Energy transport in one-dimensional disordered granular solids

Area of Science:

• Physics
• Condensed Matter Physics
• Nonlinear Dynamics

Background:

• Energy transport in disordered systems is crucial for understanding material properties.
• Granular chains offer a unique platform to study nonlinear phenomena and energy dynamics.
• Disorder significantly impacts wave propagation and energy localization.

Purpose of the Study:

• To investigate energy transport in one-dimensional disordered granular solids.
• To explore the influence of nonlinearity on energy spreading under different initial conditions.
• To identify distinct dynamical regimes governing energy transport.

Main Methods:

• Extensive numerical simulations of a polydisperse granular chain.
• Analysis of energy transport for two types of initial conditions: displacement and momentum excitation.
• Systematic variation of initial excitation amplitudes to probe nonlinear effects.

Main Results:

• Three dynamical regimes identified: near linear, weakly nonlinear, and highly nonlinear.
• Energy spreading increases with nonlinearity, but shows no clear asymptotic behavior in the weakly nonlinear regime.
• Energy detrapping observed in the weakly nonlinear regime, influencing spreading fluctuations.
• Differences in energy transport between initial conditions vanish in the highly nonlinear regime.

Conclusions:

• Nonlinearity fundamentally alters energy transport in disordered granular chains.
• The weakly nonlinear regime exhibits complex energy dynamics, including localization and detrapping.
• In the highly nonlinear regime, energy transport becomes nearly ballistic, characterized by shocklike excitations.