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Displaying 121 – 140 of 1376

Adaptive finite element relaxation schemes for hyperbolic conservation laws

Christos Arvanitis, Theodoros Katsaounis, Charalambos Makridakis (2001)

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

We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...

Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws

Christos Arvanitis, Theodoros Katsaounis, Charalambos Makridakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Ageing in the parabolic Anderson model

Peter Mörters, Marcel Ortgiese, Nadia Sidorova (2011)

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

The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time,...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy (2009)

Bulletin de la Société Mathématique de France

We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height $log t$ . In the quenched setting, we also sharply estimate the distribution of the walk at time $t$ .

Aging for interacting diffusion processes

Amir Dembo, Jean-Dominique Deuschel (2007)

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

Alcune disuguaglianze nel modello di Edwards-Anderson e in altri modelli di vetri di spin

Emilio De Santis (2000)

Bollettino dell'Unione Matematica Italiana

Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics

Vladimir Dragović (2012)

Publications de l'Institut Mathématique

Almost sure functional central limit theorem for ballistic random walk in random environment

Firas Rassoul-Agha, Timo Seppäläinen (2009)

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

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.

Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case

Jean Bourgain, Aynur Bulut (2014)

Journal of the European Mathematical Society

We extend the convergence method introduced in our works [8–10] for almost sure global well-posedness of Gibbs measure evolutions of the nonlinear Schrödinger (NLS) and nonlinear wave (NLW) equations on the unit ball in $ℝ^{d}$ to the case of the three dimensional NLS. This is the first probabilistic global well-posedness result for NLS with supercritical data on the unit ball in $ℝ^{3}$ . The initial data is taken as a Gaussian random process lying in the support of the Gibbs measure associated to the equation,...

Ammann Bars and Quasicrystals.

T. Stehling (1992)

Discrete & computational geometry

An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix, Giovanni Samaey, Dirk Roose (2011)

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

We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...

An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix, Giovanni Samaey, Dirk Roose (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

An analysis of quantum Fokker-Planck models: a Wigner function approach.

Anton Arnold, José L. López, Peter A. Markowich, Juan Soler (2004)

Revista Matemática Iberoamericana

The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time, where we adopt the viewpoint of mild solutions in this paper. Also, the admissibility of a density matrix formulation in Lindblad form with Fokker-Planck...

An analysis of the effect of ghost force oscillation on quasicontinuum error

Matthew Dobson, Mitchell Luskin (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...