Related papers: Mean squared displacement in a generalized L\'evy …
We report an analytical evaluation of the mean-squared displacement (MSD) of the particles in glasses based on their coarse grained trajectories. The calculation is conducted by means of a local random configuration-tree theory that was…
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
The three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time averaged mean square…
L\'{e}vy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In…
It is recognised now that a variety of real-life phenomena ranging from diffuson of cold atoms to motion of humans exhibit dispersal faster than normal diffusion. L\'evy walks is a model that excelled in describing such superdiffusive…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…
Random walk simulation of the Levy flight shows a linear relation between the mean square displacement <r2> and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
Experimental results for passive tracer dispersion in the turbulent surface layer under stable conditions are presented. In this case, the dispersion of tracer particles is determined by the interplay of three mechanisms: relative…
We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) $\langle x^2(t)\rangle\simeq\log^{\gamma}t$. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution…
We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position $x$ of the test particle and the process time $t$. This process thus combines the features of…
Countless processes in nature and industry, from rain droplet nucleation to plankton interaction in the ocean, are intimately related to turbulent fluctuations of local concentrations of advected matter. These fluctuations can be described…
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is…
The mean square displacement (MSD) of intruders (tracer particles) immersed in a multicomponent granular mixture made up of smooth inelastic hard spheres in a homogeneous cooling state is explicitly computed. The multicomponent granular…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…