Charles Doering

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Charles Doering is the Nicholas D. Kazarinoff Collegiate Professor of Complex Systems, Mathematics and Physics and the Director of the Center for the Study of Complex Systems. He is a Fellow of the American Physical Society, and a Fellow of the Society of Industrial and Applied Mathematics (SIAM). He uses stochastic, dynamical systems arising in biology, chemistry and physics models, as well as systems of nonlinear partial differential equations to extract reliable, rigorous and useful predictions. His research spans rigorous estimation, numerical simulations and abstract functional and probabilistic analysis.

Aaron King

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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.

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Shravan Veerapaneni

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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.

simulation of red blood cells

Snapshot from a hydrodynamic simulation of 40,000 red blood cells with the inset showing the details of a two-body interaction.

Divakar Viswanath

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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.

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Robert Krasny

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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.

This picture illustrates the instability of a vortex ring. The ring was modeled as a circular disk vortex sheet with an imposed perturbation of azimuthal wavenumber m=8. The ring’s motion was computed using a Lagrangian particle method and a treecode algorithm for fast evaluation of the induced velocity. The picture shows three isosurfaces of vorticity at a late time in the simulation. The results reveal details of the instability, in particular the relation between axial flow and collapse of the vortex core.

This picture illustrates the instability of a vortex ring. The ring was modeled as a circular disk vortex sheet with an imposed perturbation of azimuthal wavenumber m=8. The ring’s motion was computed using a Lagrangian particle method and a treecode algorithm for fast evaluation of the induced velocity. The picture shows three isosurfaces of vorticity at a late time in the simulation. The results reveal details of the instability, in particular the relation between axial flow and collapse of the vortex core.

Anna Gilbert

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Anna Gilbert is a Professor in the Department of Mathematics. Her research interests include analysis, probability, networking and algorithms. She is especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, and computational imaging.

This figure shows pulse sequence design positions for data acquisition for 3D imaging of a brain in MRI.

This figure shows pulse sequence design positions for data acquisition for 3D imaging of a brain in MRI.

Krishna Garikipati

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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.

Isogeometric analysis (weak form based-solution of PDEs with spline basis functions) of phase transformations in a battery material.

Isogeometric analysis (weak form based-solution of PDEs with spline basis functions) of phase transformations in a battery material.