1,958 research outputs found
Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices
In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the
tangent bifurcation of the band edge modes () of nonlinear Hamiltonian
lattices made of coupled oscillators. Introducing the concept of {\em
partial isochronism} which characterises the way the frequency of a mode,
, depends on its energy, , we generalize these results and
show how the bifurcation energies of these modes are intimately connected to
their degree of isochronism. In particular we prove that in a lattice of
coupled purely isochronous oscillators ( strictly constant),
the in-phase mode () never undergoes a tangent bifurcation whereas the
out-of-phase mode () does, provided the strength of the nonlinearity in
the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger
equation governing the slow modulations of small-amplitude band edge modes and
show that its nonlinear exponent is proportional to the degree of isochronism
of the corresponding orbits. This equation may be seen as a link between the
tangent bifurcation of band edge modes and the possible emergence of localized
modes such as discrete breathers.Comment: 23 pages, 1 figur
Discrete moving breather collisions in a Klein-Gordon chain of oscillators
We study collision processes of moving breathers with the same frequency,
traveling with opposite directions within a Klein-Gordon chain of oscillators.
Two types of collisions have been analyzed: symmetric and non-symmetric,
head-on collisions. For low enough frequency the outcome is strongly dependent
of the dynamical states of the two colliding breathers just before the
collision. For symmetric collisions, several results can be observed: breather
generation, with the formation of a trapped breather and two new moving
breathers; breather reflection; generation of two new moving breathers; and
breather fusion bringing about a trapped breather. For non-symmetric collisions
the possible results are: breather generation, with the formation of three new
moving breathers; breather fusion, originating a new moving breather; breather
trapping with also breather reflection; generation of two new moving breathers;
and two new moving breathers traveling as a ligand state. Breather annihilation
has never been observed.Comment: 19 pages, 12 figure
Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
The nonlinear tuned vibration absorber (NLTVA) is a recently-developed
nonlinear absorber which generalizes Den Hartog's equal peak method to
nonlinear systems. If the purposeful introduction of nonlinearity can enhance
system performance, it can also give rise to adverse dynamical phenomena,
including detached resonance curves and quasiperiodic regimes of motion.
Through the combination of numerical continuation of periodic solutions,
bifurcation detection and tracking, and global analysis, the present study
identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and
unacceptable operations. The sensitivity of these boundaries to uncertainty in
the NLTVA parameters is also investigated.Comment: Journal pape
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
Existence of multi-site intrinsic localized modes in one-dimensional Debye crystals
The existence of highly localized multi-site oscillatory structures (discrete
multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an
inverse dispersion law is proven and their linear stability is investigated.
The results are applied in the description of vertical (transverse, off-plane)
dust grain motion in dusty plasma crystals, by taking into account the lattice
discreteness and the sheath electric and/or magnetic field nonlinearity.
Explicit values from experimental plasma discharge experiments are considered.
The possibility for the occurrence of multibreathers associated with vertical
charged dust grain motion in strongly-coupled dusty plasmas (dust crystals) is
thus established. From a fundamental point of view, this study aims at
providing a first rigorous investigation of the existence of intrinsic
localized modes in Debye crystals and/or dusty plasma crystals and, in fact,
suggesting those lattices as model systems for the study of fundamental crystal
properties.Comment: 12 pages, 8 figures, revtex forma
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