scholarly journals An Asymptotic Solution to a Two-Dimensional Exit Problem Arising in Population Dynamics

1989 ◽  
Vol 49 (6) ◽  
pp. 1793-1810 ◽  
Author(s):  
H. Roozen
Keyword(s):  
Population Dynamics ◽  
Asymptotic Solution ◽  
Two Dimensional ◽  
Exit Problem

scholarly journals Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 124 ◽  
Author(s):  
Alexander Eliseev ◽  
Tatjana Ratnikova
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Solution ◽  
Regularization Method ◽  
Turning Point ◽  
Singularly Perturbed ◽  
Dimensional Case ◽  
Singularly Perturbed Problem ◽  
Two Dimensional ◽  
Limit Operator ◽  
Regularized Solution

By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution.

scholarly journals Coherence and population dynamics of chlorophyll excitations in FCP complex: Two-dimensional spectroscopy study

2015 ◽  
Vol 142 (21) ◽  
pp. 212414 ◽  
Author(s):  
Vytautas Butkus ◽  
Andrius Gelzinis ◽  
Ramūnas Augulis ◽  
Andrew Gall ◽  
Claudia Büchel ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Two Dimensional ◽  
Spectroscopy Study

An Analytical Study of the Standard k–ε Model

1990 ◽  
Vol 112 (2) ◽  
pp. 192-198 ◽  
Author(s):  
N. Takemitsu
Keyword(s):  
Experimental Data ◽  
Asymptotic Solution ◽  
Channel Flow ◽  
Analytical Study ◽  
Turbulent Channel Flow ◽  
Second Order ◽  
Two Dimensional ◽  
Ill Posed ◽  
Leading Term ◽  
Logarithmic Law

An asymptotic solution of the standard k–ε model for two-dimensional turbulent channel flow is found. Using this solution, five model constants in the model are all determined reasonably with the aid of experimental data. If an asymptotic solution with the logarithmic law as the leading term is sought for, the standard k–ε model is shown to be ill-posed since the second-order solution has divergent terms.

Crack Propagation in a Brittle Elastic Material With Defects

1999 ◽  
Vol 66 (1) ◽  
pp. 79-86 ◽  
Author(s):  
M. Valentini ◽  
S. K. Serkov ◽  
D. Bigoni ◽  
A. B. Movchan
Keyword(s):  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Isotropic Medium ◽  
Numerical Solutions ◽  
Porous Ceramics ◽  
Qualitative Description ◽  
Mode I ◽  
Pure Mode ◽  
Two Dimensional

A two-dimensional asymptotic solution is presented for determination of the trajectory of a crack propagating in a brittle-elastic, isotropic medium containing small defects. Brittleness of the material is characterized by the assumption of the pure Mode I propagation criterion. The defects are described by Po´lya-Szego¨ matrices, and examples for small elliptical cavities and circular inclusions are given. The results of the asymptotic analysis, which agree well with existing numerical solutions, give qualitative description of crack trajectories observed in brittle materials with defects, such as porous ceramics.

scholarly journals Unsteady Reversed Stagnation-Point Flow over a Flat Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Vai Kuong Sin ◽  
Chon Kit Chio
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Total Flow ◽  
Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

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