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Solitons and thermal fluctuations in strongly nonlinear solids
N Upadhyaya1, A M Turner2, V Vitelli1
1Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
This study models solitary wave propagation in anharmonic spring chains, revealing their behavior under thermal fluctuations. Analytical and simulation results show damping and diffusion, including new expansion solitary waves.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Statistical mechanics
Background:
- Solitary waves are crucial for energy transport in nonlinear systems.
- Understanding their behavior amidst thermal noise is key for materials science.
- Previous models often simplified spring interactions.
Purpose of the Study:
- To model solitary wave propagation in anharmonic spring chains with tunable interactions.
- To investigate the effects of thermal fluctuations on these waves.
- To derive and validate analytical predictions for wave dynamics.
Main Methods:
- Developed a minimal model of anharmonic springs with power law interactions.
- Treated solitary waves as quasiparticles to derive an effective Langevin equation.
- Validated analytical findings against Langevin dynamic simulations.
Main Results:
- Derived expressions for solitary wave damping rate and thermal diffusion.
- Analytical results showed strong agreement with numerical simulations.
- Discovered expansion solitary waves (antisolitons) in two-sided nonlinear spring chains, alongside compressive solitons.
Conclusions:
- The Langevin equation effectively describes solitary wave dynamics in this system.
- Thermal fluctuations significantly impact solitary wave propagation.
- The existence of both compressive and expansion solitary waves broadens understanding of nonlinear wave phenomena.
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