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

研究人员正在开发一种随机 偏微分方程（SPDE）的分布 粒子和漩涡。 这些SPDE是偏微分的 方程（偏微分方程）的抛物型，这是纠正了一个 附加波动项。 波动项必须是 从颗粒分布来看。 的优点之一 这种方法是，SPDE中的所有量都可以是 用物理术语来解释，守恒定律将成立， 对于SPDE，如果它们对于底层物理模型成立的话。 研究人员正在开发一种研究 理论物理中出现的随机系统， 动力学、化学和各种数学领域。 的 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.