2,075 research outputs found
Curvature(s) of a light wavefront in a weak gravitational field
The geometry of a light wavefront evolving from a flat wavefront under the
action of weak gravity field in the 3-space associated to a post-Newtonian
relativistic spacetime, is studied numerically by means of the ray tracing
method.Comment: 3 pages, 1 fig, Talk given by JFPS at the 12th Marcel Grossmann
conference (Paris, July, 2009), submitted to the Proceeding
Geometry of an accelerated rotating disk
We analyze the geometry of a rotating disk with a tangential acceleration in
the framework of the Special Theory of Relativity, using the kinematic linear
differential system that verifies the relative position vector of time-like
curves in a Fermi reference. A numerical integration of these equations for a
generic initial value problem is made up and the results are compared with
those obtained in other works.Comment: 10 pages, LaTeX, 2 eps figs; typos corrected, added reference, minor
changes; submitte
Comparative Analysis of Three Digital Signal Processing Techniques for 2D Combination of Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes
Ordering and finite-size effects in the dynamics of one-dimensional transient patterns
We introduce and analyze a general one-dimensional model for the description
of transient patterns which occur in the evolution between two spatially
homogeneous states. This phenomenon occurs, for example, during the
Freedericksz transition in nematic liquid crystals.The dynamics leads to the
emergence of finite domains which are locally periodic and independent of each
other. This picture is substantiated by a finite-size scaling law for the
structure factor. The mechanism of evolution towards the final homogeneous
state is by local roll destruction and associated reduction of local
wavenumber. The scaling law breaks down for systems of size comparable to the
size of the locally periodic domains. For systems of this size or smaller, an
apparent nonlinear selection of a global wavelength holds, giving rise to long
lived periodic configurations which do not occur for large systems. We also
make explicit the unsuitability of a description of transient pattern dynamics
in terms of a few Fourier mode amplitudes, even for small systems with a few
linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende
Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
In order to perform numerical simulations of the KPZ equation, in any
dimensionality, a spatial discretization scheme must be prescribed. The known
fact that the KPZ equation can be obtained as a result of a Hopf--Cole
transformation applied to a diffusion equation (with \emph{multiplicative}
noise) is shown here to strongly restrict the arbitrariness in the choice of
spatial discretization schemes. On one hand, the discretization prescriptions
for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen.
On the other hand, since the discretization is an operation performed on
\emph{space} and the Hopf--Cole transformation is \emph{local} both in space
and time, the former should be the same regardless of the field to which it is
applied. It is shown that whereas some discretization schemes pass both
consistency tests, known examples in the literature do not. The requirement of
consistency for the discretization of Lyapunov functionals is argued to be a
natural and safe starting point in choosing spatial discretization schemes. We
also analyze the relation between real-space and pseudo-spectral discrete
representations. In addition we discuss the relevance of the Galilean
invariance violation in these consistent discretization schemes, and the
alleged conflict of standard discretization with the fluctuation--dissipation
theorem, peculiar of 1D.Comment: RevTex, 23pgs, 2 figures, submitted to Phys. Rev.
Coevolution of dynamical states and interactions in dynamic networks
We explore the coupled dynamics of the internal states of a set of
interacting elements and the network of interactions among them. Interactions
are modeled by a spatial game and the network of interaction links evolves
adapting to the outcome of the game. As an example we consider a model of
cooperation, where the adaptation is shown to facilitate the formation of a
hierarchical interaction network that sustains a highly cooperative stationary
state. The resulting network has the characteristics of a small world network
when a mechanism of local neighbor selection is introduced in the adaptive
network dynamics. The highly connected nodes in the hierarchical structure of
the network play a leading role in the stability of the network. Perturbations
acting on the state of these special nodes trigger global avalanches leading to
complete network reorganization.Comment: 4 pages, 5 figures, for related material visit
http:www.imedea.uib.es/physdept
Anomalous lifetime distributions and topological traps in ordering dynamics
We address the role of community structure of an interaction network in
ordering dynamics, as well as associated forms of metastability. We consider
the voter and AB model dynamics in a network model which mimics social
interactions. The AB model includes an intermediate state between the two
excluding options of the voter model. For the voter model we find dynamical
metastable disordered states with a characteristic mean lifetime. However, for
the AB dynamics we find a power law distribution of the lifetime of metastable
states, so that the mean lifetime is not representative of the dynamics. These
trapped metastable states, which can order at all time scales, originate in the
mesoscopic network structure.Comment: 7 pages; 6 figure
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