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The Child–Langmuir limit for semiconductors : a numerical validation

María-José Cáceres, José-Antonio Carrillo, Pierre Degond (2002)

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

The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons...

The Child–Langmuir limit for semiconductors: a numerical validation

María-José Cáceres, José-Antonio Carrillo, Pierre Degond (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical...

The classic differential evolution algorithm and its convergence properties

Roman Knobloch, Jaroslav Mlýnek, Radek Srb (2017)

Applications of Mathematics

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...

The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Sebastian Franz, Fang Liu, Hans-Görg Roos, Martin Stynes, Aihui Zhou (2009)

Applications of Mathematics

Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing N for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on N × N , N × N and N × N meshes. It is shown that the combination FEM yields (up to a factor ln N ) the same order of accuracy in the associated...

The computation of Stiefel-Whitney classes

Pierre Guillot (2010)

Annales de l’institut Fourier

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

Thorsten Rohwedder (2013)

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

Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the stationary electronic Schrödinger equation. Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, i.e. within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis...

Currently displaying 61 – 80 of 543