Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

From linear to non-linear scales: analytical and numerical predictions for the weak lensing convergence

Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations which provide two simple methods to compute the probability distribution function, pdf, of the convergence. We apply one of these to the case where the density field can be described by a log-normal pdf. Next, we discuss two hierarchical models for the high-order correlations which allow one to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly non-linear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement with our theoretical predictions. We have probed various angular scales in the numerical work and considered sources at 14 different redshifts in each of two different cosmological scenarios, an open cosmology and a flat cosmology with non-zero cosmological constant. Our simulation technique employs computations of the full 3-d shear matrices along the line of sight from the source redshift to the observer and is complementary to more popular ray-tracing algorithms. Our results therefore provide a valuable cross-check for such complementary simulation techniques, as well as for our simple analytical model, from the linear to the highly non-linear regime.Comment: 20 pages, final version published in MNRA

Comment on Mie Scattering from a Sonoluminescing Bubble with High Spatial and Temporal Resolution [Physical Review E 61, 5253 (2000)]

A key parameter underlying the existence of sonoluminescence (SL)is the time relative to SL at which acoustic energy is radiated from the collapsed bubble. Light scattering is one route to this quantity. We disagree with the statement of Gompf and Pecha that -highly compressed water causes the minimum in scattered light to occur 700ps before SL- and that this effect leads to an overestimate of the bubble wall velocity. We discuss potential artifacts in their experimental arrangement and correct their description of previous experiments on Mie scattering.Comment: 10 pages, 2 figure

Using intervention mapping to develop a culturally appropriate intervention to prevent childhood obesity: the HAPPY (Healthy and Active Parenting Programme for Early Years) study.

INTRODUCTION: Interventions that make extensive use of theory tend to have larger effects on behaviour. The Intervention Mapping (IM) framework incorporates theory into intervention design, implementation and evaluation, and was applied to the development of a community-based childhood obesity prevention intervention for a multi-ethnic population. METHODS: IM was applied as follows: 1) Needs assessment of the community and culture; consideration of evidence-base, policy and practice; 2) Identification of desired outcomes and change objectives following identification of barriers to behaviour change mapped alongside psychological determinants (e.g. knowledge, self-efficacy, intention); 3) Selection of theory-based methods and practical applications to address barriers to behaviour change (e.g., strategies for responsive feeding); 4) Design of the intervention by developing evidence-based interactive activities and resources (e.g., visual aids to show babies stomach size). The activities were integrated into an existing parenting programme; 5) Adoption and implementation: parenting practitioners were trained by healthcare professionals to deliver the programme within Children Centres. RESULTS: HAPPY (Healthy and Active Parenting Programme for Early Years) is aimed at overweight and obese pregnant women (BMI > 25); consists of 12 × 2.5 hr. sessions (6 ante-natal from 24 weeks; 6 postnatal up to 9 months); it addresses mother's diet and physical activity, breast or bottle feeding, infant diet and parental feeding practices, and infant physical activity. CONCLUSION: We have demonstrated that IM is a feasible and helpful method for providing an evidence based and theoretical structure to a complex health behaviour change intervention. The next stage will be to assess the impact of the intervention on behaviour change and clinical factors associated with childhood obesity. The HAPPY programme is currently being tested as part of a randomised controlled feasibility trial

Design and performance of a multicentre, randomized controlled trial of teleconsulting.

We have designed and performed a multicentre, randomized controlled trial of teleconsulting. The trial investigated the effectiveness and cost implications in rural and inner-city settings of using videoconferencing as an alternative to general practitioner referral to a hospital specialist. The participating general practitioners referred a total of 3170 patients who satisfied the entry criteria. Of these, 1040 (33%) failed to provide consent or otherwise refused to participate in the trial. Of the patients recruited to the trial, a total of 1902 (91%) completed and returned the baseline questionnaire. Although the trial was successful in recruiting sufficient patients and in obtaining high questionnaire response rates, the findings will require careful interpretation to take account of the limits which the protocol placed on the ability of general practitioners to select patients for referral

Specific heat of the simple-cubic Ising model

We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions and with a set of experimental results. Our results include a determination of the universal amplitude ratio of the specific-heat divergences at both sides of the critical point.Comment: 20 pages, 3 figure

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.Comment: 4 pages, 3 figures on request (2 as .ps files