Enhancement of second harmonic generation efficiency: Cs(I)-doped tris(thiourea)zinc(II) sulphate crystals

The effect of dopant cesium (Cs(I)) over a concentration range from 1 to 10 mol% on the growth process, morphology, thermal and optical properties of tri(thiourea)zinc(II) sulfate (ZTS) single crystals grown by slow evaporation solution growth technique has been investigated. Incorporation of Cs(I) into the crystal lattice was well confirmed by energy dispersive X-ray spectroscopy (EDS). The lattice parameters of the as-grown crystals were obtained by single crystal X-ray diffraction analysis. The reduction in the intensities observed in powder X-ray diffraction patterns of doped specimen and slight shifts in vibrational frequencies in fourier transform infrared spectra (FT-IR) indicate the lattice stress as a result of doping. Thermal studies reveal the purity of the material and no decomposition is observed up to the melting point. High transmittance is observed in the visible region and the cut-off λ is ～280 nm. The surface morphology of the as-grown specimens was studied by scanning electron microscopy (SEM). The second harmonic generation (SHG) efficiency of the host crystal is enhanced greatly in the presence of high concentrations of the dopant.     

Transport in 3D volume-preserving flows

Summary The idea of surfaces of locally minimal flux is introduced as a key concept for understanding transport in steady three-dimensional, volume-preserving flows. Particular attention is paid to the role of the skeleton formed by the equilibrium points, selected hyperbolic periodic orbits and cantori and connecting orbits, to which many surfaces of locally minimal flux can be attached. Applications are given to spheromaks (spherical vortices) and eccentric Taylor-Couette Flow.     

Universal behaviour in families of area-preserving maps

We have investigated numerically the behaviour, as a perturbation parameter is varied, of periodic orbits of some reversible area-preserving maps of the plane. Typically, an initially stable periodic orbit loses its stability at some parameter value and gives birth to a stable orbit of twice the period. An infinite sequence of such bifurcations is accomplished in a finite parameter range. This period-doubling sequence has a universal limiting behaviour: the intervals in parameter between successive bifurcations tend to a geometric progression with a ratio of $\text{1}\text{δ}\text{=}\text{1}\text{8.721097200}$…, and when examined in the proper coordinates, the pattern of periodic points reproduces itself, asymptotically, from one bifurcation to the next when the scale is expanded by α = ?4.018076704… in one direction, and by β = 16.363896879… in another. Indeed, the whole map, including its dependence on the parameter, reproduces itself on squaring and rescaling by the three factors α, β and δ above. In the limit we obtain a universal one-parameter, area-preserving map of the plane. The period-doubling sequence is found to be connected with the destruction of closed invariant curves, leading to irregular motion almost everywhere in a neighbourhood.     

Quantum hysteresis loops in microscopic system: The loop area as a dynamical parameter

The area enclosed by hysteresis loops in a periodically forced bistable microscopic system at zero-temperature is examined by using the time dependent Hellmann-Feynman theorem and the Fourier grid Hamiltonian recipe for solving time-dependent Schrödinger equation. Effects of non-zero temperatures are explored with reference to a symmetric double well potential. The barrier crossing or, relaxation rates are shown to correlate systematically with the area of the loop. The possible use of hysteresis loop area in designing field parameters for optimal control is suggested.     

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess–Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess–Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.     

Substituent effects in the hydrosilylation of coordinated dinitrogen in a ditantalum complex: cleavage and functionalization of N2

The dinitrogen complex ([NPN]Ta)2(mu-eta1:eta2-N2)(mu-H)2, 1, (where [NPN] = (PhNSiMe2CH2)2PPh) undergoes hydrosilylation with primary and secondary alkyl- and arylsilanes, giving a new N-Si bond and a new terminal tantalum hydride derived from one Si-H unit. Various primary silanes can be employed to give isolable complexes of the general formula ([NPN]TaH)(mu-N-N-SiH(n)R(3-n))(mu-H)2(Ta[NPN]) (5, R=Bu, n = 2; 9, R=Ph, n = 2). Analogous complexes featuring secondary silanes are not isolable, because these products, and 5 and 9, are uniformly unstable toward reductive elimination of bridging hydrides as H2, followed by cleavage of the N-N bond to give ([NPN]TaH)(mu-N)(mu-N-SiH(n)R(3-n))(Ta[NPN]) (6, R=Bu, n = 2; 10, R=Ph, n = 2; 15, R=Ph, n = 1; 16, R=Ph and Me, n = 1). The bridging nitrido ligand in these complexes is itself a substrate for a second hydrosilylation when n = 2, and schemes leading to Ta(IV) complexes of the general formula ([NPN]Ta)2(mu-N-SiH2R)(mu-N-SiH2R') via elimination of H2 are reported (4, R=R'=Bu; 12, R=Bu, R' = Ph; 13, R=Bu, R' = CH2CH2SiH3). At this point, the general reaction manifold for these compounds ramifies, with distinct outcomes occurring for different R groups-[NPN] ligand amide migration from Ta to RSi affords 11, whereas stable complex 6 rearranges to give 7, in the presence of excess silane. Ethanediylbissilane reacts with 1 to give 14, isostructural to 7.     

Mode-locking and rotational chaos in networks of oscillators: A mathematical framework

Summary A mathematical framework is presented for describing mode-locking and rotational chaos in networks of oscillators. Its advantages are explained, and some key questions are identified.     

RationalR-matrices and exceptional lie algebras

We give a brief introduction to our work in math. QA/0608248: an explicit construction of certain rationalR-matrices associated with the exceptionale ₆ ande ₇ series of Lie algebras, which explains Westbury’s observation of their uniform spectral decompositions.