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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...

Mathematically Modelling The Dissolution Of Solid Dispersions

Meere, Martin, McGinty, Sean, Pontrelli, Giuseppe (2017)

Proceedings of Equadiff 14

A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design....

Maximizing multi–information

Nihat Ay, Andreas Knauf (2006)

Kybernetika

Stochastic interdependence of a probability distribution on a product space is measured by its Kullback–Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed description of the structure of probability distributions with globally maximal multi-information we obtain our main result: The exponential family...

Mean-field evolution of fermionic systems

Marcello Porta (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...

Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation

Jürg Fröhlich, Enno Lenzmann (2003/2004)

Séminaire Équations aux dérivées partielles

We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle (Newtonian)...

Metastability in reversible diffusion processes I: Sharp asymptotics for capacities and exit times

Anton Bovier, Michael Eckhoff, Véronique Gayrard, Markus Klein (2004)

Journal of the European Mathematical Society

We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form − ϵ Δ + ∇ F ( · ) ∇ on ℝ d or subsets of ℝ d , where F is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as ϵ ↓ 0 , to the capacities of suitably constructed sets. We show that these capacities...

Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues

Anton Bovier, Véronique Gayrard, Markus Klein (2005)

Journal of the European Mathematical Society

We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form − ϵ Δ + ∇ F ( · ) ∇ on ℝ d or subsets of ℝ d , where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum...

Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)

Annales de l'I.H.P. Probabilités et statistiques

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude t1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type processes....

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