Mathematical Sciences: Interacting Particle Systems

这项研究涉及相互作用粒子的应用 系统到生物学 特别是，研究人员将 构建模型来解释生物现象，如 麻疹的时间振荡和浮游生物的斑块 在海里。 另一个感兴趣的领域是与 非线性偏微分方程 通过混合 粒子在一个快速的速度和缩放空间，系统收敛 非线性偏微分方程 这使得 可以推导出偏微分方程， 准确地模拟生物系统， 快速混合的粒子系统。 相互作用的粒子系统有一种结构， 它们适用于物理学中的各种环境， 化学和生物学 有一个网格的网站，其中每一个 可以有一组固定的值。 例如，一个城市 个体可能易感染、感染或免疫 麻疹。 每个站点的价值变化率取决于 邻居的价值观，这项研究感兴趣的是， 确定随着时间的推移系统会发生什么。 这些模型 最终将使人们更好地了解全球 生态问题。

This research involves applications of interacting particle systems to biology. In particular, the investigator will construct models to explain biological phenomena such as the temporal oscillations of measles and the patchiness of plankton in the sea. Another area of interest is the connection with nonlinear partial differential equations. By mixing the particles at a fast rate and scaling space, the system converges to a nonlinear partial differential equation. This makes it possible to derive partial differential equations that more accurately model the biological systems and also to prove results about the particle systems with fast mixing. Interacting particle systems have a structure that makes them appropriate for use in a variety of contexts in physics, chemistry, and biology. There is a grid of sites, each of which can have a fixed set of values. For example, a city of individuals can be susceptible to, infected with, or immune to measles. Each site changes its value at a rate that depends on the values of its neighbors, and this research is interested in determining what happens to the system over time. These models should eventually provide a better understanding of global ecological problems.