Pressure Fronts in FPU Lattices
by
Serge Aubry
Laboratoire Léon Brillouin, CEA Saclay 91191-Gif-sur-Yvette (France)
Coauthors: Laurent Proville

We present analytical and numerical results on the dynamics without damping and with

damping of a one dimensional chain of atoms where nearest neighbour atoms are coupled

by a convex anharmonic potentials (extended FPU model). The sound velocity is assumed to

be monotonously increasing with pressure.

Pressure fronts are numerically generated by the impact at uniform positive velocity of the

FPU chain on a fixed boundary wall or equivalently by the uniform motion of

a compressive piston at a boundary. At strong damping, the system dynamics is attracted by

a stationary solution corresponding to a travelling front separating two regions at different

uniform pressures which uniformly propagates toward the low pressure region.

We analytically calculate the rate of energy dissipation for any uniformly travelling front

which is found independant of the damping. Thus, since in the limit of no damping, energy

dissipation would persist, no exact travelling front solution can exist at zero damping.

Actually, when the damping goes to zero, the front solution develops backward

in the high pressure region an oscillating tail, which extends and manifests instabilities

while it diverges in size. This oscillating tail dissipates energy as vibrations at the atomic

scale.

On the base of Rankine-Hugoniot arguments valid for the continuous approximation of this

FPU chain, we expect that long wave length travelling waves spontaneously generate such

pressure fronts after a sufficiently long time. Numerical observations confirms this fact. We

suggest that the spontaneous generation of front could be an efficient pathway for the

thermalization at the atomic level of the energy of longwavelength fluctuations in the FPU

model (except likely for exceptional integrable models such as Toda lattices).

Date received: June 5, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caum-75.