Lattice models of nonequilibrium bacterial dynamics
Lattice models of nonequilibrium bacterial dynamics
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DOI：
10.1088/1742-5468/2011/02/p02029
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
A. G. Thompson;Julien Tailleur;Michael E. Cates;R. Blythe
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文献类型：
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作者：
A. G. Thompson;Julien Tailleur;Michael E. Cates;R. Blythe
我们研究了一个自推进粒子模型，该模型在晶格上表现出运行和翻滚动力学。这种非布朗扩散的特征在于在方向变化之间具有有限持续长度的随机游走，并且受到诸如E.杆菌通过定义一类具有多个粒子种类和物种之间的嬗变的模型，我们可以重新创建这样的动力学。这些模型承认准确的分析结果，同时也形成了一个对应的运行和翻滚动力学以前的连续模型。我们解决了外部驱动的非相互作用和零范围版本的模型，并利用场论的方法来推导出更一般的相互作用的连续波动流体动力学。我们与以前的方法来运行和翻滚动力学的晶格接触，并确定一类拥挤的相互作用，跳跃率随着密度的增加而降低的稳态和线性稳定性。除了从非平衡统计力学的角度来看它的兴趣之外，这个晶格模型构成了一个有效的工具来模拟一类与细菌运动相关的相互作用的运行和翻滚模型，只要满足某些条件（我们推导出的）。
We study a model of self-propelled particles exhibiting run-and-tumble dynamics on a lattice. This non-Brownian diffusion is characterized by a random walk with a finite persistence length between changes of direction and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particles and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run-and-tumble dynamics. We solve the externally driven non-interacting and zero-range versions of the model exactly and utilize a field-theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to run-and-tumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes an efficient tool to simulate a class of interacting run-and-tumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met.