1,246 research outputs found
The Flux-Phase of the Half-Filled Band
The conjecture is verified that the optimum, energy minimizing magnetic flux
for a half-filled band of electrons hopping on a planar, bipartite graph is
per square plaquette. We require {\it only} that the graph has
periodicity in one direction and the result includes the hexagonal lattice
(with flux 0 per hexagon) as a special case. The theorem goes beyond previous
conjectures in several ways: (1) It does not assume, a-priori, that all
plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type
on-site interaction of any sign, as well as certain longer range interactions,
can be included; (3) The conclusion holds for positive temperature as well as
the ground state; (4) The results hold in dimensions if there is
periodicity in directions (e.g., the cubic lattice has the lowest energy
if there is flux in each square face).Comment: 9 pages, EHL14/Aug/9
Sequential design of computer experiments for the estimation of a probability of failure
This paper deals with the problem of estimating the volume of the excursion
set of a function above a given threshold,
under a probability measure on that is assumed to be known. In
the industrial world, this corresponds to the problem of estimating a
probability of failure of a system. When only an expensive-to-simulate model of
the system is available, the budget for simulations is usually severely limited
and therefore classical Monte Carlo methods ought to be avoided. One of the
main contributions of this article is to derive SUR (stepwise uncertainty
reduction) strategies from a Bayesian-theoretic formulation of the problem of
estimating a probability of failure. These sequential strategies use a Gaussian
process model of and aim at performing evaluations of as efficiently as
possible to infer the value of the probability of failure. We compare these
strategies to other strategies also based on a Gaussian process model for
estimating a probability of failure.Comment: This is an author-generated postprint version. The published version
is available at http://www.springerlink.co
Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares
The extreme ultraviolet portion of the solar spectrum contains a wealth of
diagnostic tools for probing the lower solar atmosphere in response to an
injection of energy, particularly during the impulsive phase of solar flares.
These include temperature and density sensitive line ratios, Doppler shifted
emission lines and nonthermal broadening, abundance measurements, differential
emission measure profiles, and continuum temperatures and energetics, among
others. In this paper I shall review some of the advances made in recent years
using these techniques, focusing primarily on studies that have utilized data
from Hinode/EIS and SDO/EVE, while also providing some historical background
and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the
Topical Issue on Solar and Stellar Flare
High-contrast imaging constraints on gas giant planet formation - The Herbig Ae/Be star opportunity
Planet formation studies are often focused on solar-type stars, implicitly
considering our Sun as reference point. This approach overlooks, however, that
Herbig Ae/Be stars are in some sense much better targets to study planet
formation processes empirically, with their disks generally being larger,
brighter and simply easier to observe across a large wavelength range. In
addition, massive gas giant planets have been found on wide orbits around early
type stars, triggering the question if these objects did indeed form there and,
if so, by what process. In the following I briefly review what we currently
know about the occurrence rate of planets around intermediate mass stars,
before discussing recent results from Herbig Ae/Be stars in the context of
planet formation. The main emphasis is put on spatially resolved polarized
light images of potentially planet forming disks and how these images - in
combination with other data - can be used to empirically constrain (parts of)
the planet formation process. Of particular interest are two objects, HD100546
and HD169142, where, in addition to intriguing morphological structures in the
disks, direct observational evidence for (very) young planets has been
reported. I conclude with an outlook, what further progress we can expect in
the very near future with the next generation of high-contrast imagers at 8-m
class telescopes and their synergies with ALMA.Comment: Accepted by Astrophysics and Space Science as invited short review in
special issue about Herbig Ae/Be stars; 12 pages incl. 5 figures, 2 tables
and reference
Parallel Low-Storage RungeâKutta Solvers for ODE Systems with Limited Access Distance
Fractal iso-contours of passive scalar in smooth random flows
We consider a passive scalar field under the action of pumping, diffusion and
advection by a smooth flow with a Lagrangian chaos. We present theoretical
arguments showing that scalar statistics is not conformal invariant and
formulate new effective semi-analytic algorithm to model the scalar turbulence.
We then carry massive numerics of passive scalar turbulence with the focus on
the statistics of nodal lines. The distribution of contours over sizes and
perimeters is shown to depend neither on the flow realization nor on the
resolution (diffusion) scale for scales exceeding . The scalar
isolines are found fractal/smooth at the scales larger/smaller than the pumping
scale . We characterize the statistics of bending of a long isoline by the
driving function of the L\"owner map, show that it behaves like diffusion with
the diffusivity independent of resolution yet, most surprisingly, dependent on
the velocity realization and the time of scalar evolution
Like-minded sources on Facebook are prevalent but not polarizing
Many critics raise concerns about the prevalence of âecho chambersâ on social media and their potential role in increasing political polarization. However, the lack of available data and the challenges of conducting large-scale field experiments have made it difficult to assess the scope of the problem 1,2. Here we present data from 2020 for the entire population of active adult Facebook users in the USA showing that content from âlike-mindedâ sources constitutes the majority of what people see on the platform, although political information and news represent only a small fraction of these exposures. To evaluate a potential response to concerns about the effects of echo chambers, we conducted a multi-wave field experiment on Facebook among 23,377 users for whom we reduced exposure to content from like-minded sources during the 2020 US presidential election by about one-third. We found that the intervention increased their exposure to content from cross-cutting sources and decreased exposure to uncivil language, but had no measurable effects on eight preregistered attitudinal measures such as affective polarization, ideological extremity, candidate evaluations and belief in false claims. These precisely estimated results suggest that although exposure to content from like-minded sources on social media is common, reducing its prevalence during the 2020 US presidential election did not correspondingly reduce polarization in beliefs or attitudes
Measurement of the Hadronic Photon Structure Function F_2^gamma at LEP2
The hadronic structure function of the photon F_2^gamma is measured as a
function of Bjorken x and of the factorisation scale Q^2 using data taken by
the OPAL detector at LEP. Previous OPAL measurements of the x dependence of
F_2^gamma are extended to an average Q^2 of 767 GeV^2. The Q^2 evolution of
F_2^gamma is studied for average Q^2 between 11.9 and 1051 GeV^2. As predicted
by QCD, the data show positive scaling violations in F_2^gamma. Several
parameterisations of F_2^gamma are in agreement with the measurements whereas
the quark-parton model prediction fails to describe the data.Comment: 4 pages, 2 figures, to appear in the proceedings of Photon 2001,
Ascona, Switzerlan
A measurement of the tau mass and the first CPT test with tau leptons
We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV
using tau pairs from Z0 decays. To test CPT invariance we compare the masses of
the positively and negatively charged tau leptons. The relative mass difference
is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.
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