Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart [PDF]
, 2021 We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada-Kawasaki-Teramoto nonlocal cross-diffusion problem converges to a solution of the usual ...
Velasco, Julián +5 more
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Numerical Methods for a Diffusive Class of Nonlocal Operators [PDF]
Journal of Scientific Computing, 2021 In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $ν$, of diffusive type. In particular, we assume $ν$ is symmetric and exponentially decaying at infinity. We consider problems posed in bounded domains and in $\R$.
Gabriela Jaramillo +2 more
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Comparison of holographic photopolymer materials by use of analytic nonlocal diffusion models [PDF]
, 2002 The one-dimensional diffusion equation governing holographic grating formation in photopolymers, which includes both nonlocal material response and generalized dependence of the rate of polymerization on the illuminating intensity, has been previously ...
Lawrence, Justin R. +3 more
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A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models [PDF]
SIAM Journal on Numerical Analysis, 2018 In this paper, we extend the idea of “geometric reconstruction” to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial inconsistency, ensures the flux balance, and satisfies energy conservation as well as the maximum principle, whereas none of existing ...
Qiang Du 0001 +3 more
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Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 20 ...
Isolda E. Cardoso, Raúl E. Vidal
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Monomer diffusion rates in photopolymer material. Part I. Low spatial frequency holographic gratings [PDF]
, 2011 For photopolymers, knowing the rate of diffusion of the active monomer is important when modeling the material evolution during recording in order to understand and optimize their performance.
Close, Ciara E. +8 more
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Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling
CoRR, 2018 Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well ...
Yunzhe Tao +3 more
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Study of the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals [PDF]
, 2004 Local and nonlocal models for the diffusion of photopolymers are applied to the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals (H-PDLCs). We retrieve the main parameters of H-PDLCs (
Kaiser, Jean-Luc +5 more
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Existence result for a nonlocal viscous Cahn-Hillard equation with a degenerate mobility [PDF]
, 2011 We study a diffusion model of phase field type, consisting of a system of two partial differential equations of second order for the particle densities and the viscosity variable, coupled by a nonlocal drift term.
Farshbaf-Shaker, Hassan +1 more
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A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates [PDF]
, 2003 We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster ...
Winter, M +3 more
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