The contraction number of a multigrid method for solving the Poisson equation

Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.Dedicated to Professor Dr.Dr.h.c. Lothar Collatz on the occasion of his 70 th birthday     

An anchoring strategy for photoswitchable biosensor technology: azobenzene-modified SAMs on Si(111)

A mild and efficient procedure has been developed to obtain covalently attached self-assembled monolayers (SAMs) on Si(111) with photochromic azobenzene head-groups. Starting from neat or diluted carboxylic acid functionalized monolayers on-chip coupling reactions were applied to attach hydroxyl-functionalized azobenzene units to the SAMs by ester bond formation. The modified surfaces were characterized by high-resolution X-ray photoelectron spectroscopy (XPS), transmission Fourier transform infrared spectroscopy (FT-IR), and contact angle measurements. Reversible cis ↔ trans isomerizations of photoswitchable SAMs were monitored by wettability measurements. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users. Dedicated with respect and compliments to Professor Helmut Schwarz on the occasion of his 65th birthday.     

Non-singular space-times with a negative cosmological constant: V. Boson stars

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.     

Coherent electromagnetic radiation from the fragments of nuclear fission

The electromagnetic radiation from two vibrating fission fragments is classically treated. The rotational and translational motion of the fragments during emission and the interference of the radiation from the two individual fragments are taken into account. It is shown that the angular distribution of the radiation contains valuable information on the fission process and that the spectral distribution depends sensitively on the damping of the shape vibration.Dedicated to Professor P. Armbruster and P. Kienle on the occasion of their 60th birthday     

Classical r-Matrices and Novikov Algebras

We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.     

Magnetic properties of nanostructured MnZn ferrite

Mn_0.5Zn_0.5Fe₂O₄ nanoparticles (10-30 nm) have been prepared via mechanochemical processing, using a mixture of two single-phase ferrites, MnFe₂O₄ and ZnFe₂O₄. SQUID measurements (field-cooled magnetization curves and hysteresis loops) were performed to follow the mechanically induced evolution of the MnFe₂O₄/ZnFe₂O₄ mixture submitted to the high-energy milling process. The resulting single MnZn nanoferrite phase was characterized by SQUID (M-H curve), Faraday balance (M-T curve) and transmission electron microscopy. The magnetic characteristics of the mechanosynthesized material were compared with those of bulk Mn_0.5Zn_0.5Fe₂O₄. It was found that the saturation magnetization of nanostructured Mn_0.5Zn_0.5Fe₂O₄ (87.2 emu/g) is lower than that of the bulk Mn_0.5Zn_0.5Fe₂O₄, but, the Néel temperature of the sample (583 K) is higher than that of the bulk Mn_0.5Zn_0.5Fe₂O₄.     

Off-equilibrium photon production during the chiral phase transition

In the early stage of ultrarelativistic heavy-ion collisions chiral symmetry is restored temporarily. During this so-called chiral phase transition, the quark masses change from their constituent to their bare values. This mass shift leads to the spontaneous non-perturbative creation of quark–antiquark pairs, which effectively contributes to the formation of the quark–gluon plasma. We investigate the photon production induced by this creation process. We provide an approach that eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable in the ultraviolet domain. The off-equilibrium photon numbers are of quadratic order in the perturbative coupling constants while a thermal production is only of quartic order. Quantitatively, we find, however, that for the most physical mass-shift scenarios and for photon momenta larger than 1 GeV the off-equilibrium processes contribute less photons than the thermal processes.