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  3. Tensor-Valued Random Fields for Continuum Physics
  • Cited by 25
Publisher:
Cambridge University Press
Online publication date:
November 2018
Print publication year:
2018
Online ISBN:
9781108555401
DOI:
https://doi.org/10.1017/9781108555401
Subjects:
Mathematics, Physics and Astronomy, Mathematical Physics, Theoretical Physics and Mathematical Physics
Series:
Cambridge Monographs on Mathematical Physics
Information

Book description

Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools.

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