17,769 research outputs found
Light-Front QCD and the Constituent Quark Model
A general strategy is described for deriving a constituent approximation to
QCD, inspired by the constituent quark model and based on light-front
quantization. Some technical aspects of the approach are discussed, including a
mechanism for obtaining a confining potential and ways in which spontaneous
chiral symmetry breaking can be manifested. (Based on a talk presented by K.G.
Wilson at ``Theory of Hadrons and Light-Front QCD,'' Polana Zgorzelisko,
Poland, August 1994.)Comment: 14 pages, LaTeX, no figure
Trees and Matchings
In this article, Temperley's bijection between spanning trees of the square
grid on the one hand, and perfect matchings (also known as dimer coverings) of
the square grid on the other, is extended to the setting of general planar
directed (and undirected) graphs, where edges carry nonnegative weights that
induce a weighting on the set of spanning trees. We show that the weighted,
directed spanning trees (often called arborescences) of any planar graph G can
be put into a one-to-one weight-preserving correspondence with the perfect
matchings of a related planar graph H.
One special case of this result is a bijection between perfect matchings of
the hexagonal honeycomb lattice and directed spanning trees of a triangular
lattice. Another special case gives a correspondence between perfect matchings
of the ``square-octagon'' lattice and directed weighted spanning trees on a
directed weighted version of the cartesian lattice.
In conjunction with results of Kenyon, our main theorem allows us to compute
the measures of all cylinder events for random spanning trees on any (directed,
weighted) planar graph. Conversely, in cases where the perfect matching model
arises from a tree model, Wilson's algorithm allows us to quickly generate
random samples of perfect matchings.Comment: 32 pages, 19 figures (minor revisions from version 1
A hybrid CA-PDE Model of chlamydia trachomatis infection in the female genital tract
Chlamydia trachomatis is amongst the most common sexually transmitted diseases in the world and when left untreated, may lead to serious sequelae particularly in women such as pelvic inflammatory disease, ectopic pregnancy and infertility. Currently, most mathematical modelling in the literature regarding Chlamydia is based on time dependent differential equations. The serious pathology associated with C. trachomatis occurs when the chlamydial infection ascends to the upper genital tract. But no modelling study has investigated the important spatial aspects of the disease. In this work, we include spatiotemporal considerations of the progression of chlamydial infection in the genital tract. This novel direction is achieved using cellular automata modelling with probabilistic decision processes. In this presentation, the modelling strategy will be described, as well as its relationship with existing models and the advances in understanding that are achieved with such a model. Such an approach provides valuable insights into disease progression and will lead to experimentally testable predictions and a basis for further investigation in this area
On the effect of the atmosphere on the evaporation of sessile droplets of water
An experimental and theoretical study into the effect of the atmosphere on the evaporation of pinned sessile droplets of water is described. The experimental work investigated the evaporation rates of sessile droplets in atmospheres of three different ambient gases (namely, helium, nitrogen and carbon dioxide) at reduced pressure (from 40 to 1000 mbar) using four different substrates(namely, aluminium, titanium, Macor and PTFE) with a wide range of thermal conductivities.Reducing the atmospheric pressure increases the diffusion coefficient of water vapour in the atmosphere and hence increases the evaporation rate. Changing the ambient gas also alters the diffusion coefficient and hence also affects the evaporation rate. A mathematical model that takes into account the effect of the atmospheric pressure and the nature of the ambient gas on the diffusion of water vapour in the atmosphere and the thermal conductivity of the substrate is developed, and its predictions are found to be in encouraging agreement with the experimental results
Grid-connected renewables, storage and the UK electricity market
This article is a critical counterpoint to an article by published by Swift-Hook in the journal of Renewable Energy entitled "Grid-connected intermittent renewables are the last to be stored". In contrast to Swift-Hook we found evidence that "grid-connected intermittent renewables" have been, and will continue to be stored when it suits the "UK market" to do so. This article is important to policy makers as energy storage (through EV battery demand side management for example) may well have an important role to play in facilitating the integration of high wind penetrations
Isoscalar scattering and the mesons from QCD
We present the first lattice QCD study of coupled isoscalar
- and -wave scattering extracted from
discrete finite-volume spectra computed on lattices which have a value of the
quark mass corresponding to MeV. In the sector we find
analogues of the experimental and states, where the
appears as a stable bound-state below threshold, and, similar
to what is seen in experiment, the manifests itself as a dip in the
cross section in the vicinity of the threshold. For
we find two states resembling the and ,
observed as narrow peaks, with the lighter state dominantly decaying to
and the heavier state to . The presence of all these
states is determined rigorously by finding the pole singularity content of
scattering amplitudes, and their couplings to decay channels are established
using the residues of the poles
The dimension of loop-erased random walk in 3D
We measure the fractal dimension of loop-erased random walk (LERW) in 3
dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related
to the uniform spanning tree and the abelian sandpile model. We simulated LERW
on both the cubic and face-centered cubic lattices; the corrections to scaling
are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change
MV "Surveyor" Cruise 71/1, 26 February - 11 April 1971. Tide gauges: geology and geophysics on the Hebridean Shelf and on the Rockall Plateau
Sampling and sensitivity analyses tools (SaSAT) for computational modelling
SaSAT (Sampling and Sensitivity Analysis Tools) is a user-friendly software package for applying uncertainty and sensitivity analyses to mathematical and computational models of arbitrary complexity and context. The toolbox is built in Matlab®, a numerical mathematical software package, and utilises algorithms contained in the Matlab® Statistics Toolbox. However, Matlab® is not required to use SaSAT as the software package is provided as an executable file with all the necessary supplementary files. The SaSAT package is also designed to work seamlessly with Microsoft Excel but no functionality is forfeited if that software is not available. A comprehensive suite of tools is provided to enable the following tasks to be easily performed: efficient and equitable sampling of parameter space by various methodologies; calculation of correlation coefficients; regression analysis; factor prioritisation; and graphical output of results, including response surfaces, tornado plots, and scatterplots. Use of SaSAT is exemplified by application to a simple epidemic model. To our knowledge, a number of the methods available in SaSAT for performing sensitivity analyses have not previously been used in epidemiological modelling and their usefulness in this context is demonstrated
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