A Probabilistic Multiscale Approach to Hysteresis in Shear Wave Propagation in Biotissue

Motivated by a problem involving wave propagation through viscoelastic biotissue, we present a theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables. The resulting systems entail probability measure-dependent partial d...

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Bibliographic Details
Published in:Multiscale modeling & simulation 2005-01, Vol.3 (2), p.395-412
Main Authors: Banks, H. T., Pinter, Gabriella A.
Format: Article
Language:English
Subjects:
Applied mathematics
Data collection
Probability distribution
Propagation
Viscoelasticity
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Summary:Motivated by a problem involving wave propagation through viscoelastic biotissue, we present a theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables. The resulting systems entail probability measure-dependent partial differential equations for which we establish well-posedness in a framework that leads readily to computationally useful approximations.
ISSN:1540-3459
1540-3467
DOI:10.1137/040603693