Key research themes
1. How does fluctuating and spatially heterogeneous diffusivity explain non-Gaussian yet Fickian diffusion behavior?
This theme investigates the mechanistic origins and mathematical modeling of diffusion processes where the mean square displacement (MSD) scales linearly with time (Fickian diffusion), yet the displacement probability distributions are non-Gaussian. A central insight is that spatial or temporal variability in the diffusivity — termed diffusing diffusivity or fluctuating diffusivity — leads to such complex behavior. Models integrating memory effects (generalized Langevin equations with fluctuating diffusivity), Lévy flight statistics, and heterogeneity generate analytical and numerical predictions matching experimental observations of anomalous diffusion in crowded and active media, relevant to cellular transport and complex fluids.
2. What are the impacts of heterogeneous and non-local diffusion processes in porous and composite media on the effective mean diffusivity?
This research direction addresses how spatial heterogeneity and microstructural complexity in porous rocks, composite materials, and biological media influence diffusion and dispersion at multiple scales. It incorporates theoretical homogenization, fractional calculus, and non-local constitutive laws to capture deviations from classical Fickian diffusion. Understanding these effects is critical in petroleum engineering, substrate transport in biological tissues, and material science where the effective diffusivity differs substantially from molecular diffusivity due to tortuosity, connectivity, and local flow dynamics.
3. How do spatial heterogeneity and surface effects influence ergodicity, self-averaging, and measured mean diffusivities in complex biological and porous media?
This theme focuses on the statistical properties of diffusion in quenched random media and heterogeneous environments where spatially variable diffusivity and trapping lead to weak ergodicity breaking and non-self-averaging behavior. Work in this area sheds light on how diffusion measurements from ensemble averages can differ from single-particle time averages due to disorder sampling constraints, and how surface interactions slow diffusion and affect fluctuations in measured mean square displacements. These insights are critical for interpreting single-molecule tracking in living cells and molecular transport in complex porous materials.