Mathematical Sciences: Statistical Mechanics and Partial Differential Equations

9403399科隆首席研究员将对偏微分方程组中的问题进行研究。这些问题是由关于大时间尺度上相互作用的随机漫步行为的直觉驱动的。朝着这个方向迈出的重要一步是理解随机环境中的随机行走。对这些问题的主要研究方法是获得适当偏微分方程解的足够精确的估计。他打算继续这项工作。这个项目的总体目标是促进对介质中扩散的理解，其中介质的一致性发生了很大变化。当两种液体混合时，混合过程是一个扩散过程。热很大程度上是通过扩散传播的。在扩散过程中，传播介质的稠度变化很大的例子有很多，石油在多孔岩石中的传播就是一个例子。另一个是污染物在地下的传播。在上面的每一个例子中，重要的是要对这种媒介中的扩散机制建立一个定性的理解。这项研究将对此做出贡献，

9403399 Conlon The principal investigator will conduct research on problems in partial differential equations. These problems are motivated by intuitions concerning the behavior of interacting random walks over large time scales. A major step in this direction would be to understand random walks in random environments. The principal investigator's approach to these problems has been to obtain sufficiently sharp estimates on solutions to appropriate partial differential equations. He intends to continue this work. The general goal of this project is to advance understanding of diffusion in a medium where the consistency of the medium changes a lot. When two liquids are mixed the process of mixing is a diffusive process. Heat propagates largely by diffusion. There are many examples of diffusive processes where the consistency of the medium of propagation changes a lot.One example is the propagation of oil through porous rock. Another is the propagation of pollutants in the ground. In each of the above examples it is important to build up a qualitative understanding of the mechanism of difdusion in such media. This study will contribute to this,