Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Binary-black-hole encounters, gravitational bursts, and maximum final spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the "residual" orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole, and the gravitational bursts in a sequence of equal mass encounters. The initial orbital configurations range from those producing an almost direct infall to others leading to numerous orbits before infall, with multiple bursts of radiation. Our sequence consists of orbits with fixed impact parameter. What varies is the initial linear momentum of the black holes. For this sequence, the final black hole of mass M_{h} gets a maximum spin parameter a/M_{h} approximately 0.823, with this maximum occurring for initial orbital angular momentum L/M_{h};{2} approximately 1.176.     

Nanostructured Ti(1-x)S(x)O(2-y)N(y) heterojunctions for efficient visible-light-induced photocatalysis

Highly visible-light-active S,N-codoped anatase-rutile heterojunctions are reported for the first time. The formation of heterojunctions at a relatively low temperature and visible-light activity are achieved through thiourea modification of the peroxo-titania complex. FT-IR spectroscopic studies indicated the formation of a Ti(4+)-thiourea complex upon reaction between peroxo-titania complex and thiourea. Decomposition of the Ti(4+)-thiourea complex and formation of visible-light-active S,N-codoped TiO(2) heterojunctions are confirmed using X-ray diffraction, Raman spectroscopy, transmission electron microscopy, and UV/vis spectroscopic studies. Existence of sulfur as sulfate ions (S(6+)) and nitrogen as lattice (N-Ti-N) and interstitial (Ti-N-O) species in heterojunctions are identified using X-ray photoelectron spectroscopy (XPS) and FT-IR spectroscopic techniques. UV-vis and valence band XPS studies of these S,N-codoped heterojunctions proved the fact that the formation of isolated S 3p, N 2p, and Π* N-O states between the valence and conduction bands are responsible for the visible-light absorption. Titanium dioxide obtained from the peroxo-titania complex exists as pure anatase up to a calcination temperature as high as 900 °C. Whereas, thiourea-modified samples are converted to S,N-codoped anatase-rutile heterojunctions at a temperature as low as 500 °C. The most active S,N-codoped heterojunction 0.2 TU-TiO(2) calcined at 600 °C exhibits a 2-fold and 8-fold increase in visible-light photocatalytic activities in contrast to the control sample and the commercial photocatalyst Degussa P-25, respectively. It is proposed that the efficient electron-hole separation due to anatase to rutile electron transfer is responsible for the superior visible-light-induced photocatalytic activities of S,N-codoped heterojunctions.     

Über En-synthesen mit Singulett-Sauerstoff [1] II. Die Farbstoff-sensibilisierte Photooxygenierung von (—)-Thujopsen und die Stereochemie der dargestellten Thujopsanole

The dye-sensitized photooxygenation of (–)-thujopsene ( 1 ) leads to two allyl hydroperoxides 16 and 17 (ratio 2:1). From the structure of the corresponding alcohols 2 and 3 it is possible to demostrate the complete stereospecificity of the addition of ¹Δ_g-oxygen to the acceptor system. In this way it is shown that 1 exists in only one conformation in solution. The production of the rearranged product 23 can be explained by Hock fission from the allyl hydroperoxides 16 or 17 following the Criegee mechanism. Under the epoxidation conditions 1 is converted mainly to the two new odorous substances (–)-3-thujopsanone ( 4 ) and (–)-3-isothujopsanone ( 5 ). A series of sesquiterpenes with the thujopsane skeleton is also described, all of which have been intercorrelated.     

Regarding Some Problems of the Kutta — Joukovskii Condition in Lifting Surface Theory

We are interested in finding the velocity distribution at the wings of an aeroplane. Within the scope of a three — dimensional linear theory we analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation (Δ +k²)Φ = 0 in ?³\s where Φ denotes the perturbation velocity potential, induced by the presence of the wings and s :=L UW with the projection L of the wings onto the (x,y)- plane and the wake W. Not all Cauchy data are given explicitly on L, respectively W. These missing Cauchy data depend on the wing circulation Γ· Γ has to be fixed by the Kutta–Joukovskii condition: Λ Φ should be finite near the trailing edge x_t of L. To fulfil this condition in a way that all appearing terms can be defined mathematically exactly and belong to spaces which are physically meaningful, we propose to fix Γ by the condition of vanishing stress intensity factors of Φ near x_t up to a certain order such that ΛΦ|_xt ?W₂^?(x_t)? L₂(x_t),?>0. In the two–dimensional case, and if L is the left half–plane in ?², we have an explicit formula to calculate Γ and we can control the regularity of Γ and Φ.     

X-ray photoelectron spectra of some Ni mono- and polynuclear complexes

The core-level photoelectron spectra for Ni(bpy)₂(OOCCMe₃)₂, Ni₂(H₂O)bpy₂(OOCCMe₃)₄, Nibpy(OOCCMe₃)₂, Ni(C₁₀H₄(CH₃)₂N(SO₂C₆H₄(CH₃), Ni₂(2,4-Lut)₂(OOCCMe₃)₄, and (2,4-Lut is 2,4-lutidine) are reported and discussed, and the role of ligands in their appearance is determined. X-ray irradiation of some complexes was found to induce removal of some pyridyl rings and oligomerization both at room and liquid nitrogen temperature. The dependence of composition on temperature was used to find correlation between ligand surrounding and the spectra.