Determination of unsteady supersonic flows around thin pointed wingsby asymptotic expansions.

1968 ◽  
Vol 5 (5) ◽  
pp. 455-460
Author(s):  
JEAN-YVES PARLANGE
Keyword(s):  
Asymptotic Expansions ◽  
Supersonic Flows

scholarly journals ASYMPTOTICS OF STRESS AND CONTINUITY FIELDS NEAR A FATIGUE GROWING CRACK IN A DAMAGED MEDIUM IN CONDITIONS OF STATE OF PLANE STRESS

2017 ◽  
Vol 19 (9.2) ◽  
pp. 97-108
Author(s):  
S.A. Igonin ◽  
L.V. Stepanova
Keyword(s):  
Fatigue Crack ◽  
Asymptotic Solution ◽  
Plane Stress ◽  
Asymptotic Expansions ◽  
Asymptotic Representation ◽  
Stress Fields ◽  
Repeated Loading ◽  
Growing Crack

In the paper asymptotic solution to the problem of growth of fatigue crack in conditions of repeated loading in a damaged medium in the coupled elasticity-damage statement of the problem is given. Asymptotic expansions of stress fields and continuity fields in which two summands are retained in asymptotic representation are derived. The problems of determination of amplitude coeffl-cients of obtained asymptotic expansions are discussed.

A method for the determination of converging factors, applied to the asymptotic expansions for the parabolic cylinder functions

1952 ◽  
Vol 48 (2) ◽  
pp. 243-254 ◽  
Author(s):  
J. C. P. Miller
Keyword(s):  
Infinite Series ◽  
Asymptotic Expansions ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Functions ◽  
Image Position

1. The method of converging factors, for hastening the convergence of slowly convergentseries and improving the accuracy of asymptotic expansions, was introduced by J. R. Airey and is well known to computers (see Airey(1) and Rosser(2)). The principle is as follows. It is required to compute a quantity which is expressed as an infinite seriesThe series may be either convergent or asymptotic and divergent.

scholarly journals Determination of the Arbitrary Constants which appear in the Asymptotic Expansions for the Functions of the Elliptic Cylinder

1921 ◽  
Vol 40 ◽  
pp. 2-8 ◽  
Author(s):  
William Marshall
Keyword(s):  
Numerical Calculation ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Series ◽  
Elliptic Cylinder ◽  
Arithmetic Computation ◽  
Image Position ◽  
Two Parameters

In an article, published some time since, the author of the present paper deduced an asymptotic expression for the functions of the elliptic cylinder, which expression took the following form:Here P and Q are certain asymptotic series, and C and a arbitrary constants. General expressions for these constants were not determined in the aforementioned article on account of the difficulties there set forth, though it was pointed out that their numerical calculation for any particular problem was simply a matter of arithmetic computation. It is the object of the present paper to deduce general expressions for these constants C and a in terms of the two parameters which appear in the defining equation for U.

Integrals with a large parameter and several nearly coincident saddle points; the continuation of uniformly asymptotic expansions

1974 ◽  
Vol 76 (1) ◽  
pp. 211-231 ◽  
Author(s):  
J. Martin
Keyword(s):  
Asymptotic Expansions ◽  
Saddle Points ◽  
Geometrical Shape ◽  
Large Parameter ◽  
Airy Functions ◽  
Regular Functions ◽  
Stokes Lines ◽  
Image Position ◽  
Actual Region

AbstractIn the contour integralf and g are regular functions of z in a neighbourhood of the contour C and of the complex parameters (α1, α2, …, αp) = α in a domain of . N is a positive parameter and asymptotic expansions are considered as N → + ∞. The method of steepest descents provides an asymptotic expansion for each fixed value of α, but this is non-uniform with respect to α near critical values α0 at which certain saddle points tend to coincidence. A more complicated expansion, involving Airy functions or generalizations thereof, is valid and uniform for α near α0. This expansion is known to be valid in a neighbourhood of α0 which does not depend on N, in contrast to certain other expansions having regions of validity which contract to a point or surface as N → ∞. It is thereby suggested that the actual region of validity has a definite geometrical shape determined by the functions f and g and the contour C, just as steepest descents expansions are valid in regions bounded by Stokes' lines. In this paper, procedures are derived for the determination of such regions, subject to assumptions concerning f, g and C. The validity of the expansion is established in regions so determined.

New insight into the generation of ship bow waves

2000 ◽  
Vol 421 ◽  
pp. 15-38 ◽  
Author(s):  
E. FONTAINE ◽  
O. M. FALTINSEN ◽  
R. COINTE
Keyword(s):  
Asymptotic Expansions ◽  
Near Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Asymptotic Approach ◽  
Dimensional Solution ◽  
First Order ◽  
Bow Waves ◽  
Insight Into

The generation of ship bow waves is studied within the framework of potential flow theory. Assuming the ship bow to be slender, or thin, a pattern of the flow is derived using the method of matched asymptotic expansions. This method leads to the determination of three different zones in which three asymptotic expansions are performed and matched. To first order with respect to the slenderness parameter, the near-field flow appears to be two-dimensional in each transverse plane along the bow. However, it is demonstrated that three-dimensional effects are important in front of the ship and must be taken into account in the composite solution. This leads to a three-dimensional correction to be added to the two-dimensional solution along the ship. The asymptotic approach is then applied to explain the structure of the bow flow in connection with experimental observations and numerical simulations.

Matched asymptotic expansions for the determination of the electromagnetic field near the edge of a patch antenna

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2050013-2050014
Author(s):  
Abderrahmane Bendali ◽  
Abdelkader Makhlouf ◽  
Sébastien Tordeux
Keyword(s):  
Electromagnetic Field ◽  
Asymptotic Expansions ◽  
Patch Antenna ◽  
Matched Asymptotic Expansions
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