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Tensor-Valued Random Fields for Continuum Physics

$145.00 (C)

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: January 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781108429856

$ 145.00 (C)
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About the Authors
  • 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.

    • Contains ideas for future research in stochastic mathematics and statistical physics, providing a starting point for Ph.D. students and researchers
    • Relevant for a broad audience interested in continuum physics, providing physical applications for mathematicians and mathematical tools for physicists
    • Includes numerous examples and applications, providing a complete description of homogenous and isotropic tensor-valued random fields
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    Product details

    • Date Published: January 2019
    • format: Hardback
    • isbn: 9781108429856
    • length: 310 pages
    • dimensions: 253 x 180 x 22 mm
    • weight: 0.71kg
    • contains: 10 b/w illus. 25 tables
    • availability: In stock
  • Table of Contents

    Introduction
    1. Introduction to continuum theories
    2. Mathematical preliminaries
    3. Mathematical results
    4. Tensor random fields in continuum theories
    References
    Index.

  • Authors

    Anatoliy Malyarenko, Mälardalens Högskola, Sweden
    Anatoliy Malyarenko is Professor of Mathematics at Mälardalens Högskola, Sweden. Previously he was a researcher at the Statistical Research Centre at Taras Shevchenko National University, and at the International Mathematical Centre of the National Academy of Science. His research interests include random functions of several variables, actuarial and financial mathematics, and computer simulation of real-world systems.

    Martin Ostoja-Starzewski, University of Illinois, Urbana-Champaign
    Martin Ostoja-Starzewski is a Professor at the Department of Mechanical Science and Engineering at the University of Illinois, Urbana-Champaign and also at the Institute for Condensed Matter Theory and Beckman Institute. He serves as Editor of Acta Mechanica, Editor of the Journal of Thermal Stresses, and Chair Managing Editor of Mathematics and Mechanics of Complex Systems. His research interests include random and fractal media, continuum theories, as well as aerospace, bio- and geo-physical applications.

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