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Tensor-Valued Random Fields for Continuum Physics (Hardcover)
Loot Price: R4,179
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Tensor-Valued Random Fields for Continuum Physics (Hardcover)
Series: Cambridge Monographs on Mathematical Physics
Expected to ship within 10 - 15 working days
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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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