166 research outputs found
Driven Intrinsic Localized Modes in a Coupled Pendulum Array
Intrinsic localized modes (ILMs), also called discrete breathers, are
directly generated via modulational instability in an array of coupled
pendulums. These ILMs can be stabilized over a range of driver frequencies and
amplitudes. They are characterized by a pi-phase difference between their
center and wings. At higher driver frequencies, these ILMs are observed to
disintegrate via a pulsating instability, and the mechanism of this breather
instability is investigated.Comment: 5 pages, 6 figure
Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond
A novel, protean, topological soliton has recently been shown to emerge in
systems of repulsive particles in cylindrical geometries, whose statics is
described by the number-theoretical objects of phyllotaxis. Here we present a
minimal and local continuum model that can explain many of the features of the
phyllotactic soliton, such as locked speed, screw shift, energy transport and,
for Wigner crystal on a nanotube, charge transport. The treatment is general
and should apply to other spiraling systems. Unlike e.g. Sine-Gornon-like
systems, our solitons can exist between non-degenerate structure, imply a power
flow through the system, dynamics of the domains it separates; we also predict
pulses, both static and dynamic. Applications include charge transport in
Wigner Crystals on nanotubes or A- to B-DNA transitions.Comment: 8 Pages, 6 Figures, Phys Rev E in pres
Energy transmission in the forbidden bandgap of a nonlinear chain
A nonlinear chain driven by one end may propagate energy in the forbidden
band gap by means of nonlinear modes. For harmonic driving at a given
frequency, the process ocurs at a threshold amplitude by sudden large energy
flow, that we call nonlinear supratransmission. The bifurcation of energy
transmission is demonstrated numerically and experimentally on the chain of
coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and
sustained by an extremely simple theory.Comment: LaTex file, 6 figures, published in Phys Rev Lett 89 (2002) 13410
Scaling, self-similar solutions and shock waves for V-shaped field potentials
We investigate a (1+1)-dimensional nonlinear field theoretic model with the
field potential It can be obtained as the universal small
amplitude limit in a class of models with potentials which are symmetrically
V-shaped at their minima, or as a continuum limit of certain mechanical system
with infinite number of degrees of freedom. The model has an interesting
scaling symmetry of the 'on shell' type. We find self-similar as well as shock
wave solutions of the field equation in that model.Comment: Two comments and one reference adde
Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment
We study experimentally and numerically the existence and stability
properties of discrete breathers in a periodic nonlinear electric line. The
electric line is composed of single cell nodes, containing a varactor diode and
an inductor, coupled together in a periodic ring configuration through
inductors and driven uniformly by a harmonic external voltage source. A simple
model for each cell is proposed by using a nonlinear form for the varactor
characteristics through the current and capacitance dependence on the voltage.
For an electrical line composed of 32 elements, we find the regions, in driver
voltage and frequency, where -peaked breather solutions exist and
characterize their stability. The results are compared to experimental
measurements with good quantitative agreement. We also examine the spontaneous
formation of -peaked breathers through modulational instability of the
homogeneous steady state. The competition between different discrete breathers
seeded by the modulational instability eventually leads to stationary
-peaked solutions whose precise locations is seen to sensitively depend on
the initial conditions
Tristability in the pendula chain
Experiments on a chain of coupled pendula driven periodically at one end
demonstrate the existence of a novel regime which produces an output frequency
at an odd fraction of the driving frequency. The new stationary state is then
obtained on numerical simulations and modeled with an analytical solution of
the continuous sine-Gordon equation that resembles a kink-like motion back and
forth in the restricted geometry of the chain. This solution differs from the
expressions used to understand nonlinear bistability where the synchronization
constraint was the basic assumption. As a result the short pendula chain is
shown to possess tristable stationary states and to act as a frequency divider.Comment: To appear in PR
Self-organized escape of oscillator chains in nonlinear potentials
We present the noise free escape of a chain of linearly interacting units
from a metastable state over a cubic on-site potential barrier. The underlying
dynamics is conservative and purely deterministic. The mutual interplay between
nonlinearity and harmonic interactions causes an initially uniform lattice
state to become unstable, leading to an energy redistribution with strong
localization. As a result a spontaneously emerging localized mode grows into a
critical nucleus. By surpassing this transition state, the nonlinear chain
manages a self-organized, deterministic barrier crossing. Most strikingly,
these noise-free, collective nonlinear escape events proceed generally by far
faster than transitions assisted by thermal noise when the ratio between the
average energy supplied per unit in the chain and the potential barrier energy
assumes small values
Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide
We study the propagation of quasi-discrete microwave solitons in a nonlinear
left-handed coplanar waveguide coupled with split ring resonators. By
considering the relevant transmission line analogue, we derive a nonlinear
lattice model which is studied analytically by means of a quasi-discrete
approximation. We derive a nonlinear Schr{\"o}dinger equation, and find that
the system supports bright envelope soliton solutions in a relatively wide
subinterval of the left-handed frequency band. We perform systematic numerical
simulations, in the framework of the nonlinear lattice model, to study the
propagation properties of the quasi-discrete microwave solitons. Our numerical
findings are in good agreement with the analytical predictions, and suggest
that the predicted structures are quite robust and may be observed in
experiments
Optimization of soliton ratchets in inhomogeneous sine-Gordon systems
Unidirectional motion of solitons can take place, although the applied force
has zero average in time, when the spatial symmetry is broken by introducing a
potential , which consists of periodically repeated cells with each cell
containing an asymmetric array of strongly localized inhomogeneities at
positions . A collective coordinate approach shows that the positions,
heights and widths of the inhomogeneities (in that order) are the crucial
parameters so as to obtain an optimal effective potential that yields
a maximal average soliton velocity. essentially exhibits two
features: double peaks consisting of a positive and a negative peak, and long
flat regions between the double peaks. Such a potential can be obtained by
choosing inhomogeneities with opposite signs (e.g., microresistors and
microshorts in the case of long Josephson junctions) that are positioned close
to each other, while the distance between each peak pair is rather large. These
results of the collective variables theory are confirmed by full simulations
for the inhomogeneous sine-Gordon system
Formation of Random Dark Envelope Solitons from Incoherent Waves
This letter reports experimental results on a new type of soliton: the random
temporal dark soliton. One excites an incoherent large-amplitude propagating
spin-wave packet in a ferromagnetic film strip with a repulsive, instantaneous
nonlinearity. One then observes the random formation of dark solitons from this
wave packet. The solitons appear randomly in time and in position relative to
the entire wave packet. They can be gray or black. For wide and/or very strong
spin-wave packets, one also observes multiple dark solitons. In spite of the
randomness of the initial wave packets and the random formation processes, the
solitons show signatures that are found for conventional coherent dark
solitons.Comment: 10 pages, 4 figures, double-spaced preprint forma
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