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Multipoint matrix Padé approximant bounds on effective anisotropic transport coefficients of two-phase media. (English) Zbl 1264.80034

Summary: It is well known that a tensor Stieltjes function f represents an effective transport coefficient q of an inhomogeneous medium consisting of two isotropic components. In this paper, we investigate multipoint matrix Padé approximants to matrix expansions of f. We prove that matrix Padé approximants to f estimate f from the top and below. Consequently the Padé approximants to q form upper and lower bounds on q. The inequalities for matrix Padé bounds on f and q are established. They reduce to the inequalities for scalar Padé approximants [the author, Z. Angew. Math. Phys. 61, No. 4, 773–780 (2010; Zbl 1264.74196)]. As an illustrative example, matrix Padé estimates of an effective conductivity of a specially laminated two-phase medium are computed.

MSC:

80M35 Asymptotic analysis for problems in thermodynamics and heat transfer
41A21 Padé approximation
80M40 Homogenization for problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
26A42 Integrals of Riemann, Stieltjes and Lebesgue type

Citations:

Zbl 1264.74196
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References:

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