106,779 research outputs found
Low Mach number flows, and combustion
We prove uniform existence results for the full Navier-Stokes equations for
time intervals which are independent of the Mach number, the Reynolds number
and the P\'eclet number. We consider general equations of state and we give an
application for the low Mach number limit combustion problem introduced by
Majda
Regularized Optimal Transport and the Rot Mover's Distance
This paper presents a unified framework for smooth convex regularization of
discrete optimal transport problems. In this context, the regularized optimal
transport turns out to be equivalent to a matrix nearness problem with respect
to Bregman divergences. Our framework thus naturally generalizes a previously
proposed regularization based on the Boltzmann-Shannon entropy related to the
Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We
call the regularized optimal transport distance the rot mover's distance in
reference to the classical earth mover's distance. We develop two generic
schemes that we respectively call the alternate scaling algorithm and the
non-negative alternate scaling algorithm, to compute efficiently the
regularized optimal plans depending on whether the domain of the regularizer
lies within the non-negative orthant or not. These schemes are based on
Dykstra's algorithm with alternate Bregman projections, and further exploit the
Newton-Raphson method when applied to separable divergences. We enhance the
separable case with a sparse extension to deal with high data dimensions. We
also instantiate our proposed framework and discuss the inherent specificities
for well-known regularizers and statistical divergences in the machine learning
and information geometry communities. Finally, we demonstrate the merits of our
methods with experiments using synthetic data to illustrate the effect of
different regularizers and penalties on the solutions, as well as real-world
data for a pattern recognition application to audio scene classification
The exponential-logarithmic equivalence classes of surreal numbers
In his monograph, H. Gonshor showed that Conway's real closed field of
surreal numbers carries an exponential and logarithmic map. Subsequently, L.
van den Dries and P. Ehrlich showed that it is a model of the elementary theory
of the field of real numbers with the exponential function. In this paper, we
give a complete description of the exponential equivalence classes in the
spirit of the classical Archimedean and multiplicative equivalence classes.
This description is made in terms of a recursive formula as well as a sign
sequence formula for the family of representatives of minimal length of these
exponential classes
A new activity phase of the blazar 3C 454.3. Multifrequency observations by the WEBT and XMM-Newton in 2007-2008
We present and analyse the WEBT multifrequency observations of 3C 454.3 in
the 2007-2008 observing season, including XMM-Newton observations and near-IR
spectroscopic monitoring, and compare the recent emission behaviour with the
past one. In the optical band we observed a multi-peak outburst in July-August
2007, and other faster events in November 2007 - February 2008. During these
outburst phases, several episodes of intranight variability were detected. A mm
outburst was observed starting from mid 2007, whose rising phase was
contemporaneous to the optical brightening. A slower flux increase also
affected the higher radio frequencies, the flux enhancement disappearing below
8 GHz. The analysis of the optical-radio correlation and time delays, as well
as the behaviour of the mm light curve, confirm our previous predictions,
suggesting that changes in the jet orientation likely occurred in the last few
years. The historical multiwavelength behaviour indicates that a significant
variation in the viewing angle may have happened around year 2000. Colour
analysis reveals a complex spectral behaviour, which is due to the interplay of
different emission components. All the near-IR spectra show a prominent Halpha
emission line, whose flux appears nearly constant. The analysis of the
XMM-Newton data indicates a correlation between the UV excess and the
soft-X-ray excess, which may represent the head and the tail of the big blue
bump, respectively. The X-ray flux correlates with the optical flux, suggesting
that in the inverse-Compton process either the seed photons are synchrotron
photons at IR-optical frequencies or the relativistic electrons are those that
produce the optical synchrotron emission. The X-ray radiation would thus be
produced in the jet region from where the IR-optical emission comes.Comment: 10 pages, 12 figures (7 included in the text, 5 in GIF format),
accepted for publication in A&
What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}
We perform an analysis of a binding energy difference called delta
V_{pn}(N,Z) =- 1/4(E(Z,N)-E(Z,N-2)-E(Z-2,N)+ E(Z-2,N-2) in the framework of a
realistic nuclear model. Using the angular-momentum and particle-number
projected generator coordinate method and the Skyrme interaction SLy4, we
analyze the contribution brought to delta V_{pn} by static deformation and
dynamic fluctuations around the mean-field ground state. Our method gives a
good overall description of delta V_{pn} throughout the chart of nuclei with
the exception of the anomaly related to the Wigner energy along the N=Z line.
The main conclusions of our analysis are that (i) the structures seen in the
systematics of delta V_{pn} throughout the chart of nuclei can be easily
explained combining a smooth background related to the symmetry energy and
correlation energies due to deformation and collective fluctuations; (ii) the
characteristic pattern of delta V_{pn} around a doubly-magic nucleus is a
trivial consequence of the asymmetric definition of delta V_{pn}, and not due
to a the different structure of these nuclei; (iii) delta V_{pn} does not
provide a very reliable indicator for structural changes; (iv) \delta V_{pn}
does not provide a reliable measure of the proton-neutron interaction in the
nuclear EDF, neither of that between the last filled orbits, nor of the one
summed over all orbits; (v) delta V_{pn} does not provide a conclusive
benchmark for nuclear EDF methods that is superior or complementary to other
mass filters such as two-nucleon separation energies or Q values.Comment: 19 pages and 12 figure
Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
We discuss the origin of pathological behaviors that have been recently
identified in particle-number-restoration calculations performed within the
nuclear energy density functional framework. A regularization method that
removes the problematic terms from the multi-reference energy density
functional and which applies (i) to any symmetry restoration- and/or
generator-coordinate-method-based configuration mixing calculation and (ii) to
energy density functionals depending only on integer powers of the density
matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]
and implemented for particle-number restoration calculations in [M. Bender, T.
Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the
viability of non-integer powers of the density matrices in the nuclear energy
density functional. Our discussion builds upon the analysis already carried out
in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)].
First, we propose to reduce the pathological nature of terms depending on a
non-integer power of the density matrices by regularizing the fraction that
relates to the integer part of the exponent using the method proposed in [D.
Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious
features brought about by the remaining fractional power. Finally, we conclude
that non-integer powers of the density matrices are not viable and should be
avoided in the first place when constructing nuclear energy density functionals
that are eventually meant to be used in multi-reference calculations.Comment: 17 pages, 12 figures, accepted for publication in PR
Planar pyrochlore: a strong-coupling analysis
Recent investigations of the two-dimensional spin-1/2 checkerboard lattice
favor a valence bond crystal with long range quadrumer order [J.-B. Fouet et
al., preprint cond-mat/0108070]. Starting from the limit of isolated
quadrumers, we perform a complementary analysis of the evolution of the
spectrum as a function of the inter quadrumer coupling j using both, exact
diagonalization (ED) and series expansion (SE) by continuous unitary
transformation. We compute (i) the ground state energy, (ii) the elementary
triplet excitations, (iii) singlet excitations on finite systems and find very
good agreement between SE and ED. In the thermodynamic limit we find a ground
state energy substantially lower than documented in the literature. The
elementary triplet excitation is shown to be gapped and almost dispersionless,
whereas the singlet sector contains strongly dispersive modes. Evidence is
presented for the low energy singlet excitations in the spin gap in the
vicinity of j=1 to result from a large downward renormalization of local
high-energy states.Comment: 4 pages REVTeX4 including 3 figures: published version (minor
changes
Peculiar properties of the Josephson junction at the transition from 0 to Pi state
It is demonstrated that in the diffusive
superconductor-ferromagnet-superconductor (S/F/S) junctions the current-phase
relation is practically sinusoidal everywhere except in a narrow region near
the 0-Pi transition. In this region the second harmonic dominates the scenario
of the 0-Pi transition. We predict a first order transition for the S/F/S
junctions with a homogeneous F barrier. However, in real junctions a small
modulation of the thickness of the barrier may favor the continious 0-Pi
transition and the realisation of the Josephson junction with an arbitrary
ground state phase difference. The performed calculations of the second
harmonic amplitude provide a natural explanation of the recent contradictory
results on the second harmonic measurements.Comment: Corrected version. To be published in PRB Rapid Communication
Isotropic Huygens dipoles and multipoles with colloidal particles
Huygens sources are elements that scatter light in the forward direction as
used in the Huygens-Fresnel principle. They have remained fictitious until
recently where experimental systems have been fabricated. In this letter, we
propose isotropic meta-atoms that act as Huygens sources. Using clusters of
plasmonic or dielectric colloidal particles, Huygens dipoles that resonate at
visible frequencies can be achieved with scattering cross-sections as high as 5
times the geometric cross-section of the particle surpassing anything
achievable with a hypothetical simple spherical particle. Examples are given
that predict extremely broadband scattering in the forward direction over a
1000 nm wavelength range at optical frequencies. These systems are important to
the fields of nanoantennas, metamaterials and wave physics in general as well
as any application that requires local control over the radiation properties of
a system as in solar cells or bio-sensing
First principles investigation of the electronic structure of La2MnNiO6: A room-temperature insulating ferromagnet
Using first principles calculations within DFT based on the full potential
APW+lo method, we calculated the electronic and magnetic structures for the
ferromagnetic and antiferromagnetic states of La2MnNiO6 and analyzed the site
projected density of states and electronic band structures. Our calculations
show that the ground state of La2MnNiO6 is ferromagnetic insulating with the
magnetization in agreement with Hund's first rule and experimental findings.Comment: 10 pages, 3 figure
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