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Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel

Tutkimustuotosvertaisarvioitu

Standard

Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. / Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf.

julkaisussa: Fractional Calculus and Applied Analysis, Vuosikerta 18, Nro 4, 01.08.2015, s. 1006-1038.

Tutkimustuotosvertaisarvioitu

Harvard

Sandev, T, Chechkin, A, Kantz, H & Metzler, R 2015, 'Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel', Fractional Calculus and Applied Analysis, Vuosikerta. 18, Nro 4, Sivut 1006-1038. https://doi.org/10.1515/fca-2015-0059

APA

Sandev, T., Chechkin, A., Kantz, H., & Metzler, R. (2015). Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Fractional Calculus and Applied Analysis, 18(4), 1006-1038. https://doi.org/10.1515/fca-2015-0059

Vancouver

Sandev T, Chechkin A, Kantz H, Metzler R. Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Fractional Calculus and Applied Analysis. 2015 elo 1;18(4):1006-1038. https://doi.org/10.1515/fca-2015-0059

Author

Sandev, Trifce ; Chechkin, Aleksei ; Kantz, Holger ; Metzler, Ralf. / Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Julkaisussa: Fractional Calculus and Applied Analysis. 2015 ; Vuosikerta 18, Nro 4. Sivut 1006-1038.

Bibtex - Lataa

@article{edefde71dbed4e74bafc3ff080cfd2e0,
title = "Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel",
abstract = "We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.",
keywords = "anomalous diffusion, continuous time random walk (CTRW), Fokker- Planck-Smoluchowski equation, Mittag-Leffler functions, multi-scaling",
author = "Trifce Sandev and Aleksei Chechkin and Holger Kantz and Ralf Metzler",
year = "2015",
month = "8",
day = "1",
doi = "10.1515/fca-2015-0059",
language = "English",
volume = "18",
pages = "1006--1038",
journal = "Fractional Calculus and Applied Analysis",
issn = "1311-0454",
publisher = "Springer Science + Business Media",
number = "4",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel

AU - Sandev, Trifce

AU - Chechkin, Aleksei

AU - Kantz, Holger

AU - Metzler, Ralf

PY - 2015/8/1

Y1 - 2015/8/1

N2 - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.

AB - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.

KW - anomalous diffusion

KW - continuous time random walk (CTRW)

KW - Fokker- Planck-Smoluchowski equation

KW - Mittag-Leffler functions

KW - multi-scaling

UR - http://www.scopus.com/inward/record.url?scp=84939133175&partnerID=8YFLogxK

U2 - 10.1515/fca-2015-0059

DO - 10.1515/fca-2015-0059

M3 - Article

VL - 18

SP - 1006

EP - 1038

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 4

ER -