LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.     

Emission,Emissionslebensdauer und Absorption von [Cr urea6]X3-Einkristallen

Emission and absorption polarization spectra as well as emission lifetimes between room temperature and 5 °K have been measured of [Cr urea₆]X₃ single crystals, where X stands for ClO ₄ ^– , J^–, NO ₃ ^– , Br^–, Cl^–, F^–, and X₃ for JSO ₄ ^3– . The strong temperature dependence of the fluorescence/phosphorescence-ratios, and of the emission lifetimes is discussed. The differences between the spectra as well as the emission lifetimes of the various salts can be attributed to an anion dependent trigonal perturbation.

Die Autoren danken dem Verband der Chemischen Industrie für finanzielle Unterstützung dieser Arbeit.     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.     

Scattering loss in Nd-doped silica based optical fibers

Rare-earth doped fibers suffer from relatively high attenuation in comparison to conventional communication fibers. In order to improve the properties of such fibers, understanding of the mechanisms involved in scattering effects is of great importance. The effect of Nd-doping, Al-codoping and of the drawing temperature on the scattering effect was investigated for several different optical fibers. To this end a measuring setup was realized which allows absolute measurements of the scattering coefficient at different positions along a fiber. Also separation of total attenuation and scattering effects is possible. The presented results indicate scattering effects as primary source for increased attenuation compared with undoped fibers.     

Relativistic orbits of classical charged bodies in a spherically symmetric electrostatic field

The orbits of a relativistic charged body in a static, spherically symmetric electric field are calculated and classified in the classical theory. Contrary to the nonrelativistic problem, we find that there is a limiting minimal value for the angular momentumL _c . Should the actual angular momentum of a charged test body be lower than this limit, the test particle will spiral into the central point charge instead of having (precessing) Keplerian orbits.     

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.     

Adaption of a diffractometer for time‐resolved X‐ray resonant magnetic scattering

A new set‐up is presented to measure element‐selective magnetization dynamics using the ALICE chamber [Grabis et al. (2003), Rev. Sci. Instrum. 74 , 4048–4051] at the BESSY II synchrotron at the Helmholtz‐Zentrum Berlin. A magnetic‐field pulse serves as excitation, and the magnetization precession is probed by element‐selective X‐ray resonant magnetic scattering. With the use of single‐bunch‐generated X‐rays a temporal resolution well below 100 ps is reached. The ALICE diffractometer environment enables investigations of thin films, described here, multilayers and laterally structured samples in reflection or diffuse scattering geometry. The combination of the time‐resolved set‐up with a cryostat in the ALICE chamber will allow temperature‐dependent studies of precessional magnetization dynamics and of damping constants to be conducted over a large temperature range and for a large variety of systems in reflection geometry.     

Bending insensitivity of fiber Bragg gratings in suspended-core optical fibers

This Letter presents simulation and experimental results that explore bending insensitivity of fiber Bragg gratings in suspended-core optical fibers. The implementation of thin silica bridge in the fibers enhances index contrast of the fiber core and reduces bending-induced strain transfer to the fiber core. This fiber design lead to a reduction of over 7 times in strain-induced fiber Bragg grating resonant peak shifts in the suspended-core fiber compared with that in standard telecommunication fiber, and an 0.14 dB bending loss at a bending radius of 6.35 mm.