17,941 research outputs found
Integrability of one degree of freedom symplectic maps with polar singularities
In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure
Selective decay by Casimir dissipation in fluids
The problem of parameterizing the interactions of larger scales and smaller
scales in fluid flows is addressed by considering a property of two-dimensional
incompressible turbulence. The property we consider is selective decay, in
which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D
flows) decays in time, while the energy stays essentially constant. This paper
introduces a mechanism that produces selective decay by enforcing Casimir
dissipation in fluid dynamics. This mechanism turns out to be related in
certain cases to the numerical method of anticipated vorticity discussed in
\cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of
selective decay is developed that uses the Lie-Poisson structure of the ideal
theory. A scale-selection operator allows the resulting modifications of the
fluid motion equations to be interpreted in several examples as parameterizing
the nonlinear, dynamical interactions between disparate scales. The type of
modified fluid equation systems derived here may be useful in modelling
turbulent geophysical flows where it is computationally prohibitive to rely on
the slower, indirect effects of a realistic viscosity, such as in large-scale,
coherent, oceanic flows interacting with much smaller eddies
Link Invariants for Flows in Higher Dimensions
Linking numbers in higher dimensions and their generalization including gauge
fields are studied in the context of BF theories. The linking numbers
associated to -manifolds with smooth flows generated by divergence-free
p-vector fields, endowed with an invariant flow measure are computed in
different cases. They constitute invariants of smooth dynamical systems (for
non-singular flows) and generalizes previous results for the 3-dimensional
case. In particular, they generalizes to higher dimensions the Arnold's
asymptotic Hopf invariant for the three-dimensional case. This invariant is
generalized by a twisting with a non-abelian gauge connection. The computation
of the asymptotic Jones-Witten invariants for flows is naturally extended to
dimension n=2p+1. Finally we give a possible interpretation and implementation
of these issues in the context of string theory.Comment: 21+1 pages, LaTeX, no figure
Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
We investigate an -particle Bose-Hubbard dimer with an additional
effective decay term in one of the sites. A mean-field approximation for this
non-Hermitian many-particle system is derived, based on a coherent state
approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in
particular the fixed point structures showing characteristic modifications of
the self-trapping transition, are analyzed. The mean-field dynamics is found to
be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio
Dynamical stability of a doubly quantized vortex in a three-dimensional condensate
The Bogoliubov equations are solved for a three-dimensional Bose-Einstein
condensate containing a doubly quantized vortex, trapped in a harmonic
potential. Complex frequencies, signifying dynamical instability, are found for
certain ranges of parameter values. The existence of alternating windows of
stability and instability, respectively, is explained qualitatively and
quantitatively using variational calculus and direct numerical solution. It is
seen that the windows of stability are much smaller for a cigar shaped
condensate than for a pancake shaped one, which is consistent with the findings
of recent experiments.Comment: 23 pages, 11 figure
Pseudo-boundaries in discontinuous 2-dimensional maps
It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently
smooth 2-dimensional area-preserving maps. When such boundaries are destroyed,
they become pseudo-boundaries. We show that pseudo-boundaries can also be found
in discontinuous maps. The origin of these pseudo-boundaries are groups of
chains of islands which separate parts of the phase space and need to be
crossed in order to move between the different sub-spaces. Trajectories,
however, do not easily cross these chains, but tend to propagate along them.
This type of behavior is demonstrated using a ``generalized'' Fermi map.Comment: 4 pages, 4 figures, Revtex, epsf, submitted to Physical Review E (as
a brief report
Poincar\'e recurrence theorem and the strong CP-problem
The existence in the physical QCD vacuum of nonzero gluon condensates, such
as , requires dominance of gluon fields with finite mean action
density. This naturally allows any real number value for the unit ``topological
charge'' characterising the fields approximating the gluon configurations
which should dominate the QCD partition function. If is an irrational
number then the critical values of the parameter for which CP is
spontaneously broken are dense in , which provides for a mechanism
of resolving the strong CP problem simultaneously with a correct implementation
of symmetry. We present an explicit realisation of this
mechanism within a QCD motivated domain model. Some model independent arguments
are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now
includes model independent argument
Spectral analysis and an area-preserving extension of a piecewise linear intermittent map
We investigate spectral properties of a 1-dimensional piecewise linear
intermittent map, which has not only a marginal fixed point but also a singular
structure suppressing injections of the orbits into neighborhoods of the
marginal fixed point. We explicitly derive generalized eigenvalues and
eigenfunctions of the Frobenius--Perron operator of the map for classes of
observables and piecewise constant initial densities, and it is found that the
Frobenius--Perron operator has two simple real eigenvalues 1 and , and a continuous spectrum on the real line . From these
spectral properties, we also found that this system exhibits power law decay of
correlations. This analytical result is found to be in a good agreement with
numerical simulations. Moreover, the system can be extended to an
area-preserving invertible map defined on the unit square. This extended system
is similar to the baker transformation, but does not satisfy hyperbolicity. A
relation between this area-preserving map and a billiard system is also
discussed.Comment: 12 pages, 3 figure
Anderson localization or nonlinear waves? A matter of probability
In linear disordered systems Anderson localization makes any wave packet stay
localized for all times. Its fate in nonlinear disordered systems is under
intense theoretical debate and experimental study. We resolve this dispute
showing that at any small but finite nonlinearity (energy) value there is a
finite probability for Anderson localization to break up and propagating
nonlinear waves to take over. It increases with nonlinearity (energy) and
reaches unity at a certain threshold, determined by the initial wave packet
size. Moreover, the spreading probability stays finite also in the limit of
infinite packet size at fixed total energy. These results are generalized to
higher dimensions as well.Comment: 4 pages, 3 figure
Surface chemistry of selected lunar regions
A completely new analysis has been carried out on the data from the Apollo 15 and 16 gamma ray spectrometer experiments. The components of the continuum background have been estimated. The elements Th, K, Fe and Mg give useful results; results for Ti are significant only for a few high Ti regions. Errors are given, and the results are checked by other methods. Concentrations are reported for about sixty lunar regions; the ground track has been subdivided in various ways. The borders of the maria seem well-defined chemically, while the distribution of KREEP is broad. This wide distribution requires emplacement of KREEP before the era of mare formation. Its high concentration in western mare soils seems to require major vertical mixing
- …