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Asymptotic Expansions

Estimated H-index: 1. The role of coordinate systems in boundary-layer theory. Saul Kaplun 6 Estimated H-index: 6.

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The asymptotic solutions of certain linear ordinary differential equations of the second order. Rudolph E. Langer 12 Estimated H-index: It is accordingly the subject of an extensive literature. In particular, the problem of the asymptotic dependence of its solutions upon the complex parameter X has been the subject of many investigations, in which for suitably restricted configurations a theory of considerable generality has been deduced.

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A familiar change Published on Dec 1, Leon Lichtenstein 1 Estimated H-index: 1. Cited By Boundary layer separation and asymptotics from to Abstract The aim of this Note is to follow the spreading of the idea of asymptotic analysis in fluid mechanics more precisely the laminar boundary layer. We will focus on the actors who worked on the problem of boundary layer separation from to Multiple scales and matched asymptotic expansions for the discrete logistic equation. Cameron L. Hall 6 Estimated H-index: 6. Estimated H-index: 4. In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly valid asymptotic solutions to autonomous and non-autonomous forms of the discrete logistic equation in the neighbourhood of a period-doubling bifurcation.

In each case, we begin by constructing a multiple scales approximation in which the fast time scale is treated as discrete, but the slow time scale is treated as continuous. The resulting multiple scales solutions are Advanced Asymptotic Methods. Published on Jan 1, Christian Kuehn 14 Estimated H-index: Asymptotic analysis is a key ingredient in capturing multiscale dynamics.

In this chapter, a collection of asymptotic and perturbation methods is presented. The focus is on the basic principles of methods and key examples to understand their application.

Table of contents

All methods can be applied in many other circumstances, and although the algebraic manipulations change, the principles of the methods tend to carry over. Finite element method. Composite materials. Keywords A. Asymptotic expansion homogenization for heterogeneous media: Computational issues and applications.

Chung, Peter W. Access to Document Link to publication in Scopus. Link to citation list in Scopus. Abstract: The fields of applications and design for piezoelectric effect grew rapidly in recent years, and these materials play an important role in countless areas of modern life. Add to Cart. Advanced Materials Research Volumes Main Theme:. Edited by:.

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Jingying Zhao. Online since:. May Cited by. Related Articles. Paper Title Pages. Abstract: In this paper, an isotropic elastic damage analysis is presented by using a meshless boundary element method BEM without internal cells. First, nonlinear boundary-domain integral equations are derived by using the fundamental solutions for undamaged, homogeneous, isotropic and linear elastic solids and the concept of normalized displacements, which results in boundary-domain integral equations without an involvement of the displacement gradients in the domain-integral.

Then, the arising domain-integral due to the damage effects is converted into a boundary integral by approximating the normalized displacements in the domain-integral by a series of prescribed radial basis functions RBF and using the radial integration method RIM. The damage variable used in the paper is the ratio of the damaged area to the total area of the material, and an exponential evolution equation for the damage variable is adopted. A numerical example is given to demonstrate the efficiency of the present meshless BEM.

Abstract: A numerical approach to solve a problem of combined heat and mass transfer in porous medium saturated with compressible fluid is presented. Transport phenomena in porous media is described using the modified Navier-Stokes equations, where for the governing momentum equation the Brinkman extended Darcy formulation is used. Abstract: The boundary element methodology is applied to the fracture mechanics of non-linear viscoelastic solids.

Nonlinearity generates an irreducible domain integral into the original boundary integral equation governing the behaviour of linear viscoelastic solids.