116 research outputs found
Numerical study of the current sheet and PSBL in a magnetotail model
The current sheet and plasma sheet boundary layer (PSBL) in a magnetotail model are discussed. A test particle code is used to study the response of ensembles of particles to a two-dimensional, time-dependent model of the geomagnetic tail, and test the proposition (Coroniti, 1985a, b; Buchner and Zelenyi, 1986; Chen and Palmadesso, 1986; Martin, 1986) that the stochasticity of the particle orbits in these fields is an important part of the physical mechanism for magnetospheric substorms. The realistic results obtained for the fluid moments of the particle distribution with this simple model, and their insensitivity to initial conditions, is consistent with this hypothesis
The phase plane of moving discrete breathers
We study anharmonic localization in a periodic five atom chain with
quadratic-quartic spring potential. We use discrete symmetries to eliminate the
degeneracies of the harmonic chain and easily find periodic orbits. We apply
linear stability analysis to measure the frequency of phonon-like disturbances
in the presence of breathers and to analyze the instabilities of breathers. We
visualize the phase plane of breather motion directly and develop a technique
for exciting pinned and moving breathers. We observe long-lived breathers that
move chaotically and a global transition to chaos that prevents forming moving
breathers at high energies.Comment: 8 pages text, 4 figures, submitted to Physical Review Letters. See
http://www.msc.cornell.edu/~houle/localization
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
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Generation of Intrinsic Vibrational Gap Modes in Three-Dimensional Ionic Crystals
The existence of anharmonic localization of lattice vibrations in a perfect
3-D diatomic ionic crystal is established for the rigid-ion model by molecular
dynamics simulations. For a realistic set of NaI potential parameters, an
intrinsic localized gap mode vibrating in the [111] direction is observed for
fcc and zinc blende lattices. An axial elastic distortion is an integral
feature of this mode which forms more readily for the zinc blende than for the
fcc structure. Molecular dynamics simulations verify that in each structure
this localized mode may be stable for at least 200 cycles.Comment: 5 pages, 4 figures, RevTeX, using epsf.sty. To be published in Phys.
Rev. B. Also available at http://www.msc.cornell.edu/~kiselev
Stepwise quantum decay of self-localized solitons
The two-phonon decay of self-localized soliton in a one-dimensional monatomic
anharmonic lattice caused by cubic anharmonicity is considered. It is shown
that the decay takes place with emission of phonon bursts. The average rate of
emission of phonons is of the order of vibrational quantum per vibrational
period. Characteristic time of the relaxation is determined by the quantum
anharmonicity parameter; this time may vary from a few (quantum lattices, large
anharmonicity) to thousands (ordinary lattices, small anharmonicity) of
vibrational periods.Comment: 6 pages, 3 figure
Optical creation of vibrational intrinsic localized modes in anharmonic lattices with realistic interatomic potentials
Using an efficient optimal control scheme to determine the exciting fields,
we theoretically demonstrate the optical creation of vibrational intrinsic
localized modes (ILMs) in anharmonic perfect lattices with realistic
interatomic potentials. For systems with finite size, we show that ILMs can be
excited directly by applying a sequence of femtosecond visible laser pulses at
THz repetition rates. For periodic lattices, ILMs can be created indirectly via
decay of an unstable extended lattice mode which is excited optically either by
a sequence of pulses as described above or by a single picosecond far-infrared
laser pulse with linearly chirped frequency. In light of recent advances in
experimental laser pulse shaping capabilities, the approach is experimentally
promising.Comment: 20 pages, 7 eps figures. Accepted, Phys. Rev.
Discrete breathers in classical spin lattices
Discrete breathers (nonlinear localised modes) have been shown to exist in
various nonlinear Hamiltonian lattice systems. In the present paper we study
the dynamics of classical spins interacting via Heisenberg exchange on spatial
-dimensional lattices (with and without the presence of single-ion
anisotropy). We show that discrete breathers exist for cases when the continuum
theory does not allow for their presence (easy-axis ferromagnets with
anisotropic exchange and easy-plane ferromagnets). We prove the existence of
localised excitations using the implicit function theorem and obtain necessary
conditions for their existence. The most interesting case is the easy-plane one
which yields excitations with locally tilted magnetisation. There is no
continuum analogue for such a solution and there exists an energy threshold for
it, which we have estimated analytically. We support our analytical results
with numerical high-precision computations, including also a stability analysis
for the excitations.Comment: 15 pages, 12 figure
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
Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity
Nonlinear localized excitations in one-dimensional diatomic lattices with
cubic and quartic nonlinearity are considered analytically by a
quasi-discreteness approach. The criteria for the occurence of asymmetric gap
solitons (with vibrating frequency lying in the gap of phonon bands) and
small-amplitude, asymmetric intrinsic localized modes (with the vibrating
frequency being above all the phonon bands) are obtained explicitly based on
the modulational instabilities of corresponding linear lattice plane waves. The
expressions of particle displacement for all these nonlinear localized
excitations are also given. The result is applied to standard two-body
potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The
comparison with previous numerical study of the anharmonic gap modes in
diatomic lattices for the standard two-body potentials is made and good
agreement is found.Comment: 24 pages in Revtex, 2 PS figure
- …