2,850 research outputs found
Jensen-Feynman approach to the statistics of interacting electrons
Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a
variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov)
inequality in order to optimize the accounting for two-particle interactions in
the calculation of canonical partition functions. It consists in a
decomposition into a reference electron system and a first-order correction.
The procedure appears to be very efficient in order to evaluate the free energy
and the orbital populations. In this work, we present numerical applications of
the method and propose to extend it using a reference energy which includes the
interaction between two electrons inside a given orbital. This is possible
thanks to our efficient recursion relation for the calculation of partition
functions. We also show that a linear reference energy, however, is usually
sufficient to achieve a good precision and that the most promising way to
improve the approach of Faussurier et al. is to apply Jensen's inequality to a
more convenient convex function.Comment: submitted to Physical Review
Photometry of supernovae in an image series : methods and application to the Supernova Legacy Survey (SNLS)
We present a technique to measure lightcurves of time-variable point sources
on a spatially structured background from imaging data. The technique was
developed to measure light curves of SNLS supernovae in order to infer their
distances. This photometry technique performs simultaneous PSF photometry at
the same sky position on an image series. We describe two implementations of
the method: one that resamples images before measuring fluxes, and one which
does not. In both instances, we sketch the key algorithms involved and present
the validation using semi-artificial sources introduced in real images in order
to assess the accuracy of the supernova flux measurements relative to that of
surrounding stars. We describe the methods required to anchor these PSF fluxes
to calibrated aperture catalogs, in order to derive SN magnitudes. We find a
marginally significant bias of 2 mmag of the after-resampling method, and no
bias at the mmag accuracy for the non-resampling method. Given surrounding star
magnitudes, we determine the systematic uncertainty of SN magnitudes to be less
than 1.5 mmag, which represents about one third of the current photometric
calibration uncertainty affecting SN measurements. The SN photometry delivers
several by-products: bright star PSF flux mea- surements which have a
repeatability of about 0.6%, as for aperture measurements; we measure relative
astrometric positions with a noise floor of 2.4 mas for a single-image bright
star measurement; we show that in all bands of the MegaCam instrument, stars
exhibit a profile linearly broadening with flux by about 0.5% over the whole
brightness range.Comment: Accepted for publication in A&A. 20 page
Supernova search at intermediate z. I. Spectroscopic analysis
We study 8 supernovae discovered as part of the International Time Programme
(ITP) project ``Omega and Lambda from Supernovae and the Physics of Supernova
Explosions'' at the European Northern Observatory (ENO). The goal of the
project is to increase the sample of intermediate redshift (0.1<z<0.4) SNe Ia
for testing properties of SNe Ia along z and for enlarging the sample in the
Hubble diagram up to large z.Comment: 2 pages, 2 figures, 1 table, to appear in ``1604-2004: Supernovae as
Cosmological Lighthouses'', (extended text upon request
Numerical Modelling of Debris Bed Water Quenching
Acknowledgements The authors would like to thank the EPSRC MEMPHIS multi-phase programme grant, the EPSRC Computational modelling for advanced nuclear power plants project, the EU FP7 projects THINS and GoFastR and ExxonMobil for helping to fund this work.Peer reviewedPublisher PD
An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion
Using an autoencoder for dimensionality reduction, this paper presents a
novel projection-based reduced-order model for eigenvalue problems.
Reduced-order modelling relies on finding suitable basis functions which define
a low-dimensional space in which a high-dimensional system is approximated.
Proper orthogonal decomposition (POD) and singular value decomposition (SVD)
are often used for this purpose and yield an optimal linear subspace.
Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more
efficiently, features or patterns in the high-fidelity model results.
Reduced-order models based on an autoencoder and a novel hybrid
SVD-autoencoder are developed. These methods are compared with the standard
POD-Galerkin approach and are applied to two test cases taken from the field of
nuclear reactor physics.Comment: 35 pages, 33 figure
Structure of 12Be: intruder d-wave strength at N=8
The breaking of the N=8 shell-model magic number in the 12Be ground state has
been determined to include significant occupancy of the intruder d-wave
orbital. This is in marked contrast with all other N=8 isotones, both more and
less exotic than 12Be. The occupancies of the 0 hbar omega neutron p1/2-orbital
and the 1 hbar omega, neutron d5/2 intruder orbital were deduced from a
measurement of neutron removal from a high-energy 12Be beam leading to bound
and unbound states in 11Be.Comment: 5 pages, 2 figure
AIR multigrid with GMRES polynomials (AIRG) and additive preconditioners for Boltzmann transport
We develop a reduction multigrid based on approximate ideal restriction (AIR)
for use with asymmetric linear systems. We use fixed-order GMRES polynomials to
approximate and we use these polynomials to build grid
transfer operators and perform F-point smoothing. We can also apply a fixed
sparsity to these polynomials to prevent fill-in.
When applied in the streaming limit of the Boltzmann Transport Equation
(BTE), with a P angular discretisation and a low-memory spatial
discretisation on unstructured grids, this "AIRG" multigrid used as a
preconditioner to an outer GMRES iteration outperforms the lAIR implementation
in hypre, with two to three times less work. AIRG is very close to scalable; we
find either fixed work in the solve with slight growth in the setup, or slight
growth in the solve with fixed work in the setup when using fixed sparsity.
Using fixed sparsity we see less than 20% growth in the work of the solve with
either 6 levels of spatial refinement or 3 levels of angular refinement. In
problems with scattering AIRG performs as well as lAIR, but using the full
matrix with scattering is not scalable.
We then present an iterative method designed for use with scattering which
uses the additive combination of two fixed-sparsity preconditioners applied to
the angular flux; a single AIRG V-cycle on the streaming/removal operator and a
DSA method with a CG FEM. We find with space or angle refinement our iterative
method is very close to scalable with fixed memory use
Two superluminous supernovae from the early universe discovered by the Supernova Legacy Survey
We present spectra and lightcurves of SNLS 06D4eu and SNLS 07D2bv, two
hydrogen-free superluminous supernovae discovered by the Supernova Legacy
Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with
a spectrum, at M_U = -22.7 is one of the most luminous SNe ever observed, and
gives a rare glimpse into the restframe ultraviolet where these supernovae put
out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but
based on the supernova spectrum, we estimate it to be at z ~ 1.5. Both
supernovae have similar observer-frame griz lightcurves, which map to restframe
lightcurves in the U-band and UV, rising in ~ 20 restframe days or longer, and
declining over a similar timescale. The lightcurves peak in the shortest
wavelengths first, consistent with an expanding blackbody starting near 15,000
K and steadily declining in temperature. We compare the spectra to theoretical
models, and identify lines of C II, C III, Fe III, and Mg II in the spectrum of
SNLS 06D4eu and SCP 06F6, and find that they are consistent with an expanding
explosion of only a few solar masses of carbon, oxygen, and other trace metals.
Thus the progenitors appear to be related to those suspected for SNe Ic. A high
kinetic energy, 10^52 ergs, is also favored. Normal mechanisms of powering
core- collapse or thermonuclear supernovae do not seem to work for these
supernovae. We consider models powered by 56Ni decay and interaction with
circumstellar material, but find that the creation and spin-down of a magnetar
with a period of 2ms, magnetic field of 2 x 10^14 Gauss, and a 3 solar mass
progenitor provides the best fit to the data.Comment: ApJ, accepted, 43 pages, 15 figure
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