The Casimir effect for thin plasma sheets and the role of the surface plasmons

We consider the Casimir force betweeen two dielectric bodies described by the plasma model and between two infinitely thin plasma sheets. In both cases in addition to the photon modes surface plasmons are present in the spectrum of the electromagnetic field. We investigate the contribution of both types of modes to the Casimir force and confirm resp. find in both models large compensations between the plasmon modes themselves and between them and the photon modes especially at large distances. Our conclusion is that the separation of the vacuum energy into plasmon and photon contributions must be handled with care except for the case of small separations.Comment: submitted to JPhysA Special Issue QFEXT'05, replaced due to a wrong Latex comman

Low-Energy Heavy-Ion Reactions and the Skyrme Effective Interaction

The Skyrme effective interaction, with its multitude of parameterisations, along with its implemen- tation using the static and time-dependent density functional (TDHF) formalism have allowed for a range of microscopic calculations of low-energy heavy-ion collisions. These calculations allow variation of the effective interaction along with an interpretation of the results of this variation informed by a comparison to experimental data. Initial progress in implementing TDHF for heavy-ion collisions necessarily used many approximations in the geometry or the interaction. Over the last decade or so, the implementations have overcome all restrictions, and studies have begun to be made where details of the effective interaction are being probed. This review surveys these studies in low energy heavy-ion reactions, finding significant effects on observables from the form of the spin-orbit interaction, the use of the tensor force, and the inclusion of time-odd terms in the density functional.Comment: submitted to Prog. Part. Nucl. Phy

Quantifying and visualising change: strain monitoring of tapestries with digital image correlation

A three-year research project at the University of Southampton (2007–2010) investigated whether monitoring techniques commonly used by engineers to assess the strength and durability of materials could be usefully applied to inform the condition assessment of historic tapestries. To date it has not been possible to obtain an objective picture of the overall condition of a tapestry; the study investigated whether it is possible to identify precursors of structural damage. The two techniques, digital image correlation (DIC) and optical fibre sensors, were used to monitor a representative wool fabric, specially woven tapestry samples, a newly woven tapestry, and historic tapestries, both in the laboratory and in situ in a historic house. This study first sets out to answer the question: can DIC be used to monitor and visualize strain in historic tapestries? It is shown that DIC can be used successfully. Secondly, it discusses the map function, a novel development which allowed the monitoring equipment to be moved, so that it could be used in situ in a historic house. Thirdly, it provides further details of the experimental work using optical fibre sensors to confirm the accuracy of the DIC technique

Renormalization group analysis of the Reynolds stress transport equation

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately

Minimal Forbidden Factors of Circular Words

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We generalize this result to the case of a circular word. We discuss several combinatorial properties of the minimal forbidden factors of a circular word. As a byproduct, we obtain a formal definition of the factor automaton of a circular word. Finally, we investigate the case of minimal forbidden factors of the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc

Simulation tools for future interferometers

For the design and commissioning of the LIGO interferometer, simulation tools have been used explicitly and implicitly. The requirement of the advanced LIGO interferometer is much more demanding than the first generation interferometer. Development of revised simulation tools for future interferometers are underway in the LIGO Laboratory. The outline of those simulation tools and applications are discussed

A new model for evolution in a spatial continuum

We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans(1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side L as L tends to infinity. Under appropriate conditions (and on a suitable timescale), we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).Comment: 63 pages, version accepted to Electron. J. Proba

Coalescent simulation in continuous space:Algorithms for large neighbourhood size

Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail