71,324 research outputs found
Generalising the logistic map through the -product
We investigate a generalisation of the logistic map as (, )
where stands for a generalisation of the ordinary product, known as
-product [Borges, E.P. Physica A {\bf 340}, 95 (2004)]. The usual product,
and consequently the usual logistic map, is recovered in the limit ,
The tent map is also a particular case for . The
generalisation of this (and others) algebraic operator has been widely used
within nonextensive statistical mechanics context (see C. Tsallis, {\em
Introduction to Nonextensive Statistical Mechanics}, Springer, NY, 2009). We
focus the analysis for at the edge of chaos, particularly at the
first critical point , that depends on the value of . Bifurcation
diagrams, sensitivity to initial conditions, fractal dimension and rate of
entropy growth are evaluated at , and connections with
nonextensive statistical mechanics are explored.Comment: 12 pages, 23 figures, Dynamics Days South America. To be published in
Journal of Physics: Conference Series (JPCS - IOP
The Jacobi identity for Dirac-like brackets
For redundant second-class constraints the Dirac brackets cannot be defined
and new brackets must be introduced. We prove here that the Jacobi identity for
the new brackets must hold on the surface of the second-class constraints. In
order to illustrate our proof we work out explicitly the cases of a fractional
spin particle in 2+1 dimensions and the original Brink-Schwarz massless
superparticle in D=10 dimensions in a Lorentz covariant constraints separation.Comment: 14 pages, Latex. Final version to be published in Int. J. Mod. Phys.
Influence of Refractory Periods in the Hopfield model
We study both analytically and numerically the effects of including
refractory periods in the Hopfield model for associative memory. These periods
are introduced in the dynamics of the network as thresholds that depend on the
state of the neuron at the previous time. Both the retrieval properties and the
dynamical behaviour are analyzed.Comment: Revtex, 7 pages, 7 figure
Radiative corrections in bumblebee electrodynamics
We investigate some quantum features of the bumblebee electrodynamics in flat
spacetimes. The bumblebee field is a vector field that leads to a spontaneous
Lorentz symmetry breaking. For a smooth quadratic potential, the massless
excitation (Nambu-Goldstone boson) can be identified as the photon, transversal
to the vacuum expectation value of the bumblebee field. Besides, there is a
massive excitation associated with the longitudinal mode and whose presence
leads to instability in the spectrum of the theory. By using the
principal-value prescription, we show that no one-loop radiative corrections to
the mass term is generated. Moreover, the bumblebee self-energy is not
transverse, showing that the propagation of the longitudinal mode can not be
excluded from the effective theory.Comment: Revised version: contains some more elaborated interpretation of the
results. Conclusions improve
Mixed-state microwave response in superconducting cuprates
We report measurements of the magnetic-field induced microwave complex
resistivity in REBaCuO thin films, with RE = Y, Sm.
Measurements are performed at 48 GHz by means of a resonant cavity in the
end-wall-replacement configuration. The magnetic field dependence is
investigated by applying a moderate (0.8 T) magnetic field along the c-axis.
The measured vortex state complex resistivity in
YBaCuO and SmBaCuO is
analyzed within the well-known models for vortex dynamics. It is shown that
attributing the observed response to vortex motion alone leads to
inconsistencies in the as-determined vortex parameters (such as the vortex
viscosity and the pinning constant). By contrast, attributing the entire
response to field-induced pair breaking leads to a nearly quantitative
description of the data.Comment: 6 pages, 4 figures, to be published in J. Supercond. as proceedings
of 8th HTSHFF (May 26th-29th, 2004, Begur, Spain
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
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