Method of matched asymptotic expansions

About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.

Asymptotic Analysis of Fields in Multi-Structures

Abstract: 1. Introduction to compound asymptotic expansions 2. A boundary value problem for the Laplacian in a multi-structure 3. Auxiliary facts from mathematical elasticity 4. Elastic multi-structure 5. Non-degenerate elastic multi-structure 6. Spectral analysis for 3D-1D multi-structures Bibliographical remarks Bibliography Index

Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations

Abstract: Recently Aronson [1] extended the concept of asymptotic speed which he and Weinberger [3], [4] had developed for nonlinear diffusion problems in population genetics, combustion and nerve propagation, to an epidemic model proposed by Kendall [11], [12] in 1957 (1965). In this model (which is a spatial version of Kermack's and McKendrick's epidemic model [13]) the aflfected individuals become immediately infectious and are removed at a constant rate. The model does not take into account that with most infectious diseases the affected individuals underlie an incubation period, before they become infective, and that they remain infective for a fixed period only. These features cannot be described by the equation considered by Aronson [1] which contains a derivative with respect to time and an integral with respect to space. It is therefore desirable to extend Aronson's and Weinberger's concept of asymptotic speed to the nonlinear integral equation t J g(u(t-s,x+y))k(s9\\y\\)dsdy

How to expand around mean-field theory using high-temperature expansions

Abstract: High-temperature expansions performed at a fixed-order parameter provide a simple and systematic way to derive and correct mean-field theories for statistical mechanical models. For models like spin glasses which have general couplings between spins, the authors show that these expansions generate the Thouless-Anderson-Palmer equations at low order. They explicitly calculate the corrections to TAP theory for these models. For ferromagnetic models, they show that their expansions can easily be converted into 1/d expansions around mean-field theory, where d is the number of spatial dimensions. Only a small finite number of graphs need to be calculated to generate each order in 1/d for thermodynamic quantities like free energy or magnetization. Unlike previous 1/d expansions, the expansions are valid in the low-temperature phases of the models considered. They consider alternative ways to expand around mean-field theory besides 1/d expansions. In contrast to the 1/d expansion for the critical temperature, which is presumably asymptotic, these schemes can be used to devise convergent expansions for the critical temperature. They also appear to give convergent series for thermodynamic quantities and critical exponents. They test the schemes using the spherical model, where their properties can be studied using exact expressions.

The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point

Abstract: The variable x is to be real and on an interval a ? x < b. The parameter X is to be large in absolute value, but otherwise unrestricted-real or complex. The matter of primary concern is to be the derivation of analytic forms which represent the solutions of the equation asymptotically as to X. By way of hypotheses it is to be assumed that the functions pj,,(x) are indefinitely differentiable on (a, b), and that the series Pj(x, X) are convergent and differentiable term by term when IXI is sufficiently large(2). It is familiar that the functional forms of the solutions of an equation (1.1) depend in large measure upon the nature of the discriminant of th-e auxiliary algebraic equation