Rigidity and Normal Modes in Random Matrix Spectra

We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is linear, and for large matrices, the normal modes are found to be Chebyshev polynomials of the second kind. We contrast this with the behaviour of a sequence of uncorrelated levels, which has a quadratic normal mode spectrum. The difference in the rigidity of random matrix spectra and sequences of uncorrelated levels can be attributed to this difference in the normal mode spectra. We illustrate this by calculating the number variance in the two cases.Comment: 12 pages, 1 LaTeX fil

Modelling a Dune Field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of La\^ayounne.Comment: 15 pages, 13 figure

Hospital food service: a comparative analysis of systems and introducing the ‘Steamplicity’ concept

Background Patient meals are an integral part of treatment hence the provision and consumption of a balanced diet, essential to aid recovery. A number of food service systems are used to provide meals and the Steamplicity concept has recently been introduced. This seeks, through the application of a static, extended choice menu, revised patient ordering procedures, new cooking processes and individual patient food heated/cooked at ward level, to address some of the current hospital food service concerns. The aim of this small-scale study, therefore, was to compare a cook-chill food service operation against Steamplicity. Specifically, the goals were to measure food intake and wastage at ward level; ‘stakeholders’ (i.e. patients, staff, etc.) satisfaction with both systems; and patients’ acceptability of the food provided. Method The study used both quantitative (self-completed patient questionnaires, n = 52) and qualitative methods (semi-structured interviews, n = 16) with appropriate stakeholders including medical and food service staff, patients and their visitors. Results Patients preferred the Steamplicity system overall and in particular in terms of food choice, ordering, delivery and food quality. Wastage was considerably less with the Steamplicity system, although care must be taken to ensure that poor operating procedures do not negate this advantage. When the total weight of food consumed in the ward at each meal is divided by the number of main courses served, at lunch, the mean intake with the cook-chill system was 202 g whilst that for the Steamplicity system was 282 g and for the evening meal, 226 g compared with 310 g. Conclusions The results of this small study suggest that Steamplicity is more acceptable to patients and encourages the consumption of larger portions. Further evaluation of the Steamplicity system is warranted. The purpose of this study was to directly compare selected aspects (food wastage at ward level; satisfaction with systems and food provided) of a traditional cook-chill food service operation against ‘Steamplicity’. Results indicate that patients preferred the ‘Steamplicty’ system in all areas: food choice, ordering, delivery, food quality and overall. Wastage was considerably less with the ‘Steamplicity’ system; although care must be taken to ensure that poor operating procedures do not negate this advantage. When the total weight of food consumed in the ward at each meal is divided by the number of main courses served, results show that at lunch, mean intake with the cook-chill system was 202g whilst that for the ‘Steamplicity’ system was 282g and for the evening meal, 226g compared with 310g

Strongly focused light beams interacting with single atoms in free space

We construct 3-D solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.Comment: 9 pages, 9 figure

Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops

We study the magnetic interaction between two superconducting concentric mesoscopic Al loops, close to the superconducting/normal phase transition. The phase boundary is measured resistively for the two-loop structure as well as for a reference single loop. In both systems Little-Parks oscillations, periodic in field are observed in the critical temperature Tc versus applied magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak 'low frequency' response shows up, which can be attributed to the inner loop supercurrent magnetic coupling to the flux of the outer loop. The amplitude of this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Co-crystallisation as a modular approach to the discovery of spin-crossover materials

Herein we present co-crystallisation as a strategy for materials discovery in the field of switchable spin crossover (SCO) systems. Using [Fe(3-bpp)2]·2A (where 3-bpp = 2,6-bis(pyrazol-3-yl)pyridine, A = BF4−/PF6−) as a starting point, a total of 11 new cocrystals have been synthesised with five different dipyridyl coformers. Eight of these systems show spin crossover behaviour, and all show dramatically different switching properties from the parent complex. The cocrystals have been studied by variable temperature single-crystal X-ray diffraction and SQUID magnetometry to develop structure–property relationships. The supramolecular architecture of the cocrystals depends on the properties of the coformer. With linear, rigid coformer molecules leading to 1D supramolecular hydrogen-bonded chains, while flexible coformers form 2D sheets and bent coformers yield 3D network structures. The SCO behaviour of the cocrystals can be modified through changing the coformer and thus co-crystallisation presents a rapid, facile and highly modular tool for the discovery of new switchable materials. The wider applicability of this strategy to the design of hybrid multifunctional materials is also discussed

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.Comment: 17 pages, Revte

Darkness visible: reflections on underground ecology

1 Soil science and ecology have developed independently, making it difficult for ecologists to contribute to urgent current debates on the destruction of the global soil resource and its key role in the global carbon cycle. Soils are believed to be exceptionally biodiverse parts of ecosystems, a view confirmed by recent data from the UK Soil Biodiversity Programme at Sourhope, Scotland, where high diversity was a characteristic of small organisms, but not of larger ones. Explaining this difference requires knowledge that we currently lack about the basic biology and biogeography of micro-organisms. 2 It seems inherently plausible that the high levels of biological diversity in soil play some part in determining the ability of soils to undertake ecosystem-level processes, such as carbon and mineral cycling. However, we lack conceptual models to address this issue, and debate about the role of biodiversity in ecosystem processes has centred around the concept of functional redundancy, and has consequently been largely semantic. More precise construction of our experimental questions is needed to advance understanding. 3 These issues are well illustrated by the fungi that form arbuscular mycorrhizas, the Glomeromycota. This ancient symbiosis of plants and fungi is responsible for phosphate uptake in most land plants, and the phylum is generally held to be species-poor and non-specific, with most members readily colonizing any plant species. Molecular techniques have shown both those assumptions to be unsafe, raising questions about what factors have promoted diversification in these fungi. One source of this genetic diversity may be functional diversity. 4 Specificity of the mycorrhizal interaction between plants and fungi would have important ecosystem consequences. One example would be in the control of invasiveness in introduced plant species: surprisingly, naturalized plant species in Britain are disproportionately from mycorrhizal families, suggesting that these fungi may play a role in assisting invasion. 5 What emerges from an attempt to relate biodiversity and ecosystem processes in soil is our extraordinary ignorance about the organisms involved. There are fundamental questions that are now answerable with new techniques and sufficient will, such as how biodiverse are natural soils? Do microbes have biogeography? Are there rare or even endangered microbes

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur