Anagram-free Graph Colouring

An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and $k$-anagram-free colouring.Comment: Version 2: Changed 'abelian square' to 'anagram' for consistency with 'Anagram-free colourings of graphs' by Kam\v{c}ev, {\L}uczak, and Sudakov. Minor changes based on referee feedbac

Derivative Expansion of the Exact Renormalization Group

The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a fixed point action have at most a countable number of solutions that are well defined for all values of the field. We apply the technique to the fixed points of one-component real scalar field theory in three dimensions. Only two non-singular solutions are found: the gaussian fixed point and an approximation to the Wilson fixed point. The latter is used to compute critical exponents, by carrying the approximation to second order. The results appear to converge rapidly.Comment: 14 pages (with figures), Plain TeX, uses psfig, 4 postscript figures appended as uuencoded compressed tar file, SHEP 93/94-16, CERN-TH.7203/94. (Added small details and minor improvements in rigour : the version to be published in Phys.Lett.B

Signatures of the collapse and revival of a spin Schr\"{o}dinger cat state in a continuously monitored field mode

We study the effects of continuous measurement of the field mode during the collapse and revival of spin Schr\"{o}dinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the collapse and revival of a spin Schr\"{o}dinger cat state.Comment: 5 pages, 2 figure

On Truncations of the Exact Renormalization Group

We investigate the Exact Renormalization Group (ERG) description of ($Z_2$ invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations $n=2,3,\dots$, obtained by expanding about the field $\varphi=0$ and discarding all powers $\varphi^{2n+2}$ and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.Comment: 15 pages (with figures), Plain TeX, uses psfig, 5 postscript figures appended as uuencoded compressed tar file, SHEP 93/94-23, CERN-TH.7281/94. (Corrections of typos, and small additions to improve readability: version to be published in Phys. Lett. B

Exploring mini rugby union coaches’ perceptions of competitive activities

The purpose of this study was to explore volunteer rugby union coaches’ perceptions of organised competitive participation during childhood. Participants were 202 under-9 (U9) mini rugby union coaches who had coached during the 2010/11 season. Coaches completed an Internet-based survey, and cluster analysis was used to identify different groups based on attitudes towards the Rugby Football Union’s current rules and proposed changes to these rules. Three distinct groups were identified based on whether they wanted to maintain the status quo (Traditionalists); maintain some elements of structure (Moderates); or have a much less structured introduction to rugby (Radicals). In total, over three quarters of coaches favoured structured elements (early specialisation), while less than a quarter favoured a less structured game (late specialisation). Only the Radical’s views matched those espoused by elite coaches and U9 players themselves, raising several issues regarding coach education for player development during childhood. In the short term there are the difficulties of aligning disparate views of U9 player development via coaching for and during competitive games. This is further complicated by the challenges of enhancing the skills of thousands of volunteer coaches with limited experience, knowledge and expertise in coaching during childhood

Equation of State for Helium-4 from Microphysics

We compute the free energy of helium-4 near the lambda transition based on an exact renormalization-group equation. An approximate solution permits the determination of universal and nonuniversal thermodynamic properties starting from the microphysics of the two-particle interactions. The method does not suffer from infrared divergences. The critical chemical potential agrees with experiment. This supports a specific formulation of the functional integral that we have proposed recently. Our results for the equation of state reproduce the observed qualitative behavior. Despite certain quantitative shortcomings of our approximation, this demonstrates that ab initio calculations for collective phenomena become possible by modern renormalization-group methods.Comment: 9 pages, 6 figures, revtex updated version, journal referenc

Use of a novel dataset to explore spatial and social variations in car type, size, usage and emissions

© 2015 The Authors. The 'MOT' vehicle inspection test record dataset recently released by the UK Department for Transport (DfT) provides the ability to estimate annual mileage figures for every individual light duty vehicle greater than 3 years old within Great Britain. Vehicle age, engine size and fuel type are also provided in the dataset and these allow further estimates to be made of fuel consumption, energy use, and per vehicle emissions of both air pollutants and greenhouse gases. The use of this data permits the adoption of a new vehicle-centred approach to assessing emissions and energy use in comparison to previous road-flow and national fuel consumption based approaches. The dataset also allows a spatial attribution of each vehicle to a postcode area, through the reported location of relevant vehicle testing stations. Consequently, this new vehicle data can be linked with socio-demographic data in order to determine the potential characteristics of vehicle owners.This paper provides a broad overview of the types of analyses that are made possible by these data, with a particular focus on distance driven and pollutant emissions. The intention is to demonstrate the very broad potential for this data, and to highlight where more focused analysis could be useful. The findings from the work have important implications for understanding the distributional impacts of transport related policies and targeting messaging and interventions for the reduction of car use

Gauge Invariance, the Quantum Action Principle, and the Renormalization Group

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective Quantum Action Principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires non-vanishing subtraction points. The difficulties encountered with non-perturbative approximations are briefly discussed.Comment: 11 pages, latex, no figures, one reference added, version to be published on Phys. Lett.

External Tank (ET) Bipod Fitting Bolted Attachment Locking Insert Performance

Following STS-107, the External Tank (ET) Project implemented corrective actions and configuration changes at the ET bipod fitting. Among the corrective actions, the existing bolt lock wire which provided resistance to potential bolt rotation was removed. The lock wire removal was because of concerns with creating voids during foam application and potential for lock wire to become debris. The bolts had been previously lubricated to facilitate assembly but, because of elimination of the lock wire, the ET Project wanted to enable the locking feature of the insert. Thus, the lubrication was removed from bolt threads and instead applied to the washer under the bolt head. Lubrication is necessary to maximize joint pre-load while remaining within the bolt torque specification. The locking feature is implemented by thread crimping in at four places in the insert. As the bolt is torqued into the insert the bolt threads its way past the crimped parts of the insert. This provides the locking of the bolt, as torque is required to loosen the joint after clamping