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Physical Applied Mathematics

This area has two complementary goals:

  1. to develop new mathematical models and methods of broad utility to science and engineering; and
  2. 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. 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. On a far larger scale, we have also been remarkably successful in unraveling some of the curious dynamics of galaxies.

Faculty

Martin Bazant Applied Mathematics, Electrokinetics, Microfluidics and Electrochemistry

John Bush Fluid Dynamics

Jörn Dunkel Physical Applied Mathematics

Anette Hosoi Fluid Dynamics, Numerical Analysis

Steven Johnson Waves, PDEs, Scientific Computing

Rodolfo Rosales Nonlinear Waves, Fluid Mechanics, Material Sciences, Numerical pde

Instructors & Postdocs

Peter Baddoo Fluid Dynamics, Complex Analysis, Machine Learning

Keaton Burns PDEs, Spectral Methods, Fluid Dynamics

Pui Tung Choi Applied and Computational Geometry, Metamaterials, Quantitative Biology, Medical Imaging

Matthew Durey Fluid mechanics, Dynamical systems

Valeri Frumkin Interfacial phenomena, fluidic shaping, hydrodynamic quantum analogs

Ousmane Kodio

Žiga Kos

David Kouskoulas Pilot Wave Theory, Water Waves, Quantum Mechanics, Fluid Mechanics, Acoustics

Zin Lin

Alexander Mietke Theoretical Biophysics, Collective Phenomena, Soft Matter

Konstantinos Papatryfonos

Daniel Pearce

Raphaël Pestourie Inverse design in nanophotonics, efficient approximate solvers in optics, deep surrogate for PDES.

Graduate Students*

Mo Chen Optimization, Scientific Computing

Davis Evans Hydrodynamic Quantum Analogs

George Stepaniants Statistical Learning of PDEs, Continuous Neural Networks

*Only a partial list of graduate students