عنوان

Tensor-valued random fields for continuum physics /

1108429858

9781108429856

9781108567800 (PDF ebook)

Tensor-valued random fields for continuum physics /

[Book]

Anatoliy Malyarenko (Mälardalen University Sweden), Martin Ostoja-Starzewski (University of Illinois).

New York, NY :

Cambridge University Press,

2019.

x, 302 pages :

illustrations ;

26 cm.

Cambridge monographs on mathematical physics

Includes bibliographical references and index.

Introduction to continuum theories -- Mathematical preliminaries -- Mathematical results -- Tensor random fields in continuum theories.

0

"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." - publisher

9781108567800

Field theory (Physics)

Geometry, Differential.

Random fields.

Tensor fields.

Field theory (Physics)

Geometry, Differential.

Random fields.

Tensor fields.

Malyarenko, Anatoliy

Ostoja-Starzewski, Martin

20200822150954.0

rda

[Book]

Y