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Approximate representations for the effective tensors of two-phase two-dimensional composites

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Approximate representations for the effective tensors of two-phase two-dimensional composites
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On the correspondence between subspace collections and Herglotz functions
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27
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
The response of many passive linear physical systems are governed by Herglotz or Stieltjes functions. Typically associated with these functions is some sort of Hilbert space, or in the case of composites, a subspace collection. Operations on Herglotz or Stieltjes function often have a parallel operation on subspace collections. Here we will explore this correspondence. Also we give representation formulas for the effective (conductivity, elastic, piezoelectric, etc.) properties of two-dimensional composites of two anisotropic phases.