Daniel Forger is a Professor in the Department of Mathematics. He is devoted to understanding biological clocks. He uses techniques from many fields, including computer simulation, detailed mathematical modeling and mathematical analysis, to understand biological timekeeping. His research aims to generate predictions that can be experimentally verified.
Aaron A. King is an Associate Professor of Ecology & Evolutionary Biology, and is affiliated with the Department of Mathematics, the Center for the Study of Complex Systems, the Center for Computational Medicine & Bioinformatics, the Fogarty International Center, and the National Institutes of Health. Prof. King develops and applies computationally intensive methods for using stochastic dynamical systems models to learn about infectious disease ecology and epidemiology. These systems are typically highly noisy and nonlinear and are frequently uncomfortably high-dimensional. Nevertheless, the King group’s approaches allow them to find out what the data have to say about the mechanisms that generate them.
His research group develops fast and scalable algorithms for solving differential and integral equations on complex moving geometries. Application areas of current interest include large-scale simulations of blood flow through arbitrary confined geometries, electrohydrodynamics of soft particles and heat flow on time-varying domains.
Divakar Viswanath is a Professor in the Department of Mathematics. His research is at the interface of scientific computation and nonlinear dynamics. The incompressible Navier-Stokes equations are a major point of current interest. Turbulent dynamics is locally unstable and bounded in phase space. In such scenarios, dynamical systems theory predicts the existence of periodic solutions (modulo symmetries). Professor Viswanath has developed algorithms to extract periodic solutions and traveling waves from turbulent dynamics. One goal of current research is to derive, implement, and demonstrate algorithms that simulate turbulent flows at higher Reynolds numbers than is currently possible. It appears that this goal will be met shortly. Professor Viswanath has a general interest in foundational numerical analysis ranging from interpolation theory to the solution of differential equations.
His research goal is to develop accurate and efficient numerical methods for computational problems in science and engineering. The methods he works on typically use the Green’s function to convert the relevant differential equation into an integral equation. Krasny develops treecode algorithms for efficient computation of long-range particle interactions. Topics of interest include fluid dynamics (vortex sheets, vortex rings, Hamiltonian chaos, geophysical flow), and electrostatics (Poisson-Boltzmann model for solvated proteins). He is also interested in modeling charge transport in organic solar cells.
His research is in computational physics, specifically biophysics (tumor growth and cell mechanics) and materials physics (battery materials, structural alloys and semiconductor materials). In these areas Garikipati’s group focuses on developing mathematical and numerical models of phenomena that can be described by continuum analyses that translate to PDEs. Usually, these are nonlinear, and feature coupled physics, for example chemo-thermo-mechanics. Our numerical techniques are mesh-based variational methods such as the finite element method and its many variants. In some problems we make connections with fine-grained models, in which case we work with kinetic Monte Carlo, molecular dynamics or electronic structure calculations in some form. In the realm of analysis, we often examine the asymptotic limits of our mathematical models, and the consistency, stability and convergence of our numerical methods.