Related papers: Comb models for transport along spiny dendrites
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
We present a \textit{mesoscopic}description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
Information to be stored and transported requires physical carriers. The quantum bit of information (qubit) can for instance be realised as the spin 1/2 degree of freedom of a massive particle like an electron or as the spin 1 polarisation…
We study the dynamics of overdamped Brownian particles interacting through soft pairwise potentials on a comb-like structure. Within the linearized Dean-Kawasaki framework, we characterize the particle density fluctuations by computing…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
A model for magnetoresistance in positionally disordered organic materials is presented and solved using percolation theory. The model describes the effects of spin flips on hopping transport by considering the effect of spin dynamics on an…
We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a…
Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an…
We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows…
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Transport phenomena in out-of-equilibrium systems is immensely important in a myriad of applications in biology, engineering and physics. Complex environments, such as the cytoplasm or porous media, can substantially affect the transport…
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property…
The notions of taxis and kinesis are introduced and used to describe two types of behavior of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favorable conditions; (ii) Kinesis is the non-directional…
We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
We present a comprehensive theory of spin transport in a non-degenerate semiconductor that is in contact with multiple ferromagnetic terminals. The spin dynamics in the semiconductor is studied during a perturbation of a general,…