Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.Comment: latex, 60 pages, 22 figure

Effect of angular momentum on equilibrium properties of a self-gravitating system

The microcanonical properties of a two dimensional system of N classical particles interacting via a smoothed Newtonian potential as a function of the total energy E and the total angular momentum L are discussed. In order to estimate suitable observables a numerical method based on an importance sampling algorithm is presented. The entropy surface shows a negative specific heat region at fixed L for all L. Observables probing the average mass distribution are used to understand the link between thermostatistical properties and the spatial distribution of particles. In order to define a phase in non-extensive system we introduce a more general observable than the one proposed by Gross and Votyakov [Eur. Phys. J. B:15, 115 (2000)]: the sign of the largest eigenvalue of the entropy surface curvature. At large E the gravitational system is in a homogeneous gas phase. At low E there are several collapse phases; at L=0 there is a single cluster phase and for L>0 there are several phases with 2 clusters. All these pure phases are separated by first order phase transition regions. The signal of critical behaviour emerges at different points of the parameter space (E,L). We also discuss the ensemble introduced in a recent pre-print by Klinko & Miller; this ensemble is the canonical analogue of the one at constant energy and constant angular momentum. We show that a huge loss of informations appears if we treat the system as a function of intensive parameters: besides the known non-equivalence at first order phase transitions, there exit in the microcanonical ensemble some values of the temperature and the angular velocity for which the corresponding canonical ensemble does not exist, i.e. the partition sum diverges.Comment: 17 pages, 11 figures, submitted to Phys. Rev.

A dynamical classification of the range of pair interactions

We formalize a classification of pair interactions based on the convergence properties of the {\it forces} acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the "usual" thermodynamic limit. For a pair interaction potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it bounded} pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the {\it pair force} is absolutely integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to this case as {\it dynamically short-range}, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the {\it dynamically long-range} case, i.e., a \leq d-1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with a > d-2 (or a < d-2), for which the PDF of the {\it difference in forces} is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.Comment: 12 pages, 1 figure; significantly shortened and focussed, additional references, version to appear in J. Stat. Phy

Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d=3, it is given by a Levy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d=2, it is given by a marginal Gaussian distribution intermediate between Gaussian and Levy laws. In d=1, it is exactly given by the Bernouilli distribution (for any particle number N) which becomes Gaussian for N>>1. Therefore, the dimension d=2 is critical regarding the statistics of the gravitational force. We generalize these results for inhomogeneous systems with arbitrary power-law density profile and arbitrary power-law force in a d-dimensional universe

Equilibrium and dynamical properties of two dimensional self-gravitating systems

A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously distributed. A phase transition from the collapsed to the homogeneous state occurs at critical energy U_c. A theoretical analysis within the canonical ensemble identifies such a transition as first order. But microcanonical simulations reveal a negative specific heat regime near $U_c$. The dynamical behaviour of the system is affected by this transition : below U_c anomalous diffusion is observed, while for U > U_c the motion of the particles is almost ballistic. In the collapsed phase, finite $N$-effects act like a noise source of variance O(1/N), that restores normal diffusion on a time scale diverging with N. As a consequence, the asymptotic diffusion coefficient will also diverge algebraically with N and superdiffusion will be observable at any time in the limit N \to \infty. A Lyapunov analysis reveals that for U > U_c the maximal exponent \lambda decreases proportionally to N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy, in spite of a clear non ergodicity of the system, a common scaling law \lambda \propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two column version with included figures : less paper waste

School screening for scoliosis: can surface topography replace examination with scoliometer?

<p>Abstract</p> <p>Background</p> <p>Clinical examination with the use of scoliometer is a basic method for scoliosis detection in school screening programs. Surface topography (ST) enables three-dimensional back assessment, however it has not been adopted for the purpose of scoliosis screening yet. The purpose of this study was to assess the usefulness of ST for scoliosis screening.</p> <p>Methods</p> <p>996 girls aged 9 to 13 years were examined, with both scoliometer and surface topography. The Surface Trunk Rotation (STR) was introduced and defined as a parameter allowing comparison with scoliometer Angle of Trunk Rotation taken as reference.</p> <p>Results</p> <p>Intra-observer error for STR parameter was 1.9°, inter-observer error was 0.8°. Sensitivity and specificity of ST were not satisfactory, the screening cut-off value of the surface topography parameter could not be established.</p> <p>Conclusions</p> <p>The study did not reveal advantage of ST as a scoliosis screening method in comparison to clinical examination with the use of the scoliometer.</p

Development of the Advancing the Patient Experience (APEX) in COPD Registry : A Modified Delphi Study

Funding statement: APEX COPD is conducted by Optimum Patient Care (OPC) Global Limited, and co-funded by OPC Global and Boehringer Ingelheim Pharmaceuticals, Inc. (BIPI). The author(s) meet criteria for authorship as recommended by the International Committee of Medical Journal Editors (ICMJE). The authors received no direct compensation related to the development of the manuscript. Writing, editorial support, and/or formatting assistance was provided by Ms. Audrey Ang of the Observational and Pragmatic Research Institute, Singapore, and Dr. Lisa Buttle of Medscript Ltd, Ireland, which was funded by BIPI. BIPI was given the opportunity to review the manuscript for medical and scientific accuracy as well as intellectual property considerations. Acknowledgments The author(s) meet criteria for authorship as recommended by the International Committee of Medical Journal Editors (ICMJE). We thank Dr. Alvaro Aranda (Hospital Auxilio Mutuo, San Juan, Puerto Rico) for his scientific and clinical contributions during the drafting of this manuscript. We also thank Ms. Audrey Ang for editorial assistance, Ms. Bronte Sawyer for project coordination, and Dr. Lisa Buttle for assistance with drafting the article. Dr. Ruth B. Murray is acknowledged for her substantial contribution to the interpretation, summarization and presentation of data in this article and significant intellectual input to the manuscript. She has provided her final approval of the version to be published and agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Dr. Ruth B. Murray is the founder and director of Medscript Ltd., a company that provided writing and editorial support for APEX COPD publications.Peer reviewedPostprin

Epidemiology and cost of herpes zoster and postherpetic neuralgia among patients treated in primary care centres in the valencian community of Spain

<p>Abstract</p> <p>Background</p> <p>Data on the epidemiology and costs related to herpes zoster (HZ) and postherpetic neuralgia (PHN) in Spain are scarce; therefore, studies are needed to evaluate the epidemiological and economic impact of HZ and its most common complication, PHN. The present study aimed to estimate the clinical and economic burden of HZ and PHN in Valencia (Spain).</p> <p>Methods</p> <p>We prospectively analyzed the burden of HZ and PHN and their attributable costs in patients from 25 general practices in the Autonomous Community of Valencia serving 36,030 persons aged > 14 years. All patients with a clinical diagnosis of HZ who attended these centers between December 1^st2006 and November 30^th2007 were asked to participate. Patients included were followed for 1 year.</p> <p>Results</p> <p>Of the 130 cases of HZ followed up, continued pain was experienced by 47.6% (95% confidence interval (CI) = 35.6-56.7%) at 1 month after rash onset, by 14.5% (95% CI = 7.8-1.2%) at 3 months, by 9.0% (95% CI = 3.7-14.3%) at 6 months, and by 5.9% (95% CI = 1.5-10.3%) at 12 months. The percentage of patients with PHN increased with age, from 21.4% (95% CI = 8.3-40) in patients < 50 years to 59.2% (95% CI = 44.4-74) in patients ≥ 70 years. The estimated total cost for the 130 HZ cases during the follow-up period was €49,160 ($67,349). Mean cost per patient was €378 (range 53-2,830) ($517, range 73-3,877).</p> <p>Conclusions</p> <p>This study shows that PHN is a relatively common complication of HZ and that both conditions combined give rise to a significant clinical and economic burden for patients and providers.</p

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

Screening for Gonorrhea: Recommendation Statement

The U.S. Preventive Services Task Force (USPSTF) recommends that clinicians screen all sexually active women, including those who are pregnant, for gonorrhea infection if they are at increased risk for infection (that is, if they are young or have other individual or population risk factors; see Clinical Considerations for further discussion of risk factors). B recommendation