论文标题
加热方程和旋转旋转球的布朗运动
Heat equation and Brownian motion of an overdamped rotating sphere
论文作者
论文摘要
在蛋白质，各向异性胶体，介电理论和液晶等领域中，既可以翻译和旋转的布朗刚体的治理方程。在本文中，描述浓度演变的部分微分方程是从可能存在潜在场的粘性介质中经历布朗运动的球体的随机微分方程得出的。潜在的场可以是颗粒之间的相互作用，也可以是外部施加的。对于可以由向量（$ s^2 $）指定的粒子，而对需要旋转矩阵的粒子（$ so（3）$）指定的粒子进行了一次派生。派生显示了概率密度和浓度，ITO和Stratonovich演算之间的重要差异，并获得了Piola-type身份以完成推导。
The governing equations of Brownian rigid bodies that both translate and rotate are of interest in fields such as self-assembly of proteins, anisotropic colloids, dielectric theory, and liquid crystals. In this paper, the partial differential equation that describes the evolution of concentration is derived from the stochastic differential equation of a sphere experiencing Brownian motion in a viscous medium where a potential field may be present. The potential field may be either interactions between particles or applied externally. The derivation is performed once for particles whose orientation can be specified by a vector ($S^2$), and again for particles which require a rotation matrix ($SO(3)$). The derivation shows the important difference between probability density and concentration, the Ito and Stratonovich calculus, and a Piola-type identity is obtained to complete the derivation.
