285 research outputs found
Surrogate Test to Distinguish between Chaotic and Pseudoperiodic Time Series
In this communication a new algorithm is proposed to produce surrogates for
pseudoperiodic time series. By imposing a few constraints on the noise
components of pseudoperiodic data sets, we devise an effective method to
generate surrogates. Unlike other algorithms, this method properly copes with
pseudoperiodic orbits contaminated with linear colored observational noise. We
will demonstrate the ability of this algorithm to distinguish chaotic orbits
from pseudoperiodic orbits through simulation data sets from theR\"{o}ssler
system. As an example of application of this algorithm, we will also employ it
to investigate a human electrocardiogram (ECG) record.Comment: Accepted version, to appear in Phys. Rev.
On kinks and other travelling-wave solutions of a modified sine-Gordon equation
We give an exhaustive, non-perturbative classification of exact
travelling-wave solutions of a perturbed sine-Gordon equation (on the real line
or on the circle) which is used to describe the Josephson effect in the theory
of superconductors and other remarkable physical phenomena. The perturbation of
the equation consists of a constant forcing term and a linear dissipative term.
On the real line candidate orbitally stable solutions with bounded energy
density are either the constant one, or of kink (i.e. soliton) type, or of
array-of-kinks type, or of "half-array-of-kinks" type. While the first three
have unperturbed analogs, the last type is essentially new. We also propose a
convergent method of successive approximations of the (anti)kink solution based
on a careful application of the fixed point theorem.Comment: Latex file, 25 pages, 4 figures. Final version to appear in
"Meccanica
Magnetic translation groups in an n-dimensional torus
A charged particle in a uniform magnetic field in a two-dimensional torus has
a discrete noncommutative translation symmetry instead of a continuous
commutative translation symmetry. We study topology and symmetry of a particle
in a magnetic field in a torus of arbitrary dimensions. The magnetic
translation group (MTG) is defined as a group of translations that leave the
gauge field invariant. We show that the MTG on an n-dimensional torus is
isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x
Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible
unitary representations of the MTG on a three-torus and apply the
representation theory to three examples. We shortly describe a representation
theory for a general n-torus. The MTG on an n-torus can be regarded as a
generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in
Journal of Mathematical Physic
Pseudoperiodic Words and a Question of Shevelev
We generalize the familiar notion of periodicity in sequences to a new kind
of pseudoperiodicity, and we prove some basic results about it. We revisit the
results of a 2012 paper of Shevelev and reprove his results in a simpler and
more unified manner, and provide a complete answer to one of his previously
unresolved questions. We consider finding words with specific pseudoperiod and
having the smallest possible critical exponent. Finally, we consider the
problem of determining whether a finite word is pseudoperiodic of a given size,
and show that it is NP-complete
Giant vortex state in perforated aluminum microsquares
We investigate the nucleation of superconductivity in a uniform perpendicular
magnetic field H in aluminum microsquares containing a few (2 and 4) submicron
holes (antidots). The normal/superconducting phase boundary T_c(H) of these
structures shows a quite different behavior in low and high fields. In the low
magnetic field regime fluxoid quantization around each antidot leads to
oscillations in T_c(H), expected from the specific sample geometry, and
reminiscent of the network behavior. In high magnetic fields, the T_c(H)
boundaries of the perforated and a reference non-perforated microsquare reveal
cusps at the same values of Phi/Phi_0 (where Phi is the applied flux threading
the total square area and Phi_0 is the superconducting flux quantum), while the
background on T_c(H) becomes quasi-linear, indicating that a giant vortex state
is established. The influence of the actual geometries on T_c(H) is analyzed in
the framework of the linearized Ginzburg-Landau theory.Comment: 14 pages, 6 PS figures, RevTex, accepted for publication in Phys.
Rev.
On the Pseudoperiodic Extension of u^l = v^m w^n
We investigate the solution set of the pseudoperiodic extension of the classical Lyndon and Sch"utzenberger word equations. Consider u_1 ... u_l = v_1 ... v_m w_1 ... w_n, where u_i is in {u, theta(u)} for all 1 = 12 or m,n >= 5 and either m and n are not both even or not all u_i\u27s are equal, all solutions are pseudoperiodic
Dynamics of projectable functions: Towards an atlas of wandering domains for a family of Newton maps
We present a one-parameter family of transcendental entire
functions with zeros, whose Newton's method yields wandering domains,
coexisting with the basins of the roots of . Wandering domains for
Newton maps of zero-free functions have been built before by, e.g., Buff and
R\"uckert based on the lifting method. This procedure is suited to our Newton
maps as members of the class of projectable functions (or maps of the
cylinder), i.e. transcendental meromorphic functions in the complex
plane that are semiconjugate, via the exponential, to some map , which
may have at most a countable number of essential singularities.
In this paper we make a systematic study of the general relation (dynamical
and otherwise) between and , and inspect the extension of the
logarithmic lifting method of periodic Fatou components to our context,
especially for those of finite-type. We apply these results to characterize
the entire functions with zeros whose Newton's method projects to some map
which is defined at both and . The family is the
simplest in this class, and its parameter space shows open sets of
-values in which the Newton map exhibits wandering or Baker domains,
in both cases regions of initial conditions where Newton's root-finding method
fails.Comment: 34 pages, 9 figure
- …