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Key research themes
1. How does heterogeneous and spatially dependent diffusion impact anomalous diffusion and steady-state behaviors with stochastic resetting?
This research theme focuses on diffusion processes where the diffusivity varies with spatial position, often following a power law, and how stochastic resetting modifies these dynamics. It is crucial because many natural and biological systems exhibit spatial heterogeneity affecting diffusion, and resetting introduces non-equilibrium steady states. Understanding these phenomena addresses fundamental questions about transitions to stationarity, scaling laws of mean squared displacement (MSD), and probability density function (PDF) behaviors in anomalous diffusion contexts.
Key finding: This paper presents exact analytical results for the MSD and PDF of a heterogeneous diffusion process (HDP) with position-dependent diffusivity following a power-law form combined with Poissonian resetting. It demonstrates... Read more
Key finding: This study analyzes diffusion in systems with slower surface diffusion than bulk diffusion, modeled via a CTRW combined with heterogeneous waiting times on membrane surfaces, some exhibiting anomalous subdiffusion. It reveals... Read more
Key finding: By analytically investigating nonlinear diffusion equations with diffusivity depending on concentration via a power law with exponent γ, this work demonstrates that anomalous diffusion arises when γ is positive but less than... Read more
Key finding: This paper introduces a general model-less method to characterize diffusion regimes (normal, subdiffusion, superdiffusion) by monitoring the time evolution of the spatial width of particle distributions, without requiring... Read more
2. What are the effects of obstacle crowding and environmental heterogeneity on transient anomalous diffusion and ergodicity breaking in tracer particle dynamics?
This theme explores how non-inert obstacles, crowding, and binding interactions alter diffusion of tracer particles in heterogeneous crowded media, leading to transient subdiffusion, ergodicity breaking, and non-Gaussian transport properties. It is essential for understanding particle mobility in biological cells, porous media, and complex fluids where spatial obstruction and heterogeneous interactions dominate, impacting biochemical reaction kinetics and transport.
Key finding: Through computer simulations, this work shows that tracer diffusion in crowded environments of immobile obstacles displays transient anomalous diffusion strongly dependent on both obstacle volume fraction and tracer-obstacle... Read more
Key finding: This comprehensive review places classical Einstein diffusion coefficients in the context of both equilibrium and nonequilibrium systems, highlighting scenarios where diffusivity depends non-trivially on factors like... Read more
3. How does active matter and complex environmental structuring modulate particle diffusion mechanisms including non-monotonic size dependence and multi-scale coupling in reaction-diffusion systems?
This theme examines diffusion in active fluids where self-propelling particles drive non-equilibrium fluctuations, and heterogeneous reaction-diffusion media where discrete sources and multi-scale cell structures interplay. Key questions involve how particle size, substrate structure, and reaction kinetics coupled with nonlinear or discrete environments affect particle transport properties, including emergent non-monotonic diffusion coefficients, transport efficiency, and front propagation limits. Insights here inform biological transport, material design, and ecological dispersal modeling.
Key finding: Experimental investigations show that passive particle diffusion in bacterial suspensions exhibits a striking non-monotonic dependence on particle size, with an intermediate size range diffusing faster than both smaller and... Read more
Key finding: This paper derives an exact analytical solution for reaction-diffusion fronts propagating through media with spatially discrete point-like sources, contrasting it with continuum homogenized models. It demonstrates that... Read more
Key finding: Extending Leighton’s surface diffusion model, this study analytically models diffusion generated by two sizes of random cellular flows (granulation and supergranulation) on the solar surface. It introduces a dimensionless... Read more