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We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases…
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…
We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We obtain…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
We present a real-space method for first-principles nano-scale electronic transport calculations. We use the non-equilibrium Green's function method with density functional theory and implement absorbing boundary conditions (ABCs, also…
The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of…
Water flow in plant tissues takes place in two different physical domains separated by semipermeable membranes: cell insides and cell walls. The assembly of all cell insides and cell walls are termed symplast and apoplast, respectively.…
Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of graphene and other fascinating materials afterwards. While most previous work is devoted to the…
The method of nonequilibrium Greens functions allows for a spatial and energetical resolution of the electron current in Quantum Cascade Lasers. While scattering does not change the spatial position of carriers, the entire spatial evolution…
In an increasingly interconnected world, understanding congestion-related phenomena in transportation and their underlying mechanisms is crucial for improving efficiency. As the transportation system becomes denser, different modes of…
To describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry…
Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method.…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
The generic mechanisms of anomalous transport in porous media are investigated by computer simulations of two-dimensional model systems. In order to bridge the gap between the strongly idealized Lorentz model and realistic models of porous…
Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for…