应用数学理学博士（物理应用数学）

我们部门在以下各个领域都取得了重大进展。我们已经开发了一个理论框架来描述非线性电渗流的感应电荷机理。我们在仿生研究中的工作重点是阐明昆虫和鸟类利用其在微观尺度上进行流体运输的机制。数字微流体和纳米技术中的这些和其他活动已在生物启发性材料（如单向超疏水表面）和设备（如“芯片实验室”和微型泵）中得到应用。运输现象理论提供了多种有用的数学技术，例如用于集体运动的连续方程，用于多体流体动力相互作用的有效数值方法，混沌混合的度量以及带电双层的渐近分析。纳米光子学是研究与波长相同长度尺度的介质中电磁波现象的研究，并且
Our department has made major advances in each of the following areas. We've developed a theoretical framework to describe the induced-charge mechanism for nonlinear electro-osmotic flow. Our work in biomimetics focuses on elucidating mechanisms exploited by insects and birds for fluid transport on a micro-scale. These and other activities in digital microfluidics and nanotechnology have applications in biologically inspired materials such as a unidirectional super-hydrophobic surface, and devices such as the lab-on-a-chip' and micropumps. The theory of transport phenomena} provides a variety of useful mathematical techniques, such as continuum equations for collective motion, efficient numerical methods for many-body hydrodynamic interactions, measures of chaotic mixing, and asymptotic analysis of charged double layers. Nanophotonics is the study of electromagnetic wave phenomena in media structured on the same lengthscale as the wavelength, and is an active area of study in our group, for example to allow unprecedented control over light from ultra-low-power lasers to hollow-core optical fibers. New mathematical tools may be useful here, to give rigorous theorems for optical confinement and to understand the limit where quantum and atomic-scale phenomena become significant. Granular materials provide challenging problems of collective dynamics far from equilibrium. The intermediate nature (between solid and fluid) of dense granular matter defies traditional statistical mechanics and existing continuum models from fluid dynamics and solid elasto-plasticity. Despite two centuries of research in engineering, no known general continuum model describes flow fields in multiple situations (say, in silo drainage and in shear cells), let alone diffusion or mixing of discrete particles. A fundamental challenge is to derive continuum equations from microscopic mechanisms, analogous to collisional kinetic theory of simple fluids.