36,948 research outputs found
Decay of distance autocorrelation and Lyapunov exponents
This work presents numerical evidences that for discrete dynamical systems
with one positive Lyapunov exponent the decay of the distance autocorrelation
is always related to the Lyapunov exponent. Distinct decay laws for the
distance autocorrelation are observed for different systems, namely exponential
decays for the quadratic map, logarithmic for the H\'enon map and power-law for
the conservative standard map. In all these cases the decay exponent is close
to the positive Lyapunov exponent. For hyperbolic conservative systems, the
power-law decay of the distance autocorrelation tends to be guided by the
smallest Lyapunov exponent.Comment: 7 pages, 8 figure
Black string corrections in variable tension braneworld scenarios
Braneworld models with variable tension are investigated, and the corrections
on the black string horizon along the extra dimension are provided. Such
corrections are encrypted in additional terms involving the covariant
derivatives of the variable tension on the brane, providing profound
consequences concerning the black string horizon variation along the extra
dimension, near the brane. The black string horizon behavior is shown to be
drastically modified by the terms corrected by the brane variable tension. In
particular, a model motivated by the phenomenological interesting case
regarding Eotvos branes is investigated. It forthwith provides further physical
features regarding variable tension braneworld scenarios, heretofore concealed
in all previous analysis in the literature. All precedent analysis considered
uniquely the expansion of the metric up to the second order along the extra
dimension, what is able to evince solely the brane variable tension absolute
value. Notwithstanding, the expansion terms aftermath, further accomplished in
this paper from the third order on, elicits the successive covariant
derivatives of the brane variable tension, and their respective coupling with
the extrinsic curvature, the Weyl tensor, and the Riemann and Ricci tensors, as
well as the scalar curvature. Such additional terms are shown to provide sudden
modifications in the black string horizon in a variable tension braneworld
scenarioComment: 12 pages, 5 figures, accepted in PR
Notes on the Two-brane Model with Variable Tension
Motivated by possible extensions of the braneworld models with two branes, we
investigate some consequences of a variable brane tension using the well
established results on consistency conditions. By a slight modification of the
usual stress-tensor used in order to derive the braneworld sum rules, we find
out some important constraints obeyed by time dependent brane tensions. In
particular it is shown that the tensions of two Randall-Sundrum like branes
obeying, at the same time, an Eotvos law, aggravate the fine tuning problem.
Also, it is shown that if the hidden brane tension obeys an Eotvos law, then
the visible brane has a mixed behavior allowing a bouncing-like period at early
times while it is dominated by an Eotvos law nowadays. To finalize, we discuss
some qualitative characteristics which may arise in the scope of dynamical
brane tensions, as anisotropic background and branons production.Comment: 7 pages, 1 figure, accepted for publication in Physical Review
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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