Search Results - subject:"Fractional diffusion equation"

Some insights in superdiffusive transport

Marseguerra, M.; Zoia, A. - In: Physica A: Statistical Mechanics and its Applications 377 (2007) 1, pp. 1-14

) approach to anomalous diffusion, we compare the analytical solution of the approximated fractional diffusion equation (FDE …

Persistent link: https://www.econbiz.de/10011060648

On Hilfer's objection to the fractional time diffusion equation

Barkai, E.; Sokolov, I.M. - In: Physica A: Statistical Mechanics and its Applications 373 (2007) C, pp. 231-236

Hilfer [Physica A 329 (2003) 35] claims to give an example of a continuous time random walk (CTRW) model with long-tailed waiting time probability density that approaches a Gaussian behavior in the continuum limit. Rigorous limit theorems, derived previously, show however that in the limit of...

Persistent link: https://www.econbiz.de/10010588919

Fractional nonlinear diffusion equation, solutions and anomalous diffusion

Silva, A.T.; Lenzi, E.K.; Evangelista, L.R.; Lenzi, M.K.; … - In: Physica A: Statistical Mechanics and its Applications 375 (2007) 1, pp. 65-71

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and,...

Persistent link: https://www.econbiz.de/10010590403

Fractional diffusion equation and Green function approach: Exact solutions

Lenzi, E.K.; Mendes, R.S.; Gonçalves, G.; Lenzi, M.K.; … - In: Physica A: Statistical Mechanics and its Applications 360 (2006) 2, pp. 215-226

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function …

Persistent link: https://www.econbiz.de/10011064517

Solution of a modified fractional diffusion equation

Langlands, T.A.M. - In: Physica A: Statistical Mechanics and its Applications 367 (2006) C, pp. 136-144

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to ….M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I … of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of …

Persistent link: https://www.econbiz.de/10010588851

Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion

Abe, Sumiyoshi; Thurner, Stefan - In: Physica A: Statistical Mechanics and its Applications 356 (2005) 2, pp. 403-407

Einstein's theory of Brownian motion is revisited in order to formulate a generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally...

Persistent link: https://www.econbiz.de/10010588842

Some exact results for the trapping of subdiffusive particles in one dimension

Yuste, S.B; Acedo, L - In: Physica A: Statistical Mechanics and its Applications 336 (2004) 3, pp. 334-346

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with...

Persistent link: https://www.econbiz.de/10011059868

On anomalous transport on comb structures

Reynolds, A.M - In: Physica A: Statistical Mechanics and its Applications 334 (2004) 1, pp. 39-45

New transport properties of regular comb structures (associated with transport processes at the threshold of percolation and driven by temporally correlated noise) are identified. These include the first realization of transitions from normal diffusion to either anomalous diffusion or to...

Persistent link: https://www.econbiz.de/10010591209

Tsallis and Rényi entropies in fractional diffusion and entropy production

Essex, Christopher; Schulzky, Christian; Franz, Astrid; … - In: Physica A: Statistical Mechanics and its Applications 284 (2000) 1, pp. 299-308

The entropy production rate for fractional diffusion processes using Shannon entropy was calculated previously, which showed an apparently counter intuitive increase with the transition from dissipative diffusion behaviour to reversible wave propagation. Rényi and Tsallis entropies, which have...

Persistent link: https://www.econbiz.de/10010872061

Boundary value problems for fractional diffusion equations

Metzler, Ralf; Klafter, Joseph - In: Physica A: Statistical Mechanics and its Applications 278 (2000) 1, pp. 107-125

The fractional diffusion equation is solved for different boundary value problems, these being absorbing and reflecting … employed. The separation of variables is studied for a fractional diffusion equation with a potential term, describing a …

Persistent link: https://www.econbiz.de/10010872398