Mathematical Sciences: Infinite Particle Systems and Hydrodynamics

首席研究员正在研究一种 随机伊辛模型的宏观方程。 研究 在不同相共存低温下的问题 表明不同相的液滴根据 到某种“平均曲率运动”偏微分方程。 相关问题 可以为该模型或其适当的 变化，如简单的排除速度变化或 Ginzburg-Landau模型 另一个有趣的问题是 非对称简单排斥守恒律的推导 速度的变化。 分析一个 这个模型中的标记粒子也很有趣。 统计力学中的一个重要任务是导出 流体从其分子结构的演化。 在 在分子水平上，流体由大量分子组成 按照物理定律运动。 显微镜下，分子 不停地碰撞，并在一个随机 比如时尚 由于质量、动量和 熵，分子设法以这样一种方式组织自己， 形成大规模的流动模式。 各种漫画 将研究流体的模型，以导出其宏观 从它们的微观结构演化而来， 严谨的时尚

The principal investigator is working on the derivation of a macroscopic equation for the stochastic Ising model. Studies of the problem at low temperatures where different phases coexist indicate that the droplets of different phases evolve according to some type of "motion by mean curvature" PDE. Related problems can be proposed for either this model or its appropriate variations such as simple exclusions with speed change or the Ginzburg-Landau model. Another problem of interest is the derivation of conservation laws for asymmetric simple exclusions with speed changes. Analyzing the asymptotic behavior of a tagged particle in this model is also of great interest. An important task in statistical mechanics is to derive the evolution of a fluid from its molecular structure. At the molecular level, a fluid consists of a large number of molecules moving according to physical laws. Microscopically, molecules collide incessantly and move somewhat erratically in a random like fashion. Due to conservation laws of mass, momentum and entropy, molecules manage to organize themselves in such a way as to form a flow pattern on a large scale. Various Caricature models of a fluid will be studied to derive their macroscopic evolution from their microscopic structure in a mathematically rigorous fashion.