Continuous dependence estimates for nonlinear fractional convection-diffusion equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.Comment: In this version we have corrected Example 3.4 explaining the link with the results in [51,59

Estimating the density scaling exponent of viscous liquids from specific heat and bulk modulus data

It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propto F(rho^gamma/T) [Schroder et al., arXiv:0803.2199]. We here show how to calculate the exponent gamma from bulk modulus and specific heat data, either measured as functions of frequency in the metastable liquid or extrapolated from the glass and liquid phases to a common temperature (close to the glass transition temperature). Thus an exponent defined from the response to highly nonlinear parameter changes may be determined from linear response measurements

The Late-time Expansion of the Ejecta of SN 1987A

The evolution of the shape and size of the ejecta of SN 1987A is analyzed over a period of ~ 8 years based on HST images and spectra taken between 1278 and 4336 days after the supernova outburst. We combine both proprietary and archival HST data obtained with the FOC, WFPC2 and STIS. The low resolution near-UV prism FOC spectrum obtained at day 3043 has not been described previously. Although the FWHM of the ejecta grew linearly over the time span studied, the appearance of the SN envelope also changed markedly with wavelength. At visible wavelengths (lambda ~ 5000 Angstrom) the ejecta became progressively more elongated, reaching an ellipticity epsilon ~ 0.25 by day 4000. In the near-UV (lambda ~ 2500 AA), the ejecta remained closely circular (epsilon <= 0.1) and ~ 50% larger in angular extent than in the visible. The FOC prism observations show that the large extent of the SN envelope is confined to a grouping of resonance lines spanning Mg I 2852, Mg II 2795,2802 and several Fe II multiplets -- thereby confirming that the larger size of the debris in the near-UV is due to scattering in these optically thick transitions compared to the optically thin forbidden and semi-forbidden transitions that dominate the visible spectrum. The available data are not of sufficient quality to detect the slight deviation from linear expansion expected for the outermost regions of the near-UV images as predicted by Chugai et al. (1997).Comment: Accepted for publication in A&A. 8 pages with 5 figures. Latex using Springer's A&A macros v4.0

Caught in the act: a helium-reionizing quasar near the line of sight to Q0302-003

We report the discovery of a quasar at z=3.050+/-0.003, closely coincident in redshift with the isolated low-opacity feature seen near z~3.056 in the otherwise black portion of the HeII Gunn-Peterson absorption trough seen toward the z=3.286 background quasar Q0302-003, located 6.5' away on the sky. We explore plausible models for the HeIII ionization zone created by this neighboring quasar and its interception with the line of sight toward Q0302-003. At its present brightness of V=20.5 and separation of D=3.2 Mpc, the quasar can readily account for the opacity gap in the HeII absorption spectrum of Q0302-003, provided it has been active for t_Q > 10^7 y. This is the first clear detection of the `transverse' proximity effect and imprint of a quasar on the intervening absorption detected along an adjacent line of sight

All-optical phase-regenerative multicasting of 40 Gbit/s DPSK signal in a degenerate phase sensitive amplifier

We demonstrate all-optical 1-to-5 differential phase-shift keyed (DPSK) wavelength multicasting at 40 Gbit/s using a degenerate four-wave mixing (FWM) based phase sensitive amplifier (PSA). Phase regenerative properties are reported with a sensitivity improvement of more that 10 dB

Saturation effects in degenerate phase sensitive fiber optic parametric amplifiers

We experimentally study saturation effects in degenerate phase sensitive amplifiers, revealing and explaining a gain regime suitable for all-optical signal processing functions such as phase regeneration

Experimental investigation of cut-off phenomena in non-linear photonic crystal fibers

The modal cut-off is investigated experimentally in a series of high quality non-linear photonic crystal fibers. We demonstrate a suitable measurement technique to determine the cut-off wavelength and verify it by inspecting the near field of the modes that may be excited below and above the cut-off. We observe a double peak structure in the cut-off spectra, which is attributed to a splitting of the higher order modes. The cut-off is measured for seven different fiber geometries with different pitches and relative hole size, and a very good agreement with recent theoretical work is found.Comment: 3 pages including 1 table and 4 figures. Accepted for Optics Letter

All-optical phase and amplitude regeneration properties of a 40 Gbit/s DPSK black-box phase sensitive amplifier

We experimentally study the pure amplitude and phase regeneration capabilities of a blackbox degenerate four wave mixing (FWM) based bit-rate-flexible phase sensitive amplifier (PSA) for a 40 Gbit/s differential phase-shift keyed (DPSK) signal

Survival of patients with small cell lung cancer undergoing lung resection in England, 1998–2009

Introduction: Chemotherapy or chemoradiotherapy is the recommended treatment for small cell lung cancer (SCLC), except in stage I disease where clinical guidelines state there may be a role for surgery based on favourable outcomes in case series. Evidence supporting adjuvant chemotherapy in resected SCLC is limited but this is widely offered. Methods: Data on 359 873 patients who were diagnosed with a first primary lung cancer in England between 1998 and 2009 were grouped according to histology (SCLC or non-SCLC (NSCLC)) and whether they underwent a surgical resection. We explored their survival using Kaplan-Meier analysis and Cox regression, adjusting for age, sex, comorbidity and socioeconomic status. Results: The survival of 465 patients with resected SCLC was lower than patients with resected NSCLC (5-year survival 31% and 45%, respectively), but much higher than patients of either group who were not resected (3%). The difference between resected SCLC and NSCLC diminished with time after surgery. Survival was superior for the subgroup of 198 'elective' SCLC cases where the diagnosis was most likely known before resection than for the subgroup of 267 'incidental' cases where the SCLC diagnosis was likely to have been made after resection. Conclusions: These data serve as a natural experiment testing the survival after surgical management of SCLC according to NSCLC principles. Patients with SCLC treated surgically for early stage disease may have survival outcomes that approach those of NSCLC, supporting the emerging clinical practice of offering surgical resection to selected patients with SCLC