On the absence of the Eshelby property for slender non-ellipsoidal inhomogeneities

2008 ◽  
Vol 464 (2093) ◽  
pp. 1079-1088 ◽  
Author(s):  
Igor V Andrianov ◽  
Ivan I Argatov ◽  
Dieter Weichert
Keyword(s):  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
Asymptotic Model ◽  
Inhomogeneity Problem

The method of matched asymptotic expansions is applied to construct an asymptotic model for the Eshelby inhomogeneity problem in the case of a slender sufficiently rigid inhomogeneity. On the basis of the obtained asymptotic model, it is shown that the only infinitesimal perturbations of the elongated ellipsoid that preserve constancy of stresses inside the inhomogeneity are those into another elongated ellipsoid.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Cusp formation for the undercooled Stefan problem in two and three dimensions

1997 ◽  
Vol 8 (1) ◽  
pp. 1-21 ◽  
Author(s):  
JUAN J. L. VELÁZQUEZ
Keyword(s):  
Stefan Problem ◽  
Asymptotic Expansions ◽  
Three Dimensions ◽  
Matched Asymptotic Expansions ◽  
Cusp Formation

We consider in this paper the classical one-phase Stefan problem in dimensions two and three in the undercooled situation. By means of matched asymptotic expansions, a mechanism of cusp formation is presented for interfaces that are initially smooth.

Nearly equilibrium dissociating boundary-layer flows by the method of matched asymptotic expansions

1966 ◽  
Vol 26 (4) ◽  
pp. 793-806 ◽  
Author(s):  
George R. Inger
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansions ◽  
High Speed ◽  
Numerical Solutions ◽  
The Body ◽  
Matched Asymptotic Expansions ◽  
Form Analysis ◽  
Perturbation Problem ◽  
Valid Solution ◽  
Non Equilibrium

The approach to equilibrium in a non-equilibrium-dissociating boundary-layer flow along a catalytic or non-catalytic surface is treated from the standpoint of a singular perturbation problem, using the method of matched asymptotic expansions. Based on a linearized reaction rate model for a diatomic gas which facilitates closed-form analysis, a uniformly valid solution for the near equilibrium behaviour is obtained as the composite of appropriate outer and inner solutions. It is shown that, under near equilibrium conditions, the primary non-equilibrium effects are buried in a thin sublayer near the body surface that is described by the inner solution. Applications of the theory are made to the calculation of heat transfer and atom concentrations for blunt body stagnation point and high-speed flat-plate flows; the results are in qualitative agreement with the near equilibrium behaviour predicted by numerical solutions.

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