Asymptotic Analysis - Volume 37, issue 3-4

Authors: Brassart, Matthieu

Article Type: Research Article

Abstract: We study the transport of particles in time‐dependent random media in the so‐called weak coupling limit. We show how a limiting irreversible dynamic of Boltzmann's type can be derived from a reversible dynamic of Schrödinger's type. The homogenization is performed at the level of Wigner transforms for a mixed states formulation. We obtain a simple modelization of the influence of microscopic chaos on physical observables by means of a space–time Fourier transform of a covariance associated with the random variations.

Keywords: semi‐classical limit, Wigner transform, Schrödinger equation, Boltzmann equation, random media, weak coupling limit

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 189-214, 2004

Authors: Korotyaev, Evgeni

Article Type: Research Article

Abstract: For the Schrödinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one‐to‐one and onto. Moreover, we show that the resonances in any bounded domain in $\mathbb{C}$ ‐ are so‐called free parameters.

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 215-226, 2004

Authors: Bayada, G. | Benhaboucha, N. | Chambat, M.

Article Type: Research Article

Abstract: We have studied the asymptotic behaviour of a coupling between a thin film of fluid and an adjacent thin porous medium. This situation appears in boundary lubrication problems. We show that there is a critical value between the size of the microstructure of the porous medium, the free fluid gap and the thickness of the porous medium. Moreover it is shown that an actual geometry can always be described by that critical value for which a modified Reynolds equation is proved. Numerical calculations show the difference between our model and two other models proposed in mechanical literature. Résumé. On …étudie le comportement asymptotique d'un écoulement fluide constité d'une couche poreuse mince adjacente à un milieu fluide mince. Cette géométrie est caractéristique d'un écoulement lubrifié “limite”. On met en évidence l'existence d'un rapport critique entre la taille de la microstructure du milieu poreux et les deux épaisseurs, rapport pour lequel une équation de Reynolds modifiée est obtenue. De plus il est montré qu'on peut toujours pour une géométrie réelle donnée se placer dans ce cas critique. Enfin, on présente des simulations numériques qui mettent en évidence les différences entre le modèle présenté ici et deux autres utilisés en mécanique. Show more

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 227-256, 2004

Authors: Da Lio, Francesca | Inwon Kim, Christina | Slepčev, Dejan

Article Type: Research Article

Abstract: This paper is concerned with the asymptotic behavior as ε→0 of the solutions of nonlocal reaction–diffusion equations of the form ut −Δu+ε−2 f(u,ε∫0 u)=0 in O×(0,T) associated with nonlinear oblique derivative boundary conditions. We show that such behavior is described in terms of an interface evolving with normal velocity depending not only on its curvature but also on the measure of the set it encloses. To this purpose we introduce a weak notion of motion of hypersurfaces with nonlocal normal velocities depending on the volume they enclose, which extends the geometric definition of generalized motion of hypersurfaces in bounded domains …introduced by G. Barles and the first author to solve a similar problem with local normal velocities depending on the normal direction and the curvature of the front. We also establish comparison and existence theorems of viscosity solutions to initial‐boundary value problems for some singular degenerate nonlocal parabolic pde's with nonlinear Neumann‐type boundary conditions. Show more

Keywords: front propagation, nonlocal reaction–diffusion equations, asymptotic behavior, geometrical approach, level‐set approach, Neumann boundary condition, angle boundary condition, viscosity solutions

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 257-292, 2004

Authors: Rousse, Vidian

Article Type: Research Article

Abstract: In the Born–Oppenheimer approximation context, we study the propagation of Gaussian wave packets through the simplest type of eigenvalue avoided crossings of an electronic Hamiltonian 𝒞4 in the nuclear position variable. It yields a two‐parameter problem: the mass ratio ε4 between electrons and nuclei and the minimum gap δ between the two eigenvalues. We prove that, up to first order, the Landau–Zener formula correctly predicts the transition probability from a level to another when the wave packet propagates through the avoided crossing in the two different regimes: δ being asymptotically either smaller or greater than ε when both …go to 0. Show more

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 293-328, 2004

Authors: Liess, Otto

Article Type: Research Article

Abstract: We study decay estimates for Fourier transforms of smooth densities defined on surfaces with uniplanar singularities.

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 329-362, 2004

Article Type: Other

Citation: Asymptotic Analysis, vol. 37, no. 3-4, pp. 363-363, 2004