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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 31, 2004
Accession Number
ADA446722

Entities

People

  • Gabriella A> Pinter
  • H. Thomas Banks

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Computational Science
  • Continuous Spectra
  • Differential Equations
  • Hysteresis
  • Inverse Problems
  • Materials
  • Mechanical Properties
  • Partial Differential Equations
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Secondary Waves
  • Topology
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis