Mathematical Sciences: Stochastic Partial Differential Equations -- A Particle Systems Approach

研究人员正在开发一种用于颗粒和漩涡分布的随机偏微分方程组(SPDEs)的微积分。这些单项微分方程组是抛物型偏微分方程组，通过附加的涨落项进行修正。涨落项必须从颗粒分布中推导出来。这种方法的优点之一是，SPDE中的所有量都可以用物理术语来解释，如果守恒定律适用于基本的物理模型，那么SPDE将适用于守恒定律。这位研究人员正在开发一种研究随机系统的方法，这些系统出现在理论物理、流体力学、化学和数学的各个领域。模型中的量可以用物理术语来解释，这应该有助于分析。

The investigator is developing a calculus of stochastic partial differential equations (SPDEs) for the distribution of particles and vortices. These SPDEs are partial differential equations (PDEs) of parabolic type which are corrected by an additional fluctuation term. The fluctuation term has to be derived from the particle distribution. One of the advantages of this approach is that all quantities in the SPDE can be interpreted in physical terms, and conservation laws will hold for the SPDE if they hold for the underlying physical model. The investigator is developing a method of studying stochastic systems which arise in theoretical physics, fluid dynamics, chemistry and various fields of mathematics. The quantities in the models can be interpreted in physical terms, which should help in the analysis.