Anatoliy Malyarenko

Tensor-Valued Random Fields for Continuum Physics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 6. Dezember 2018
• Englisch
• ISBN-13: 9781108567800
• Artikelnr.: 56527601

Autorenporträt

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.

Inhaltsangabe

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