Isotropic model of fractional transport in two-dimensional bounded domains

Journal Article · Tue Jan 01 04:00:00 EST 2013 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.87.052115· OSTI ID:1097507

Kullberg, A. ^[1]; Del-Castillo-Negrete, Diego B ^[2]

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1. University of California, Los Angeles
2. ORNL

A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1097507
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 87; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

ADVECTION-DISPERSION EQUATIONS
ANOMALOUS DIFFUSION
FLUCTUATIONS
PLASMA TURBULENCE
TOKAMAK