Tensor-Valued Random Fields for Continuum Physics

Name: Tensor-Valued Random Fields for Continuum Physics
SKU: 28279659
Price: 364.99 AUD
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Hardback

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Cambridge Monographs on Mathematical Physics

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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.

Author Biography:

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 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.

Release date Australia

December 6th, 2018

Author

Audience

Professional & Vocational

Illustrations

Worked examples or Exercises; 25 Tables, black and white; 7 Halftones, black and white; 3 Line drawings, black and white

Pages

310

Series

Cambridge Monographs on Mathematical Physics

Dimensions

180x253x22

ISBN-13

9781108429856

Product ID

28279659

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