Pressure Fronts in 1D Damped Nonlinear Lattices

TL;DR

This paper investigates pressure front propagation in 1D damped nonlinear lattices, revealing analytical relations between impact velocity, compression, front velocity, and energy dissipation, which depend only on the coupling potential.

Contribution

It provides the first analytical relations for pressure fronts in damped nonlinear lattices, showing their independence from damping forces.

Findings

Traveling pressure fronts are numerically and analytically characterized.

Three key relations between impact velocity, compression, front velocity, and energy dissipation are derived.

Traveling front solutions require damping to exist.

Abstract

The propagation of pressure fronts (impact solutions) in 1D chains of atoms coupled by anharmonic potentials between nearest neighbor and submitted to damping forces preserving uniform motion, is investigated. Travelling fronts between two regions at different uniform pressures are found numerically and well approximate analytically. It is proven that there are three analytical relations between the impact velocity, the compression, the front velocity and the energy dissipation which only depend on the coupling potential and are \textit{independent} of the damping. Such travelling front solutions cannot exist without damping.