Superdiffusive transport and energy localization in disordered granular crystals

Area of Science:

• Nonlinear Dynamics
• Condensed Matter Physics
• Wave Propagation

Background:

• Disordered granular crystals exhibit complex wave dynamics.
• Localization phenomena in linear and weakly nonlinear systems are well-understood.
• Strongly nonlinear systems present unique challenges for studying wave localization.

Purpose of the Study:

• Investigate energy spreading of localized excitations in 1D disordered granular crystals.
• Compare wave dynamics under different disorder types (uncorrelated and correlated) and initial conditions (displacement and velocity excitations).
• Differentiate localization phenomena in strongly nonlinear systems from linear and weakly nonlinear counterparts.

Main Methods:

• Simulated wave dynamics in 1D granular crystal chains with three distinct disorder types.
• Analyzed energy spreading using the second moment (m̃(2)) and inverse participation ratio (P(-1)).
• Examined behavior under varying precompression levels (weakly and strongly nonlinear regimes) and initial excitation types.

Main Results:

• In weakly nonlinear chains, displacement excitations show disorder-dependent energy oscillations, unlike velocity excitations which follow standard power-law scaling.
• Strongly nonlinear chains exhibit superdiffusive dynamics with scaling relations for m̃(2) and P(-1).
• Partial energy localization occurs in strongly nonlinear systems, with distinct patterns for displacement and velocity excitations, but not in the sonic-vacuum regime.

Conclusions:

• Strongly nonlinear granular systems display fundamentally different localization behaviors compared to linear systems.
• The type of initial excitation critically influences energy spreading in weakly nonlinear granular crystals.
• Superdiffusion and partial localization characterize wave packet dynamics in strongly nonlinear disordered granular chains.