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Detecting early kidney allograft fibrosis with multi-b-value spectral diffusion MRI. [PDF]
Sci RepLiu MM +16 more
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Diffusion, Cross-diffusion and Competitive Interaction
Journal of Mathematical Biology, 2006The cross-diffusion competition systems were introduced by Shigesada et al. [J. Theor. Biol. 79, 83-99 (1979)] to describe the population pressure by other species. In this paper, introducing the densities of the active individuals and the less active ones, we show that the cross-diffusion competition system can be approximated by the reaction ...
Iida, Masato +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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Bifurcation of Reaction Cross-Diffusion Systems
International Journal of Bifurcation and Chaos, 2017This paper is devoted to a reaction cross-diffusion system under Neumann boundary conditions. Firstly, the existence and multiplicity of spatially nonhomogeneous/homogeneous steady-state solutions are investigated by means of Lyapunov–Schmidt reduction.
Zou, Rong, Guo, Shangjiang
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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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Study on a Cross Diffusion Parabolic System
Acta Mathematicae Applicatae Sinica, English Series, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Li, Hsiao, Ling, Warnecke, Gerald
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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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