Asymptotic Analysis - Volume 10, issue 3

Authors: Parisse, B.

Article Type: Research Article

Abstract: On s'intéresse ici à l'étude lorsque h→0 (en limite semi-classique) de l'opérateur de Dirac défini sur C∞ (R3 ;C4 ) par: (1) Dt (h)=Σ3 j=1 αj (hDj +tAj )+α4 +V(x).I4 , en présence d'un champ magnétique B = rot A nul en-dehors d'un cylindre (ici les αj désignent des matrices 4 × 4 qui anticommutent). Dans le cas de l'opérateur de Schrödinger en dimension 2, si le champ magnétique est nul en-dehors d'un disque, B. Helffer a montré qu'il peut apparaître un effet de flux qui décale les valeurs propres de l'opérateur sans champ magnétique, cet effet …de flux est nommé effet d'Aharonov-Bohm. On montre ici qu'il en est de même pour l'opérateur de Dirac et on verra qu'en limite non-relativiste l'effet d'Aharonov-Bohm provoque un découplage des valeurs propres (qui sont de multiplicité paire en l'absence de champ magnétique). Show more

DOI: 10.3233/ASY-1995-10301

Citation: Asymptotic Analysis, vol. 10, no. 3, pp. 199-224, 1995

Authors: Amar, M. | Bellettini, G.

Article Type: Research Article

Abstract: We determine the Γ-limit as ε→0 of the sequence ∫Ω [εϕ2 (x,∇u)+ε−1 u2 (1−u2 )]dx of functionals defined on H1 (Ω). The free energy density ϕ has linear growth, is convex and positively homogeneous of degree one in the second variable and is upper semi-continuous in the first variable. The Γ-limit can be interpreted as a generalized total variation with discontinuous coefficients on the class of the characteristic functions of sets of finite perimeter. The proof is based on some variational properties of the generalized total variation strictly related to the upper semi-continuity of ϕ and on constructing a suitable …approximation of ϕ, from above. Show more

DOI: 10.3233/ASY-1995-10302

Citation: Asymptotic Analysis, vol. 10, no. 3, pp. 225-243, 1995

Authors: Petkov, Vesselin

Article Type: Research Article

Abstract: We examine the scattering phase related to metric perturbations of the Laplacian and we obtain a Weyl type formula with oscillating term related to absolutely periodic trajectories.

DOI: 10.3233/ASY-1995-10303

Citation: Asymptotic Analysis, vol. 10, no. 3, pp. 245-261, 1995

Authors: Perthame, B. | Pulvirenti, M.

Article Type: Research Article

Abstract: We build aN-particle stochastic system subject to a multibody interaction. The postcollisional repartition is performed so that the one-particle density function solves a scalar conservation law in a suitable limit of hydrodynamical type. In the kinetic limit, we recover a relaxation model which approximates the scalar. conservation. law. Our proof relies on a direct estimate of the L1 distance between the one-particle density function and its kinetic limit, using an appropriate joint process.

DOI: 10.3233/ASY-1995-10304

Citation: Asymptotic Analysis, vol. 10, no. 3, pp. 263-278, 1995

Authors: Henry, J. | Louro, B.

Article Type: Research Article

Abstract: We consider a Nernst-Planck-Poisson system modelling ion migration through biological membranes, in the one dimensional case. The model includes both the effects of biochemical reaction between ions and of fixed charges. We state the existence of solutions under either an imposed potential condition or an imposed current condition. We study the asymptotical behaviour of solutions in the limit of electroneutrality. Non-uniform convergence gives rise to jump in the potential, known as Donnan potential. Finally we give correctors which describe the charged boundary layers.

DOI: 10.3233/ASY-1995-10305

Citation: Asymptotic Analysis, vol. 10, no. 3, pp. 279-302, 1995