722 research outputs found
Obtaining Breathers in Nonlinear Hamiltonian Lattices
We present a numerical method for obtaining high-accuracy numerical solutions
of spatially localized time-periodic excitations on a nonlinear Hamiltonian
lattice. We compare these results with analytical considerations of the spatial
decay. We show that nonlinear contributions have to be considered, and obtain
very good agreement between the latter and the numerical results. We discuss
further applications of the method and results.Comment: 21 pages (LaTeX), 8 figures in ps-files, tar-compressed uuencoded
file, Physical Review E, in pres
Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
Discrete breathers are time-periodic, spatially localized solutions of
equations of motion for classical degrees of freedom interacting on a lattice.
They come in one-parameter families. We report on studies of energy properties
of breather families in one-, two- and three-dimensional lattices. We show that
breather energies have a positive lower bound if the lattice dimension of a
given nonlinear lattice is greater than or equal to a certain critical value.
These findings could be important for the experimental detection of discrete
breathers.Comment: 10 pages, LaTeX, 4 figures (ps), Physical Review Letters, in prin
Dimension dependent energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. We study the existence of energy thresholds for discrete breathers,
i.e., the question whether, in a certain system, discrete breathers of
arbitrarily low energy exist, or a threshold has to be overcome in order to
excite a discrete breather. Breather energies are found to have a positive
lower bound if the lattice dimension d is greater than or equal to a certain
critical value d_c, whereas no energy threshold is observed for d<d_c. The
critical dimension d_c is system dependent and can be computed explicitly,
taking on values between zero and infinity. Three classes of Hamiltonian
systems are distinguished, being characterized by different mechanisms
effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure
Observation of breathers in Josephson ladders
We report on the observation of spatially-localized excitations in a ladder
of small Josephson junctions. The excitations are whirling states which persist
under a spatially-homogeneous force due to the bias current. These states of
the ladder are visualized using a low temperature scanning laser microscopy. We
also compute breather solutions with high accuracy in corresponding model
equations. The stability analysis of these solutions is used to interpret the
measured patterns in the I-V characteristics
Limit cycles in the presence of convection, a travelling wave analysis
We consider a diffusion model with limit cycle reaction functions, in the
presence of convection. We select a set of functions derived from a realistic
reaction model: the Schnakenberg equations. This resultant form is
unsymmetrical. We find a transformation which maps the irregular equations into
model form. Next we transform the dependent variables into polar form. From
here, a travelling wave analysis is performed on the radial variable. Results
are complex, but we make some simple estimates.
We carry out numerical experiments to test our analysis. An initial `knock'
starts the propagation of pattern. The speed of the travelling wave is not
quite as expected. We investigate further. The system demonstrates distinctly
different behaviour to the left and the right. We explain how this phenomenon
occurs by examining the underlying behaviour.Comment: 20 pages, 5 figure
Nonlinear Fano resonance and bistable wave transmission
We consider a discrete model that describes a linear chain of particles
coupled to a single-site defect with instantaneous Kerr nonlinearity. We show
that this model can be regarded as a nonlinear generalization of the familiar
Fano-Anderson model, and it can generate the amplitude depended bistable
resonant transmission or reflection. We identify these effects as the nonlinear
Fano resonance, and study its properties for continuous waves and pulses.Comment: 9 pages, 14 figure, submitted to Phys. Rev.
Discrete breathers in dissipative lattices
We study the properties of discrete breathers, also known as intrinsic
localized modes, in the one-dimensional Frenkel-Kontorova lattice of
oscillators subject to damping and external force. The system is studied in the
whole range of values of the coupling parameter, from C=0 (uncoupled limit) up
to values close to the continuum limit (forced and damped sine-Gordon model).
As this parameter is varied, the existence of different bifurcations is
investigated numerically. Using Floquet spectral analysis, we give a complete
characterization of the most relevant bifurcations, and we find (spatial)
symmetry-breaking bifurcations which are linked to breather mobility, just as
it was found in Hamiltonian systems by other authors. In this way moving
breathers are shown to exist even at remarkably high levels of discreteness. We
study mobile breathers and characterize them in terms of the phonon radiation
they emit, which explains successfully the way in which they interact. For
instance, it is possible to form ``bound states'' of moving breathers, through
the interaction of their phonon tails. Over all, both stationary and moving
breathers are found to be generic localized states over large values of ,
and they are shown to be robust against low temperature fluctuations.Comment: To be published in Physical Review
Breather Statics and Dynamics in Klein--Gordon Chains with a Bend
In this communication, we examine a nonlinear model with an impurity
emulating a bend. We justify the geometric interpretation of the model and
connect it with earlier work on models including geometric effects. We focus on
both the bifurcation and stability analysis of the modes that emerge as a
function of the strength of the bend angle, but we also examine dynamical
effects including the scattering of mobile localized modes (discrete breathers)
off of such a geometric structure. The potential outcomes of such numerical
experiments (including transmission, trapping within the bend as well as
reflection) are highlighted and qualitatively explained. Such models are of
interest both theoretically in understanding the interplay of breathers with
curvature, but also practically in simple models of photonic crystals or of
bent chains of DNA.Comment: 14 pages, 16 figure
Tunable Pinning of Burst-Waves in Extended Systems with Discrete Sources
We study the dynamics of waves in a system of diffusively coupled discrete
nonlinear sources. We show that the system exhibits burst waves which are
periodic in a traveling-wave reference frame. We demonstrate that the burst
waves are pinned if the diffusive coupling is below a critical value. When the
coupling crosses the critical value the system undergoes a depinning
instability via a saddle-node bifurcation, and the wave begins to move. We
obtain the universal scaling for the mean wave velocity just above threshold.Comment: 4 pages, 5 figures, revte
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