624 research outputs found
Nonlinear Lattices Generated from Harmonic Lattices with Geometric Constraints
Geometrical constraints imposed on higher dimensional harmonic lattices
generally lead to nonlinear dynamical lattice models. Helical lattices obtained
by such a procedure are shown to be described by sine- plus linear-lattice
equations. The interplay between sinusoidal and quadratic potential terms in
such models is shown to yield localized nonlinear modes identified as intrinsic
resonant modes
Observations on Tetragonal (Fe, Ni, Co)1+xS, Mackinawite
In this paper the writers have discussed the stability of mackinawite, the importance of the cation : anion ratio in its structure on the basis of the analytical data, and the relation of the α-transforma-tion of hexagonal FeSx to the transformation temperatures of natural mackinawites
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
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
Compositional Variations in Natural Mackinawite and the Results of Heating Experiments
The compositions of natural mackinawites, (Fe,Ni,Co,Cu)1+x S, from 14 different localities are presented. Heating experiments were performed and the temperature of observed breakdown to pyr-rhotite does not appear to be a function of cation proportions. Indeed, the "breakdown" is not isochemical and involves the addition of sulfur from the surrounding minerals and therefore, is not representative of the upper thermal stability of mackinawite. In most natural occurrences, mackinawite occurs with chalco-pyrite. Based on phase chemistry, this would appear to be a metastable assemblage. However, recent developments, particularly in the Cu—Fe—S system, suggest that at low temperatures several reactions may occur which could thereby permit the stable existence of this assemblage
A Rich Example of Geometrically Induced Nonlinearity: From Rotobreathers and Kinks to Moving Localized Modes and Resonant Energy Transfer
We present an experimentally realizable, simple mechanical system with linear
interactions whose geometric nature leads to nontrivial, nonlinear dynamical
equations. The equations of motion are derived and their ground state
structures are analyzed. Selective ``static'' features of the model are
examined in the context of nonlinear waves including rotobreathers and
kink-like solitary waves. We also explore ``dynamic'' features of the model
concerning the resonant transfer of energy and the role of moving intrinsic
localized modes in the process
Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones
(LJ) anharmonic lattices. Numerical simulations reveal the presence of high
energy strongly localized ``discrete'' kink-solitons (DK), which move with
supersonic velocities that are proportional to kink amplitudes. For small
amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous''
kink-soliton solutions of the modified Korteweg-de Vries equation. For high
amplitudes, we obtain a consistent description of these DK's in terms of
approximate solutions of the lattice equations that are obtained by restricting
to a bounded support in space exact solutions with sinusoidal pattern
characterized by the ``magic'' wavenumber . Relative displacement
patterns, velocity versus amplitude, dispersion relation and exponential tails
found in numerical simulations are shown to agree very well with analytical
predictions, for both FPU and LJ lattices.Comment: Europhysics Letters (in print
Discrete breathers in dc biased Josephson-junction arrays
We propose a method to excite and detect a rotor localized mode
(rotobreather) in a Josephson-junction array biased by dc currents. In our
numerical studies of the dynamics we have used experimentally realizable
parameters and included self-inductances. We have uncovered two families of
rotobreathers. Both types are stable under thermal fluctuations and exist for a
broad range of array parameters and sizes including arrays as small as a single
plaquette. We suggest a single Josephson-junction plaquette as an ideal system
to experimentally investigate these solutions.Comment: 5 pages, 5 figure, to appear June 1, 1999 in PR
A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations
A new class of 1D discrete nonlinear Schrdinger Hamiltonians
with tunable nonlinerities is introduced, which includes the integrable
Ablowitz-Ladik system as a limit. A new subset of equations, which are derived
from these Hamiltonians using a generalized definition of Poisson brackets, and
collectively refered to as the N-AL equation, is studied. The symmetry
properties of the equation are discussed. These equations are shown to possess
propagating localized solutions, having the continuous translational symmetry
of the one-soliton solution of the Ablowitz-Ladik nonlinear
Schrdinger equation. The N-AL systems are shown to be suitable
to study the combined effect of the dynamical imbalance of nonlinearity and
dispersion and the Peierls-Nabarro potential, arising from the lattice
discreteness, on the propagating solitary wave like profiles. A perturbative
analysis shows that the N-AL systems can have discrete breather solutions, due
to the presence of saddle center bifurcations in phase portraits. The
unstaggered localized states are shown to have positive effective mass. On the
other hand, large width but small amplitude staggered localized states have
negative effective mass. The collison dynamics of two colliding solitary wave
profiles are studied numerically. Notwithstanding colliding solitary wave
profiles are seen to exhibit nontrivial nonsolitonic interactions, certain
universal features are observed in the collison dynamics. Future scopes of this
work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn
Experimental Demonstration of Macroscopic Quantum Coherence in Gaussian States
We witness experimentally the presence of macroscopic coherence in Gaussian
quantum states using a recently proposed criterion (E.G. Cavalcanti and M.
Reid, Phys. Rev. Lett. 97, 170405 (2006)). The macroscopic coherence stems from
interference between macroscopically distinct states in phase space and we
prove experimentally that even the vacuum state contains these features with a
distance in phase space of shot noise units (SNU). For squeezed
states we found macroscopic superpositions with a distance of up to
SNU. The proof of macroscopic quantum coherence was investigated
with respect to squeezing and purity of the states.Comment: 5 pages, 6 figure
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