Sentence examples for using the asymptotic expansion from inspiring English sources

The homogenization procedure is justified using the asymptotic expansion method.

In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique.

331, 641 646] for in-plane periodic rigid perfectly plastic plates is justified using the asymptotic expansion method.

The effective properties of these composites are identified using the asymptotic expansion homogenization method in two steps.

The structure of adiabatic premixed flames within porous inert media is investigated using the asymptotic expansion method.

This paper aims to model and compute the effective electro-mechanical properties of Macro Fiber Composite (MFC) transducers using the Asymptotic Expansion Homogenization (AEH) method.

(32) Using the asymptotic expansions (29) for large β, we get W bigl(-beta^{2} bigr)sim frac{i}{sqrt{ab} beta }cos biggl[ biggl( frac{b}{a}-1 biggr) beta biggr], and hence the zeros of (W s)) are a sequence (s_{n}=-beta_{n}^{2}), (n=1,2,ldots ) , such that beta_{n}sim biggl n-frac{1}{2} biggl n-frac{1}{{b-a}quad mbiggrs } nrightarrow +infrac{api

Higher order weak deformations Since our definition of weak deformations was motivated by semiclassical considerations one could perhaps consider refinements of this method using the asymptotic expansions of Hagedorn [31,32] and his followers; this could then lead to "higher order" weak deformations, depending on the number of terms that are retained.

Miki in [22] exploits a formula for the Fermat quotient (frac{a^{p}-a}{p}) modulo (p^{2}), Shiratani-Yokoyama in [23] employs p-adic analysis, Gessel in [21] bases his work on two different expressions for Stirling numbers of the second kind (S_{2} (n,k )), and Dunne-Schubert in [15] uses the asymptotic expansion of some special polynomials coming from the quantum field theory computations.

b Using the asymptotic standard error assuming the null hypothesis.

We present a simple example in which the higher order topological derivatives of the total potential energy are obtained analytically and by using the proposed asymptotic expansion.