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This study constructs traveling waves, including front waves and pulse waves, in a spring slider-block friction model. Explicit formulas for wave speed and form are derived in a simplified limit.

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Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Traveling waves are fundamental phenomena in various physical systems.
  • Friction models, such as the spring slider-block model, are crucial for understanding phenomena like earthquakes.
  • Previous studies have explored wave propagation in simplified friction models.

Purpose of the Study:

  • To explicitly construct traveling front and pulse waves in a spring slider-block model.
  • To derive analytical formulas for wave speed and form.
  • To investigate the connection between these waves and localized seismic events.

Main Methods:

  • Utilized a piecewise-linear spinodal friction force to model the system.
  • Explicitly constructed front waves (kinks) and pulse waves.
  • Derived analytical solutions in the anticontinuum limit.

Main Results:

  • Successfully constructed explicit formulas for front waves (kinks) and pulse waves.
  • Obtained explicit formulas for wave speed and wave form in the anticontinuum limit.
  • Demonstrated that pulse waves emerge from the matching of two traveling fronts.

Conclusions:

  • The study provides an explicit analytical framework for understanding traveling waves in a simplified friction model.
  • The findings offer insights into the dynamics of localized wave phenomena.
  • The work establishes a link to localized waves relevant to earthquake fault modeling.