Topic
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.
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TL;DR: Theoretical results for heat transfer from a circular cylinder oscillating in an unbounded viscous fluid which is otherwise at rest are given in this article, where the amplitude of the oscillation is assumed small compared to the radius of the cylinder, which for most of the examples considered is assumed to be at a constant temperature.
53 citations
TL;DR: In this article, a plane sound wave is incident upon two semi-infinite rigid plates, lying along y = 0, x > 0 and y = -h, x < 0, respectively, where (x, y) are two-dimensional Cartesian coordinates.
53 citations
TL;DR: In this article, a generalisation of the Mullins-Sekerka problem to model phase separation in multi-component systems is proposed, which includes equilibrium equations in bulk, the Gibbs-Thomson relation on the interfaces, Young's law at triple junctions, together with a dynamic law of Stefan type.
Abstract: We propose a generalisation of the Mullins–Sekerka problem to model phase separation in multi-component systems. The model includes equilibrium equations in bulk, the Gibbs–Thomson relation on the interfaces, Young's law at triple junctions, together with a dynamic law of Stefan type. Using formal asymptotic expansions, we establish the relationship to a transition layer model known as the Cahn-Hilliard system. We introduce a notion of weak solutions for this sharp interface model based on integration by parts on manifolds, together with measure theoretical tools. Through an implicit time discretisation, we construct approximate solutions by stepwise minimisation. Under the assumption that there is no loss of area as the time step tends to zero, we show the existence of a weak solution.
52 citations
TL;DR: In this paper, it was shown that three identically-constructed pairs of expansions exist for solving the Mathieu equation: one pair in terms of trigonometrical functions, one pair on terms of Hermite functions of a real variable, and another pair on the Hermite function of an imaginary variable.
Abstract: Straight forward and systematic procedures are developed for finding asymptotic expansions of Mathieu functions and their characteristic numbers. In particular, it is shown that three identically-constructed pairs of expansions exist for Solutions to the Mathieu equation: one pair in terms of trigonometrical functions, one pair in terms of Hermite functions of a real variable, and one pair in terms of Hermite functions of an imaginary variable. By linking these different expansions together in regions where they overlap, the behaviour of Mathieu functions can be investigated over the entire ränge of the independent variable.
52 citations
TL;DR: In this article, matched asymptotic expansions were used to look into the problem of the scattering of plane SH waves by topographic irregularities of a restricted range in an otherwise plane half-space when the characteristic length dimension of the irregularity is much smaller than the wavelength of the incident wave.
Abstract: Summary
The method of matched asymptotic expansions is used to look into the problem of the scattering of plane SH waves by topographic irregularities of a restricted range in an otherwise plane half-space when the characteristic length dimension of the irregularity is much smaller than the wavelength of the incident wave In contrast to previous work the slope of the irregularity remains arbitrary Expressions for the near and far scattered fields are obtained Comparison between this theory and the regular perturbation technique (which also assumes that the irregularity has a small slope) show that both agree when the slope is small but differ in the general case Results are given for irregularities in the shape of triangles, trapezia and semicircles
52 citations