Accelerating oscillatory fronts in a nonlinear sonic vacuum with strong nonlocal effects.

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Wave propagation

Background:

• Oscillatory fronts are observed in various physical systems.
• Nonlocal interactions can significantly alter wave propagation dynamics.
• Understanding front acceleration is crucial for modeling complex systems.

Purpose of the Study:

• To describe and explore accelerating oscillatory fronts in sonic vacua with nonlocal interactions.
• To derive analytical scaling laws for front propagation and oscillatory tails.
• To investigate the threshold amplitude required for front initiation.

Main Methods:

• Consideration of a discrete model: a chain of particles with linear springs and fixed ends.
• Harmonic excitation in the transverse direction to initiate front propagation.
• Continuum approximation to derive analytical scaling laws.
• Analysis of a simplified discrete model reduced to a completely integrable nonlinear system.

Main Results:

• Observation of accelerated propagation of the excitation front with an almost monochromatic oscillatory tail.
• Front position follows the scaling law l(t) ∼ t(4/3).
• Oscillatory tail exhibits constant frequency and wavelength scaling as λ ∼ t(1/3).
• Identification of a threshold excitation amplitude for front propagation initiation.

Conclusions:

• Nonlocal effects are responsible for the observed scaling laws in accelerating oscillatory fronts.
• The derived analytical results provide a quantitative understanding of the phenomenon.
• Nonlinear sonic vacua with nonlocal interactions are likely common in periodic lattices due to their simplicity.