Related papers: Comb model with slow and ultraslow diffusion
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
We study diffusion on comb lattices of arbitrary dimension. Relying on the loopless structure of these lattices and using first-passage properties, we obtain exact and explicit formulae for the Laplace transforms of the propagators…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
It is investigated the statistical properties of random walks evolving on real configurations of a crumpled wire rigidly jammed in two dimensions. These crumpled hierarchical structures with complex topology are obtained from a metallic…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of…
Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
Diffusion of particles in complex fluids and gels is difficult to describe and often lies beyond the scope of the classical Stokes-Einstein relation. One of the main lines of research over the past few decades has sought to relate…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, H\"ollig or non-Fourier type. Classical weak solutions to such problems are…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…
The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa systems are investigated by molecular dynamics simulations. Using both the asymptotic behaviour of the mean-squared displacement of the particles and the…