138 research outputs found
Three predictions on July 2012 Federal Elections in Mexico based on past regularities
Electoral systems are subject of study for physicist and mathematicians in
last years given place to a new area: sociophysics. Based on previous works of
the author on the Mexican electoral processes in the new millennium, he found
three characteristics appearing along the 2000 and 2006 preliminary dataset
offered by the electoral authorities, named PREP: I) Error distributions are
not Gaussian or Lorentzian, they are characterized for power laws at the center
and asymmetric lobes at each side. II) The Partido Revolucionario Institucional
(PRI) presented a change in the slope of the percentage of votes obtained when
it go beyond the 70% of processed certificates; hence it have an improvement at
the end of the electoral computation. III) The distribution of votes for the
PRI is a smooth function well described by Daisy model distributions of rank
in all the analyzed cases, presidential and congressional elections in
2000, 2003 and 2006. If all these characteristics are proper of the Mexican
reality they should appear in the July 2012 process. Here I discuss some
arguments on why such a behaviors could appear in the present processComment: 6 pages, one tabl
Intruder States and their Local Effect on Spectral Statistics
The effect on spectral statistics and on the revival probability of intruder
states in a random background is analysed numerically and with perturbative
methods. For random coupling the intruder does not affect the GOE spectral
statistics of the background significantly, while a constant coupling causes
very strong correlations at short range with a fourth power dependence of the
spectral two-point function at the origin.The revival probability is
significantly depressed for constant coupling as compared to random coupling.Comment: 18 pages, 10 Postscript figure
On the locus formed by the maximum heights of projectile motion with air resistance
We present an analysis on the geometrical place formed by the set of maxima
of the trajectories of a projectile launched in a media with linear drag. Such
a place, the locus of apexes, is written in term of the Lambert function in
polar coordinates, confirming the special role played by this function in the
problem. In order to characterize the locus, a study of its curvature is
presented in two parameterizations, in terms of the launch angle and in the
polar one. The angles of maximum curvature are compared with other important
angles in the projectile problem. As an addendum, we find that the synchronous
curve in this problem is a circle as in the drag-free case.Comment: 7 pages, 6 color eps figures. Synchronous curve added. Typos and
style corrected
Fluctuating dynamics at the quasiperiodic onset of chaos, Tsallis q-statistics and Mori's q-phase thermodynamics
We analyze the fluctuating dynamics at the golden-mean transition to chaos in
the critical circle map and find that trajectories within the critical
attractor consist of infinite sets of power laws mixed together. We elucidate
this structure assisted by known renormalization group (RG) results. Next we
proceed to weigh the new findings against Tsallis' entropic and Mori's
thermodynamic theoretical schemes and observe behavior to a large extent richer
than previously reported. We find that the sensitivity to initial conditions
has the form of families of intertwined q-exponentials, of which we determine
the q-indexes and the generalized Lyapunov coefficient spectra. Further, the
dynamics within the critical attractor is found to consist of not one but a
collection of Mori's q-phase transitions with a hierarchical structure. The
value of Mori's `thermodynamic field' variable q at each transition corresponds
to the same special value for the entropic index q. We discuss the relationship
between the two formalisms and indicate the usefulness of the methods involved
to determine the universal trajectory scaling function and/or the ocurrence and
characterization of dynamical phase transitions.Comment: Resubmitted to Physical Review E. The title has been changed slightly
and the abstract has been extended. There is a new subsection following the
conclusions that explains the role and usefulness of the q-statistics in the
problem studied. Other minor changes througout the tex
Evanescent wave approach to diffractive phenomena in convex billiards with corners
What we are going to call in this paper "diffractive phenomena" in billiards
is far from being deeply understood. These are sorts of singularities that, for
example, some kind of corners introduce in the energy eigenfunctions. In this
paper we use the well-known scaling quantization procedure to study them. We
show how the scaling method can be applied to convex billiards with corners,
taking into account the strong diffraction at them and the techniques needed to
solve their Helmholtz equation. As an example we study a classically
pseudointegrable billiard, the truncated triangle. Then we focus our attention
on the spectral behavior. A numerical study of the statistical properties of
high-lying energy levels is carried out. It is found that all computed
statistical quantities are roughly described by the so-called semi-Poisson
statistics, but it is not clear whether the semi-Poisson statistics is the
correct one in the semiclassical limit.Comment: 7 pages, 8 figure
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