Asymptotic Decomposition of Pfaffian Systems with a Small Parameter

1995 ◽  
pp. 305-338
Author(s):  
Yu. A. Mitropolsky ◽  
A. K. Lopatin
Keyword(s):  
Small Parameter ◽  
Asymptotic Decomposition ◽  
Pfaffian Systems

Asymptotic decomposition of differential systems with a small parameter

1987 ◽  
Vol 39 (2) ◽  
pp. 162-170
Author(s):  
Yu. A. Mitropol'skii ◽  
A. K. Lopatin
Keyword(s):  
Small Parameter ◽  
Asymptotic Decomposition ◽  
Differential Systems

ASYMPTOTIC METHODS FOR MICROPOLAR FLUIDS IN A TUBE STRUCTURE

2004 ◽  
Vol 14 (05) ◽  
pp. 735-758 ◽  
Author(s):  
D. DUPUY ◽  
G. P. PANASENKO ◽  
R. STAVRE
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Small Parameter ◽  
Asymptotic Methods ◽  
Steady Motion ◽  
Asymptotic Decomposition ◽  
Micropolar Fluids ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Tube Structure

The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Small Parameter ◽  
Pipe Flow ◽  
Quantitative Estimation ◽  
Reynolds Numbers ◽  
Power Law Model ◽  
Viscosity Function ◽  
Small Reynolds Numbers ◽  
Title Problem ◽  
Flow Enhancement ◽  
Method Of Small Parameter

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

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