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.

Multi-point Taylor Expansions of Analytic Functions

Abstract: Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in several points as well as Taylor-Laurent expansions.

Uniform asymptotic expansions for the Barnes double gamma function

Abstract: We develop uniform asymptotic approximations for the Barnes double gamma function for various parameter values. This involves the use of the method of matched asymptotic expansions to solve the defining functional difference equation in various asymptotic regions. The resulting solutions provide extremely accurate approximations to the double gamma function. We also give applications of our results to functional difference equations that arise in the theory of moving contact lines and acoustic wave diffraction.

Boundary conditions for the Child-Langmuir sheath model

Abstract: A collision-free space-charge sheath formed by cold ions at a negative surface is considered. The method of matched asymptotic expansions is applied, small parameter being the ratio of the electron temperature to the sheath voltage. Two expansions are considered, one describing bulk of the sheath where the electron density is exponentially small as compared to the ion density, and another describing the outer section of the sheath in which the densities are comparable. Boundary conditions for equations describing the bulk are found such that the model have exponential accuracy. A physical meaning of these conditions is that the ions are accelerated in the outer section from the Bohm velocity to twice the Bohm velocity and that the voltage drop, in the outer section equals (3/2)(kT/sub e//e). The model predicts the electric field and ion velocity at the surface and the thickness of the ion layer to the accuracy of several percent for sheath voltages exceeding 3(kT/sub e//e).

Approximations to wave propagation through doubly-periodic arrays of scatterers

Abstract: The propagation of waves through a doubly-periodic array of identical rigid scatterers is considered in the case that the field equation is the two-dimensional Helmholtz equation. The method of matched asymptotic expansions is used to obtain the dispersion relation corresponding to wave propagation through an array of scatterers of arbitrary shape that are each small relative to both the wavelength and the array periodicity. The results obtained differ from those obtained from homogenization in that there is no requirement that the wavelength be much smaller than the array periodicity, and hence it is possible to examine phenomena, such as band gaps, that are associated with the array periodicity.