Mathematical Biology

• Experimental, computational and mathematical Neuroscience (synaptic dynamics, neronal plasticity, neuronal networks and applications to the visual cortex, persistant localized activity in excitatory networks, electrical activity in excitable cells)
• Developmental Biology (patterning, reaction-diffusion equations)
• Biological Fluid Dynamics (microvascular blood flow and oxygen delivery, immersed boundary/continuum methods)

Calculated oxygen distributions in the tissue surrounding three-dimensional arrays of capillaries

Fluid Dynamics

• Interfacial flows and microhydrodynamics (jet breakup, bubble dynamics, surfactants, interfacial instabilities, thin films, electrohydrodynamics)
• Reactive flow & combustion (droplet burning, flame modulation, ignition and extinction, turbulent flame modeling, detonation dynamics, front tracking)
• Particulate flows (granular flows, sedimentation)

Wave Propagation

• Underwater acoustics (inverse scattering, matched field processing, target detection and localization)
• Electromagnetics (microwave heating and processing of ceramics, scattering from complex objects and dispersive materials, ultrafast optical communications, solitons in optical fibers)

Applied Analysis

CAMS Numerical Methods Research

• Dynamical Systems (swept volumes (CAD/CAM), bifurcation and chaos in biological and mechanical systems, fractal geometry, traffic modeling)
• Differential Geometry (web geometry, analysis and computer-aided representation of surfaces)
• Numerical Analysis (methods and algorithms for simulation of physical systems, computer-aided geometric design, analysis of algorithms)
• Nonlinear Functional Analysis (topological and variational methods, applications to nonlinear ordinary and partial differential equations)

Statistics

• Reliability and performance analysis (modeling, repairable systems, survival analysis)
• Time series and signal processing (forecasting, pattern recognition, nonlinear modeling)
• Computational statistical analysis (MCMC, Regression Splines, CART)