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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Mach Fronts in Random Media with Fractal and Hurst Effects.

Junren Ran1, Martin Ostoja-Starzewski2, Yuriy Povstenko3

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Fractal and Fractional
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Summary
This summary is machine-generated.

Transient second sound phenomena in random media were studied. Moving heat sources create stochastic Mach wedges, differing from those in homogeneous materials, offering insights into heat transfer dynamics.

Keywords:
Hurst effectMach frontfractalrandom mediasupersonic

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Area of Science:

  • Thermodynamics
  • Statistical Physics
  • Wave Phenomena

Background:

  • Second sound describes heat propagation in certain materials, influenced by material properties.
  • Moving heat sources can induce complex wave phenomena.
  • Material randomness, particularly in relaxation time, affects wave propagation dynamics.

Purpose of the Study:

  • To investigate transient second sound phenomena caused by moving heat sources in randomly heterogeneous media.
  • To model spatial randomness in relaxation time using advanced statistical field theories.
  • To analyze the impact of material randomness on wave patterns, specifically Mach wedges.

Main Methods:

  • Utilizing the Maxwell-Cattaneo model for heat transport.
  • Solving the model with second-order central differencing for numerical accuracy.
  • Employing Cauchy or Dagum random fields to represent spatial material randomness.
  • Analyzing stochastic fluctuations in Mach wedge formation.

Main Results:

  • Demonstrated that spatial randomness in relaxation time significantly alters second sound wave propagation.
  • Quantified the stochastic fluctuations in Mach wedges generated by moving heat sources in random media.
  • Compared these fluctuations to the deterministic Mach wedges observed in homogeneous media.

Conclusions:

  • Material randomness introduces significant deviations in transient second sound phenomena.
  • The study provides a framework for understanding heat wave behavior in complex, disordered materials.
  • Simulation movies illustrate the dynamic evolution of these stochastic wave patterns.