Main Research Areas

The focus of CAMS research is roughly divided into five application areas.

Mathematical Biology

Experimental, Computational and Mathematical Neuroscience

  • Neuronal dynamics, synaptic plasticity, neuronal networks
  • Electrical activity in excitable cells, calcium dynamics
  • Interaction between electrical dynamics and gene expression
  • Applications to visual cortex, central pattern generators, spreading cortical depression and circadian rhythms

Biological Fluid Dynamics

  • Immersed interface/continuum methods
  • Biomechanics and tissue engineering
  • Cell and vesicle dynamics

Developmental Biology

  • Morphogenetic patterning, embryogenesis

Members: Bose, Diekman, Lushi, MacLaurin, Matveev, Wicke, Young, Jaquette

(External Members: Booth, Bunker, Garnier, Golowasch, Holzapfel, Nadim, Rotstein, Russell, Sachs)

Fluid Dynamics

Interfacial Flows

  • Fast/multiscale numerical methods
  • Analysis and simulation of jet breakup, bubble dynamics, surfactant effects
  • Modeling, analysis and simulation of thin films and wetting phenomena
  • Fluid-structure interaction
  • Electrohydrodynamics and electrokinetics
  • Geophysical fluid dynamics

Multiphase and Reactive Flows

  • Flame-flow interaction, droplet burning, ignition
  • Cryogenic fluids for rocket propulsion technology
  • Micro- and nano-fluidics
  • Complex fluids

Numerical Methods and PDE Analysis

  • Boundary integral, volume of fluid, level set methods
  • Convergence and error estimates for numerical methods
  • Fast/multiscale methods
  • Well-posedness for interfacial flows
  • Analysis of singularity formation

(see also Complex Flows and Soft Matter page)

Members: Afkhami, Askham, Bechtold, Booty, Bukiet, Choi, Cummings, Jiang, Kondic, Luke, Lushi, Oza, 

Petropoulos, Shirokoff, Siegel, Wang, Young

 

(External Members: Diez, Farokhirad, Gor, Huang, Marras, Meegoda, Mema, Pak, 

Papageorgiou, Rosato, Sanei, Shakib,  Tafuni, Vanden-Broeck, Voronov, Wang H., Wang Q.,Wylie)

Wave Propagation

Underwater Acoustics and Ocean Waves

  • Inverse scattering, matched field processing, target detection and localization
  • Surface and internal waves
  • Data assimilation

Electromagnetics

  • Finite element and domain decomposition methods
  • Fast algorithms, fast multipole and related methods
  • Effective media, homogenization, dispersive media
  • Scattering from complex objects

Nonlinear Optics

  • Ultrafast optical communications
  • Solitons in optical fibers

Front Propagation

  • Traveling waves in reaction-diffusion systems
  • Population dynamics
  • Flame dynamics and detonation

Members: Askham, Booty, Boubendir, Choi, Frederick, Goodman, Jiang, 

Nguyen, Michalopoulou, Petropoulos, Turc 

(External Members: Ahluwalia, Erneux, Moore)

Materials Science

Soft Matter

  • Molecular dynamics simulations of granular materials
  • Modeling and asymptotics for liquid crystal systems
  • Mesoscopic phases in polymer systems
  • Biomaterials

Energy Driven Pattern Formation

  • Analysis of variational problems with long-range forces
  • Modeling, analysis and simulation of magnetic systems
  • Numerical methods for interfacial phenomena in solids
  • Large deviations, rare events and nucleation phenomena

(see also Complex Flows and Soft Matter page)

Members: Afkhami, Booty, Cummings, Kondic, Muratov, Shirokoff, Siegel, Young 

(External Members: Rosato, Wylie)

Optimization

Numerical Methods

  • Optimal transport
  • Inverse problems

Applications

  • Gradient flow systems
  • Optimization in dynamical systems (parameter estimation; Lyapanov stability; model fitting)
  • Large deviations
  • Optimal filter design

Members: Askham, Diekman, Cummings, Frederick, Hamfeldt, Kondic, 

MacLaurin, Michalopoulou, Muratov, Oza, Shirokoff

 

Statistics and Data Science

Biostatistics

  • Multivariate methods
  • Clinical trials and Longitudinal Data Analysis
  • Microarray and Proteomics analysis
  • Generalized Additive Models and Semi-parametric methods

High dimensional data

  • Multiple testing and False Discovery Rate
  • Analysis of massive datasets
  • Variable selection

Spatial statistics

  • Analysis of spatial point patterns
  • Spatial anomaly detection

Survival Analysis

  • Copulas and competing risk models
  • Bootstrap of survival data
  • Empirical likelihood
  • High dimensional censored data analysis
  • Reliability models

Members: Dhar, Guo, Jin, Loh, Shang, Subramanian, Wang

(External Member: Roychoudhury)