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Ecological modeling and Lagrangian approach

Boris Arkhipov, Viacheslav Solbakov, Mikhail Solov’ev, Dmitry Shapochkin (2013)

Open Mathematics

A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the...

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the...

Effective saturation for composite porous media

Micol Amar, Roberto Gianni (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper is devoted to the study of the homogenization of a porous medium, composed of different materials arranged in a periodic structure. This provides the profile of the saturation function for the limit material.

Effects of In-plane Elastic Stress and Normal External Stress on Viscoelastic Thin Film Stability

F. Closa, F. Ziebert, E. Raphaël (2012)

Mathematical Modelling of Natural Phenomena

Motivated by recent experiments on the electro-hydrodynamic instability of spin-cast polymer films, we study the undulation instability of a thin viscoelastic polymer film under in-plane stress and in the presence of either a close by contactor or an electric field, both inducing a normal stress on the film surface. We find that the in-plane stress affects both the typical timescale of the instability and the unstable wavelengths. The film stability...

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