Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Vernetzung und Abbau von Polyäthylenterephthalat durch Elektronenbestrahlung

Zusammenfassung PÄT-Folien wurden in Luft, Stickstoff und Vakuum bei 20 °C mit 1 MeV-Elektronen bestrahlt. Untersucht wurden Löslichkeit und Viskosität von Proben, die unmittelbar nach der Bestrahlung gelöst wurden.In allen untersuchten Fällen trat bei hohen Bestrahlungsdosen ein unlöslicher, d. h. vernetzter Anteil auf, dessen Ausbildung jedoch durch in den Proben enthaltene Feuchtigkeit verzögert werden kann. Bei niedrigen Bestrahlungsdosen bewirkt Feuchtigkeit einen Abbau des Polymeren, wie durch Viskositätsmessungen gezeigt wird.Aus den Gel-Messungen wurde derp ₀/q ₀-Wert für Bestrahlung in Luft, Stickstoff und Vakuum zu 1,05 bestimmt.Die Änderung des Gel-Anteils bei Lagerung der Proben zwischen Bestrahlung und Lösung wird diskutiert.

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Summary Polyethyleneterephthalate samples were irradiated in air, nitrogen and vacuum at 20 °C with 1 MeV electrons. The solubility of the samples and the viscosity of the solutions were studied immediately after irradiation. At high doses an insoluble crosslinked part was always observed. Crosslinking was delayed by moisture in the samples. At low irradiation doses moisture causes chain scission as shown by viscosity measurements. The ratiop ₀/q ₀ of degradation to crosslinking in the case of irradiation in air, nitrogen and vacuum was found by gel measurements to be 1.05. The insoluble gel-part changes with increasing storage time of the samples between irradiation and solution.

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Herrn Diplom-PhysikerH. Fischer sei an dieser Stelle für wertvolle Anregungen und Diskussionen besonders gedankt.     

Synthesis and characterization of water-soluble phenylene-vinylene-based singlet oxygen sensitizers for two-photon excitation

[reaction: see text] The synthesis and characterization of water-soluble singlet oxygen sensitizers with a phenylene-vinylene motif is presented. The principal motivation for this study was to better understand specific features of a water-soluble molecule that influence the photosensitized production of singlet oxygen upon nonlinear, two-photon excitation of that molecule. To achieve water solubility, sensitizers were synthesized with ionic as well as nonionic substituents. In the ionic approach, salts of N-methylated pyridine, benzothiazole, and 1-methyl-piperazine moieties were used, as were aryl-substituted sulfonic acid moieties. In the nonionic approach, aryl-substituted triethylene glycol moieties were used. Selected photophysical properties of the compounds synthesized were determined, including singlet oxygen quantum yields. Of the molecules examined, the most efficient singlet oxygen sensitizers had triethylene glycol units as the functional group that imparted water solubility. Molecules containing the ionic moieties did not make singlet oxygen in appreciable yield nor did they efficiently fluoresce. Rather, for these latter molecules, rapid charge-transfer-mediated non-radiative processes appear to dominate excited state deactivation.     

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.     

Theoretical stability,thin film synthesis and transport properties of the Mon +1GaCn MAX phase

The phase stability of Mo_{n +1}GaC_n has been investigated using ab‐initio calculations. The results indicate stability for the Mo₂GaC phase only, with a formation enthalpy of –0.4 meV per atom. Subsequent thin film synthesis of Mo₂GaC was performed through magnetron sputtering from elemental targets onto Al₂O₃ [0001], 6H‐SiC [0001] and MgO [111] substrates within the temperature range of 500 °C and 750 °C. High structural quality films were obtained for synthesis on MgO [111] substrates at 590 ºC. Evaluation of transport properties showed a superconducting behavior with a critical temperature of approximately 7 K, reducing upon the application of an external magnetic field. The results point towards the first superconducting MAX phase in thin film form. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality

A study is made of a recent integral identity of B. Helffer and J. Sjöstrand, which for a not yet fully determined class of probability measures yields a formula for the covariance of two functions (of a stochastic variable); in comparison with the Brascamp-Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover deduced from the obtained abstract expression for the range projection. As a corollary, a generalised version of Brascamp-Lieb's inequality is obtained. For a certain class of measures occuring in statistical mechanics, explicit criteria for the Witten-Laplacians are found from the Persson-Agmon formula, from compactness of embeddings and from the Weyl calculus, which give results for closed range, strict positivity, essential self-adjointness and domain characterisations.Supported by TMR grant FMRX-CT960001 of the European Commision, PDE and QM at Université de Paris-Sud, France; partly by the Danish Natural Sciences Research Council, grant 9700987.