Center for Applied Mathematics and Statistics (CAMS) Main Research Areas

Mathematical Biology

CAMS Mathematical Biology Research
  • 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

CAMS Fluid Dynamics Research
  • 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)

Numerical simulation of the kinetics of droplet formation in polymer-liquid crystal mixtures


Wave Propagation

CAMS Wave Propagation Research
  • 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)

Ambiguity surface generated by matched field processing of an exhaustive search for unknown source range and depth


Applied Analysis

CAMS Dynamical Systems Research

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)

Mesoscopic Model for Pattern Formation in Materials


Statistics

CAMS Statistics Research
  • 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)

The Mean Remaining Life function MRL(x) ≡ E(X-x | X > x)