Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility.
Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy
We consider the following problem: where Φ: Ω ⊂ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
Random hysteresis loops
Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order , the size of the system, the “critical” hysteresis loop becomes random.
Random matrices and permutations, matrix integrals and integrable systems
Random matrices, non-colliding processes and queues
Random spatial growth with paralyzing obstacles
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 walk in a strongly inhomogeneous environment and invasion percolation
Random walk on a discrete torus and random interlacements.
Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit.
Random walks in a Dirichlet environment.
Random walks on finite rank solvable groups
We establish the lower bound , for the large times asymptotic behaviours of the probabilities of return to the origin at even times , 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 , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to .)
Random walks on trees and matchings.
Randomly interacting particle systems : the uniqueness regime
Rapid mixing of Swendsen-Wang dynamics in two dimensions [Book]
Rationality, property rights and thermodynamic approach to the market equilibrium.
Reconstruction des phases en cristallographie par maximum d'entropie
Recurrence of distributional limits of finite planar graphs.
Reduced and extended weak coupling limit
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 energy functionals for a three-dimensional fast rotating Bose Einstein condensates
Reduced resistive MHD in Tokamaks with general density
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.