Photonic crystal fiber with a hybrid honeycomb cladding

We consider an air-silica honeycomb lattice and demonstrate a new approach to the formation of a core defect. Typically, a high or low-index core is formed by adding a high-index region or an additional air-hole (or other low-index material) to the lattice, but here we discuss how a core defect can be formed by manipulating the cladding region rather than the core region itself. Germanium-doping of the honeycomb lattice has recently been suggested for the formation of a photonic band-gap guiding silica-core and here we experimentally demonstrate how an index-guiding silica-core can be formed by fluorine-doping of the honeycomb lattice.Comment: 5 pages including 3 figures. Accepted for Optics Expres

Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports

We demonstrate a new class of hollow-core Bragg fibers that are composed of concentric cylindrical silica rings separated by nanoscale support bridges. We theoretically predict and experimentally observe hollow-core confinement over an octave frequency range. The bandwidth of bandgap guiding in this new class of Bragg fibers exceeds that of other hollow-core fibers reported in the literature. With only three rings of silica cladding layers, these Bragg fibers achieve propagation loss of the order of 1 dB/m.Comment: 9 pages including 5 figure

Dietary determinants of changes in waist circumference adjusted for body mass index - a proxy measure of visceral adiposity

Background Given the recognized health effects of visceral fat, the understanding of how diet can modulate changes in the phenotype “waist circumference for a given body mass index (WCBMI)”, a proxy measure of visceral adiposity, is deemed necessary. Hence, the objective of the present study was to assess the association between dietary factors and prospective changes in visceral adiposity as measured by changes in the phenotype WCBMI. Methods and Findings We analyzed data from 48,631 men and women from 5 countries participating in the European Prospective Investigation into Cancer and Nutrition (EPIC) study. Anthropometric measurements were obtained at baseline and after a median follow-up time of 5.5 years. WCBMI was defined as the residuals of waist circumference regressed on body mass index, and annual change in WCBMI (¿WCBMI, cm/y) was defined as the difference between residuals at follow-up and baseline, divided by follow-up time. The association between energy, energy density (ED), macronutrients, alcohol, glycemic index (GI), glycemic load (GL), fibre and ¿WCBMI was modelled using centre-specific adjusted linear regression, and random-effects meta-analyses to obtain pooled estimates. Men and women with higher ED and GI diets showed significant increases in their WCBMI, compared to those with lower ED and GI [1 kcal/g greater ED predicted a ¿WCBMI of 0.09 cm (95% CI 0.05 to 0.13) in men and 0.15 cm (95% CI 0.09 to 0.21) in women; 10 units greater GI predicted a ¿WCBMI of 0.07 cm (95% CI 0.03 to 0.12) in men and 0.06 cm (95% CI 0.03 to 0.10) in women]. Among women, lower fibre intake, higher GL, and higher alcohol consumption also predicted a higher ¿WCBMI. Conclusions Results of this study suggest that a diet with low GI and ED may prevent visceral adiposity, defined as the prospective changes in WCBMI. Additional effects may be obtained among women of low alcohol, low GL, and high fibre intake

Laudatores Temporis Acti, or Why Cosmology is Alive and Well - A Reply to Disney

A recent criticism of cosmological methodology and achievements by Disney (2000) is assessed. Some historical and epistemological fallacies in the said article have been highlighted. It is shown that---both empirically and epistemologically---modern cosmology lies on sounder foundations than it is portrayed. A brief historical account demonstrates that this form of unsatisfaction with cosmology has had a long tradition, and rather meagre results in the course of the XX century.Comment: 11 pages, no figures; a criticism of astro-ph/0009020; Gen. Rel. Grav., accepted for publicatio

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Metal enrichment and evolution in four z > 6.5 quasar sightlines observed with JWST/NIRSpec

We present JWST/NIRSpec R$\approx$2700 spectra of four high-redshift quasars: VDES J0020-3653 (z = 6.860), DELS J0411-0907(z = 6.825), UHS J0439+1634 (z = 6.519) and ULAS J1342+0928 (z = 7.535). The exquisite data quality, signal-to-noise ratio of 50-200, and large $0.86\!~\mu{\rm m}\le \lambda \le 5.5\!~\mu{\rm m}$ spectral coverage allows us to identify between 13 and 17 intervening and proximate metal absorption line systems in each quasar spectrum, with a total number of 61 absorption-line systems detected at $2.42<z<7.48$ including the highest redshift intervening OI $\lambda$1302 and MgII systems at $z=7.37$ and $z=7.44$. We investigate the evolution of the metal enrichment in the epoch of reionization at $z>6$ and find: i) A continued increase of the low-ionization OI, CII, and SiII incidence, ii) Decreasing high-ionization CIV and SiIV incidence with a transition from predominantly high- to low-ionization at $z\approx6.0$, and iii) a constant MgII incidence across all redshifts. The observations support a change in the ionization state of the intergalactic medium in the EoR rather than a change in metallicity. The abundance ratio of [Si/O] in five $z>6$ absorption systems show enrichment signatures produced by low-mass Pop III pair instability supernovae, and possibly Pop III hypernovae. In the Gunn-Peterson troughs we detect transmission spikes where Ly$\alpha$ photons can escape. From 22 absorption systems at $z>5.7$, only a single low-ionization system out of 13 lies within 2000 km s$^{-1}$ from a spike, while four high-ionization systems out of nine lie within $\sim$2000 km s$^{-1}$ from a spike. This confirms that galaxies responsible for the heavy elements that are transported into the circumgalactic medium lie in predominantly in high-density, neutral environments, while lower density environments are ionized without being polluted by metals at $z\approx$ 6-7. [abridged]Comment: 50 pages including 30 pages of appendices. Submitted to A&

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure