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In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
Cosmic ray (CR) transport is usually modeled with a single diffusion coefficient, but this description captures only the growth of the variance and not the full transport process. Distinct transport mechanisms can share the same effective…
While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
Brownian motion in confinement and at interfaces is a canonical situation, encountered from fundamental biophysics to nanoscale engineering. Using the Lorenz-Mie framework, we optically record the thermally-induced tridimensional…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
A major open problem in biophysics is to understand the highly heterogeneous transport of many structures inside living cells, such as endosomes. We find that mathematically it is described by spatio-temporal heterogeneous fractional…
We discuss certain kinds of diffusions on hyperbolic spaces, associated random walks on discrete groups of isometries of the latter, and their Martin boundaries.
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…
Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise…
Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions.…
Active adaptive matter has attracted considerable interest due to its rich, largely unexplained dynamics and its relevance to a wide range of synthetic and biological materials. An important subclass of such systems consists of active…
Random motion in disordered media is sensitive to the presence of obstacles that prevent atoms, molecules, and other particles from moving freely in space. When obstacles are static, a sharp transition between confined motion and free…
We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacles density…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two…
A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…