各向同性和各向异性环境中自推进运动的几何方法
A geometric approach to self-propelled motion in isotropic and anisotropic environments
摘要：
我们提出了一个几何的角度来描述运动的自推进粒子在d维匀速运动。我们利用的事实，即传达粒子的运动方向的矢量执行随机行走的$(d-1)$维流形。我们表明，粒子进行各向同性扩散的d维，如果流形对应于一个超球。相比之下，我们发现，自推进粒子表现出各向异性扩散，如果这个流形对应于一个变形的超球体（例如椭圆）。这种简单的方法提供了一个统一的框架来处理各向同性以及各向异性扩散的粒子以恒定的速度在任何维度上移动。
英文摘要：
We propose a geometric perspective to describe the motion of self-propelled particles moving at constant speed in d dimensions. We exploit the fact that the vector that conveys the direction of motion of the particle performs a random walk on a $(d-1)$-dimensional manifold. We show that the particle performs isotropic diffusion in d-dimensions if the manifold corresponds to a hypersphere. In contrast, we find that the self-propelled particle exhibits anisotropic diffusion if this manifold corresponds to a deformed hypersphere (e.g. an ellipsoid). This simple approach provides an unified framework to deal with isotropic as well as anisotropic diffusion of particles moving at constant speed in any dimension.
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