A Study of the N=2N=2 Kazakov-Migdal Model

We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In contrast to our earlier work on the subject we have chosen here {\it not} to integrate out the gauge fields but to keep them in the Monte Carlo simulation. This allows us to measure observables associated with the gauge fields and thereby address the problem of the local $Z_2$ symmetry present in the model. We confirm our previous result that the model has a line of first order phase transitions terminating in a critical point. The adjoint plaquette has a clear discontinuity across the phase transition, whereas the plaquette in the fundamental representation is always zero in accordance with Elitzur's theorem. The density of small $Z_2$ monopoles shows very little variation and is always large. We also find that the model has extra local U(1) symmetries which do not exist in the case of the standard adjoint theory. As a result, we are able to show that two of the angles parameterizing the gauge field completely decouple from the theory and the continuum limit defined around the critical point can therefore not be `QCD'.Comment: 11 pages, UTHEP-24

Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter \l, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of \l the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.Comment: 20 pages, LaTeX, Imperial/TP/92-93/5

National Evaluation of the Capacity Building Programme in English Local Government: Evaluation of the National Programmes: Annex 2: Evaluation of the National Programmes

The report is one of a series of outputs from the national evaluation of the CBP, being undertaken by a team of researchers at the Policy Research Institute (PRI) at Leeds Metropolitan University and the Cities Research Unit at the University of West of England. The Capacity Building Programme for local government was launched in 2003 as a joint Department for Communities and Local Government (DCLG) / Local Government Association (LGA) initiative to support capacity building and improvement activities within local authorities in England. The evaluation of the Capacity Building Programme has been underway since late 2004. A scoping phase was conducted until May 2005, including a short evaluation of the Pilot Programmes. The main phase of the evaluation commenced in September 2005 and encompassed four main phases (see Section 1.3: p10)

Role of inertia in two-dimensional deformation and breakup of a droplet

We investigate by Lattice Boltzmann methods the effect of inertia on the deformation and break-up of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is {\em necessary} for break-up, so that at zero Reynolds number the droplet deforms indefinitely without breaking. We identify two different routes to breakup via two-lobed and three-lobed structures respectively, and give evidence for a sharp transition between these routes as parameters are varied.Comment: 4 pages, 4 figure

Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval Δt\Delta t

The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval \Dt was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as $n!$. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is not excluded that for number of the potentials the expansion is convergent. For the polynomial potentials \Dt-expansion is certainly asymptotic one. The coefficients increase in this case as $\Gamma(n \frac{L-2}{L+2})$, where $L$ is the order of the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe

Numerical Solution of a Complete Formulation of Flow in a Perfusion Bone-Tissue Bioreactor Using Lattice Boltzmann Equation Method

We report the key findings from numerical solutions of a model of transport within an established perfusion bioreactor design. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell attachment. It also includes the experimentally determined internal (Poly-L-Lactic Acid (PLLA)) scaffold boundary, together with the external vessel and flow-port boundaries. Our findings, obtained using parallel lattice Boltzmann equation method, relate to (i) whole-device, steady-state flow and species distribution and (ii) the properties of the scaffold. In particular the results identify which elements of the problem may be addressed by coarse grained methods such as the Darcy approximation and those which require a more complete description. The work demonstrates that appropriate numerical modelling will make a key contribution to the design and development of large scale bioreactors.Comment: 9 pages, 3 figure

Stable chromium isotopic composition of meteorites and metal-silicate experiments: Implications for fractionation during core formation

We present new mass independent and mass dependent Cr isotope compositions for meteorites measured by double spike thermal ionisation mass spectrometry. Small differences in both mass independent 53Cr and 54Cr relative to the Bulk Silicate Earth are reported and are very similar to previously published values. Carbonaceous chondrites are characterised by an excess in 54Cr compared to ordinary and enstatite chondrites which make mass independent Cr isotopes a useful tool for distinguishing between meteoritic groups. Mass dependent stable Cr isotope compositions for the same samples are also reported. Carbonaceous and ordinary chondrites are identical within uncertainty with average δ53Crδ53Cr values of −0.118±0.040‰−0.118±0.040‰ and −0.143±0.074‰−0.143±0.074‰ respectively. The heaviest isotope compositions are recorded by an enstatite chondrite and a CO carbonaceous chondrite, both of which have relatively reduced chemical compositions implying some stable Cr isotope fractionation related to redox processes in the circumstellar disk. The average δ53Crδ53Cr values for chondrites are within error of the estimate for the Bulk Silicate Earth (BSE) also determined by double spiking. The lack of isotopic difference between chondritic material and the BSE provides evidence that Cr isotopes were not fractionated during core formation on Earth. A series of high-pressure experiments was also carried out to investigate stable Cr isotope fractionation between metal and silicate and no demonstrable fractionation was observed, consistent with our meteorites data. Mass dependent Cr isotope data for achondrites suggest that Cr isotopes are fractionated during magmatic differentiation and therefore further work is required to constrain the Cr isotopic compositions of the mantles of Vesta and Mars.

Self-Similar Bootstrap of Divergent Series

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal stability of the self-similar renormalization procedure. The latter is to be repeated as many times as it is necessary in order to convert into closed self-similar expressions all sums from the series considered. This multiple and complete renormalization is called self-similar bootstrap. The method is illustrated by several examples from statistical physics.Comment: 1 file, 22 pages, RevTe