Skip to content
Register Sign in Wishlist

Tensor-Valued Random Fields for Continuum Physics

$116.00 ( ) USD

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: November 2018
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108567800

$ 116.00 USD ( )
Adobe eBook Reader

You will be taken to for this purchase
Buy eBook Add to wishlist

Other available formats:

Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
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
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: November 2018
    • format: Adobe eBook Reader
    • isbn: 9781108567800
    • contains: 10 b/w illus. 25 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

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

  • 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.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.