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.     

Effect of Magnetic Co–CoO Particles on the Carrier Transport in Monolayer Graphene

Physics of the Solid State - Electrodeposition of cobalt on monolayer graphene synthesized by chemical vapor deposition produces Co–CoO/graphene composite structures, which is accompanied by...     

On the definition of the resonance with examples two-channel models

In an exactly solvable model of separable potentials a two channel scattering problem is solved in l = 0 state. The location and the width of a resonance are then defined in three different ways and the resonance parameters so extracted are then compared. This problem is of interest vis-a-vis the Δ(3, 3) resonance parameters.     

Tests of resonance recognition criteria in coupled channel problems with separable potentials

Exactly soluble two-body two-channel problems are set up with separable potentials. Resonance is defined theoretically then the empirical resonance recognition criteria used in two-body data analyses are tested. Results are summarized in the last section of the paper.     

Selective O-deallylation of dihydropyrazoles by molecular iodine in the presence of active N-allyl and formyl groups

Selective O-deallylation of dihydropyrazoles has been achieved by use of iodine (10 mol%) in PEG-400 as ecofriendly solvent. Iodine (10 mol%) in dimethyl sulfoxide at 100 °C also afforded O-deallylation with aromatization compatible with highly reactive N-allyl and formyl groups. The function of iodine in the synthesis of substituted pyrazoles under different conditions is described.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.     

Chalcogen Stabilized bis-Hydridoborate Complexes of Cobalt: Analogues of Tetracyclo[4.3.0.02,4.03,5]nonane

Treatment of Li[BH₃ER] (E=Se or Te, R=Ph; E=S, R=CH₂Ph) with [Cp*CoCl]₂ led to the formation of hydridoborate complexes, [{CoCp*Ph}{Cp*Co}{μ-EPh}{μ-κ²-E,H-EBH₃}], 1a and 1 b ( 1 a : E=Se; 1 b : E=Te) and a bis-hydridoborate species [Cp*Co{μ-κ²-Se,H-SeBH₃}]₂, 2 . All the complexes, 1 a , 1 b and 2 are stabilized by β-agostic type interaction in which 1 b represents a novel bimetallic borate complex with a rare B−Te bond. QTAIM analysis furnished direct proof for the existence of a shared and dative B-chalcogen and Co-chalcogen interactions, respectively. In parallel to the formation of the hydridoborate complexes, the reactions also yielded tetracyclic species, [Cp*Co{κ³-E,H,H-E(BH₂)₂-C₅Me₅H₃}], 3 a and 3 b ( 3 a : E=Se and 3 b : E=S), wherein the bridgehead boron atoms are surrounded by one chalcogen, one cobalt and two carbon atoms of a cyclopentane ring. Molecules 3 a and 3 b are best described as the structural mimic of tetracyclo[4.3.0.0^2,4.0^3,5]nonane having identical structure and similar valence electron counts.     

Thermodynamic reassessment of the Al–Zr binary system

Journal of Thermal Analysis and Calorimetry - Based on the data of the literature reports, the Al–Zr binary system has been re-assessed thermodynamically through the CALPHAD (CALculations of...     

Unexpected dimerization of 1,3‐dimethyl‐5‐methylenebarbituric acid revealed by a combined experimental and computational study

A comparison of experimental and calculated ¹³C‐nuclear magnetic resonance chemical shifts reveals the molecular structure of a dimer that was obtained by an unexpected dimerization of 1,3‐dimethyl‐5‐methylenebarbituric acid. Furthermore, the puckering angle of the cyclobutane unit linking the six‐membered rings is discussed in detail. The influence of substituents on 1,3‐position of the cyclobutane ring on the puckering angle is demonstrated based on 1,1,3,3‐tetramethylcyclobutane. Copyright © 2015 John Wiley & Sons, Ltd.