Wave-packet spreading in disordered soft architected structures

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Wave propagation

Background:

• Studying disordered mechanical lattices with multiple degrees-of-freedom (DoFs) is crucial for understanding complex wave phenomena.
• Recent experiments highlight the importance of nonlinearities and DoF coupling in such systems.
• Existing models often simplify lattices to single DoFs, limiting their applicability.

Purpose of the Study:

• To analyze the dynamical and chaotic behavior of a disordered 1D elastic mechanical lattice with coupled translational and rotational waves.
• To investigate the influence of nonlinearities and disorder on wave-packet spreading and energy transport.
• To explore the potential of such lattices as platforms for controlling energy transfer in heterogeneous media.

Main Methods:

• Developing a theoretical model for a 1D elastic lattice with two DoFs per site and strong geometrical nonlinearities.
• Simulating wave propagation using single-site initial excitations on the rotational DoF to induce nonlinear coupling.
• Quantifying chaotic behavior through the evolution of the finite-time maximum Lyapunov exponent.

Main Results:

• Nonlinear coupling between translational and rotational DoFs induces rich wave-packet spreading in disordered lattices.
• In the weakly nonlinear regime, energy spreading is driven by DoF coupling, unlike single-DoF Klein-Gordon lattices.
• Strong nonlinearities lead to near-ballistic wave-packet behavior, and persistent chaos is observed, though its strength diminishes over time.

Conclusions:

• Disordered, nonlinear lattices with multiple DoFs provide a versatile platform for studying energy transport.
• The nonlinear coupling mechanism offers a novel approach to control energy spreading in complex media.
• Findings contribute to understanding wave dynamics and energy localization in heterogeneous materials.