Asymptotic Analysis - Volume 80, issue 3-4

Authors: Ammari, Habib | Garapon, Pierre | Kang, Hyeonbae | Lee, Hyundae

Article Type: Research Article

Abstract: In this paper we derive high-order asymptotic expansions of the effective viscosity properties of a dilute periodic suspension composed of freely-suspended arbitrarily shaped particles dispersed in an incompressible Newtonian fluid. High-order terms are not only function of the viscous moment tensor but also of a distortion tensor that characterizes the periodic array.

Keywords: effective viscosity, dilute suspension, viscous moment tensor, high-order expansions

DOI: 10.3233/ASY-2012-1101

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 189-211, 2012

Authors: Yoshitomi, Kazushi

Article Type: Research Article

Abstract: We study inverse scattering problems for the singular rank-one perturbations of a selfadjoint operator. We obtain a necessary and sufficient condition for a given function to be the scattering phase shift of a singular rank-one perturbation of the operator.

Keywords: scattering theory, inverse problems, singular perturbation

DOI: 10.3233/ASY-2012-1112

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 213-221, 2012

Authors: Wright, Paul

Article Type: Research Article

Abstract: In this article we prove an important inequality regarding the Ruelle operator in hyperbolic flows. This was already proven briefly by Mark Pollicott and Richard Sharp in a low dimensional case [Amer. J. Math. 120 (1998), 1019–1042], but we present a clearer proof of the inequality, filling in gaps and explaining the ideas in more detail, and extend the inequality to higher-dimensional flows. This inequality is necessary to prove a proposition about the analyticity of Ruelle zeta functions.

Keywords: Ruelle's lemma, dynamical systems, axiom A flow, symbolic dynamics, Ruelle operator, transfer operator, zeta function

DOI: 10.3233/ASY-2012-1113

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 223-236, 2012

Authors: Le Bris, Claude | Legoll, Frédéric | Thomines, Florian

Article Type: Research Article

Abstract: We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of periodic coefficients.

Keywords: weakly stochastic homogenization, two-scale expansion

DOI: 10.3233/ASY-2012-1114

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 237-267, 2012

Authors: Korotyaev, Evgeny L.

Article Type: Research Article

Abstract: We consider the Schrödinger operator with a periodic potential p on the real line. We assume that p belongs to the real Sobolev space Hm on the circle for some m≥−1. We determine the sharp asymptotics of the quasimomentum and the Titchmarsh–Weyl functions, the Bloch functions at high energy.

Keywords: quasimomentum, integrated density of states, periodic potential

DOI: 10.3233/ASY-2012-1115

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 269-287, 2012

Authors: Gómez, D. | Pérez, E. | Shaposhnikova, T.A.

Article Type: Research Article

Abstract: Let uε be the solution of the Poisson equation in a domain periodically perforated along a manifold γ=Ω∩{x1 =0}, with a nonlinear Robin type boundary condition on the perforations (the flux here being O(ε−κ )σ(x,uε )), and with a Dirichlet condition on ∂Ω. Ω is a domain of Rn with n≥3, the small parameter ε, that we shall make to go to zero, denotes the period, and the size of each cavity is O(εα ) with α≥1. The function σ involving the nonlinear process is a C1 (Ω¯ ×R) function and the parameter κ∈R. Depending on the values …of α and κ, the effective equations on γ are obtained; we provide a critical relation between both parameters which implies a different average of the process on γ ranging from linear to nonlinear. For each fixed κ a critical size of the cavities which depends on n is found. As ε→0, we show the convergence of uε in the weak topology of H1 and construct correctors which provide estimates for convergence rates of solutions. All this allows us to derive convergence for the eigenelements of the associated spectral problems in the case of σ a linear function. Show more

Keywords: boundary homogenization, porous media, nonlinear flux, spectral analysis

DOI: 10.3233/ASY-2012-1116

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 289-322, 2012

Authors: Chacha, Djamal Ahmed | Miloudi, Madjda

Article Type: Research Article

Abstract: The aim of this paper is to extend the results obtained by Miara [Arch. Ration. Mech. Anal. 142 (1998), 331–353] and Lods and Miara [Arch. Ration. Mech. Anal. 142 (1998), 335–374] on the asymptotic analysis of nonlinearly elastic shells to the nonhomogeneous anisotropic case. To this end, we use the Hellinger–Reissner variational principle.

Keywords: asymptotic expansion, anisotropic shell, Hellinger–Reissner, nonlinear elasticity

DOI: 10.3233/ASY-2012-1119

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 323-346, 2012

Authors: Ouksel, Leila

Article Type: Research Article

Abstract: We examine the decay of the energy for wave equations on a bounded domain Rn , connected through one point to a rod modelled by a segment of R. It is shown that the energy decreases at least as the inverse logarithm of time. This result is obtained using a dissipative condition of the Neumann type on the boundary of the domain.

Keywords: logarithmic stabilisation, wave equations, Carleman inequality, interpolation inequality

DOI: 10.3233/ASY-2012-1152

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 347-376, 2012

Article Type: Other

Citation: Asymptotic Analysis, vol. 80, no. 3-4, pp. 377-378, 2012