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A Mixed-Culture Biofilm Model with Cross-Diffusion
Bulletin of Mathematical Biology, 2015We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given.
Rahman, Kazi A. +2 more
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Cross Diffusion-Stresses Effects
Defect and Diffusion Forum, 2007Three cross diffusion-stresses effects are considered: mobility-stress effect, flux-stress effect and vacancy-stress effect. The value of the migration volume for vacancies in Al is found from atomistic computer simulation. A cross vacancy-stress effect is applied to the process of the pores growth and dissolution in Ni-based superalloys.
Boris S. Bokstein +5 more
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Negative refractoriness in excitable systems with cross-diffusion
Biophysics, 2009The results of numerical experiments with mathematical models of excitable systems with cross-diffusion are presented. It was shown that the refractoriness in such systems may be negative. The effects of negative refractoriness on the propagation and interaction of waves are demonstrated.
M A, Tsyganov +2 more
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2016
Cross-diffusion models are systems of strongly coupled parabolic equations. In Sect. 4.1, we present some known examples arising in cell biology and thermodynamics. The derivation of these models from on-lattice models or fluid equations for mixtures is sketched in Sect. 4.2, using results from Ostrander, SIAM Undergrad, Res, 4, 2011, [53], Jackson and
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Cross-diffusion models are systems of strongly coupled parabolic equations. In Sect. 4.1, we present some known examples arising in cell biology and thermodynamics. The derivation of these models from on-lattice models or fluid equations for mixtures is sketched in Sect. 4.2, using results from Ostrander, SIAM Undergrad, Res, 4, 2011, [53], Jackson and
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Cross-diffusion models: Analytic and multiscale problems
Mathematical Models and Methods in Applied Sciences, 2018A presentation of a special issue on the derivation of cross-diffusion models and on the related analytical problems is proposed in this note. A brief introduction to motivations and recently published literature is presented in the first part. Subsequently, a concise description of the contents of the papers published in the issue follows.
Bellomo, N., Tao, Y., Winkler, M.
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Regularity of Solutions to a Class of Cross Diffusion Systems
SIAM Journal on Mathematical Analysis, 2005Interior Hölder continuity of weak bounded solutions to a class of parabolic systems of the type \[ \vec u_t = \nabla . (A(\vec u)\nabla \vec u) + F(\vec u)\quad \text{on}\quad \Omega_T = \Omega \times (0,T) \tag{1} \] is proved under interesting structural conditions on the main part of the considered systems. Here \(A(\vec u)= (P_{ij}(\vec u))_{i,j=1,
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On the Cross-diffusion and Soret Effect in Multicomponent Mixtures
Microgravity Science and Technology, 2008The model of convection in a multicomponent fluid is considered taking into account the cross-diffusion and the Soret effect. It is shown that the cross-diffusion coefficients can be eliminated by a linear change of composition and the thermal diffusion coefficients.
Ryzhkov, Ilya, Shevtsova, Valentina
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PEB model with cross-diffusion
SPIE Proceedings, 2003ABSTRACT In multi-component chemical systems, thermodynamic fluxes linearly depend on thermodynamic forces through thematrix of Onsagers coefficients. By applying Onsager s relationship to the PEB diffusion of acid and other relevantchemical components, we deducted a generalization of the traditional PEB diffusion-reaction equations.
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Cross-diffusion in the two-variable Oregonator model
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013We explore the effect of cross-diffusion on pattern formation in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction. For high negative cross-diffusion of the activator (the activator being attracted towards regions of increased inhibitor concentration) we find, depending on the values of the parameters, Turing patterns, standing ...
Berenstein, Igal +1 more
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Numerical Solution of Nonlinear Cross Diffusion Problems
2019This paper considered cross-diffusion equations. With those equations the concentration development in a certain region during an interesting time-interval can be described.
Günter Bärwolff, Julia Baumbach
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