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Random spatial growth with paralyzing obstacles

J. van den Berg, Y. Peres, V. Sidoravicius, M. E. Vares (2008)

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

We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with others (there is no ‘inter-green’ competition). The red substance remains passive as long as it is isolated. However, when a green cluster comes in touch with the red substance, it is immediately invaded by the latter, stops growing and starts to act as a red...

Random walks on finite rank solvable groups

Ch. Pittet, Laurent Saloff-Coste (2003)

Journal of the European Mathematical Society

We establish the lower bound p 2 t ( e , e ) ≿ exp ( − t 1 / 3 ) , for the large times asymptotic behaviours of the probabilities p 2 t ( e , e ) of return to the origin at even times 2 t , for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r .)

Reduced and extended weak coupling limit

Jan Dereziński, Wojciech De Roeck (2007)

Banach Center Publications

The main aim of our lectures is to give a pedagogical introduction to various mathematical formalisms used to describe open quantum systems: completely positive semigroups, dilations of semigroups, quantum Langevin dynamics and the so-called Pauli-Fierz Hamiltonians. We explain two kinds of the weak coupling limit. Both of them show that Hamiltonian dynamics of a small quantum system interacting with a large resevoir can be approximated by simpler dynamics. The better known reduced weak coupling...

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

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

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Regularity analysis for systems of reaction-diffusion equations

Thierry Goudon, Alexis Vasseur (2010)

Annales scientifiques de l'École Normale Supérieure

This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi’s method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere...

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