1,316 research outputs found
On the non-convergence of the Wang-Landau algorithms with multiple random walkers
This paper discusses some convergence properties in the entropic sampling
Monte Carlo methods with multiple random walkers, particularly in the
Wang-Landau (WL) and algorithms. The classical algorithms are modified by
the use of independent random walkers in the energy landscape to calculate
the density of states (DOS). The Ising model is used to show the convergence
properties in the calculation of the DOS, as well as the critical temperature,
while the calculation of the number by multiple dimensional integration
is used in the continuum approximation. In each case, the error is obtained
separately for each walker at a fixed time, ; then, the average over
walkers is performed. It is observed that the error goes as .
However, if the number of walkers increases above a certain critical value
, the error reaches a constant value (i.e. it saturates). This occurs
for both algorithms; however, it is shown that for a given system, the
algorithm is more efficient and accurate than the similar version of the WL
algorithm. It follows that it makes no sense to increase the number of walkers
above a critical value , since it does not reduces the error in the
calculation. Therefore, the number of walkers does not guarantee convergence.Comment: 10 pages, 12 figures, Regular Articl
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Uncertainty quantification is a critical missing component in radio
interferometric imaging that will only become increasingly important as the
big-data era of radio interferometry emerges. Statistical sampling approaches
to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling,
can in principle recover the full posterior distribution of the image, from
which uncertainties can then be quantified. However, for massive data sizes,
like those anticipated from the Square Kilometre Array (SKA), it will be
difficult if not impossible to apply any MCMC technique due to its inherent
computational cost. We formulate Bayesian inference problems with
sparsity-promoting priors (motivated by compressive sensing), for which we
recover maximum a posteriori (MAP) point estimators of radio interferometric
images by convex optimisation. Exploiting recent developments in the theory of
probability concentration, we quantify uncertainties by post-processing the
recovered MAP estimate. Three strategies to quantify uncertainties are
developed: (i) highest posterior density credible regions; (ii) local credible
intervals (cf. error bars) for individual pixels and superpixels; and (iii)
hypothesis testing of image structure. These forms of uncertainty
quantification provide rich information for analysing radio interferometric
observations in a statistically robust manner. Our MAP-based methods are
approximately times faster computationally than state-of-the-art MCMC
methods and, in addition, support highly distributed and parallelised
algorithmic structures. For the first time, our MAP-based techniques provide a
means of quantifying uncertainties for radio interferometric imaging for
realistic data volumes and practical use, and scale to the emerging big-data
era of radio astronomy.Comment: 13 pages, 10 figures, see companion article in this arXiv listin
Optical polarimetric monitoring of the type II-plateau SN 2005af
Aims. Core-collapse supernovae may show significant polarization that implies
non-spherically symmetric explosions. We observed the type II-plateau SN 2005af
using optical polarimetry in order to verify whether any asphericity is present
in the supernova temporal evolution. Methods. We used the IAGPOL imaging
polarimeter to obtain optical linear polarization measurements in R (five
epochs) and V (one epoch) broadbands. Interstellar polarization was estimated
from the field stars in the CCD frames. The optical polarimetric monitoring
began around one month after the explosion and lasted ~30 days, between the
plateau and the early nebular phase. Results. The weighted mean observed
polarization in R band was [1.89 +/- 0.03]% at position angle (PA) 54 deg.
After foreground subtraction, the level of the average intrinsic polarization
for SN 2005af was ~0.5% with a slight enhancement during the plateau phase and
a decline at early nebular phase. A rotation in PA on a time scale of days was
also observed. The polarimetric evolution of SN 2005af in the observed epochs
is consistent with an overall asphericity of ~20% and an inclination of ~30
deg. Evidence for a more complex, evolving asphericity, possibly involving
clumps in the SN 2005af envelope, is found.Comment: 6 pages, 5 figures, to be published A&
Further Criteria for the Existence of Steady Line-Driven Winds
In Paper I, we showed that steady line-driven disk wind solutions can exist
by using "simple" models that mimic the disk environment. Here I extend the
concepts introduced in Paper I and discuss many details of the analysis of the
steady/unsteady nature of 1D line-driven winds. This work confirms the results
and conclusions of Paper I, and is thus consistent with the steady nature of
the 1D streamline line-driven disk wind models of Murray and collaborators and
the 2.5D line-driven disk wind models of Pereyra and collaborators. When
including gas pressures effects, as is routinely done in time-dependent
numerical models, I find that the spatial dependence of the nozzle function
continues to play a key role in determining the steady/unsteady nature of
supersonic line-driven wind solutions. I show here that the
existence/nonexistence of local wind solutions can be proved through the nozzle
function without integrating the equation of motion. This work sets a detailed
framework with which we will analyze, in a following paper, more realistic
models than the "simple" models of Paper I.Comment: 30 pages, 5 figures, accepted for publication by The Astrophysical
Journa
Dissociative Adsorption: A Solvable Model
A model of "hot"-dimer deposition in one dimension, introduced by Pereyra and
Albano, is modified to have an unbounded dissociation range. The resulting
dynamical equations are solved exactly. A related k-mer dissociation model is
also introduced and its solution obtained as a quadrature.Comment: TeX (plain
Self-similarity of single-channel transmission for electron transport in nanowires
We demonstrate that the single-channel transmission in the resonance
tunneling regime exhibits self-similarity as a function of the nanowire length
and the energy of incident electrons. The self-similarity is used to design the
nonlinear transformation of the nanowire length and energy which, on the basis
of known values of transmission for a certain region on the energy-length
plane, yields transmissions for other regions on this plane. Test calculations
with a one-dimensional tight-binding model illustrate the described
transformations. Density function theory based transport calculations of Na
atomic wires confirm the existence of the self-similarity in the transmission
Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
In this work we present a theoretical analysis of the convergence of the
Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced
years ago to calculate the density of states in statistical models. We study
the dynamical behavior of the error in the calculation of the density of
states.We conclude that the source of the saturation of the error is due to the
decreasing variations of the refinement parameter. To overcome this limitation,
we present an analytical treatment in which the refinement parameter is scaled
down as a power law instead of exponentially. An extension of the analysis to
the N-fold way variation of the method is also discussed.Comment: 7 pages, 5 figure
Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
In this communication, the convergence of the 1/t and Wang - Landau
algorithms in the calculation of multidimensional numerical integrals is
analyzed. Both simulation methods are applied to a wide variety of integrals
without restrictions in one, two and higher dimensions. The errors between the
exact and the calculated values of the integral are obtained and the efficiency
and accuracy of the methods are determined by their dynamical behavior. The
comparison between both methods and the simple sampling Monte Carlo method is
also reported. It is observed that the time dependence of the errors calculated
with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative
agreement with the simple sampling Monte Carlo method. It is also showed that
the error for the Wang - Landau algorithm saturates in time evidencing the
non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure
The influence of the “hot”-dimer adsorption mechanism on the kinetics of a monomer-dimer surface reaction
“Hot” dimers are molecules which after adsorption dissociate and each of the remaining “hot” monomers fly apart up to a maximum distance R from the original adsorption site. The influence of the “hot”-dimer adsorption mechanism on relevant aspects of the bimolecular catalyzed reaction of the type A − (1/2)B2(“hot”) → AB is studied by means of the Monte-Carlo simulation technique. The temporal evolution of both the reactant's coverages as well as the rate of AB-production is evaluated and discussed. Due to the enhanced probability of “hot” species for encounters with other adsorbed particles, the rate of AB-production becomes faster when increasing R. This behavior may be relevant in the dynamic of some catalyzed reactions such as for example the oxidation of carbon monoxide on transition metal surfaces, i.e. A≡CO, B2≡O2, and AB≡CO2. Also the sticking coefficient of “hot” dimers and the average distance traveled by the “hot” monomers are evaluated and discussed.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada
- …