183 research outputs found
Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic
hypergeometric matrix inverse with applications to bilateral basic
hypergeometric series. This matrix inversion result was directly extracted from
an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and
involves two infinite matrices which are not lower-triangular. The present
paper features three different multivariable generalizations of the above
result. These are extracted from Gustafson's A_r and C_r extensions and of the
author's recent A_r extension of Bailey's 6-psi-6 summation formula. By
combining these new multidimensional matrix inverses with A_r and D_r
extensions of Jackson's 8-phi-7 summation theorem three balanced
very-well-poised 8-psi-8 summation theorems associated with the root systems
A_r and C_r are derived.Comment: 24 page
A new multivariable 6-psi-6 summation formula
By multidimensional matrix inversion, combined with an A_r extension of
Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7
summation is derived. By a polynomial argument this 8-phi-7 summation is
transformed to another multivariable 8-phi-7 summation which, by taking a
suitable limit, is reduced to a new multivariable extension of the
nonterminating 6-phi-5 summation. The latter is then extended, by analytic
continuation, to a new multivariable extension of Bailey's very-well-poised
6-psi-6 summation formula.Comment: 16 page
Universality and Critical Phenomena in String Defect Statistics
The idea of biased symmetries to avoid or alleviate cosmological problems
caused by the appearance of some topological defects is familiar in the context
of domain walls, where the defect statistics lend themselves naturally to a
percolation theory description, and for cosmic strings, where the proportion of
infinite strings can be varied or disappear entirely depending on the bias in
the symmetry. In this paper we measure the initial configurational statistics
of a network of string defects after a symmetry-breaking phase transition with
initial bias in the symmetry of the ground state. Using an improved algorithm,
which is useful for a more general class of self-interacting walks on an
infinite lattice, we extend the work in \cite{MHKS} to better statistics and a
different ground state manifold, namely , and explore various different
discretisations. Within the statistical errors, the critical exponents of the
Hagedorn transition are found to be quite possibly universal and identical to
the critical exponents of three-dimensional bond or site percolation. This
improves our understanding of the percolation theory description of defect
statistics after a biased phase transition, as proposed in \cite{MHKS}. We also
find strong evidence that the existence of infinite strings in the Vachaspati
Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all
discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included.
also available on
http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g
New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation
(abridged) The heating mechanism at high densities during M dwarf flares is
poorly understood. Spectra of M dwarf flares in the optical and
near-ultraviolet wavelength regimes have revealed three continuum components
during the impulsive phase: 1) an energetically dominant blackbody component
with a color temperature of T 10,000 K in the blue-optical, 2) a smaller
amount of Balmer continuum emission in the near-ultraviolet at lambda 3646
Angstroms and 3) an apparent pseudo-continuum of blended high-order Balmer
lines. These properties are not reproduced by models that employ a typical
"solar-type" flare heating level in nonthermal electrons, and therefore our
understanding of these spectra is limited to a phenomenological interpretation.
We present a new 1D radiative-hydrodynamic model of an M dwarf flare from
precipitating nonthermal electrons with a large energy flux of erg
cm s. The simulation produces bright continuum emission from a
dense, hot chromospheric condensation. For the first time, the observed color
temperature and Balmer jump ratio are produced self-consistently in a
radiative-hydrodynamic flare model. We find that a T 10,000 K
blackbody-like continuum component and a small Balmer jump ratio result from
optically thick Balmer and Paschen recombination radiation, and thus the
properties of the flux spectrum are caused by blue light escaping over a larger
physical depth range compared to red and near-ultraviolet light. To model the
near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer
lines, we include the extra Balmer continuum opacity from Landau-Zener
transitions that result from merged, high order energy levels of hydrogen in a
dense, partially ionized atmosphere. This reveals a new diagnostic of ambient
charge density in the densest regions of the atmosphere that are heated during
dMe and solar flares.Comment: 50 pages, 2 tables, 13 figures. Accepted for publication in the Solar
Physics Topical Issue, "Solar and Stellar Flares". Version 2 (June 22, 2015):
updated to include comments by Guest Editor. The final publication is
available at Springer via http://dx.doi.org/10.1007/s11207-015-0708-
Gravitational excitons from extra dimensions
Inhomogeneous multidimensional cosmological models with a higher dimensional
space-time manifold are investigated under dimensional reduction. In the
Einstein conformal frame, small excitations of the scale factors of the
internal spaces near minima of an effective potential have a form of massive
scalar fields in the external space-time. Parameters of models which ensure
minima of the effective potentials are obtained for particular cases and masses
of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20
pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97
High-Energy Aspects of Solar Flares: Overview of the Volume
In this introductory chapter, we provide a brief summary of the successes and
remaining challenges in understanding the solar flare phenomenon and its
attendant implications for particle acceleration mechanisms in astrophysical
plasmas. We also provide a brief overview of the contents of the other chapters
in this volume, with particular reference to the well-observed flare of 2002
July 23Comment: This is the introductory article for a monograph on the physics of
solar flares, inspired by RHESSI observations. The individual articles are to
appear in Space Science Reviews (2011
Low-energy cutoffs in electron spectra of solar flares: statistical survey
The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data base
(February 2002 -- May 2006) has been searched to find solar flares with weak
thermal components and flat photon spectra. Using a regularised inversion
technique, we determine the mean electron flux distribution from count spectra
of a selection of events with flat photon spectra in the 15--20 keV energy
range. Such spectral behaviour is expected for photon spectra either affected
by photospheric albedo or produced by electron spectra with an absence of
electrons in a given energy range, e.g. a low-energy cutoff in the mean
electron spectra of non-themal particles. We have found 18 cases which exhibit
a statistically significant local minimum (a dip) in the range of 10--20 keV.
The positions and spectral indices of events with low-energy cutoff indicate
that such features are likely to be the result of photospheric albedo. It is
shown that if the isotropic albedo correction was applied, all low-energy
cutoffs in the mean electron spectrum were removed and hence the low energy
cutoffs in the mean electron spectrum of solar flares above 12 keV cannot
be viewed as real features in the electron spectrum. If low-energy cutoffs
exist in the mean electron spectra, the energy of low energy cutoffs should be
less than 12 keV.Comment: 9 pages, 5 figures, submitted to Solar Physic
Exploring the Possible Impact of Unbalanced Open-Label Drop-In of Glucose-Lowering Medications on EXSCEL Outcomes
Background: EXSCEL (Exenatide Study of Cardiovascular Event Lowering) assessed the impact of once-weekly exenatide 2 mg versus placebo in patients with type 2 diabetes mellitus, while aiming for glycemic equipoise. Consequently, greater drop-in of open-label glucose-lowering medications occurred in the placebo group. Accordingly, we explored the potential effects of their unbalanced use on major adverse cardiovascular events (MACE), defined as cardiovascular death, nonfatal myocardial infarction or nonfatal stroke, and all-cause mortality (ACM), given that some of these agents are cardioprotective. Methods: Cox hazard models were performed by randomized treatment for drug classes where >5% open-label drop-in glucose-lowering medication occurred, and for glucagon-like peptide-1 receptor agonists (GLP-1 RAs; 3.0%) using three methodologies: drop-in visit right censoring, inverse probability for treatment weighting (IPTW), and applying drug class risk reductions. Results: Baseline glucose-lowering medications for the 14 752 EXSCEL participants (73.1% with previous cardiovascular disease) did not differ between treatment groups. During median 3.2 years follow-up, open-label drop-in occurred in 33.4% of participants, more frequently with placebo than exenatide (38.1% versus 28.8%), with metformin (6.1% versus 4.9%), sulfonylurea (8.7% versus 6.9%), dipeptidyl peptidase-4 inhibitors (10.6% versus 7.5%), SGLT-2i (10.3% versus 8.1%), GLP-1 RA (3.4% versus 2.4%), and insulin (13.8% versus 9.4%). The MACE effect size was not altered meaningfully by right censoring, but the favorable HR for exenatide became nominally significant in the sulfonylurea and any glucose-lowering medication groups, while the ACM HR and p-values were essentially unchanged. IPTW decreased the MACE HR from 0.91 (P=0.061) to 0.85 (P=0.008) and the ACM HR from 0.86 (P=0.016) to 0.81 (P=0.012). Application of literature-derived risk reductions showed no meaningful changes in MACE or ACM HRs or P values, although simulations of substantially greater use of drop-in cardioprotective glucose-lowering agents demonstrated blunting of signal detection. Conclusions: EXSCEL-observed HRs for MACE and ACM remained robust after right censoring or application of literature-derived risk reductions, but the exenatide versus placebo MACE effect size and statistical significance were increased by IPTW. Effects of open-label drop-in cardioprotective medications need to be considered carefully when designing, conducting, and analyzing cardiovascular outcome trials of glucose-lowering agents under the premise of glycemic equipoise. Registration: URL: https://www.clinicaltrials.gov; Unique identifier: NCT01144338
Recent Advances in Understanding Particle Acceleration Processes in Solar Flares
We review basic theoretical concepts in particle acceleration, with
particular emphasis on processes likely to occur in regions of magnetic
reconnection. Several new developments are discussed, including detailed
studies of reconnection in three-dimensional magnetic field configurations
(e.g., current sheets, collapsing traps, separatrix regions) and stochastic
acceleration in a turbulent environment. Fluid, test-particle, and
particle-in-cell approaches are used and results compared. While these studies
show considerable promise in accounting for the various observational
manifestations of solar flares, they are limited by a number of factors, mostly
relating to available computational power. Not the least of these issues is the
need to explicitly incorporate the electrodynamic feedback of the accelerated
particles themselves on the environment in which they are accelerated. A brief
prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011
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