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 ππ,KK‾,ηη\pi\pi, K\overline{K}, \eta\eta scattering and the σ,f0,f2\sigma, f_0, f_2 mesons from QCD

We present the first lattice QCD study of coupled isoscalar $\pi\pi,K\overline{K},\eta\eta$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_\pi\sim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $\sigma$ and $f_0(980)$ states, where the $\sigma$ appears as a stable bound-state below $\pi\pi$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $\pi\pi$ cross section in the vicinity of the $K\overline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2'(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $\pi\pi$ and the heavier state to $K\overline{K}$. 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

Dynamic flow distortion investigation in an S-duct using DDES and SPIV data

The dynamic flow distortion generated within convoluted aero-engine intakes can affect the performance and operability of the engine. There is a need for a better understanding of the main flow mechanisms which promote flow distortion at the exit of S-shaped intakes. This paper presents a detailed analysis of the main coherent structures in an S-duct flow field based on a Delayed Detached Eddy Simulation (DDES). The DDES capability to capture the characteristics of the highly unsteady flow field is demonstrated against high resolution, synchronous Stereoscopic Particle Image Velocimetry (SPIV) measurements at the Aerodynamic Interface Plane (AIP). The flow field mechanisms responsible for the main AIP perturbations are identified. Clockwise and counter-clockwise stream-wise vortices are alternately generated around the separation region at a frequency of St=0.53, which promotes the swirl switching at the AIP. Spanwise vortices are also shed from the separation region at a frequency of St=1.06, and convect downstream along the separated centreline shear layer. This results in a vertical modulation of the main loss region and a fluctuation of the velocity gradient between the high and low velocity flow at the AIP