37,869 research outputs found
Information entropy of classical versus explosive percolation
We study the Shannon entropy of the cluster size distribution in classical as
well as explosive percolation, in order to estimate the uncertainty in the
sizes of randomly chosen clusters. At the critical point the cluster size
distribution is a power-law, i.e. there are clusters of all sizes, so one
expects the information entropy to attain a maximum. As expected, our results
show that the entropy attains a maximum at this point for classical
percolation. Surprisingly, for explosive percolation the maximum entropy does
not match the critical point. Moreover, we show that it is possible determine
the critical point without using the conventional order parameter, just
analysing the entropy's derivatives.Comment: 6 pages, 6 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
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
New Algorithms for Computing a Single Component of the Discrete Fourier Transform
This paper introduces the theory and hardware implementation of two new
algorithms for computing a single component of the discrete Fourier transform.
In terms of multiplicative complexity, both algorithms are more efficient, in
general, than the well known Goertzel Algorithm.Comment: 4 pages, 3 figures, 1 table. In: 10th International Symposium on
Communication Theory and Applications, Ambleside, U
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