All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 14 Next

Displaying 261 – 280 of 498

Showing per page

Nonlocal quadratic evolution problems

Piotr Biler, Wojbor Woyczyński (2000)

Banach Center Publications

Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...

Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena

Nicolas Besse, Norbert J. mauser, Eric Sonnendrücker (2007)

International Journal of Applied Mathematics and Computer Science

We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows thenumerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian...

Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field...

On a variant of Korn’s inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We state and prove a Korn-like inequality for a vector field in a bounded open set of ℝ N , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are...

On a variant of Korn's inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We state and prove a Korn-like inequality for a vector field in a bounded open set of ℝ N , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case...

On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz (2003)

Banach Center Publications

In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

John W. Barrett, James F. Blowey, Harald Garcke (2001)

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

We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with...

Currently displaying 261 – 280 of 498