Macroscopic dynamics and bifurcations of active particle systems
活性粒子系统的宏观动力学和分叉
基本信息
- 批准号:EP/M006883/1
- 负责人:
- 金额:$ 48.55万
- 依托单位:
- 依托单位国家:英国
- 项目类别:Research Grant
- 财政年份:2015
- 资助国家:英国
- 起止时间:2015 至 无数据
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The living world presents many examples of large assemblies of coordinated agents such as insect swarms, bird flocks or crowds and, at a more microscopic scale, swarming bacterial colonies or collectively migrating cells. These agents resemble particles composing inert matter but a striking difference is that they produce their own motion. They are generically referred to as active particles. Like herds and flocks, most active particle systems exhibit self-organized collective motion. The mechanisms by which self-organization emerges are still poorly understood. Current research on this question is intense. In this work, we view the emergence of self-organization as a bifurcation from a non-coordinated state of the system to a collectively coordinated one. Bifurcations are intimately related to what physicists call phase transitions, i. e. abrupt changes of the state of a system when its environmental parameters are changed. Everyday examples are changes of state of matter such as water changing from liquid to vapor when its temperature crosses the boiling temperature. In nature, animals groups may change from a random motion state (when they are foraging for food for instance) to a coordinated motion state (when they want to escape the attack of a predator) in a similar way. Our goal is to study mathematical models for active particle systems. We aim to develop macroscopic descriptions of these systems when the number of particles is large and to analyse their bifurcation from disordered to collective motion. Indeed, when the number of agents is large, it is neither possible nor efficient to follow each agent individually. Macroscopic models describe the evolution of statistical averages such as the mean density or velocity of the particles and are computationally much more efficient. Their rigorous derivation involves complex mathematical tools of kinetic theory but they give rise to an efficient way of analysing bifurcations. Like for matter, there are many different types of bifurcations in active particle systems. In this proposal, we will focus on two specific but important examples. The first one is symmetry-breaking bifurcations when a system state changes its underlying symmetry. The second one is bifurcation due to jamming, which occurs when finite sized particles reach the density where they are all in contact with each other as in dense crowds for instance. To test the general character of our findings, we will also investigate other kinds of bifurcations, by looking at systems of rigid bodies interacting through attitude coordination, having collective sperm-cell dynamics as an application in mind. The nature of mathematical models varies according to which state of the system they are adapted to. When several states are present simultaneously, they are separated by abrupt transition interfaces. To numerically approximate such situations, numerical methods that are uniformly accurate across the transition interface will be developed. They will allow us to validate the models by comparing them with real data in two selected applications, namely collective sperm-cell dynamics and pedestrian dynamics. In these two examples, we will showcase the usefulness of the models by using them to anticipate the outcome of various strategies of action aiming to change the collective behaviour of the system.
生物世界中有许多协调媒介的大型集合体,如昆虫群、鸟群或群体,在更微观的尺度上,还有成群的细菌菌落或集体迁移的细胞。这些物质类似于组成惰性物质的粒子,但一个显著的区别是它们产生自己的运动。它们通常被称为活性粒子。像牛群和羊群一样,大多数活跃的粒子系统都表现出自组织的集体运动。自组织出现的机制仍然知之甚少。目前对这一问题的研究非常深入。在这项工作中,我们认为出现的自组织作为一个分叉,从一个非协调状态的系统,以集体协调。分叉与物理学家所谓的相变密切相关,即。e.当系统的环境参数改变时,系统状态的突然变化。日常的例子是物质状态的变化,如水在其温度超过沸点时从液体变成蒸汽。在自然界中,动物群体可以以类似的方式从随机运动状态(例如当它们觅食时)转变为协调运动状态(当它们想要逃避捕食者的攻击时)。我们的目标是研究主动粒子系统的数学模型。我们的目标是发展这些系统的宏观描述时,粒子的数量是大的,并分析其从无序到集体运动的分歧。事实上,当代理人的数量很大时,单独跟踪每个代理人既不可能也没有效率。宏观模型描述了统计平均值的演变,例如粒子的平均密度或速度,并且在计算上更有效。他们的严格推导涉及复杂的数学工具的动力学理论,但他们产生了一个有效的方法来分析分叉。像物质一样,在活跃的粒子系统中有许多不同类型的分叉。在本建议中,我们将重点介绍两个具体但重要的例子。第一种是当系统状态改变其基本对称性时的破缺分岔。第二种是由于堵塞而产生的分叉,当有限尺寸的颗粒达到密度时,它们都彼此接触,例如在密集的人群中。为了检验我们发现的一般特征,我们还将研究其他类型的分叉,通过观察通过姿态协调相互作用的刚体系统,将集体精子细胞动力学作为一种应用。数学模型的性质根据它们所适应的系统状态而变化。当几个状态同时存在时,它们被突然的过渡界面分开。为了在数值上近似这种情况,将开发在过渡界面上具有一致精度的数值方法。它们将使我们能够通过将模型与两个选定应用中的真实的数据进行比较来验证模型,即集体精子细胞动力学和行人动力学。在这两个例子中,我们将展示模型的有用性,通过使用它们来预测旨在改变系统集体行为的各种行动策略的结果。
项目成果
期刊论文数量(10)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Phase Transitions in a kinetic flocking model of Cucker-Smale type
Cucker-Smale 型动力学植绒模型中的相变
- DOI:10.48550/arxiv.1510.04009
- 发表时间:2015
- 期刊:
- 影响因子:0
- 作者:Barbaro A
- 通讯作者:Barbaro A
A new model for the emergence of blood capillary networks
毛细血管网络出现的新模型
- DOI:10.3934/nhm.2021001
- 发表时间:2021
- 期刊:
- 影响因子:1
- 作者:Aceves-Sanchez P
- 通讯作者:Aceves-Sanchez P
Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation.
- DOI:10.1007/s11538-020-00805-z
- 发表时间:2020-09-25
- 期刊:
- 影响因子:3.5
- 作者:Aceves-Sanchez P;Degond P;Keaveny EE;Manhart A;Merino-Aceituno S;Peurichard D
- 通讯作者:Peurichard D
Pedestrian Models based on Rational Behaviour
基于理性行为的行人模型
- DOI:10.48550/arxiv.1808.07426
- 发表时间:2018
- 期刊:
- 影响因子:0
- 作者:Bailo R
- 通讯作者:Bailo R
Incompressible limit of a continuum model of tissue growth with segregation for two cell populations
两个细胞群分离的组织生长连续模型的不可压缩极限
- DOI:10.25418/crick.11619099
- 发表时间:2020
- 期刊:
- 影响因子:0
- 作者:A Chertock
- 通讯作者:A Chertock
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Pierre Degond其他文献
Simulation of a resonant tunneling diode using an entropic quantum drift-diffusion model
- DOI:
10.1007/s10825-006-0088-4 - 发表时间:
2006-12-09 - 期刊:
- 影响因子:2.500
- 作者:
Pierre Degond;Samy Gallego;Florian Méhats - 通讯作者:
Florian Méhats
Numerical simulations of the ionospheric striation model in a non-uniform magnetic field
- DOI:
10.1016/j.cpc.2006.07.022 - 发表时间:
2007-01-15 - 期刊:
- 影响因子:
- 作者:
Christophe Besse;Jean Claudel;Pierre Degond;Fabrice Deluzet;Gérard Gallice;Christian Tessieras - 通讯作者:
Christian Tessieras
Quasi-neutral fluid models for current-carrying plasmas
- DOI:
10.1016/j.jcp.2004.11.011 - 发表时间:
2005-05-20 - 期刊:
- 影响因子:
- 作者:
Pierre Crispel;Pierre Degond;Marie-Hélène Vignal - 通讯作者:
Marie-Hélène Vignal
Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited
- DOI:
10.1016/j.jnnfm.2010.02.007 - 发表时间:
2010-05-01 - 期刊:
- 影响因子:
- 作者:
Pierre Degond;Alexei Lozinski;Robert G. Owens - 通讯作者:
Robert G. Owens
An existence result for a strongly coupled parabolic system arising in nonequilibrium thermodynamics
- DOI:
10.1016/s0764-4442(97)84605-8 - 发表时间:
1997-07-01 - 期刊:
- 影响因子:
- 作者:
Pierre Degond - 通讯作者:
Pierre Degond
Pierre Degond的其他文献
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