Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

Mapping a Homopolymer onto a Model Fluid

We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and an external, confining, field are present, and then show how a general pair interaction can be introduced perturbatively, making use of a Mayer expansion. Through a diagrammatic analysis, we shall show how constitutive equations derived for the polymeric system are equivalent to the Ornstein-Zernike and P.Y. equations for a simple fluid, and find the implications of such a mapping for the simple situation of Van der Waals mean field model for the fluid.Comment: 12 pages, 3 figure

Gestational age at delivery and special educational need: retrospective cohort study of 407,503 schoolchildren

<STRONG>Background</STRONG> Previous studies have demonstrated an association between preterm delivery and increased risk of special educational need (SEN). The aim of our study was to examine the risk of SEN across the full range of gestation. <STRONG>Methods and Findings</STRONG> We conducted a population-based, retrospective study by linking school census data on the 407,503 eligible school-aged children resident in 19 Scottish Local Authority areas (total population 3.8 million) to their routine birth data. SEN was recorded in 17,784 (4.9%) children; 1,565 (8.4%) of those born preterm and 16,219 (4.7%) of those born at term. The risk of SEN increased across the whole range of gestation from 40 to 24 wk: 37–39 wk adjusted odds ratio (OR) 1.16, 95% confidence interval (CI) 1.12–1.20; 33–36 wk adjusted OR 1.53, 95% CI 1.43–1.63; 28–32 wk adjusted OR 2.66, 95% CI 2.38–2.97; 24–27 wk adjusted OR 6.92, 95% CI 5.58–8.58. There was no interaction between elective versus spontaneous delivery. Overall, gestation at delivery accounted for 10% of the adjusted population attributable fraction of SEN. Because of their high frequency, early term deliveries (37–39 wk) accounted for 5.5% of cases of SEN compared with preterm deliveries (<37 wk), which accounted for only 3.6% of cases. <STRONG>Conclusions</STRONG> Gestation at delivery had a strong, dose-dependent relationship with SEN that was apparent across the whole range of gestation. Because early term delivery is more common than preterm delivery, the former accounts for a higher percentage of SEN cases. Our findings have important implications for clinical practice in relation to the timing of elective delivery

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

Weak point disorder in strongly fluctuating flux-line liquids

We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid of relativistic charged bosons in 2+1 dimensions [P. Benetatos and M. C. Marchetti, Phys. Rev. B 64, 054518, (2001)]. In this model, flux lines are allowed to be arbitrarily curved and can even form closed loops. Point defects can be scalar or polar. In the latter case, the direction of their dipole moments can be random or correlated. Within the Gaussian approximation of our hydrodynamic model, we calculate disorder-induced corrections to the correlation functions of the flux-line fields and the elastic moduli of the flux-line liquid. We find that scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease the tilt modulus.Comment: 15 pages, submitted to Pramana-Journal of Physics for the special volume on Vortex State Studie

Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.