Related papers: Anomalous Diffusion with Absorbing Boundary
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The…
We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
A sheet of glassy polymers placed in a solvent shows swelling behaviors quite different from that of soft polymers (rubbers and gels). (1) Non-Fickian diffusion (called case II diffusion): As solvent permeates into the sample, a sharp front…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit…
It has been recently shown that a colloidal monolayer, e.g., formed at a fluid interface or by means of a suitable confining potential, exhibits anomalous collective diffusion. This is a consequence of the hydrodynamic interactions mediated…
This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
We investigate $(2+1)$-dimensional discretized directed polymers in Gaussian random media. By numerically calculating the probability distribution function of overlap between two independent and identical systems on a common random…
We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, $t$, and Planck's constant, $\hbar$, and allows a…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…