Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes

A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑_m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H¹ (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi-infinite screens ∑_m. The (2N × 2N)-Fourier symbol matrix ??_?? contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑_m.     

Rheology of gelling polymers in the Zimm model

In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model [B. H. Zimm, J. Chem. Phys. 24, 269 (1956)]. for randomly cross-linked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erdos-Renyi random graphs or three-dimensional bond percolation. Within this model the critical behavior of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size n with n. We investigate these scaling relations numerically and conclude that the scaling exponents are independent of the hydrodynamic interaction strength. The numerically determined exponents agree well with experimental data for branched polymers. However, we show that this traditional model of polymer physics is not able to yield a critical divergence at the gel point of the viscosity for a polydisperse dilute solution of gelation clusters. A generally accepted scaling relation for the Zimm exponent of the viscosity is thereby disproved.     

Effect of the Media on the Quantum Yield of Singlet Oxygen (O2(1Δg)) Production by 9H‐Fluoren‐9‐one: Solvents and Solvent Mixtures

We have investigated the effect of a series of 18 solvents and mixtures of solvents on the production of singlet molecular oxygen (O₂(¹Δ_g), denoted as ¹O₂) by 9H‐fluoren‐9‐one (FLU). The normalized empirical parameter E derived from E_T(30) has been chosen as a measure of solvent polarity using Reichardt's betaine dyes. Quantum yields of ¹O₂ production (Φ_Δ) decrease with increasing solvent polarity and protic character as a consequence of the decrease of the quantum yield of intersystem crossing (Φ_ISC). Values of Φ_Δ of unity have been found in alkanes. In nonprotic solvents of increasing polarity, Φ_ISC and, therefore, Φ_Δ decrease due to solvent‐induced changes in the energy levels of singlet and triplet excited states of FLU. This compound is a poor ¹O₂ sensitizer in protic solvents, because hydrogen bonding considerably increases the rate of internal conversion from the singlet excited state, thus diminishing Φ_Δ to values much lower than those in nonprotic solvents of similar polarity. In mixtures of cyclohexane and alcohols, preferential solvation of FLU by the protic solvent leads to a fast decrease of Φ_Δ upon addition of increasing amounts of the latter.     

Elastic and inelastic backscattering of slow electrons from silicon

The elastic and inelastic backscattering from Si(111) surfaces and evaporated amorphous silicon were measured as a function of the primary energyE _p (30eVE _p 200eV). A detailed evaluation of the amplitude of the volume plasmon lossA _vp was carried out in the loss spectra. In contrast to single crystals amorphous silicon produces a smooth curve as function of the energy, both for the elastic backscattered electron current and forA _vp (E).To interpret the measured curves for the amorphous Si calculations were made for the elastic scattering and for the excitation probability of the volume plasmon in a randium-jellium-model. In the case of elastic scattering a random distribution of atoms is assumed. In the case of inelastic scattering the free electron model is used. Double scattering processes are included. The comparison between theory and experiment shows satisfactory agreement for elastic scattering. The energy dependent excitation probability of the volume plasmon is excellently represented by this model.     

Biosynthetic Production of [N2,1,3,7,9-15N]Guanosine and [1,3,7,9-15N]inosine and conversion into [N6,1,3,7,9-15N]adenosine for structure elucidation of RNA by heteronuclear NMR

A procedure was developed for the biosynthetic preparation of ¹⁵N-labelled guanosine and inosine through the action of a mutant Bacillus subtilis strain. Crude [N²,1,3,7,9-¹⁵N]guanosine and [1,3,7,9-¹⁵N]inosine were isolated from the culture filtrate by precipitation and anion-exchange chromatography (Scheme 1). No cell lysis and no enzymatic degradation was necessary. The per-isobutyrylated derivatives 1 and 2 were isolated from a complex mixture, purified by virtue of their different lipophilicity, and separated in three steps involving normal-and reversed-phase silica-gel chromatography. One litre of complex nutrient medium yielded 8.44 mmol of guanosine derivative and 2.84 mmol of inosine derivative with high average ¹⁵N enrichment (83.5 and 91.9 atom-%, resp.). [N⁶,1,3,7,9-¹⁵N]Adenosine ( 4 ) was obtained from 2′,3′,5′-tri-O-isobutyryl[1,3,7,9-¹⁵N]inosine ( 1 ) through the ammonolysis of its 1,2,4-triazolyl derivative with aqueous ¹⁵NH₃ (Scheme 2).     

Shear modulus determination in model hydrogels by means of elongated magnetic nanoprobes

The mechanical characterization of complex soft matter by quasi-static magnetometry using nanoscopic magnetic probes is demonstrated for model hydrogels doped with two types of elongated magnetic nanoparticles. Chemically crosslinked poly(acrylamide) (PAAm) hydrogels serve as the matrix in which nickel nanorods or weakly magnetized hematite (α-Fe₂O₃) ellipsoids are embedded as local probes. We investigated the swelling behavior of the ferrogels in order to verify that their equilibrium swelling degree in water is not influenced by the probes, shows a good correlation with the Frenkel–Flory–Rehner model. The proposed magnetomechanical method relies on a correlation between the shear modulus of the PAAm hydrogel matrix and the coercive fields of the corresponding isotropic ferrogels. By extending the Stoner–Wohlfarth model for single-domain blocked magnetic particles by a term for particle rotation in an elastic matrix, information on the shear modulus of the matrix can be obtained. Comparison of the results with the expected relation from rubber elasticity theory illustrates both the general potential as well as the limits of the approach. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

This paper gives a first numerical comparison of the Discontinuous-Galerkin-(DG) and Spectral-Difference-Method (SD) under almost equivalent conditions for smooth test cases.