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.

Mathematical Justification of the Rayleigh Conductivity Model for Perforated Plates in Acoustics

Abstract: This paper is devoted to the mathematical justification of the usual models predicting the effective reflection and transmission of an acoustic wave by a low porosity multiperforated plate Some previous intuitive approximations require that the wavelength be large compared with the spacing separating two neighboring apertures In particular, we show that this basic assumption is not mandatory Actually, it is enough to assume that this distance is less than a half-wavelength The main tools used are the method of matched asymptotic expansions and lattice sums for the Helmholtz equations Some numerical experiments illustrate the theoretical derivations

Motion of a Curved Vortex Filament: Higher-Order Asymptotics

Abstract: Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated based on the Euler equations Using the method of matched asymptotic expansions in a small parameter ∈, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(∈ 3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account In the localized induction approximation, this is reducible to a completely integrable evolution equation among the localized induction hierarchy

The motion of a non-isolated vortex on the beta-plane

Abstract: The trajectory of a non-isolated monopole on the beta-plane is calculated as an asymptotic expansion in the ratio of the strength of the vortex to the beta-eect. The method of matched asymptotic expansions is used to solve the equations of motion in two regions of the flow: a near eld where the beta-eect enters as a rst-order forcing in relative vorticity, and a wave eld in which the dominant balance is a linear one between the beta-eect and the rate of change of relative vorticity. The resulting trajectory is computed for Gaussian and Rankine vortices.

The perturbation of electromagnetic fields at distances that are large compared with the object's size

Abstract: We rigorously derive the leading order terms in asymptotic expansions for the scattered electric and magnetic fields in the presence of a small object at distances that are large compared to its size. Our expansions hold for fixed wavenumber when the scatterer is a (lossy) homogeneous dielectric object with constant material parameters or a perfect conductor. We also derive the corresponding leading order terms in expansions for the fields for a low frequency problem when the scatterer is a non�lossy homogeneous dielectric object with constant material parameters or a perfect conductor. In each case we express our results in terms of polarisation tensors.