14 research outputs found
On the driven Frenkel-Kontorova model: II. Chaotic sliding and nonequilibrium melting and freezing
The dynamical behavior of a weakly damped harmonic chain in a spatially
periodic potential (Frenkel-Kontorova model) under the subject of an external
force is investigated. We show that the chain can be in a spatio-temporally
chaotic state called fluid-sliding state. This is proven by calculating
correlation functions and Lyapunov spectra. An effective temperature is
attributed to the fluid-sliding state. Even though the velocity fluctuations
are Gaussian distributed, the fluid-sliding state is clearly not in equilibrium
because the equipartition theorem is violated. We also study the transition
between frozen states (stationary solutions) and=7F molten states
(fluid-sliding states). The transition is similar to a first-order phase
transition, and it shows hysteresis. The depinning-pinning transition
(freezing) is a nucleation process. The frozen state contains usually two
domains of different particle densities. The pinning-depinning transition
(melting) is caused by saddle-node bifurcations of the stationary states. It
depends on the history. Melting is accompanied by precursors, called
micro-slips, which reconfigurate the chain locally. Even though we investigate
the dynamics at zero temperature, the behavior of the Frenkel-Kontorova model
is qualitatively similar to the behavior of similar models at nonzero
temperature.Comment: Written in RevTeX, 13 figures in PostScript, appears in PR
On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities
The dynamical behavior of a harmonic chain in a spatially periodic potential
(Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of
an external force and a velocity proportional damping is investigated. We do
this at zero temperature for long chains in a regime where inertia and damping
as well as the nearest-neighbor interaction and the potential are of the same
order. There are two types of regular sliding states: Uniform sliding states,
which are periodic solutions where all particles perform the same motion
shifted in time, and nonuniform sliding states, which are quasi-periodic
solutions where the system forms patterns of domains of different uniform
sliding states. We discuss the properties of this kind of pattern formation and
derive equations of motion for the slowly varying average particle density and
velocity. To observe these dynamical domains we suggest experiments with a
discrete ring of at least fifty Josephson junctions.Comment: Written in RevTeX, 9 figures in PostScrip