Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Fractional Fokker-Planck equation, solution, and application.

E Barkai1

  • 1Department of Chemistry and Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study solves the fractional Fokker-Planck equation (FFPE) using an integral transformation, providing insights into subdiffusive particle behavior in complex systems. The FFPE offers a practical tool for describing anomalous transport phenomena.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Ergodic properties of Brownian motion under stochastic resetting.

Physical review. E·2024
Same author

Restart Expedites Quantum Walk Hitting Times.

Physical review letters·2023
Same author

Measurement-induced quantum walks.

Physical review. E·2022
Same author

Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model.

Entropy (Basel, Switzerland)·2021
Same author

Hitchhiker model for Laplace diffusion processes.

Physical review. E·2020
Same author

Infinite ergodic theory for heterogeneous diffusion processes.

Physical review. E·2019

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Anomalous Transport

Background:

  • Fractional Fokker-Planck equation (FFPE) models subdiffusion.
  • Subdiffusion arises from external forces and thermal baths.
  • Previous work by Metzler et al. introduced the FFPE.

Purpose of the Study:

  • To present an integral transformation solution for the FFPE.
  • To investigate particle behavior under various force fields.
  • To explore fractional first passage time problems.

Main Methods:

  • Integral transformation based on Lévy's generalized central limit theorem.
  • Analysis of force-free, uniform, and harmonic fields.
  • Comparison with continuous time random walk (CTRW) solutions.

Related Experiment Videos

Main Results:

  • An exact solution for the CTRW is derived.
  • The FFPE solution is mapped from the ordinary Fokker-Planck equation solution.
  • Fractional and integer first passage times are related.

Conclusions:

  • The FFPE is compatible with the Scher-Montroll approach for dispersive transport.
  • The FFPE is applicable to various disordered systems.
  • The FFPE serves as a practical tool for complex transport phenomena.