L1L^1 contraction for bounded (non-integrable) solutions of degenerate parabolic equations

We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms. As opposed to previous results, our results apply without any integrability assumption on the %(the positive part of the difference of) solutions. They take the form of partial Duhamel formulas and can be seen as quantitative extensions of finite speed of propagation local $L^1$ contraction results for scalar conservation laws. A key ingredient in the proofs is a new and non-trivial construction of a subsolution of a fully non-linear (dual) equation. Consequences of our results are maximum and comparison principles, new a priori estimates, and in the non-local case, new existence and uniqueness results

Analysis and assessment of film materials and associated manufacturing processes for a solar sail

Candidate resin manufacturers and film producers were surveyed to determine the availability of key materials and to establish the capabilities of fabricators to prepare ultrathin films of these materials within the capacity/cost/time constraints of the Halley program. Infrared spectra of three candidate samples were obtained by pressing each sample against an internal reflection crystal with the polymer sandwiched between the crystal and the metal backing. The sample size was such that less than one-fourth of the surface of the crystal was covered with the sample. This resulted in weak spectra requiring a six-fold expansion. Internal reflection spectra of the three samples were obtained using both a KRS-5 and a Ge internal reflection crystal. Subtracted infrared spectra of the three samples are presented

Investigating CXOU J163802.6-471358: a new pulsar wind nebula in the Norma region?

We present the first analysis of the extended source CXOU J163802.6--471358, which was discovered serendipitously during the {\em Chandra} X-ray survey of the Norma region of the Galactic spiral arms. The X-ray source exhibits a cometary appearance with a point source and an extended tail region. The complete source spectrum is fitted well with an absorbed power law model and jointly fitting the {\em Chandra} spectrum of the full source with one obtained from an archived {\em XMM-Newton} observation results in best fit parameters $N_{\rm H}$ $=1.5^{+0.7}_{-0.5}\times10^{23} \text{cm}{^{-2}}$ and $\Gamma=1.1^{+0.7}_{-0.6}$ (90$$ confidence uncertainties). The unabsorbed luminosity of the full source is then $L_X\sim 4.8\times10^{33}d_{10}^2$ergs s$^{-1}$ with $d_{10}=d/10$kpc, where a distance of 10 kpc is a lower bound inferred from the large column density. The radio counterpart found for the source using data from the Molonglo Galactic Plane Survey epoch-2 (MGPS-2) shows an elongated tail offset from the X-ray emission. No infrared counterpart was found. The results are consistent with the source being a previously unknown pulsar driving a bow shock through the ambient medium

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

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

Strategies for aeroelastic parameter identification from bridge deck free vibration data

Author's manuscript version. The version of record is available from the publisher via: doi:10.1016/S0167-6105(01)00091-5. Copyright © 2001 Elsevier Science Ltd. All rights reserved.Several techniques for identification of aerodynamic derivatives (ADs) from free vibration test data are compared using simulated data and test data obtained from wind tunnel tests. These identification methods include system identification from one degree of freedom or two degree of freedom response to either transient excitation or to turbulent buffeting. The experimental and analytical difficulties involved in each method are highlighted and suggestions made for the best approach to determination of ADs in both model and full-scale studies. Time domain methods using step relaxation provided the best results as long as air-flow turbulence does not cause severe signal to noise ratio problems with the free vibration decay. When, as in full-scale, the turbulence is the primary forcing function, time domain and frequency domain methods can be used to recover the full set of ADs concerning vertical and torsional respons