891 research outputs found
Superposition Formulas for Darboux Integrable Exterior Differential Systems
In this paper we present a far-reaching generalization of E. Vessiot's
analysis of the Darboux integrable partial differential equations in one
dependent and two independent variables. Our approach provides new insights
into this classical method, uncovers the fundamental geometric invariants of
Darboux integrable systems, and provides for systematic, algorithmic
integration of such systems. This work is formulated within the general
framework of Pfaffian exterior differential systems and, as such, has
applications well beyond those currently found in the literature. In
particular, our integration method is applicable to systems of hyperbolic PDE
such as the Toda lattice equations, 2 dimensional wave maps and systems of
overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major
improvements to other
Understanding the magnetic resonance spectrum of nitrogen vacancy centers in an ensemble of randomly-oriented nanodiamonds
Nanodiamonds containing nitrogen vacancy (NV-) centers show promise for a
number of emerging applications including targeted in vivo imaging and
generating nuclear spin hyperpolarization for enhanced NMR spectroscopy and
imaging. Here, we develop a detailed understanding of the magnetic resonance
behavior of NV- centers in an ensemble of nanodiamonds with random crystal
orientations. Two-dimensional optically detected magnetic resonance
spectroscopy reveals the distribution of energy levels, spin populations, and
transition probabilities that give rise to a complex spectrum. We identify
overtone transitions that are inherently insensitive to crystal orientation and
give well-defined transition frequencies that access the entire nanodiamond
ensemble. These transitions may be harnessed for high-resolution imaging and
generation of nuclear spin hyperpolarization. The data are well described by
numerical simulations from the zero- to high-field regimes, including the
intermediate regime of maximum complexity. We evaluate the prospects of
nanodiamond ensembles specifically for nuclear hyperpolarization and show that
frequency-swept dynamic nuclear polarization may transfer a large amount of the
NV- center's hyperpolarization to nuclear spins by sweeping over a small region
of its spectrum.Comment: 6 pages, 5 figure
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Based on the algebraico-categorical (:sheaf-theoretic and sheaf
cohomological) conceptual and technical machinery of Abstract Differential
Geometry, a new, genuinely background spacetime manifold independent, field
quantization scenario for vacuum Einstein gravity and free Yang-Mills theories
is introduced. The scheme is coined `third quantization' and, although it
formally appears to follow a canonical route, it is fully covariant, because it
is an expressly functorial `procedure'. Various current and future Quantum
Gravity research issues are discussed under the light of 3rd-quantization. A
postscript gives a brief account of this author's personal encounters with
Rafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating
Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly
written that the Editor for this volume is Daniele Oriti, with CUP as
publisher. I apologize for the mistake.
Solar flares with and without SOHO/LASCO coronal mass ejections and type II shocks
We analyse of a set of radio rich (accompanied by type IV or II bursts) solar
flares and their association with SOHO/LASCO Coronal Mass Ejections in the
period 1998 2000. The intensity, impulsiveness and energetics of these events
are investigated. We find that, on the average, flares associated both with
type IIs and CMEs are more impulsive and more energetic than flares associated
with type IIs only (without CME reported), as well as flares accompanied by
type IV continua but not type II shocks. From the last two classes, flares with
type II bursts (without CMEs reported) are the shortest in duration and the
most impulsive.Comment: Advances in Space Research, Volume 38, Issue 5, p. 1007-101
`Iconoclastic', Categorical Quantum Gravity
This is a two-part, `2-in-1' paper. In Part I, the introductory talk at
`Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international
theoretical physics conference is presented in paper form (without references).
In Part II, the more technical talk, originally titled ``Abstract Differential
Geometric Excursion to Classical and Quantum Gravity'', is presented in paper
form (with citations). The two parts are closely entwined, as Part I makes
general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic
Approaches to Quantum Gravity'' international theoretical physics conference,
Athens, Greece (summer 2004
Charged Particle Production in Proton-, Deuteron-, Oxygen- and Sulphur-Nucleus Collisions at 200 GeV per Nucleon
The transverse momentum and rapidity distributions of net protons and
negatively charged hadrons have been measured for minimum bias proton-nucleus
and deuteron-gold interactions, as well as central oxygen-gold and
sulphur-nucleus collisions at 200 GeV per nucleon. The rapidity density of net
protons at midrapidity in central nucleus-nucleus collisions increases both
with target mass for sulphur projectiles and with the projectile mass for a
gold target. The shape of the rapidity distributions of net protons forward of
midrapidity for d+Au and central S+Au collisions is similar. The average
rapidity loss is larger than 2 units of rapidity for reactions with the gold
target. The transverse momentum spectra of net protons for all reactions can be
described by a thermal distribution with `temperatures' between 145 +- 11 MeV
(p+S interactions) and 244 +- 43 MeV (central S+Au collisions). The
multiplicity of negatively charged hadrons increases with the mass of the
colliding system. The shape of the transverse momentum spectra of negatively
charged hadrons changes from minimum bias p+p and p+S interactions to p+Au and
central nucleus-nucleus collisions. The mean transverse momentum is almost
constant in the vicinity of midrapidity and shows little variation with the
target and projectile masses. The average number of produced negatively charged
hadrons per participant baryon increases slightly from p+p, p+A to central
S+S,Ag collisions.Comment: 47 pages, submitted to Z. Phys.
Bose-Einstein correlations of pion pairs in central Pb+Pb collisions at CERN SPS energies
Measurements of Bose-Einstein correlations of pion pairs in central Pb+Pb
collisions were performed with the NA49 detector at the CERN SPS for beam
energies of 20A, 30A, 40A, 80A, and 158A GeV. Correlation functions were
measured in the longitudinally co-moving ``out-side-long'' reference frame as a
function of rapidity and transverse momentum in the forward hemisphere of the
reaction. Radius and correlation strength parameters were obtained from fits of
a Gaussian parametrization. The results show a decrease of the radius
parameters with increasing transverse momentum characteristic of strong radial
flow in the pion source. No striking dependence on pion-pair rapidity or beam
energy is observed. Static and dynamic properties of the pion source are
obtained from simultaneous fits with a blast-wave model to radius parameters
and midrapidity transverse momentum spectra. Predictions of hydrodynamic and
microscopic models of Pb+Pb collisions are discussed.Comment: 22 pages, 23 figure
Phase-space dependence of particle-ratio fluctuations in Pb+Pb collisions from 20A to 158A GeV beam energy
A novel approach, the identity method, was used for particle identification
and the study of fluctuations of particle yield ratios in Pb+Pb collisions at
the CERN Super Proton Synchrotron (SPS). This procedure allows to unfold the
moments of the unknown multiplicity distributions of protons (p), kaons (K),
pions () and electrons (e). Using these moments the excitation function of
the fluctuation measure [A,B] was measured, with A and
B denoting different particle types. The obtained energy dependence of
agrees with previously published NA49 results on the related
measure . Moreover, was found to depend
on the phase space coverage for [K,p] and [K,] pairs. This feature most
likely explains the reported differences between measurements of NA49 and those
of STAR in central Au+Au collisions
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