Mixed moments of characteristic polynomials of random unitary matrices

Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table

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

Improved measurement results for the Avogadro constant using a 28Si-enriched crystal

New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of $N_A = 6.022 140 76(12) \times 10^{23}$ mol$^{-1}$. The X-ray crystal density method has thus achieved the target relative standard uncertainty of $2.0 \times 10^{-8}$ necessary for the realization of the definition of the new kilogram.Comment: postprint, 22 page, 3 figures, 14 table

The preparation of HEMA-MPC films for ocular drug delivery

There is a need to prolong drug residence time using a biocompatible formulation in the subconjunctival space after surgery to treat glaucoma. Drug releasing discs were prepared with 2-(hydroxyethyl)methacrylate (HEMA) and 2-methacryloyl-oxyethyl phosphorylcholine (MPC). The ratio of bound water (Wb) to free water (Wf) ratio increased from 1:0.3 to 1:6.8 with increasing MPC (0 to 50%, w/w). The optimal balance between water content, SR and mechanical strength were obtained with 10% MPC (w/w) hydrogels. Water-alcohol mixtures were examined to facilitate loading of poorly soluble drugs, and they showed greater hydrogel swelling than either water or alcohol alone. The SR was 1.2 ± 0.02 and 3.3 ± 0.1 for water and water:ethanol (1:1) respectively. HEMA-MPC (10%) discs were loaded with dexamethasone using either water:ethanol (1:1) or methanol alone. Drug release was examined in an outflow rig model that mimics the subconjunctival space in the eye. Dexamethasone loading increased from 0.3 to 1.9 mg/disc when the solvent was changed from water:ethanol (1:1) to methanol with the dexamethasone half-life (t½) increasing from 1.9 to 9.7 days respectively. These encouraging results indicate that HEMA-MPC hydrogels have the potential to sustain the residence time of a drug in the subconjunctival space of the eye

Phylogeographic Study of Apodemus ilex (Rodentia: Muridae) in Southwest China

BACKGROUND: The Mountains of southwest China have complex river systems and a profoundly complex topography and are among the most important biodiversity hotspots in the world. However, only a few studies have shed light on how the mountains and river valleys promote genetic diversity. Apodemus ilex is a fine model for investigating this subject. METHODOLOGY/PRINCIPAL FINDINGS: To assess the genetic diversity and biogeographic patterns of Apodemus ilex, the complete cytochrome b gene sequences (1,140 bp) were determined from 203 samples of A. draco/ilex that were collected from southwest China. The results obtained suggested that A. ilex and A. draco are sistergroups and diverged from each other approximately 2.25 million years ago. A. ilex could be divided into Eastern and Western phylogroups, each containing two sub-groups and being widespread in different geographical regions of the southern Hengduan Mountains and the western Yunnan - Guizhou Plateau. The population expansions of A. ilex were roughly from 0.089 Mya to 0.023 Mya. CONCLUSIONS: Our result suggested that A. ilex is a valid species rather than synonym of A. draco. As a middle-high elevation inhabitant, the phylogenetic pattern of A. ilex was strongly related to the complex geographical structures in southwest China, particularly the existence of deep river valley systems, such as the Mekong and Salween rivers. Also, it appears that the evolutionary history of A. ilex, such as lineage divergences and population expansions were strongly affected by climate fluctuation in the Late Pleistocene

Vascular risk factors in glaucoma: the results of a national survey

Background The role of vascular risk factors in glaucoma is still being debated. To assess the importance of vascular risk factors in patients with primary open-angle glaucoma (POAG), data from the medical history of 2,879 POAG patients and 973 age-matched controls were collected and analyzed. Methods Design: observational survey. Setting: 35 Italian academic centers. Study population: POAG patients and age-matched controls. In order to reduce bias consecutive patients were included. Observation procedures: data concerning vascular risk factors were collected for all patients with a detailed questionnaire. A complete ophthalmological examination with assessment of intraocular pressure (IOP), visual field, optic disc, and systemic blood pressure was performed. Main outcome measures: the ESH-ESC (European Society of Hypertension-European Society of Cardiology) guidelines were used to calculate the level of cardiovascular risk. Crude and adjusted estimates of the odds ratios (OR) were calculated for all cardiovascular risk factors in POAG and controls. Results The study included 2,879 POAG patients and 973 controls. POAG cases had a significantly higher systolic and diastolic blood pressure (p=0.001) and systolic perfusion pressure (p=0.02) as compared with controls. Also mean IOP was significantly higher in the POAG group (p=0.01), while diastolic perfusion pressure was not significantly different in the two groups. Myopia was more prevalent in the POAG group (23 vs 18%, p=0.005) as well as a positive family history for glaucoma (26 vs 12%, p= 0.004). POAG patients tended to have a higher cardiovascular risk than controls: 63% of glaucoma cases vs 55% of controls (OR: 1.38, p=0.005) had a “high” or “very high” cardiovascular risk. Conclusions The level of cardiovascular risk was significantly higher in glaucoma patients than in controls

The design, construction, and commissioning of the KATRIN experiment

The KArlsruhe TRItium Neutrino (KATRIN) experiment, which aims to make a direct and model-independent determination of the absolute neutrino mass scale, is a complex experiment with many components. More than 15 years ago, we published a technical design report (TDR) [1] to describe the hardware design and requirements to achieve our sensitivity goal of 0.2 eV at 90% C.L. on the neutrino mass. Since then there has been considerable progress, culminating in the publication of first neutrino mass results with the entire beamline operating [2]. In this paper, we document the current state of all completed beamline components (as of the first neutrino mass measurement campaign), demonstrate our ability to reliably and stably control them over long times, and present details on their respective commissioning campaigns

A new 28Si single crystal: counting the atoms for the new kilogram definition

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