(2+1)-D propagation of spatio-temporal solitary waves including higher-order corrections

We study the propagation of bright two-dimensional spatio-temporal solitary waves using a higher-order multi-dimensional non-linear Schrödinger equation. Starting directly from Maxwell's equations, a multiple-scales derivation is presented which results in a generalized first-order vectorial evolution equation that is valid for the non-linear spatio-temporal propagation of a predominantly linearly polarized electric field with large spatial and temporal bandwidths. A reduced version of this full equation including the higher-order linear and non-linear effects of third- and fourth-order dispersion, space–time focusing, shock, stimulated Raman scattering, and ultrafast quintic index saturation, is solved numerically via a modified split-step algorithm. Material parameters corresponding to those of fused silica at λf=1.55 m are used, with the addition of a negative quintic saturation term. Without quintic saturation, the non-linear spatio-temporal wave broadens under the action of the higher-order space–time effects. In addition, in the absence of Raman scattering, the wave undergoes collapse until arrested by the remaining higher-order terms. Frequency down-shifting and spatio-temporal broadening due to Raman scattering are found to have the greatest effect on non-linear spatio-temporal wave propagation. Nevertheless, we demonstrate that quintic saturation effectively stabilizes the wave such that broadening is reduced considerably, permitting nearly stationary propagation over many confocal distances, albeit with substantial down-shift. The resulting spatio-temporal solitary waves should be useful for applications in ultrafast all-optical switching and logic, and the generalized evolution equations will provide a refined starting point for the study of spatio-temporal phenomena in other areas as well.     

197AU,57Fe and121Sb Mössbauer study of gold minerals and ores

A survey of the¹⁹⁷Au Mössbauer spectra of naturally occurring gold species is given. Gold minerals have been studied as natural specimens or as synthetic analogues. Gold impurities have been identified in pyrites and arsenopyrites. An example of the use of¹²¹Sb, and⁵⁷Fe Mössbauer spectroscopy in characterizing gold-bearing ore minerals is given.     

Single-beam thermowave analysis of semiconductors

The paper describes a new single-beam thermowave technique based on a two-frequency modulation of the laser beam used for both excitation and detection of the photothermal response in a sample. This technique provides frequency transformation to the low-frequency region and, to a certain degree, phase sensitivity without applying the lock-in detection method. This single-beam technique is proved to yield substantial evidence in the field of laser annealing of semiconductors such as the annealing threshold, the defects generated by the ultrafast solidification and the homogeneity of the laser beam applied for irradiation.     

Overdetermined problems with possibly degenerate ellipticity, a geometric approach

Given an open bounded connected subset Ω of ℝⁿ, we consider the overdetermined boundary value problem obtained by adding both zero Dirichlet and constant Neumann boundary data to the elliptic equation −div(A(|∇u|)∇u)=1 in Ω. We prove that, if this problem admits a solution in a suitable weak sense, then Ω is a ball. This is obtained under fairly general assumptions on Ω and A. In particular, A may be degenerate and no growth condition is required. Our method of proof is quite simple. It relies on a maximum principle for a suitable P-function, combined with some geometric arguments involving the mean curvature of ∂Ω.     

Composition distributions within poly(vinylidene fluoride) spherulites as grown in blends with poly(methyl methacrylate)

Upon crystalline solidification of one component in a homogeneously molten polymer blend, composition profiles develop outside (i.e., in the rest melt) and behind (i.e., within the spherulites) the crystal growth front. The present article is devoted to the detailed verification and the interpretation of these distributions and their temporal development inside growing spherulites. To this end, the energy dispersive X‐ray emission (EDX) of suitable elements has been recorded locally resolved in a scanning electron microscope and evaluated correspondingly. The investigations were performed at the melt homogeneous blend of poly(vinylidene fluoride) (PVDF) as crystallizing and poly(methyl methacrylate) (PMMA) as steadily amorphous component. If the spherulites are not volume filling, the mean PMMA content 〈?_PMMA〉 inside the PVDF spherulites is for all blends about 0.2 below the starting composition. ?_PMMA increases however slightly from the center of a spherulite to its border. That increase reflects the PMMA concentration in front of the spherulite surface, which increases likewise with time, and is clearly above the initial composition. There is at the spherulite surface, consequently, a remarkable jump in composition from the spherulite internal to its amorphous surroundings. It may amount up to 0.5. With volume filling spherulites, a slight variation of the composition from the center of a spherulite to its border is observed, too. This proves that also at these conditions composition profiles develop in the spherulite's surroundings. They remain however so weak that they do not inhibit crystallization even in its later stages. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 338–346, 2006     

Multinuclear enantiopure titanium self‐assembly complexes—synthesis,characterization and application to organic synthesis

Hexa‐ and nonanuclear titanium complexes were obtained by self‐assembly of titanium(IV)‐tert‐butoxide and D ‐mandelic acid. Suitable single crystals of these complexes were characterized by X‐ray structure analysis. When used with these complexes, aldol adducts were isolated with a high degree of regioselectivity in direct aldol additions of aromatic and aliphatic aldehydes to functionalized unsymmetrical ketones. High syn‐diastereoselectivities were obtained in aldol additions of enolizable aldehydes with hydroxyacetone and methoxyacetone. Copyright © 2007 John Wiley & Sons, Ltd.