19,203 research outputs found
A method to construct refracting profiles
We propose an original method for determining suitable refracting profiles
between two media to solve two related problems: to produce a given wave front
from a single point source after refraction at the refracting profile, and to
focus a given wave front in a fixed point. These profiles are obtained as
envelopes of specific families of Cartesian ovals. We study the singularities
of these profiles and give a method to construct them from the data of the
associated caustic.Comment: 12 pages, 5 figure
Degree of randomness: numerical experiments for astrophysical signals
Astrophysical and cosmological signals such as the cosmic microwave
background radiation, as observed, typically contain contributions of different
components, and their statistical properties can be used to distinguish one
from the other. A method developed originally by Kolmogorov is involved for the
study of astrophysical signals of randomness of various degrees. Numerical
performed experiments based on the universality of Kolmogorov distribution and
using a single scaling of the ratio of stochastic to regular components, reveal
basic features in the behavior of generated signals also in terms of a critical
value for that ratio, thus enable the application of this technique for various
observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio
Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems
We study a particular return map for a class of low dimensional chaotic
models called Kolmogorov Lorenz systems, which received an elegant general
Hamiltonian description and includes also the famous Lorenz63 case, from the
viewpoint of energy and Casimir balance. In particular it is considered in
detail a subclass of these models, precisely those obtained from the Lorenz63
by a small perturbation on the standard parameters, which includes for example
the forced Lorenz case in Ref.[6]. The paper is divided into two parts. In the
first part the extremes of the mentioned state functions are considered, which
define an invariant manifold, used to construct an appropriate Poincare surface
for our return map. From the experimental observation of the simple orbital
motion around the two unstable fixed points, together with the circumstance
that these orbits are classified by their energy or Casimir maximum, we
construct a conceptually simple skeletal dynamics valid within our sub class,
reproducing quite well the Lorenz map for Casimir. This energetic approach
sheds some light on the physical mechanism underlying regime transitions. The
second part of the paper is devoted to the investigation of a new type of
maximum energy based long term predictions, by which the knowledge of a
particular maximum energy shell amounts to the knowledge of the future
(qualitative) behaviour of the system. It is shown that, in this respect, a
local analysis of predictability is not appropriate for a complete
characterization of this behaviour. A perspective on the possible extensions of
this type of predictability analysis to more realistic cases in (geo)fluid
dynamics is discussed at the end of the paper.Comment: 21 pages, 14 figure
Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds
The obstruction to the existence of global action-angle coordinates of
Abelian and noncommutative (non-Abelian) completely integrable systems with
compact invariant submanifolds has been studied. We extend this analysis to the
case of noncompact invariant submanifolds.Comment: 13 pages, to be published in J. Math. Phys. (2007
First images on the sky from a hyper telescope
We show star images obtained with a miniature ``densified pupil imaging
interferometer'' also called a hyper-telescope. The formation of such images
violates a ``golden rule of imaging interferometers'' which appeared to forbid
the use of interferometric arrangements differing from a Fizeau interferometer.
These produce useless images when the sub-apertures spacing is much wider than
their size, owing to diffraction through the sub-apertures. The hyper-telescope
arrangement solves these problems opening the way towards multi-kilometer
imaging arrays in space. We experimentally obtain an intensity gain of 24 +- 3X
when a densified-pupil interferometer is compared to an equivalent Fizeau-type
interferometer and show images of the double star alpha Gem. The initial
results presented confirm the possibility of directly obtaining high resolution
and high dynamic range images in the recombined focal plane of a large
interferometer if enough elements are used.Comment: 6 pages, LaTeX, standard A&A macros + BibTeX macros. Accepted for
publication in Astronomy and Astrophysics Supplement
Demonstration of an inductively coupled ring trap for cold atoms
We report the first demonstration of an inductively coupled magnetic ring trap for cold atoms. A uniform, ac magnetic field is used to induce current in a copper ring, which creates an opposing magnetic field that is time-averaged to produce a smooth cylindrically symmetric ring trap of radius 5 mm. We use a laser-cooled atomic sample to characterize the loading efficiency and adiabaticity of the magnetic potential, achieving a vacuum-limited lifetime in the trap. This technique is suitable for creating scalable toroidal waveguides for applications in matter-wave interferometry, offering long interaction times and large enclosed areas
Investigation of double beta decay with the NEMO-3 detector
The double beta decay experiment NEMO~3 has been taking data since February
2003. The aim of this experiment is to search for neutrinoless
() decay and investigate two neutrino double beta decay in
seven different isotopically enriched samples (Mo, Se,
Ca, Zr, Cd, Te and Nd). After analysis of
the data corresponding to 3.75 y, no evidence for decay in the
Mo and Se samples was found. The half-life limits at the 90%
C.L. are y and y, respectively.
Additionally for decay the following limits at the 90% C.L.
were obtained, y for Ca, y
for Zr and y for Nd. The
decay half-life values were precisely measured for all investigated isotopes.Comment: 12 pages, 4 figures, 5 tables; talk at conference on "Fundamental
Interactions Physics" (ITEP, Moscow, November 23-27, 2009
On products of skew rotations
Let , be two time-independent Hamiltonians with one
degree of freedom and , be the one-parametric groups of
shifts along the orbits of Hamiltonian systems generated by , . In
some problems of population genetics there appear the transformations of the
plane having the form under some
conditions on , . We study in this paper asymptotical properties of
trajectories of .Comment: 13 pages, 10 figure
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