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)

Booth, Bose, Bukiet, Bunker, Golowasch, Holzapfel, Huang, Matveev, Miura, Muratov, Nadim, Wylie.

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)
• Numerical methods (boundary integral, volume of fluid, phase field)
• Analysis of PDE of fluid flow.
• Materials science.

Afkhami, Bechtold, Blackmore, Booty, Bukiet, Chaves, Choi, Cummings, Diez, Fazioli, Huang, Kondic, Luke, Meegoda, Muratov, Papageorgiou, Rosato, Siegel, Vanden-Broeck, Wylie, Young.

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

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)
• Numerical methods (fast algorithms)

Agrawal, Boubenir, Erneux, Goodman, Horntrop, Jiiang, Kriegsmann, Michalopoulou, Moore, Petropoulos, Turc.

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

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)
• Analysis of PDE.

Andrushkiw, Blackmore.

Statistics

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

Dhar, Dios, Jain, Johnson, Loh, Subramanian.

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