A Pregenerator for Burgers Equation¶Forced by Conservative Noise

We consider the stationarity of a Burgers equation with an external random force of gradient type in one space dimension. The expected stationary measure is the white noise measure on the space of tempered distributions. As a consequence, the nonlinearity of the formal equation u _t +λu u _x =νu _xx +η _x is ill-defined. Introducing a pregenerator we can formulate a generalized martingale problem leading to a meaningful version of the formal equation which was an open problem. Received: 9 March 2001 / Accepted: 10 October 2001     

Heavy element research at GSI — Recent results and perspectives

The nuclear shell model predicts that the next doubly magic shellclosure beyond ²⁰⁸Pb is at a proton number between Z=114 and 126 and at a neutron number N=184. The outstanding aim of experimental investigations is the exploration of this region of spherical ‘Superheavy Elements’. This article describes the experiments that were performed recently at the GSI SHIP. They resulted in an unambiguous identification of elements 110 to 112. They were negative so far in searching for elements 113, 116, and 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism are also presented.     

Synthesis and solid-state organization of coil-ring-coil block copolymers

Shape-persistent macrocycles based on the phenyl-ethynyl-butadienyl backbone containing two extraannular hydroxyl groups were prepared by the oxidative coupling of the appropriate phenylethynyl oligomers. Carbodiimide-directed coupling with independently synthesized polystyrene carboxylic acid oligomers led to ABA coil-ring-coil block copolymers in which the central macrocycle serves as rigid and the polystyrene oligomers as flexible elements. Depending on the size of the coil blocks, these structures aggregate in cyclohexane into supramolecular hollow cylindrical brushes in which the rigid core is surrounded by the flexible matrix. However, in the solid state it is not possible to identify a morphology in which isolated channels based on aggregated macrocycles are embedded in a matrix of polystyrene. Detailed X-ray and electron diffraction studies on samples prepared from a solution in cyclohexane under equilibrium conditions show that the material adopts a lamellar morphology in the solid state in which columns of macrocycles are aggregated into layers which are separated by polystyrene.     

Solvent triggering between conformational states in amphiphilic shape-persistent macrocycles

The amphiphilic shape-persistent macrocycle 1 containing four phenol-OH groups as polar side groups and four hexyloxy groups as nonpolar side groups in an adaptable arrangement was recrystallized from solvents of different polarity. X-ray crystallography reveals that the conformation of the macrocycle is solvent dependent such that in the pyridine solvate only two of the nonpolar side groups point outward while in the THF solvate all four of them point outward. Moreover, in the latter case the three-dimensional packing leads to the formation of a supramolecular channel structure with a large pore size.     

Simultaneous Raman and fluorescence spectroscopy of single conjugated polymer chains

Simultaneous surface enhanced Raman scattering (SERS) and fluorescence is demonstrated from single conjugated polymer chains. As resonance enhancement of SERS depends on the spectral overlap of the polymer's absorption and the incident laser, resonance Raman and fluorescence effectively probe the absorbing and emitting part of the polymer, respectively. The optical phonon energies change along the polymer chain, providing a window to spatially track excited state relaxation. Whereas a mean spatial redistribution of the excitation is witnessed by a change in vibronic fingerprint following interchromophoric energy transfer, intrachromophoric exciton self-trapping leaves the vibrations unchanged.     

Self-intersecting geodesics and entropy of the geodesic flow

Given a symmetric Finsler metric on T^2 whose geodesic flow has zero topological entropy, we show that the lift in the universal covering R^2 →T^2 of any closed geodesic on T^2 must be an embedded curve in R^2.     

Synthesis and Mesophase Properties of Intraanular Functionized Shape-persistent Macrocycles Containing Dibenzo [fg,op] naphthacenes

IntroductionDiscotic liquid crystals can exhibit both columnarand nematic mesophases. The columnar mesophaseshave wider potential applications to conducting andphotoconducting systems, optical data storage, light-emitting diodes, photovoltaic solar cells,…