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  • Key words. Padé approximants, Stieltjes function, composites, bounds, effective conductivities.  (1)
  • composite medium  (1)
  • dielectric constants  (1)
  • effective properties  (1)
Collection
Keywords
Publisher
Years
  • 1
    Electronic Resource
    Electronic Resource
    S-Continued Fraction Method for the Investigation of a Complex Dielectric Constant of Two-Components Composite (1997)
    Springer
    Acta applicandae mathematicae 49 (1997), S. 55-83 
    Details
    ISSN: 1572-9036
    Keywords: composite medium ; bounds ; dielectric constants ; Stieltjes function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this contribution is to examine the S-continued fraction method of obtaining bounds on the effective dielectric constant εe of a two-phase composite for the case where the dielectric coefficients ε1and ε2 of both components are either complex or real. The starting point for our study is a power expansion of εe (z) at(z)=0 (z)=ε2/ε1-1. The obtained S-continued fraction bounds have an interesting mathematical structure convenient for theoretical and numerical investigations of εe. They also agree with the earlier estimations reported by Bergman and Milton. Specific examples of calculation of bounds on εe by theS-continued fraction method are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005861519473
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  • 2
    Electronic Resource
    Electronic Resource
    Effective Conductivity of Nonlinear Two-Phase Media: Homogenization and Two-Point Padé Approximants (2000)
    Springer
    Acta applicandae mathematicae 61 (2000), S. 295-315 
    Details
    ISSN: 1572-9036
    Keywords: effective properties ; homogenization ; composites ; conductivities ; bounds, Padé approximants ; continued fractions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is a study of the quasilinear transport equation, for instance the stationary heat equation. For periodically microheterogeneous media asymptotic homogenization has been performed with the local problem formulated as a minimization problem. The Golden–Papanicolaou integral representation theorem and some bounds developed for the linear equation have been extended. Two-point Padé approximants have been used to calculate bounds. Examples are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006487103815
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  • 3
    Electronic Resource
    Electronic Resource
    Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity (1998)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 49 (1998), S. 137-155 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Padé approximants, Stieltjes function, composites, bounds, effective conductivities.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. By employing special continued fractions to two Stieltjes series with nonzero radii of convergence the inequalities for two- and three-point Padé approximants have been derived. These inequalities constitute an extension of the relevant relations valid for one-point Padé approximants [1,Cor.17.1] and two-point Padé ones [23, Th.1]. The Padé approximants inequalities achieved have been applied to the theory of inhomogeneous media for establishing of the new bounds on the effective transport coefficient of two-phase composite materials. As an example the low order estimations of the effective conductivity of a square array of cylinders have been computed and compared with the corresponding ones evaluated in [24].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050085
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