Mathematical Sciences: Studies in Continuum Mechanics and Partial Differential Equations

首席研究员将继续他的重要工作， 偏微分方程，出现在各个领域， 连续介质力学 特别是，他将应用先进的 数学工具来研究多相流的一般理论 热力学，因为它涉及到界面动力学， 涉及融化和冻结的现象。 他还将 研究一些不寻常的偏微分方程， 存在于多孔介质的流动和生物扩散中。 首席研究员的工作涉及发展 并研究数学模型，试图描述这种 复杂的物理现象，如晶体的生长， 刻面和角，融化-冻结波的演变，以及 更一般地，在介质中创建有序结构 通过弯曲的前缘在介质中移动。 举个例子，试着定量地描述 如果你把一根热线穿过一块冰就会发生。 这是一个 包括融化和重新冻结的复杂过程， 很难研究，因为熔化的和 未融化的冰对电线的温度非常敏感， 其他因素

The principal investigator will continue his important work on the partial differential equations that arise in various areas of continuum mechanics. In particular, he will apply advanced mathematical tools to study the general theory of multiphase thermomechanics as it relates to interfacial dynamics and phenomena involving melting and freezing. He will also investigate some unusual partial differential equations that are found in flows through porous media and in biological dispersal. The work of the principal investigator concerns the development and study of mathematical models that attempt to describe such complicated physical phenomena as the growth of crystals with facets and corners, the evolution of a melting-freezing wave, and more generally the creation of ordered structures in media through the action of curved fronts that move through the media. As an example, think of trying to describe quantitatively what happens if you draw a hot wire through a block of ice. It is a complicated process involving melting and re-freezing, which is difficult to study because the boundary between the melted and unmelted ice is so sensitive to the temperature of the wire and other factors.