Modélisation d'écoulements polyphasiques en milieu poreux par un système de problèmes unilatéraux
Modélisation du champ de retard à la condensation d'un supraconducteur par un problème de bifurcation
Modelli matematici per la diffusione e il trasporto di particelle cariche
Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary
In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.
Modelling bioremediation of polluted soils in unsaturated condition and its effect on the soil hydraulic properties
We study the unsaturated flow of an incompressible liquid carrying a bacterial population through a porous medium contaminated with some pollutant. The biomass grows feeding on the pollutant and affecting at the same time all the physics of the flow. We formulate a mathematical model in a one-dimensional setting and we prove an existence theorem for it. The so-called fluid media scaling approach, often used in the literature, is discussed and its limitations are pointed out on the basis of a specific...
Modelling geophysical flows in the equatorial zone
We present here a series of works which aims at describing geophysical flows in the equatorial zone, taking into account the dominating influence of the earth rotation. We actually proceed by successive approximations computing for each model the response of the fluid to the strong Coriolis penalisation. The main difficulty is due to the spatial variations of the Coriolis acceleration : in particular, as it vanishes at the equator, fast oscillations are trapped in a thin strip of latitudes.
Modelling of a collage problem.
Modelling of convective phenomena in forest fire.
We present a model coupling the fire propagation equations in a bidimensional domain representing the surface, and the air movement equations in a three dimensional domain representing an air layer. As the air layer thickness is small compared with its length, an asymptotic analysis gives a three dimensional convective model governed by a bidimensional equation verified by a stream function. We also present the numerical simulations of these equations.
Modelling of Plant Growth with Apical or Basal Meristem
Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...
Modelling of singularities in elastoplastic materials with fatigue
The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional...
Modelling of the Czochralski flow.
Modelling of the interaction of small and large eddies in two dimensional turbulent flows
Modelling the electromagnetic behaviour of SiFe alloys using the Preisach theory and the principle of loss seperation.
Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents
Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...
Models for phase separation and their mathematics.
Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare...
Modification of unfolding approach to two-scale convergence
Two-scale convergence is a powerful mathematical tool in periodic homogenization developed for modelling media with periodic structure. The contribution deals with the classical definition, its problems, the ``dual'' definition based on the so-called periodic unfolding. Since in the case of domains with boundary the unfolding operator introduced by D. Cioranescu, A. Damlamian, G. Griso does not satisfy the crucial integral preserving property, the contribution proposes a modified unfolding operator...
Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation.
Modified step variational iteration method for solving fractional biochemical reaction model.
Modified wave operators for nonlinear Schrödinger equations in one and two dimensions.