Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.     

Single Crystal X-ray Study of 6-Phenyl-4-(p-tolyl)pyridin-2(1H)-one

Crystallography Reports - The title compound 6-phenyl-4-(p-tolyl)pyridin-2(1H)-one was synthesized via one-pot, three component reaction of (E)-1-phenyl-3-(p-tolyl)-2-propen-1-one, ethyl...     

Erratum to: Analytic Calculations of the Branching Ratio and CP Violation in $$B_s^0 \to {K^{*0}}{\overline K ^{*0}}$$ B s 0 → K * 0 K ¯ * 0 Decay

Physics of Atomic Nuclei -     

Encapsulating Au‐Fe3O4 Nanodots into AIE‐active Supramolecular Assemblies: Ambient Visible‐light Harvesting “Dip‐Strip” Photocatalyst for C−C/C−N Bond Formation Reactions

The present study demonstrates the development of a supramolecular porous ensemble consisting of hetero‐oligophenylene derivative 6 and Au‐Fe₃O₄ nanodots. Supramolecular assemblies of AIE‐active hetero‐oligophenylene derivative 6 served as reactors for the generation of Au‐Fe₃O₄ nanodots. The as prepared supramolecular ensemble functioned as an efficient recyclable photocatalytic system for C(sp²)?H bond activation of anilines for the construction of quinoline carboxylates. Interestingly, the “dip catalyst” prepared by depositing PTh‐co‐PANI‐6: Au‐Fe₃O₄ nanodots on a filter paper served as a recyclable strip (up to 10 cycles) for C?C/C?N bond formation reaction.     

Photonic true-time delay unit for broadband adaptive nulling in antenna arrays

An Opto-VLSI-based (VLSI: very-large-scale-integration) tunable true-time delay (TTD) generation unit used for adaptive null steering in phased array antennas is presented. The system is based on continuous tunable optical TTD technique. Arbitrary multiple true-time delays to generate multiple broadband nulls can simultaneously be synthesised for each antenna element. The proposed structured are characterised both theoretically and experimentally. Experimental results demonstrating the principle of the true-time delay for null generations are presented. The maximum time delay measured for a wavelength tuning from 1530 to 1560 nm is 9.5 ns.     

Magnetic ordering in a model of superlattice Fe/V with the negative interlayer exchange interaction

For the first time several basic types of temperature dependence of spontaneous (resultant) magnetization in a magnetic superlattice model are revealed for various values of an interlayer exchange interaction.     

Ab initio study of the chemical states of water on Cr2O3(0 0 0 1): From the isolated molecule to saturation coverage

The reactivity of the (0 0 0 1)-Cr–Cr₂O₃ surface towards water was studied by means of periodic DFT + U. Several water coverages were studied, from 1.2H₂O/nm² to 14.1H₂O/nm², corresponding to ¼, 1, 2 and 3 water/Cr at the (0 0 0 1)-Cr₂O₃ surface, respectively. With increasing coverage, water gradually completes the coordination sphere of the surface Cr atoms from 3 (dry surface) to 4 (1.2 and 4.7H₂O/nm²), 5 (9.4H₂O/nm²) and 6 (14.1H₂O/nm²). For all studied coverages, water replaces an O atom from the missing above plane. At coverages 1.2 and 4.7H₂O/nm², the Cr–O_s (surface oxygen) acid–base character and bond directionality govern the water adsorption. The adsorption is molecular at the lowest coverage. At 4.7H₂O/nm², molecular and dissociative states are isoenergetic. The activation energy barrier between the two states being as low as 12 kJ/mol, allowing protons exchanges between the OH groups, as evidenced by ab inito molecular dynamics at room temperature. At coverages of 9.4 and 14.1H₂O/nm², 1D- (respectively, 2D-) water networks are formed. The resulting surface terminations are –Cr(OH)₂ and –Cr(OH)₃– like, respectively. The increased stability of those terminations as compared to the previous ones are due to the stabilization of the adsorbed phase through a H-bond network and to the increase in the Cr coordination number, stabilizing the Cr (t_2g) orbitals in the valence band. An atomistic thermodynamic approach allows us to specify the temperature and water pressure domains of prevalence for each surface termination. It is found that the –Cr(OH)₃-like, –Cr(OH)₂ and anhydrous surfaces may be stabilized depending on (T, P) conditions. Calculated energies of adsorption and OH frequencies are in good agreement with published experimental data and support the full hydroxylation model, where the Cr achieves a 6-fold coordination, at saturation.     

Synthesis, cyclic voltammetry, and UV–Vis studies of ferrocene-dithiafulvalenes as anticipated electron-donor materials

Abstract  

New ferrocenyl ketones were obtained as precursors of novel π-conjugated ferrocene-dithiafulvalene (Fc-DTF) and π-extended-ferrocenedithia-fulvalenes (π-exFc-DTF) as electron-donor conducting materials from ferrocene by a direct aroylation process using the Friedel–Crafts reaction. Novel Fc-DTF conjugates were synthesized using the Wittig–Horner reaction and their structures were determined. The redox behavior of the ferrocenyl carbonyl compounds Fc-DTF and Fc-π-exDTF was investigated in comparison to the parent ferrocene by means of cyclic voltammetry. A one-electron redox behavior was observed for carbonylferrocenes as one wave potential, while a two-electron process was observed as two oxidation waves for the conjugates. Introduction of electron-withdrawing groups led to increasing E _pa values and decreasing ΔE _p values. The UV–Vis spectra of some compounds were studied in comparison with ferrocene. The absorption spectra showed a red-shift with a slight increase in the absorption intensities.