Mathematical Sciences: Statistical Mechanics and Partial Differential Equations

小行星9403399 主要研究者将对偏微分方程中的问题进行研究。这些问题的动机是关于大时间尺度上相互作用的随机游动行为的直觉。在这个方向上的一个重要步骤是理解随机环境中的随机游动。 主要研究人员的方法来解决这些问题已经获得足够尖锐的估计适当的偏微分方程的解决方案。他打算继续这项工作。 该项目的总体目标是促进对介质中扩散的理解，其中介质的一致性变化很大。当两种液体混合时，混合过程是扩散过程。热主要通过扩散传播.有许多扩散过程的例子，其中传播介质的稠度变化很大。一个例子是石油通过多孔岩石的传播。另一个是污染物在地下的传播。在上述每一个例子中，重要的是要建立一个定性的理解，在这种介质中的分歧机制。这项研究将有助于这一点，

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,