8,553 research outputs found
Global stability analysis of birhythmicity in a self-sustained oscillator
We analyze global stability properties of birhythmicity in a self-sustained
system with random excitations. The model is a multi-limit cycles variation of
the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions
in brain waves. We show that the two frequencies are strongly influenced by the
nonlinear coefficients and . With a random excitation, such as
a Gaussian white noise, the attractor's global stability is measured by the
mean escape time from one limit-cycle. An effective activation energy
barrier is obtained by the slope of the linear part of the variation of the
escape time versus the inverse noise-intensity 1/D. We find that the
trapping barriers of the two frequencies can be very different, thus leaving
the system on the same attractor for an overwhelming time. However, we also
find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201
Violation of the Leggett-Garg Inequality in Neutrino Oscillations
The Leggett-Garg inequality, an analogue of Bell's inequality involving
correlations of measurements on a system at different times, stands as one of
the hallmark tests of quantum mechanics against classical predictions. The
phenomenon of neutrino oscillations should adhere to quantum-mechanical
predictions and provide an observable violation of the Leggett-Garg inequality.
We demonstrate how oscillation phenomena can be used to test for violations of
the classical bound by performing measurements on an ensemble of neutrinos at
distinct energies, as opposed to a single neutrino at distinct times. A study
of the MINOS experiment's data shows a greater than violation over
a distance of 735 km, representing the longest distance over which either the
Leggett-Garg inequality or Bell's inequality has been tested.Comment: Updated to match published version. 6 pages, 2 figure
Helicity, polarization, and Riemann-Silberstein vortices
Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime
where the complex form of a free electromagnetic field given by F=E+iB is null
(F.F=0), and they can indeed be interpreted as the collective history swept out
by moving vortex lines of the field. Formally, the nullity condition is similar
to the definition of "C-lines" associated with a monochromatic electric or
magnetic field, which are curves in space where the polarization ellipses
degenerate to circles. However, it was noted that RS vortices of monochromatic
fields generally oscillate at optical frequencies and are therefore
unobservable while electric and magnetic C-lines are steady. Here I show that
under the additional assumption of having definite helicity, RS vortices are
not only steady but they coincide with both sets of C-lines, electric and
magnetic. The two concepts therefore become one for waves of definite frequency
and helicity. Since the definition of RS vortices is relativistically invariant
while that of C-lines is not, it may be useful to regard the vortices as a
wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on
Singular Optics; minor changes from v.
Weak Lensing by High-Redshift Clusters of Galaxies - I: Cluster Mass Reconstruction
We present the results of a weak lensing survey of six high-redshift (z >
0.5), X-ray selected clusters of galaxies. We have obtained ultra-deep R-band
images of each cluster with the Keck Telescope, and have measured a weak
lensing signal from each cluster. From the background galaxy ellipticities we
create two-dimensional maps of the surface mass density of each cluster. We
find that the substructure seen in the mass reconstructions typically agree
well with substructure in both the cluster galaxy distributions and X-ray
images of the clusters. We also measure the one-dimensional radial profiles of
the lensing signals and fit these with both isothermal spheres and "universal"
CDM profiles. We find that the more massive clusters are less compact and not
as well fit by isothermal spheres as the less massive clusters, possibly
indicating that they are still in the process of collapse.Comment: 43 pages, 15 figures, uses aastex, submitted to ApJ 4 color plates
produced here as jpg's, larger versions of the jpgs can be found at
http://www.mpa-garching.mpg.de/~clow
Inflationary Reheating in Grand Unified Theories
Grand unified theories may display multiply interacting fields with strong
coupling dynamics. This poses two new problems: (1) What is the nature of
chaotic reheating after inflation, and (2) How is reheating sensitive to the
mass spectrum of these theories ? We answer these questions in two interesting
limiting cases and demonstrate an increased efficiency of reheating which
strongly enhances non-thermal topological defect formation, including monopoles
and domain walls. Nevertheless, the large fluctuations may resolve this
monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which
non-thermal destabilsation of discrete symmetries occurs at reheating.Comment: 4 pages, 5 ps figures - 1 colour, Revtex. Further (colour & 3-D)
figures available from http://www.sissa.it/~bassett/reheating/ . Matched to
version to appear in Phys. Rev. let
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