Page 1 Next
Paula B. Cohen (1999)
Journal de théorie des nombres de Bordeaux
In this paper we extend to arbitrary number fields a construction of Bost-Connes of a -dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.
Carol Bezuidenhout, Geoffrey Grimmett (1999)
Annales de l'I.H.P. Probabilités et statistiques
Piotr Biler, Tadeusz Nadzieja (1993)
Colloquium Mathematicae
We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.
Daniel Bouche, Alain Decoster, Laurent Desvillettes, Valeria Ricci (2013)
MathematicS In Action
We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.
J.-P. Hennart, J. Jaffre, J.E. Roberts (1988)
Numerische Mathematik
Knill, Oliver (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Martin Campos Pinto (2007)
International Journal of Applied Mathematics and Computer Science
This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1+1)-dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport...
M. Malik-Garbi, O. Agam (2012)
Mathematical Modelling of Natural Phenomena
We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a discrete analog of the continuous dynamics of evaporation of thin liquid films. Within mean field approximation the dynamics of this model, averaged over many realizations of the growing cluster, reduces to that of the idealized evaporation model in which surface tension is neglected. However fluctuations beyond the mean field level play an important role, and...
François Golse, Shi Jin, C. David Levermore (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating...
François Golse, Shi Jin, C. David Levermore (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating...
И. Г. Корепанов (1994)
Zapiski naucnych seminarov POMI
Maciej Ławryńczuk (2007)
International Journal of Applied Mathematics and Computer Science
This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used...
Boldrini, Jose Luiz, da Silva, Patricia Nunes (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Sébastien Breteaux (2014)
Annales de l’institut Fourier
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
Michel Mehrenberger, Eric Violard (2007)
International Journal of Applied Mathematics and Computer Science
We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
David J. Knezevic, Endre Süli (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for...
Laurent Boudin, Francesco Salvarani (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
In this work, we use the methods of nonequilibrium statistical mechanics in order to derive an equation which models some mechanisms of opinion formation. After proving the main mathematical properties of the model, we provide some numerical results.
Dario Benedetto, Emanuele Caglioti, Mario Pulvirenti (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this short note we correct a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so called quasi-elastic limit, presented by the same authors in reference[1]. The equation we derived is however correct so that, the rigorous analysis on this equation, which constituted the main purpose of that paper, remains unchanged.
P. Maynar, M. I. García de Soria (2011)
Mathematical Modelling of Natural Phenomena
The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also...
J. Beltrán, C. Landim (2008)
Annales de l'I.H.P. Probabilités et statistiques
We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.
Page 1 Next