Interacting Particle Systems and Stochastic PDEs

相互作用的粒子系统和随机偏微分方程

• 批准号: EP/N028457/1
• 负责人: Mathew Joseph
• 金额: $ 11.92万
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FN028457%2F1
• 关键词: Interacting; Particle; Systems; Stochastic; PDEs

The heat equation is a mathematical equation used to describe the flow of heat through a purely conducting substance. This equation and many variations of it have been studied for around two hundred years, and the mathematical theory is now well developed. Over the last few decades mathematicians and physicists have been interested in the more realistic stochastic heat equation which considers the effect of having impurities randomly scattered in the medium. Certain transformations of this equation are also used to describe many other physical phenomena, for example motion of a turbulent fluid, deposition of snow and bacterial growth.Although many advances have been made in our understanding of the stochastic heat equation, much more remains to be discovered. One of the goals of this proposal is to describe features of this equation for a wide class of impurities in the medium. The proposal also looks into ways of approximating this equation so that one can simulate the equation on a computer, which in turn will give us further intuition on its behaviour. We shall also explore connections of this equation to other systems exhibiting randomness.

热方程是一个数学方程，用来描述热量在纯导电物质中的流动。这个方程和它的许多变体已经被研究了大约200年，数学理论现在已经很发达了。在过去的几十年里，数学家和物理学家一直对更现实的随机热方程感兴趣，它考虑了杂质在介质中随机分散的影响。这个方程的某些变换也被用来描述许多其他的物理现象，例如湍流的运动、雪的沉积和细菌的生长。尽管我们对随机热方程的理解取得了许多进展，但仍有更多的东西有待发现。本建议的目标之一是描述介质中各种杂质的该方程的特征。该提案还研究了近似该方程的方法，以便人们可以在计算机上模拟该方程，这反过来将使我们对其行为有进一步的直观认识。我们还将探讨这个方程与其他表现出随机性的系统之间的联系。

项目成果

An invariance principle for the stochastic heat equation

• DOI: 10.1007/s40072-018-0118-9
• 发表时间: 2018-05
• 期刊: Stochastics and Partial Differential Equations: Analysis and Computations
• 作者: Mathew Joseph

An approximation result for a class of stochastic heat equations with colored noise

一类带有有色噪声的随机热方程的近似结果

• DOI: 10.1214/17-aap1376
• 发表时间: 2018
• 期刊: The Annals of Applied Probability
• 作者: Foondun M