Intrinsic Langevin dynamics of rigid inclusions on curved surfaces.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Balázs Németh, Ronojoy Adhikari
{"title":"Intrinsic Langevin dynamics of rigid inclusions on curved surfaces.","authors":"Balázs Németh, Ronojoy Adhikari","doi":"10.1103/PhysRevE.111.045418","DOIUrl":null,"url":null,"abstract":"<p><p>The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic particles on liquid-liquid interfaces. Here we construct intrinsic Langevin equations for an oriented rigid inclusion on a fixed curved surface using Cartan's method of moving frames. We first derive the Hamiltonian equations of motion for the translational and rotational momenta in the body frame. Surprisingly, surface curvature couples the linear and angular momenta of the inclusion. We then add to the Hamiltonian equations linear friction, white noise, and arbitrary configuration-dependent forces and torques to obtain intrinsic Langevin equations of motion in phase space. We provide the integrability conditions, made nontrivial by surface curvature, for the forces and torques to admit a potential, thus distinguishing between passive and active stochastic motion. We derive the corresponding Fokker-Planck equation in geometric form and obtain fluctuation-dissipation relations that ensure Gibbsian equilibrium. We extract the overdamped equations of motion by adiabatically eliminating the momenta from the Fokker-Planck equation, showing how a peculiar cancellation leads to the naively expected Smoluchowski limit. The overdamped equations can be used for accurate and efficient intrinsic Brownian dynamics simulations of passive, driven, and active diffusion processes on curved surfaces. Our work generalizes to the collective dynamics of many inclusions on curved surfaces.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"111 4-2","pages":"045418"},"PeriodicalIF":2.4000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.045418","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

Abstract

The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic particles on liquid-liquid interfaces. Here we construct intrinsic Langevin equations for an oriented rigid inclusion on a fixed curved surface using Cartan's method of moving frames. We first derive the Hamiltonian equations of motion for the translational and rotational momenta in the body frame. Surprisingly, surface curvature couples the linear and angular momenta of the inclusion. We then add to the Hamiltonian equations linear friction, white noise, and arbitrary configuration-dependent forces and torques to obtain intrinsic Langevin equations of motion in phase space. We provide the integrability conditions, made nontrivial by surface curvature, for the forces and torques to admit a potential, thus distinguishing between passive and active stochastic motion. We derive the corresponding Fokker-Planck equation in geometric form and obtain fluctuation-dissipation relations that ensure Gibbsian equilibrium. We extract the overdamped equations of motion by adiabatically eliminating the momenta from the Fokker-Planck equation, showing how a peculiar cancellation leads to the naively expected Smoluchowski limit. The overdamped equations can be used for accurate and efficient intrinsic Brownian dynamics simulations of passive, driven, and active diffusion processes on curved surfaces. Our work generalizes to the collective dynamics of many inclusions on curved surfaces.

曲面上刚性夹杂物的本征朗之万动力学。
约束在曲面上移动的刚性包涵体的随机动力学在生物和软物质物理学中有许多应用,从被动或主动膜蛋白的扩散到液-液界面上的电泳颗粒的运动。本文用Cartan的运动框架法构造了固定曲面上定向刚体的内禀朗之万方程。我们首先推导了物体坐标系中平移动量和转动动量的哈密顿运动方程。令人惊讶的是,表面曲率耦合了包体的线动量和角动量。然后,我们在哈密顿方程中加入线性摩擦、白噪声和任意构型相关的力和力矩,以获得相空间中固有的朗之万运动方程。我们提供了可积性条件,使曲面曲率非平凡,力和扭矩承认一个势,从而区分被动和主动随机运动。导出了相应的几何形式的Fokker-Planck方程,得到了保证吉本平衡的涨落-耗散关系。我们通过绝热消除福克-普朗克方程中的动量来提取过阻尼运动方程,展示了一种特殊的消去如何导致天真地期望斯摩鲁霍夫斯基极限。该过阻尼方程可用于精确、有效地模拟曲面上被动、驱动和主动扩散过程的本征布朗动力学。我们的工作推广到曲面上许多内含物的集体动力学。
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 求助全文
来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信