scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: The induction of electric currents in the oceans is considered to be of major interest and may also throw light upon the conductivity structure of the mantle as mentioned in this paper, and state of the art recommendations are made on what appears to be the best methods to use and these are demonstrated by using simple analogies.
Abstract: Summary. The induction of electric currents in the oceans is considered to be of major interest and may also throw light upon the conductivity structure of the mantle. Two aspects are considered: (1) induction by the solar quiet variations which have principal periods of 24, 12, 8 and 6 hr, and (2) induction by the ocean tides which principally have a semi-diurnal lunar period of 12.45 hr. Two classes of model may be devised: those in which the oceans are considered to be insulated from the mantle, and those in which there is a true electrical connection between the two. It appears that methods of calculating the electric currents are outstripping conductivity models. State of the art recommendations are made on what appears to be the best methods to use and these are demonstrated by using simple analogies. Particular attention is called to the Hewson-Browne technique for solving the integral equations which often emerge. It is noted that the formulations of the integral equations are variations of Weaver's method for plane configurations. Problems in which the ocean is isolated can be solved adequately by the zeroth order of the method of matched asymptotic expansions. Curiously this latter technique is simple in principle, involves only the numerical solution of a partial differential equation on the surface of the globe, and has been fecund in producing solutions for a variety of models. Induction by the ocean tides is also considered. Recommendations are made on the most promising lines appearing in present-day theories.

21 citations

Journal ArticleDOI
TL;DR: In this article, an asymptotic theory that describes the kinetics of first-order phase transitions is presented. But the main difference between the two is that the Lifshits-Slezov theory uses for the first integral of the kinetic equation an approximate solution of the characteristic equation, which is valid in the entire range of sizes except for the blocking point, i.e., it uses a nonuniformly applicable approximation.
Abstract: We construct an asymptotic theory that describes the kinetics of first-order phase transitions. The theory is a considerable refinement of the well-known Lifshits-Slezov theory. The main difference between the two is that the Lifshits—Slezov theory uses for the first integral of the kinetic equation an approximate solution of the characteristic equation, which is valid in the entire range of sizes except for the blocking point, i.e., it uses a nonuniformly applicable approximation. At the same time, the behavior of the characteristic solution near the blocking point determines the asymptotic behavior of the size distribution function of the nuclei for the new phase. Our theory uses a uniformly applicable solution of the characteristic equation, a solution valid at long times over the entire range of sizes. This solution is used to find the asymptotic behavior of all basic properties of first-order phase transitions: the size distribution function, the average nucleus size, and the nucleus density.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of the location of the far-field boundary and of the model-fluid assumption are assessed accurately, and the effect of Prandtl number, viscosity law, and level of free-stream temperature on the solutions are also studied.
Abstract: Laminar flow along a 90-deg corner, formed by the intersection of two semi-infinite flat plates, is analyzed, under the assumption of shock-free supersonic flow. The analysis is based on the method of matched asymptotic expansions. Numerical solutions are obtained for the streamwise self-similar corner flow, using the ADI method. Appropriate mapping functions are employed, so that the far-field boundary conditions are imposed at true infinity. Results are presented for subsonic and supersonic flows, with adiabatic as well as heat-transfer wall conditions. The effects of location of the far-field boundary and of the model-fluid assumption are assessed accurately. Effects of Prandtl number, viscosity law, and level of freestream temperature on the solutions are also studied. The numerical method developed is efficient and the optimization techniques implemented have wider applications. A numerical "compressibility-transformation" is also suggested for obtaining a suitable finite-difference grid for highly supersonic flows.

21 citations

Journal ArticleDOI
TL;DR: In this article, the free surface deformation and flow field caused by the impulsive horizontal motion of a rigid vertical plate into a horizontal strip of inviscid, incompressible fluid, initially at rest, is studied in the small time limit using the method of matched asymptotic expansions.
Abstract: The free surface deformation and flow field caused by the impulsive horizontal motion of a rigid vertical plate into a horizontal strip of inviscid, incompressible fluid, initially at rest, is studied in the small time limit using the method of matched asymptotic expansions. It is found that three different asymptotic regions are necessary to describe the flow. There is a main, O(1) sized, outer region in which the flow is singular at the point where the free surface meets the plate. This leads to an inner region, centered on the point where the free surface initially meets the plate, with size of O(it log t). To resolve the singularities that arise in this inner region, it is necessary to analyse further the flow in an inner-inner region, with size of O(t), again centered upon the wetting point of the nascent rising jet. The solutions of the boundary value problems in the two largest regions are obtained analytically. The solution of the parameter-free nonlinear boundary value problem that arises in the inner-inner region is obtained numerically.

21 citations


Network Information
Related Topics (5)
Partial differential equation
70.8K papers, 1.6M citations
90% related
Differential equation
88K papers, 2M citations
89% related
Boundary value problem
145.3K papers, 2.7M citations
86% related
Bounded function
77.2K papers, 1.3M citations
84% related
Nonlinear system
208.1K papers, 4M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835