Page 1

Displaying 1 – 9 of 9

Showing per page

Mathematical and numerical studies of non linear ferromagnetic materials

Patrick Joly, Olivier Vacus (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous...

Méthodes géométriques dans l’étude des équations d’Einstein

Serge Alinhac (2003/2004)

Séminaire Bourbaki

L’étude de l’équation des ondes et de ses perturbations a montré l’importance d’un certain nombre d’objets géométriques, tels que les cônes sortants et rentrants, les champs de Lorentz, des repères isotropes adaptés, etc. Parmi les systèmes d’équations hyperboliques non linéaires, les équations d’Einstein jouent un rôle central ; leur étude a nécessité, dans le cas d’un espace-temps courbe, la construction d’objets analogues à ceux du cas plat, cônes, repères adaptés, etc. La construction de ces...

Modulation of the Camassa-Holm equation and reciprocal transformations

Simonetta Abenda, Tamara Grava (2005)

Annales de l’institut Fourier

We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...

Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux

Adimurthi, Rajib Dutta, G. D. Veerappa Gowda, Jérôme Jaffré (2014)

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

For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone...

Multi-scale Modelling for Threshold Dependent Differentiation

A. Q. Cai, Y. Peng, J. Wells, X. Dai, Q. Nie (2009)

Mathematical Modelling of Natural Phenomena

The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc,...

Currently displaying 1 – 9 of 9

Page 1