Physical Modeling
Mathematical research in physical modeling focuses on the formulation and analysis of mathematical representations of problems motivated by other branches of science and engineering. In addition to generating novel problems with new computational and analytical challenges, constructing accurate models for complex systems may uncover the need for fundamental extensions to the governing equations.
Multiscale modeling is one very active area of current research, which focuses on bridging results from different types of mathematical models applicable to microscopic- vs. large-scale properties of problems. Examples include: estimates of macroscopic properties of materials from molecular structure and quantum mechanics, descriptions of population dynamics from behaviors of individuals, and homogenized effective properties of media derived from details of spatially varying in homogeneities.
Some of the other challenging aspects in current studies in physical modeling include: the influence of randomness and stochastic processes, simplifying high-dimensional models, and understanding the influences of complex and dynamic problem geometries.
Some of the primary areas of application of physical modeling at Duke include: quantum mechanics, fluid dynamics, astrophysics and biological/physiological systems. Studies in physical modeling draw extensively on techniques from analysis, probability, partial differential equations, dynamical systems and computational methods.
Faculty

J. Thomas Beale
Professor Emeritus of Mathematics
Keywords in this area
boundary integral methods, motion of fluid interfaces, equations of incompressible flow, convergence of numerical methods for fluid flow

Robert Calderbank
Charles S. Sydnor Professor of Computer Science
Keywords in this area
wireless communications, data storage, detection and estimation

Gregory Joseph Herschlag
Phillip Griffiths Assistant Research Professor
Keywords in this area
physical modeling, fluids flow across dynamic channels, surface catalysis, molecular dynamics, stochastic boundary conditions

Jianfeng Lu
Associate Professor of Mathematics
Keywords in this area
electronic structure models, multiscale modeling and simulations, rare events simulation, computational physics, kinetic equations, nonlinear Schroedinger equations, quantum chemistry, computational statistical mechanics

Jonathan Christopher Mattingly
Professor of Mathematics
Keywords in this area
Stochastic and Random PDEs, Stochastic Dynamical Systems, Fluid Mechanics

James H. Nolen
Associate Professor of Mathematics
Keywords in this area
asymptotic analysis

Arlie O. Petters
Benjamin Powell Professor of Mathematics
Keywords in this area
gravity, light, geometric lensing, stochastic lensing, black holes, extra dimensions

Amanda Randles
Alfred Winborne and Victoria Stover Mordecai Assistant Professor of Biomedical Sciences

Thomas Peter Witelski
Professor in the Department of Mathematics
Keywords in this area
fluid dynamics