Enhanced Pulse Propagation in Non-Linear Arrays of Oscillators

TL;DR

This paper investigates how pulse propagation in nonlinear oscillator arrays is affected by array type, coupling to thermal environments, and pulse amplitude, revealing diverse behaviors in pulse speed and localization.

Contribution

It provides a detailed analysis of pulse dynamics in different nonlinear arrays and how thermal coupling influences pulse speed and localization, highlighting new effects based on array type.

Findings

Hard arrays support faster, more localized pulses than harmonic or soft arrays.

Pulse speed varies with amplitude: speeds up in hard, unchanged in harmonic, slows in soft arrays.

Thermal environment coupling can either slow down or speed up pulses depending on array type.

Abstract

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (1D) or energy front (2D) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays.