A generalized approach to beam wave interaction with a dielectric interface

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higherorder components that cause angular beam deflection. Any bounded, symmetric beam, which is not necessarily Gaussian, can be comprised in terms of an angular spectrum of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. The procedure is applied to a Cauchy profile, and analytical results are given. Comparison with previous results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.     

Das Eigenwertproblem der selbstadjungierten linearen Differentialgleichung vierter Ordnung

Ohne ZusammenfassungErster Teil der von der philosophischen Fakultät der Universität Leipzig als Inaugural-Dissertation zugelassenen Arbeit Über einige Eigenwertprobleme und ihre Anwendung in der Variationsrechnung.     

Conformational and electronic consequences in crafting extended, π-conjugated, light-harvesting macrocycles

The synthesis of a new series of free‐base, Ni^II and Zn^II 2,3,12,13‐tetra(ethynyl)‐5,10,15,20‐tetraphenyl porphyrins is described. Upon heating, two of the four ethynyl moieties undergo Bergman cyclization to afford the monocyclized 2,3‐diethynyl‐5,20‐diphenylpiceno[10,11,12,13,14,15‐jklmn]porphyrin in 30 %, 10 %, and trace yields, respectively. The structures of all products were investigated by using quantum chemical calculations and the free‐base analogue was isolated and crystallized; all compounds show significant deviation from the idealized planar structure. No fully‐cyclized bispiceno[20,1,2,3,4,5,10,11,12,13,14,15‐fghij]porphyrin was isolated from the reaction mixture. To understand why only two of the four enthynyl groups undergo Bergman cyclization, the reaction coordinates were examined by using DFT at the PWPW91/cc‐pVTZ(‐f) level coupled to a continuum solvation model. The barrier to cyclization of the second pair of ethynyl groups was found to be 5.5 kcal mol^?1 higher than the first, suggesting a negative cooperative effect and significantly slower rate for the second cyclization. Cyclization reactions for model porphyrin–enediynes with ethene‐ and H‐functionality substitutions at the meso‐phenyl rings were also examined, and found to have a similar barrier to diradical formation for the second cyclization event as for the first in these highly planar molecules. By enforcing an artificial 30° cant in two of the pyrrole rings of the porphyrin, the second barrier was increased by 2 kcal mol^?1 in the ethene model system; this suggests that the disruption of the π conjugation of the extended porphyrin structure is the cause of the increased barrier to the second cyclization event.     

K0 production in e+e− annihilations at 30 GeV center of mass energy

Inclusive K⁰-production has been measured in e⁺e^- annihilation at a center of mass energy of about W = 30 GeV. The ratio of K⁰ + K⁰ production to μ⁺μ^- production is R_K0 = 5.6 ± 1.1 (statist. error) ± 0.8 (system.error) This value is about a factor of three higher than R_K0 at W = 7 GeV. The cross sections (s/β) dσ/dx is consistent with a scaling behaviour.     

Λ, Λ production in e+e− annihilation at 33 GeV centre of mass energy

Performing a PWA of the π^?π^?π⁺ system over the ^?tp/p range 0.2 to 0.4 GeV² we find evidence for a J^P = 0^? ,J^G=1^? meson of mass 1342 ± 20 MeV and width 220 ±70 MeV decaying into ?π. This state is produced by natural parity exchange with a slope similar to that of elastic scattering. It can be interpreted as a radial excitation of the π meson (π′).     

A measurement of σtot(e+e− → hadrons) for cm energies between 12.0 and 36.7 GeV

The ration R = σ(e⁺e^? → hadrons)σ_μμ was measured between 12.0 and 36.7 GeV c.m. energy W with a precision of typically ± 5.2%. R is found to be constant with an average R = 4.01 ± 0.03 (stat) ± (syst.) for W ? 14 GeV. Quarks are found to be point-like, the mass parameter describing a possible quark form-factor being larger than 186 GeV. Fits including QCD corrections and a weak neutral-current contribution are presented.     

A finite element formulation based on the Cosserat point theory

The theory of Cosserat points is the basis of a 3D finite element formulation for large deformations in structural mechanics, that recently was presented by [1]. First investigations [2] have revealed, that this formulation is free of showing undesired locking or hourglassing-phenomena. It additionally shows excellent behaviour for any type of incompressible material, for large deformations and sensitive structures such as plates or shells. The formulation initially was restricted to a Neo-Hookean material. This work will present the extension to a general elastic Ogden material and the verification of the chosen model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)