The Anderson model of localization: a challenge for modern eigenvalue methods

We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.Comment: 16 LaTeX pages with 3 figures include

Forecasting constraints from the cosmic microwave background on eternal inflation

We forecast the ability of cosmic microwave background (CMB) temperature and polarization datasets to constrain theories of eternal inflation using cosmic bubble collisions. Using the Fisher matrix formalism, we determine both the overall detectability of bubble collisions and the constraints achievable on the fundamental parameters describing the underlying theory. The CMB signatures considered are based on state-of-the-art numerical relativistic simulations of the bubble collision spacetime, evolved using the full temperature and polarization transfer functions. Comparing a theoretical cosmic-variance-limited experiment to the WMAP and Planck satellites, we find that there is no improvement to be gained from future temperature data, that adding polarization improves detectability by approximately 30%, and that cosmic-variance-limited polarization data offer only marginal improvements over Planck. The fundamental parameter constraints achievable depend on the precise values of the tensor-to-scalar ratio and energy density in (negative) spatial curvature. For a tensor-to-scalar ratio of $0.1$ and spatial curvature at the level of $10^{-4}$, using cosmic-variance-limited data it is possible to measure the width of the potential barrier separating the inflating false vacuum from the true vacuum down to $M_{\rm Pl}/500$, and the initial proper distance between colliding bubbles to a factor $\pi/2$ of the false vacuum horizon size (at three sigma). We conclude that very near-future data will have the final word on bubble collisions in the CMB.Comment: 14 pages, 6 figure

Fused filament fabrication: Comparison of methods for determining the interfacial strength of single welded tracks

The mechanical properties of plastic-based additively manufactured specimens have been widely discussed. However, there is still no standard that can be used to determine properties such as the interfacial strength of adjacent tracks and also to exclude the influence of varying manufacturing conditions. In this paper, a proposal is made to determine the interfacial strength using specimens with only one track within a layer. For this purpose, so-called single-wall specimens of polylactide were characterised under tensile load and the interfacial area between the adjacent layers was determined using three methods. It turned out that the determination of the interfacial area via the fracture surface is the most accurate method for determining the interfacial strength. The measured interfacial strengths were compared with the bulk material strength and it was found that the bulk material strength can be achieved under optimal conditions in the FFF process. It was also observed that with increasing nozzle temperature, the simultaneous printing of specimens influences the interfacial strength. To conclude, this method allows to measure the interfacial strength without superimposing the influence of voids. However, for example, the interfacial strength within a layer cannot be determined

Development of an Injection Molding Process for Long Glass Fiber-Reinforced Phenolic Resins

Glass fiber-reinforced phenolic resins are well suited to substitute aluminum die-cast materials. They meet the high thermomechanical and chemical demands that are typically found in combustion engine and electric drive train applications. An injection molding process development for further improving their mechanical properties by increasing the glass fiber length in the molded part was conducted. A novel screw mixing element was developed to improve the homogenization of the long fibers in the phenolic resin. The process operation with the mixing element is a balance between the desired mixing action, an undesired preliminary curing of the phenolic resin, and the reduction of the fiber length. The highest mixing energy input leads to a reduction of the initial fiber length L(0) = 5000 μm to a weighted average fiber length of L(p) = 571 μm in the molded part. This is an improvement over L(p) = 285 μm for a short fiber-reinforced resin under comparable processing conditions. The mechanical characterization shows that for the long fiber-reinforced materials, the benefit of the increased homogeneity outweighs the disadvantages of the reduced fiber length. This is evident from the increase in tensile strength from σ(m) = 21 MPa to σ(m) = 57 MPa between the lowest and the highest mixing energy input parameter settings

Compounding of short fiber reinforced phenolic resin by using specific mechanical energy input as a process control parameter

For a newly developed thermoset injection molding process, glass fiber-reinforced phenolic molding compounds with fiber contents between 0 wt% and 60 wt% were compounded. To achieve a comparable remaining heat of the reaction in all compound formulations, the specific mechanical energy input (SME) during the twin-screw extruder compounding process was used as a control parameter. By adjusting the extruder screw speed and the material throughput, a constant SME into the resin was targeted. Validation measurements using differential scanning calorimetry showed that the remaining heat of the reaction was higher for the molding compounds with low glass fiber contents. It was concluded that the SME was not the only influencing factor on the resin crosslinking progress during the compounding. The material temperature and the residence time changed with the screw speed and throughput, and most likely influenced the curing. However, the SME was one of the major influence factors, and can serve as an at-line control parameter for reactive compounding processes. The mechanical characterization of the test specimens revealed a linear improvement in tensile strength up to a fiber content of 40–50 wt%. The unnotched Charpy impact strength at a 0° orientation reached a plateau at fiber fractions of approximately 45 wt%

Development of an injection molding process for long glass fiber-reinforced phenolic resins

Glass fiber-reinforced phenolic resins are well suited to substitute aluminum die-cast materials. They meet the high thermomechanical and chemical demands that are typically found in combustion engine and electric drive train applications. An injection molding process development for further improving their mechanical properties by increasing the glass fiber length in the molded part was conducted. A novel screw mixing element was developed to improve the homogenization of the long fibers in the phenolic resin. The process operation with the mixing element is a balance between the desired mixing action, an undesired preliminary curing of the phenolic resin, and the reduction of the fiber length. The highest mixing energy input leads to a reduction of the initial fiber length L0 = 5000 μm to a weighted average fiber length of Lp = 571 μm in the molded part. This is an improvement over Lp = 285 μm for a short fiber-reinforced resin under comparable processing conditions. The mechanical characterization shows that for the long fiber-reinforced materials, the benefit of the increased homogeneity outweighs the disadvantages of the reduced fiber length. This is evident from the increase in tensile strength from σm = 21 MPa to σm = 57 MPa between the lowest and the highest mixing energy input parameter settings

Linearly polarized X-ray flares following short gamma-ray bursts

Soft X-ray flares were detected to follow the short-duration gamma-ray burst GRB 050724. The temporal properties of the flares suggest that they are likely due to the late time activity of the central engine. We argue that if short GRBs are generated through compact star mergers, as is supported by the recent observations, the jet powering the late X-ray flares must be launched via magnetic processes rather than via neutrino-antineutrino annihilations. As a result, the X-ray flares following short GRBs are expected to be linearly polarized. The argument may also apply to the X-ray flares following long GRBs. Future observations with the upcoming X-ray polarimeters will test this prediction.Comment: 4 pages (no figure), accepted for publication in ApJL, typos correcte

Compound-Specific Chlorine Isotope Analysis of the Herbicides Atrazine, Acetochlor, and Metolachlor

A gas chromatography-single quadrupole mass spectrometry method was developed and validated for compound-specific chlorine isotope analysis (Cl-CSIA) of three chlorinated herbicides, atrazine, acetochlor, and metolachlor, which are widespread contaminants in the environment. For each compound, the two most abundant ions containing chlorine (202/200 for atrazine, 225/223 for acetochlor, and 240/238 for metolachlor) and a dwell time of 30 ms were determined as optimized MS parameters. A limit of precise isotope analysis for ethyl acetate solutions of 10 mg/L atrazine, 10 mg/L acetochlor, and 5 mg/L metolachlor could be reached with an associated uncertainty between 0.5 and 1 . To this end, samples were measured 10-fold and bracketed with two calibration standards that covered a wide range of δ37Cl values and for which amplitudes matched those of the samples within 20% tolerance. The method was applied to investigate chlorine isotope fractionation during alkaline hydrolysis of metolachlor, which showed a shift in δ37Cl of +46 after 98% degradation, demonstrating that chlorine isotope fractionation could be a sensitive indicator of transformation processes even when limited degradation occurs. This method, combined with large-volume solid-phase extraction (SPE), allowed application of Cl-CSIA to environmentally relevant concentrations of widespread herbicides (i.e., 0.5-5 μg/L in water before extraction). Therefore, the combination of large-volume SPE and Cl-CSIA is a promising tool for assessing the transformation processes of these pollutants in the environment

A Chandra Search for Coronal X Rays from the Cool White Dwarf GD 356

We report observations with the Chandra X-ray Observatory of the single, cool, magnetic white dwarf GD 356. For consistent comparison with other X-ray observations of single white dwarfs, we also re-analyzed archival ROSAT data for GD 356 (GJ 1205), G 99-47 (GR 290 = V1201 Ori), GD 90, G 195-19 (EG250 = GJ 339.1), and WD 2316+123 and archival Chandra data for LHS 1038 (GJ 1004) and GD 358 (V777 Her). Our Chandra observation detected no X rays from GD 356, setting the most restrictive upper limit to the X-ray luminosity from any cool white dwarf -- L_{X} < 6.0 x 10^{25} ergs/s, at 99.7% confidence, for a 1-keV thermal-bremsstrahlung spectrum. The corresponding limit to the electron density is n_{0} < 4.4 x 10^{11} cm^{-3}. Our re-analysis of the archival data confirmed the non-detections reported by the original investigators. We discuss the implications of our and prior observations on models for coronal emission from white dwarfs. For magnetic white dwarfs, we emphasize the more stringent constraints imposed by cyclotron radiation. In addition, we describe (in an appendix) a statistical methodology for detecting a source and for constraining the strength of a source, which applies even when the number of source or background events is small.Comment: 27 pages, 4 figures, submitted to the Astrophysical Journa