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Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar steepest descent method and double scaling limit, we obtain Painleve asymptotics in two transitio...
We study the qualitative properties of the generalized transition fronts for the reaction diffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transitio...
We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with ...
We study the qualitative properties of the generalized transition fronts for the reactiondiffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transition...
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-fro...
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomog...
We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogenei...
Abstract: We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,...,L\}$ into disjoint intervals. Each interval can either split or merge with one of i...
Abstract: A dyadic tile of order n is any rectangle obtained from the unit square by n successive bisections by horizontal or vertical cuts. Let each dyadic tile of order n be available with probabili...
Abstract: For many random constraint satisfaction problems such as random satisfiability or random graph or hypergraph coloring, the best current estimates of the threshold for the existence of soluti...
A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al. [Phys. Rev. Lett. 96, 145701 (2006)] to exhibit a phase transition at a critical value of the coupling...
The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier-Stokes flow on a three-periodic domain.
We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...
In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all usual situations,involve uniform limits, with respe...
We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...

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