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Marangoni Convection in a Photo-Chemically Reacting Liquid

A. A. Golovin, V. A. Volpert (2008)

Mathematical Modelling of Natural Phenomena

Marangoni convection caused by a photochemical reaction of the type A ⇌ h ν B in a deep liquid layer is studied. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that increasing the rate of the direct reaction, for example, by increasing the light intensity, destabilizes the steady state and causes convective motion of the fluid, whereas increasing the rate of the inverse reaction stabilizes the steady state. A weakly nonlinear analysis...

Mathematical analysis of the stabilization of lamellar phases by a shear stress

V. Torri (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette - Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments.

Mathematical analysis of the stabilization of lamellar phases by a shear stress

V. Torri (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette-Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments. ...

Mathematical models for laser-plasma interaction

Rémi Sentis (2005)

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

We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the...

Mathematical models for laser-plasma interaction

Rémi Sentis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the...

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