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

John Everett Dolbow

Professor of Civil and Environmental Engineering

Keywords in this area
fracture, lipid membranes

Gregory Joseph Herschlag

Visiting Assistant Professor of Mathematics

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 in Trinity College of Arts and Sciences

Keywords in this area
gravity, light, geometric lensing, stochastic lensing, black holes, extra dimensions

Thomas Peter Witelski

Professor in the Department of Mathematics

Keywords in this area
fluid dynamics

Haizhao Yang

Visiting Assistant Professor in the Department of Mathematics

Keywords in this area
Modeling in materials science at atomic scale

Zhennan Zhou

William W. Elliott Assistant Research Professor

Keywords in this area
semi-classical methods in quantum dynamics, multi-scale methods for physics models, band crossing for Bloch electrons, kinetic theory, Born-Oppenheimer approximation, numerical methods for conservation law