6,907 research outputs found
The SO(N) principal chiral field on a half-line
We investigate the integrability of the SO(N) principal chiral model on a
half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well
as pure Dirichlet or Neumann) lead to infinitely many conserved charges
classically in involution. We use an anomaly-counting method to show that at
least one non-trivial example survives quantization, compare our results with
the proposed reflection matrices, and, based on these, make some preliminary
remarks about expected boundary bound-states.Comment: 7 pages, Late
Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow
A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan-Arnolâd Hamiltonian flows and for boundaryless submanifolds
Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps
We develop a Melnikov method for volume-preserving maps with codimension one
invariant manifolds. The Melnikov function is shown to be related to the flux
of the perturbation through the unperturbed invariant surface. As an example,
we compute the Melnikov function for a perturbation of a three-dimensional map
that has a heteroclinic connection between a pair of invariant circles. The
intersection curves of the manifolds are shown to undergo bifurcations in
homologyComment: LaTex with 10 eps figure
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
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by 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
Stability of non-time-reversible phonobreathers
Non-time reversible phonobreathers are non-linear waves that can transport
energy in coupled oscillator chains by means of a phase-torsion mechanism. In
this paper, the stability properties of these structures have been considered.
It has been performed an analytical study for low-coupling solutions based upon
the so called {\em multibreather stability theorem} previously developed by
some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms
the analytical predictions and gives a detailed picture of the existence and
stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010
Universal diffusion near the golden chaos border
We study local diffusion rate in Chirikov standard map near the critical
golden curve. Numerical simulations confirm the predicted exponent
for the power law decay of as approaching the golden curve via principal
resonances with period (). The universal
self-similar structure of diffusion between principal resonances is
demonstrated and it is shown that resonances of other type play also an
important role.Comment: 4 pages Latex, revtex, 3 uuencoded postscript figure
Renormalisation scheme for vector fields on T2 with a diophantine frequency
We construct a rigorous renormalisation scheme for analytic vector fields on
the 2-torus of Poincare type. We show that iterating this procedure there is
convergence to a limit set with a ``Gauss map'' dynamics on it, related to the
continued fraction expansion of the slope of the frequencies. This is valid for
diophantine frequency vectors.Comment: final versio
Statistical mechanical aspects of joint source-channel coding
An MN-Gallager Code over Galois fields, , based on the Dynamical Block
Posterior probabilities (DBP) for messages with a given set of autocorrelations
is presented with the following main results: (a) for a binary symmetric
channel the threshold, , is extrapolated for infinite messages using the
scaling relation for the median convergence time, ;
(b) a degradation in the threshold is observed as the correlations are
enhanced; (c) for a given set of autocorrelations the performance is enhanced
as is increased; (d) the efficiency of the DBP joint source-channel coding
is slightly better than the standard gzip compression method; (e) for a given
entropy, the performance of the DBP algorithm is a function of the decay of the
correlation function over large distances.Comment: 6 page
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