14,937 research outputs found
Sums of variables at the onset of chaos
We explain how specific dynamical properties give rise to the limit
distribution of sums of deterministic variables at the transition to chaos via
the period-doubling route. We study the sums of successive positions generated
by an ensemble of initial conditions uniformly distributed in the entire phase
space of a unimodal map as represented by the logistic map. We find that these
sums acquire their salient, multiscale, features from the repellor preimage
structure that dominates the dynamics toward the attractors along the
period-doubling cascade. And we explain how these properties transmit from the
sums to their distribution. Specifically, we show how the stationary
distribution of sums of positions at the Feigebaum point is built up from those
associated with the supercycle attractors forming a hierarchical structure with
multifractal and discrete scale invariance properties.Comment: arXiv admin note: text overlap with arXiv:1312.071
Confluence of the right internal iliac vein into a compressed left common iliac vein
The authors describe the abnormal confluence of the right internal iliac vein into a left common iliac vein compressed by
the overlying right common iliac artery. The prevalence of this combination of abnormalities, evaluated in cadavers and in
living subjects by CT, was 0.9%. The possible obstacle to venous pelvic return by these anomalies is pointed out
Anomalous metastability in a temperature-driven transition
Langer theory of metastability provides a description of the lifetime and
properties of the metastable phase of the Ising model field-driven transition,
describing the magnetic field-driven transition in ferromagnets and the
chemical potential-driven transition of fluids. An immediate further step is to
apply it to the study of a transition driven by the temperature, as the one
underwent by the two-dimensional Potts model. For this model a study based on
the analytical continuation of the free energy (Meunier, Morel 2000) predicts
the anomalous vanishing of the metastable temperature range in the limit of
large system size, an issue that has been controversial since the eighties.
With a parallel-GPU algorithm we compare the Monte Carlo dynamics with the
theory, obtaining agreement and characterizing the anomalous system size
dependence. We discuss the microscopic origin of these metastable phenomena,
essentially different with respect to the Ising case.Comment: 5 pages, 3 figure
Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems
We construct new stationary weak solutions of the 3D Euler equation with
compact support. The solutions, which are piecewise smooth and discontinuous
across a surface, are axisymmetric with swirl. The range of solutions we find
is different from, and larger than, the family of smooth stationary solutions
recently obtained by Gavrilov and Constantin-La-Vicol; in particular, these
solutions are not localizable. A key step in the proof is the construction of
solutions to an overdetermined elliptic boundary value problem where one
prescribes both Dirichlet and (nonconstant) Neumann data
Optimization of the ionization time of an atom with tailored laser pulses: a theoretical study
How fast can a laser pulse ionize an atom? We address this question by
considering pulses that carry a fixed time-integrated energy per-area, and
finding those that achieve the double requirement of maximizing the ionization
that they induce, while having the shortest duration. We formulate this
double-objective quantum optimal control problem by making use of the Pareto
approach to multi-objetive optimization, and the differential evolution genetic
algorithm. The goal is to find out how much a precise time-profiling of
ultra-fast, large-bandwidth pulses may speed up the ionization process with
respect to simple-shape pulses. We work on a simple one-dimensional model of
hydrogen-like atoms (the P\"oschl-Teller potential), that allows to tune the
number of bound states that play a role in the ionization dynamics. We show how
the detailed shape of the pulse accelerates the ionization process, and how the
presence or absence of bound states influences the velocity of the process
Phase ordering and symmetries of the Potts model
We have studied the ordering of the q-colours Potts model in two dimensions
on a square lattice. On the basis of our observations we propose that if q is
large enough the system is not able to break global and local null
magnetisation symmetries at zero temperature: when q<4 the system forms domains
with a size proportional to the system size while for q>4 it relaxes towards a
non-equilibrium phase with energy larger than the ground state energy, in
agreement with the previous findings of De Oliveira et al. (M. J. de Oliveira,
A. Petri, T. Tome, Europhys. Lett., 65, 20 (2004)).Comment: 6 pages, 3 figures; minor text rewordings and changes in figures
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