English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Anomalous transport is usually described either by models of continuous timerandom walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE).The asymptotic relation between properly scaled CTRW and fractional diffusionprocess has been worked out via various approaches widely discussed inliterature. Here, we focus on a correspondence between CTRWs and time and spacefractional diffusion equation stemming from two different methods aimed toaccurately approximate anomalous diffusion processes. One of them is the MonteCarlo simulation of uncoupled CTRW with a L\'evy $\alpha$-stable distributionof jumps in space and a one-parameter Mittag-Leffler distribution of waitingtimes. The other is based on a discretized form of a subordinated Langevinequation in which the physical time defined via the number of subsequent stepsof motion is itself a random variable. Both approaches are tested for theirnumerical performance and verified with known analytical solutions for theGreen function of a space-time fractional diffusion equation. The comparisondemonstrates trade off between precision of constructed solutions andcomputational costs. The method based on the subordinated Langevin equationleads to a higher accuracy of results, while the CTRW framework with aMittag-Leffler distribution of waiting times provides efficiently anapproximate fundamental solution to the FFPE and converges to the probabilitydensity function of the subordinated process in a long-time limit.

Subordinated diffusion and CTRW asymptotics