Traveling waves in a spring-block chain sliding down a slope

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.