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
This area has two complementary goals- to develop new mathematical models and methods of broad utility to science and engineering, and to make fundamental advances in the mathematical and physical sciences themselves. 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.