Exploring Embedded Uncertainty Quantification Methods on Next-Generation Computer Architectures
Abstract not provided.
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Jump to search filtersFractional diffusion on bounded domains
Fractional Calculus and Applied Analysis
The mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. This paper discusses the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.
The exit-time problem for a Markov jump process
European Physical Journal: Special Topics
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
The exit-time problem for a Markov jump process
European Physical Journal. Special Topics
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Additionally, such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Finally, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
Optimization?Based Coupling of Nonllocall and Locall diffusion models
Abstract not provided.
Optimization?Based Coupling of Nonlocal and Local Diffusion Models
Abstract not provided.
Formulation analysis and computation of an Optimization Based Local to Nonlocal Coupling Method
Abstract not provided.
Nonlocal non?symmetric diffusion Matthematical Analysis and Stochastic Interpretation
Abstract not provided.
Finite range jump processes and volume-constrained diffusion problems
Stochastic Processes and their Applications
Abstract not provided.
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