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

Operator Lévy motion and multiscaling anomalous diffusion.

M M Meerschaert1, D A Benson, B Baeumer

  • 1Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084, USA. mcubed@unr.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary
This summary is machine-generated.

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

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

Electronic journal of mathematical analysis and applications·2015
Same author

TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION.

Transactions of the American mathematical society·2014
Same author

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

Fractional calculus & applied analysis·2013
Same author

Multidimensional advection and fractional dispersion.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same author

Results of treatment with tamsulosin in men with acute urinary retention.

Techniques in urology·2002
Same author

Mitogen-activated protein kinase kinase 4 metastasis suppressor gene expression is inversely related to histological pattern in advancing human prostatic cancers.

Cancer research·2001

Anomalous diffusion exhibits directional scaling rates due to heavy-tailed particle jumps. Operator stable motions model this, showing different dispersion rates in principal directions, crucial for understanding tracer movement in aquifers.

Area of Science:

  • Physics
  • Mathematics
  • Geophysics

Background:

  • Anomalous diffusion is characterized by heavy-tailed (power-law) particle jumps.
  • Particle jump scaling rates can differ across directions.
  • Natural aquifer tracer movement shows varying scaling rates parallel and perpendicular to flow.

Purpose of the Study:

  • To introduce and analyze operator stable motions as a model for anomalous diffusion with directional scaling.
  • To describe the governing equations for these motions, incorporating generalized fractional operators.
  • To provide a mathematical framework for understanding anisotropic dispersion in natural systems.

Main Methods:

  • Operator stable motions are defined as limits of d-dimensional random jumps.
  • Scale invariance is characterized by c(H)Y(t)=Y(ct) with a dxd matrix H.

Related Experiment Videos

  • Eigenvalues of H determine directional diffusion rates proportional to t(1/alpha(j)).

    • Main Results:

    • Operator stable motions exhibit different Fickian or super-Fickian diffusion rates in principal directions.
    • The governing equation involves a spatial dispersion operator mixing fractional derivatives of varying orders.
    • Specific cases include fractional Laplacian with directional mixing and the Riesz potential.

    Conclusions:

    • Operator stable motions provide a framework for anomalous diffusion with anisotropic scaling.
    • The generalized fractional operator captures directional dispersion observed in natural aquifers.
    • This model enhances understanding of solute transport in heterogeneous media.