Dynamics of ordered systems and topological defects
We study large-scale collective effects emerging from the presence of topological defects in system with persistent order. We are developing non-singular field theories to describe the dynamics of topological defects from the order parameters associated to different discrete rotational and translational symmetries.
First-time passage problems and anomalous diffusion
We study the anomalous diffusion and first-passage time problems of particles in disordered media or under confinement. The diffusing entities could be passive or active (self-propelled) Brownian particles interacting with each other or their environment. Using stochastic toy models, we address fundamental questions in such systems concerning the long-time behavior of the mean-square displacement in relation to the topology of the embedding space, dispersion and mixing of particles, escape and first-passage time problems in confinement.
Interfacial processes
Other projects involve modelling various interfacial processes in multi-phase systems using level-set or phase field methods and geared toward geophysical applications of fluid-rock interfaces and rock deformation. We aim to develop a theoretical framework for deriving the governing balance laws at the fluid-rock interfaces where dissolution/precipitation reactions are coupled with flow and deformation.