Abstract
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 ones 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 ones Tokarzewski (ZAMP 61:773–780, 2010). As an illustrative example, matrix Padé estimates of an effective conductivity of a specially laminated two-phase medium are computed.
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Tokarzewski, S. Multipoint matrix Padé approximant bounds on effective anisotropic transport coefficients of two-phase media. Z. Angew. Math. Phys. 64, 167–178 (2013). https://doi.org/10.1007/s00033-012-0214-z
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DOI: https://doi.org/10.1007/s00033-012-0214-z