Diffusion of Zinc in Doped NaCl Crystals
Viera Paulíny-Tothová (1966)
Matematicko-fyzikálny časopis
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Viera Paulíny-Tothová (1966)
Matematicko-fyzikálny časopis
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Liljana Stefanovska, Toma Grcev, Sonja Gegovska-Zajkova (2002)
Visual Mathematics
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Hrabě, Jan
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An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability...
Hideki Murakawa (2009)
Kybernetika
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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems....
Kůs, Pavel, Dolejší, Vít
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Rybář, Vojtěch, Vejchodský, Tomáš
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We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed...
Thierry Goudon, Antoine Mellet (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.