scholarly journals Multiple scales and matched asymptotic expansions for the discrete logistic equation

2016 ◽  
Vol 85 (2) ◽  
pp. 1345-1362 ◽  
Author(s):  
Cameron L. Hall ◽  
Christopher J. Lustri
Keyword(s):  
Asymptotic Expansions ◽  
Multiple Scales ◽  
Logistic Equation ◽  
Matched Asymptotic Expansions

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.

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