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On a Model of Leukemia Development with a Spatial Cell Distribution

A. Ducrot, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation...

On the Mathematical Analysis and Optimization of Chemical Vapor Infiltration in Materials Science

Adi Ditkowski, David Gottlieb, Brian W. Sheldon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present an analysis of the partial differential equations that describe the Chemical Vapor Infiltration (CVI) processes. The mathematical model requires at least two partial differential equations, one describing the gas phase and one corresponding to the solid phase. A key difficulty in the process is the long processing times that are typically required. We address here the issue of optimization and show that we can choose appropriate pressure and temperature to minimize these...

On the modeling of the transport of particles in turbulent flows

Thierry Goudon, Frédéric Poupaud (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.

On the modeling of the transport of particles in turbulent flows

Thierry Goudon, Frédéric Poupaud (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.

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