":"<div><p>Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in <i>d</i>-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03344-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-024-03344-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0

Abstract

Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
反常随机飞行和时间分数运行翻滚方程
随机飞行(也称奔跑和翻滚行走或传输过程)表示在任何泊松时间内改变方向的有限速度随机运动。这些 d 维模型的研究给出了在任何空间维度上都有效的问题的一般表述。本文的目的是将这种一般分析扩展到动力学方程的非局部广义化所产生的时间分数过程。时间分数方程解的概率解释导致了原始传输过程的时间变化版本。所获得的结果清楚地说明了时间分数导数在这种随机运动中所起的作用。它们显示出一种反常行为,有助于描述统计物理学和生物学中出现的若干复杂系统。我们尤其关注被称为电报过程的一维随机飞行,研究经典电报方程的时间分数版本,并为其随机解提供合适的解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
期刊最新文献
Condensation in Zero-Range Processes with a Fast Rate Lattice Fundamental Measure Theory Beyond 0D Cavities: Dimers on Square Lattices Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Heavy-Tailed Interaction Fluctuations of the Occupation Density for a Parking Process A Consistent Kinetic Fokker–Planck Model for Gas Mixtures
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1