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Marisa Eisenberg

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Marisa Eisenberg is an assistant professor in the Department of Epidemiology, and in the Department of Mathematics. Her research revolves around mathematical epidemiology, focus on using and developing parameter estimation and identifiability techniques to model disease dynamics. Her group builds multi-scale models of infectious disease, including HPV, cholera and other environmentally driven diseases.

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Likelihood surface exhibiting issues of unidentifiability—colors indicate goodness-of-fit, and the white line shows the values taken by an optimization algorithm as it navigates the surface.

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Silas Alben

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Silas Alben is an Associate Professor in the Department of Mathematics, and the Director of the Applied & Interdisciplinary Mathematics program. He uses theoretical analysis, and develops numerical methods and models of problems arising from biology, especially biomechanics and engineering. Some of his group’s current applications are piezoelectric flags, flag fluttering in inviscid channel flow, snake locomotion and jet-propelled swimming.

Equilibrium configurations of actuated bilayers with general initial shapes. S. Alben, Adv. Comp. Math., 2014

Equilibrium configurations of actuated bilayers with general initial shapes. S. Alben, Adv. Comp. Math., 2014

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Victoria Booth

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Victoria Booth is an Associate Professor in the Department of Mathematics and the Department of Anesthesiology. Her interdisciplinary research in mathematical and computational neurosciences focuses on constructing and analyzing biophysical models of neurons and neural networks in order to quantitatively probe experimental hypothesis and provide experimentally-testable predictions. Her research provides continuous reciprocal interactions between modeling and experimental results.

Prof. Booth and her colleagues are constructing neurophysiologically based models of the neuronal networks and neurotransmitter interactions in the brainstem and the hypothalamus that regulate wake and sleep states. She is also addressing the question of the influence of intrinsic neuron properties and network topology on the generation of spatio-temporal activity patterns in large-scale neural networks.

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Daniel Forger

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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.

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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.

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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.

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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.