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: In this article, the authors considered the convective flow in multiple immiscible liquid layers in a differentially heated shallow rectangular cavity with rigid and insulated upper and lower boundaries, and used matched asymptotic expansions to determine the flow in two distinct regions: the core region characterized by parallel flow; and the end-wall regions where flow turns around.
28 citations
01 Sep 2001
TL;DR: In this article, a method for the decomposition of unified state-feedback singularly perturbed systems is presented, based on the small-gain theorem, and a sufficient condition for robust stability is derived such that the composite state feedback renders the closed-loop system asymptotically stable.
Abstract: A method for the decomposition of unified state-feedback singularly perturbed systems is presented. Based on the small-gain theorem, a sufficient condition for robust stability is derived such that the composite state feedback renders the closed-loop singularly perturbed system asymptotically stable. With this method there is no need to consider two different approaches for continuous-time and discrete-time domains. An example illustrates the methodology.
28 citations
TL;DR: In this article, a nonlinear differential equation which governs the equilibrium of two closely spaced drops, suspended from two circular rings, and maintained at electric potentials ± V is considered, and when the potential reaches a critical value V m, experiments show that the drops coalesce and the equation has, in fact, no solutions for V > V m.
Abstract: A nonlinear differential equation which governs the equilibrium of two closely spaced drops, suspended from two circular rings, and maintained at electric potentials ± V is considered. When the potential reaches a critical value V m , experiments show that the drops coalesce and the equation has, in fact, no solutions for V > V m . Two limiting cases are studied. At first we consider drops which at zero potential difference, are films of zero curvature. In this case it is shown that the equation may not have a unique solution for V m . In the second case we study drops which are nearly touching when there is no potential difference, with non-zero curvature. Using the method of matched asymptotic expansions, it is shown that when the drops are about to coalesce, the original separation distance is reduced by one-half. Thus the drops are not drawn out as might have been expected from experiments on isolated drops.
28 citations
TL;DR: In this paper, an alternate approach to the method of asymptotic expansions for the study of a singularly perturbed, linear system with multiparameters and multi-time scales is developed.
28 citations
TL;DR: In this article, the singularly perturbed Boussinesq equation was investigated in terms of the approximate symmetry perturbation method and the approximate direct method and series reduction solutions were derived.
Abstract: We investigate the singularly perturbed Boussinesq equation in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions and similarity reduction equations of different orders display formal coincidence for both methods. Series reduction solutions are consequently derived. For the approximate symmetry perturbation method, similarity reduction equations of the zero order are equivalent to the Painleve IV, Painleve I, and Weierstrass elliptic equations. For the approximate direct method, similarity reduction equations of the zero order are equivalent to the Painleve IV, Painleve II, Painleve I, or Weierstrass elliptic equations. The approximate direct method yields more general approximate similarity reductions than the approximate symmetry perturbation method.
28 citations