8,400 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
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
Multiscale statistical analysis of coronal solar activity
Multi-filter images from the solar corona are used to obtain temperature maps
which are analyzed using techniques based on proper orthogonal decomposition
(POD) in order to extract dynamical and structural information at various
scales. Exploring active regions before and after a solar flare and comparing
them with quiet regions we show that the multiscale behavior presents distinct
statistical properties for each case that can be used to characterize the level
of activity in a region. Information about the nature of heat transport is also
be extracted from the analysis.Comment: 24 pages, 18 figure
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
Clustering transition in a system of particles self-consistently driven by a shear flow
We introduce a simple model of active transport for an ensemble of particles
driven by an external shear flow. Active refers to the fact that the flow of
the particles is modified by the distribution of particles itself. The model
consists in that the effective velocity of every particle is given by the
average of the external flow velocities felt by the particles located at a
distance less than a typical radius, . Numerical analysis reveals the
existence of a transition to clustering depending on the parameters of the
external flow and on . A continuum description in terms of the number
density of particles is derived, and a linear stability analysis of the density
equation is performed in order to characterize the transitions observed in the
model of interacting particles.Comment: 11 pages, 2 figures. To appear in PR
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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