8,120 research outputs found
Probing the basins of attraction of a recurrent neural network
A recurrent neural network is considered that can retrieve a collection of
patterns, as well as slightly perturbed versions of this `pure' set of patterns
via fixed points of its dynamics. By replacing the set of dynamical
constraints, i.e., the fixed point equations, by an extended collection of
fixed-point-like equations, analytical expressions are found for the weights
w_ij(b) of the net, which depend on a certain parameter b. This so-called basin
parameter b is such that for b=0 there are, a priori, no perturbed patterns to
be recognized by the net. It is shown by a numerical study, via probing sets,
that a net constructed to recognize perturbed patterns, i.e., with values of
the connections w_ij(b) with b unequal zero, possesses larger basins of
attraction than a net made with the help of a pure set of patterns, i.e., with
connections w_ij(b=0). The mathematical results obtained can, in principle, be
realized by an actual, biological neural net.Comment: 17 pages, LaTeX, 2 figure
Tumbling of a rigid rod in a shear flow
The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity
limit. Following Burgers, the Master Equation is derived for the probability
distribution of the orientation of the rod. The equation contains one
dimensionless number, the Weissenberg number, which is the ratio of the shear
rate and the orientational diffusion constant. The equation is solved for the
stationary state distribution for arbitrary Weissenberg numbers, in particular
for the limit of high Weissenberg numbers. The stationary state gives an
interesting flow pattern for the orientation of the rod, showing the interplay
between flow due to the driving shear force and diffusion due to the random
thermal forces of the fluid. The average tumbling time and tumbling frequency
are calculated as a function of the Weissenberg number. A simple cross-over
function is proposed which covers the whole regime from small to large
Weissenberg numbers.Comment: 22 pages, 9 figure
Conserving Approximations in Time-Dependent Density Functional Theory
In the present work we propose a theory for obtaining successively better
approximations to the linear response functions of time-dependent density or
current-density functional theory. The new technique is based on the
variational approach to many-body perturbation theory (MBPT) as developed
during the sixties and later expanded by us in the mid nineties. Due to this
feature the resulting response functions obey a large number of conservation
laws such as particle and momentum conservation and sum rules. The quality of
the obtained results is governed by the physical processes built in through
MBPT but also by the choice of variational expressions. We here present several
conserving response functions of different sophistication to be used in the
calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio
Atomic quasi-Bragg diffraction in a magnetic field
We report on a new technique to split an atomic beam coherently with an
easily adjustable splitting angle. In our experiment metastable helium atoms in
the |{1s2s}^3S_1 M=1> state diffract from a polarization gradient light field
formed by counterpropagating \sigma^+ and \sigma^- polarized laser beams in the
presence of a homogeneous magnetic field. In the near-adiabatic regime, energy
conservation allows the resonant exchange between magnetic energy and kinetic
energy. As a consequence, symmetric diffraction of |M=0> or |M=-1> atoms in a
single order is achieved, where the order can be chosen freely by tuning the
magnetic field. We present experimental results up to 6th order diffraction (24
\hbar k momentum splitting, i.e., 2.21 m/s in transverse velocity) and present
a simple theoretical model that stresses the similarity with conventional Bragg
scattering. The resulting device constitutes a flexible, adjustable,
large-angle, three-way coherent atomic beam splitter with many potential
applications in atom optics and atom interferometry.Comment: 4 pages, 5 figure
Age, Metallicity, and the Distance to the Magellanic Clouds From Red Clump Stars
We show that the luminosity dependence of the red clump stars on age and
metallicity can cause a difference of up to < ~0.6 mag in the mean absolute I
magnitude of the red clump between different stellar populations. We show that
this effect may resolve the apparent ~0.4 mag discrepancy between red
clump-derived distance moduli to the Magellanic Clouds and those from, e.g.,
Cepheid variables. Taking into account the population effects on red clump
luminosity, we determine a distance modulus to the LMC of 18.36 +/- 0.17 mag,
and to the SMC of 18.82 +/- 0.20 mag. Our alternate red clump LMC distance is
consistent with the value (m-M){LMC} = 18.50 +/- 0.10 adopted by the HST
Cepheid Key Project. We briefly examine model predictions of red clump
luminosity, and find that variations in helium abundance and core mass could
bring the Clouds closer by some 0.10--0.15 mag, but not by the ~0.4 mag that
would result from setting the mean absolute I-magnitude of the Cloud red clumps
equal to the that of the Solar neighborhood red clump.Comment: Accepted for publication in The Astrophysical Journal Letters, AASTeX
4.0, 10 pages, 1 postscript figur
Spin-polarized stable phases of the 2-D electron fluid at finite temperatures
The Helmholtz free energy F of the interacting 2-D electron fluid is
calculated nonperturbatively using a mapping of the quantum fluid to a
classical Coulomb fluid [Phys. Rev. Letters, vol. 87, 206404 (2001)]. For
density parameters rs such that rs<~25, the fluid is unpolarized at all
temperatures t=T/EF where EF is the Fermi energy. For lower densities, the
system becomes fully spin polarized for t<~0.35, and partially polarized for
0.35<t< 2, depending on the density. At rs ~25-30, and t ~0.35, an ''ambispin''
phase where F is almost independent of the spin polarization is found. These
results support recent claims, based on quantum Monte Carlo results, for a
stable, fully spin-polarized fluid phase at T = 0 for rs larger than about
25-26.Comment: Latex manuscript (4-5 pages) and two postscript figures; see also
http://nrcphy1.phy.nrc.ca/ims/qp/chandre/chnc
Waiting and Residence Times of Brownian Interface Fluctuations
We report on the residence times of capillary waves above a given height
and on the typical waiting time in between such fluctuations. The measurements
were made on phase separated colloid-polymer systems by laser scanning confocal
microscopy. Due to the Brownian character of the process, the stochastics vary
with the chosen measurement interval . In experiments, the discrete
scanning times are a practical cutoff and we are able to measure the waiting
time as a function of this cutoff. The measurement interval dependence of the
observed waiting and residence times turns out to be solely determined by the
time dependent height-height correlation function . We find excellent
agreement with the theory presented here along with the experiments.Comment: 5 figure
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