Faculty

Developing efficient CFD algorithms for fluid flows, including central schemes, kinetic schemes and relaxation schemes; exact capturing of shocks and contact discontinuities; low numerical diffusion methods; meshless or grid-free methods; Lattice Boltzman method; non-standard finite difference methods; aerodynamic shape optimization; algorithms for turbulence simulation.

Calculus of Variations, Partial Differential Equations and geometric analysis.

Variational models and PDE models are widely employed in different branches of physics and engineering applications, from models in material sciences ( fracture models, micro-magnetics ) to image reconstruction, impedance tomography, invisibility cloaking etc. A theoretical understanding of the relevant functional from the calculus of variation and PDE perspective both facilitates and in turn is facilitated by the qualitative understanding of the physical phenomena involved.

I am also interested in some toy models in quantum field theory that leads to interesting geometric variational problems, like nonlinear sigma-models etc.

Experimental mechanics, Image based def.rmation measurements, Large strain plasticity, Granular mechanics.

Uncertainty quantification and analysis – Theory, Numerics, Software, Applications; Bayesian Inference and Data Assimilation; Dynamic data-driven stochastic ocean modeling; Cyclone track prediction; Optimal routing of marine and aerial vehicles.

Matrix analysis & Numerical methods, Sampling & Estimation in high dimensions, Optical properties & Condensed matter, Computational physics.

Computational methods in medical imaging, medical image processing (reconstruction/analysis), physiological signal processing, photoacoustic tomography, and diffuse optical tomography.

Sirtuins in Cardiovascular diseases.

Cell division and fate in plants and yeasts.