10,739 research outputs found
Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures
A proposal for the Hamilton-Jacobi theory in the context of the covariant
formulation of Hamiltonian systems is done. The current approach consists in
applying Dirac's method to the corresponding action which implies the inclusion
of second-class constraints in the formalism which are handled using the
procedure of Rothe and Scholtz recently reported. The current method is applied
to the nonrelativistic two-dimensional isotropic harmonic oscillator employing
the various symplectic structures for this dynamical system recently reported.Comment: 17 pages, no figure
Local continuity laws on the phase space of Einstein equations with sources
Local continuity equations involving background fields and variantions of the
fields, are obtained for a restricted class of solutions of the
Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the
concept of the adjoint of a differential operator. Such covariant conservation
laws are generated by means of decoupled equations and their adjoints in such a
way that the corresponding covariantly conserved currents possess some
gauge-invariant properties and are expressed in terms of Debye potentials.
These continuity laws lead to both a covariant description of bilinear forms on
the phase space and the existence of conserved quantities. Differences and
similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page
On a new fixed point of the renormalization group operator for area-preserving maps
The breakup of the shearless invariant torus with winding number
is studied numerically using Greene's residue criterion in
the standard nontwist map. The residue behavior and parameter scaling at the
breakup suggests the existence of a new fixed point of the renormalization
group operator (RGO) for area-preserving maps. The unstable eigenvalues of the
RGO at this fixed point and the critical scaling exponents of the torus at
breakup are computed.Comment: 4 pages, 5 figure
La Costa Brava en la antigüedad, en particular la zona entre Blanes y San Feliu de GuÃxols: La villa romana de Tossa (estudio de conjunto)
Non-diffusive transport in plasma turbulence: a fractional diffusion approach
Numerical evidence of non-diffusive transport in three-dimensional, resistive
pressure-gradient-driven plasma turbulence is presented. It is shown that the
probability density function (pdf) of test particles' radial displacements is
strongly non-Gaussian and exhibits algebraic decaying tails. To model these
results we propose a macroscopic transport model for the pdf based on the use
of fractional derivatives in space and time, that incorporate in a unified way
space-time non-locality (non-Fickian transport), non-Gaussianity, and
non-diffusive scaling. The fractional diffusion model reproduces the shape, and
space-time scaling of the non-Gaussian pdf of turbulent transport calculations.
The model also reproduces the observed super-diffusive scaling
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
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