May 8-10

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Abstracts

Author: Diego del-Castillo-Negrete
Requested Type: Poster
Submitted: 2023-03-31 15:08:51

Co-authors: M. Yang and G. Zhang

Contact Info:
Oak Ridge National Laboratory
PO Box 2008
Oak Ridge, TN   37831-6305
USA

Abstract Text:
The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this poster we present an accurate and efficient numerical method for computing this probability for systems described by Fokker-Planck equations modeling local transport (e.g., diffusion) or nonlocal transport (e.g., Landau-fluid or non-diffusive turbulent transport closures). The method is based on the direct evaluation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the corresponding forward SDE (stochastic differential equations). In the case of local transport, the SDE are driven by Brownian motion and in case of nonlocal transport, depending on the nonlocal kernel, by compound Poisson processes or alpha-stableLevy processes. We illustrate and benchmark the proposed method with numerical examples of transport in magnetized plasmas in toroidal geometry.

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