Method of Generating N-dimensional Isochronous Nonsingular Hamiltonian Systems

In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obtained through the Ω-modified procedure is equivalent to constrained Newtonian systems. Even though such systems admit isochronous oscillations, they are effectively one degree of freedom systems due to the constraints. Then we generalize the procedure in terms of Ω _i -modified Hamiltonians and identify suitable canonically conjugate coordinates such that the constructed Ω _i -modified Hamiltonian is nonsingular and the corresponding Newton's equation of motion is constraint free. The procedure is first illustrated for two dimensional systems and subsequently extended to N-dimensional systems. The general solution of these systems are obtained by integrating the underlying equations and is shown to admit isochronous as well as amplitude independent quasiperiodic solutions depending on the choice of parameters.     

Thermodynamics of textures in superfluid 3He

The contribution of the textures in the B-phase of superfluid ³He to the specific heat has been calculated. The specific heat is found to be divergent near T_c.     

Evaluation of one-centre electron interaction integrals over slater type atomic orbitals

Simplified expressions for one-centre electron interaction integrals in general and Slater-Condon parameters as well as repulsion integrals of the type (aa|aa) in particular have been obtained over Slater-type atomic orbitals. Results calculated using these expressions are in agreement with those due to other authors.     

Hydrogen atom abstraction from Piperazine by hydroxyl radical: a theoretical investigation

Dual level of quantum mechanical calculations have been carried out for hydrogen abstraction from Piperazine [HN(CH₂CH₂)₂NH] initiated by OH radical. Geometry optimisation and frequency calculations of all species involved in the titled reaction have been performed at M06-2X/6-31+G(d,p) level of theory. For the accuracy in the thermochemistry and kinetics data, single-point energy calculations have been further carried out at coupled cluster CCSD(T) method along with 6-311G(d,p) basis set. An energy profile diagram for the reaction has been plotted along with pre-reactive and post-reactive complexes at entrance and exit channels. Intrinsic reaction coordinates (IRCs) calculations have been performed for identification of real transition states that connect it via reactant to product. Our result shows that the H-atom abstraction takes place from the C–H position of Piperazine. The rate constant is calculated using canonical transition state theory (CTST) is found to be 2.86 × 10^?10 cm³ molecule^?1 s^?1 which is in good agreement with the reported experimental rate constant (2.38 ± 0.28) × 10^?10 cm³ molecule^?1 s^?1 at 298 K. We have also reported rate constant for the temperature range 300–500 K. Using group-balance isodesmic reaction, the standard enthalpies of formation for Piperazine and product radicals generated by hydrogen abstraction are reported. The branching ratios for both reaction channel (i.e. H-abstraction from –CH₂ and –NH position of Piperazine) are found to be 93% and 7%, respectively. The calculated atmospheric life time of Piperazine is found to be 0.97 hour.     

Effect of polysorbate plasticizer on the structural and ion conduction properties of PEO–NH<Subscript>4</Subscript>PF<Subscript>6</Subscript> solid polymer electrolyte

Effects of a new plasticizer, polysorbate 80, on the structural and electrochemical properties of PEO–NH₄PF₆ polymer electrolyte system have been investigated. X-ray diffraction studies show significant increase in amorphicity of the solid polymer electrolyte on introduction of the plasticizer, which is also supported by lesser-dense spherulites observed in the SEM micrographs. The room temperature ionic conductivity of the electrolyte shows an increase of about two orders of magnitude (σ_max～10^?5 S/cm) on plasticization. The frequency dependence of the conductivity has been found to obey the Jonscher’s power law and slower backward ion hopping on plasticization. The polymer electrolyte shows protonic conduction as confirmed using cyclic voltammetry study. The studies show that polysorbate 80 is a promising plasticizer for semicrystalline polymer electrolytes.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Effect of high‐energy light‐ion irradiation on SI‐GaAs and GaAs:Cr as observed by Raman spectroscopy

The structural evolutions of high‐energy (50 MeV) lithium ion (Li³⁺) irradiated undoped semi‐insulating GaAs (SI‐GaAs) and chromium‐doped SI‐GaAs (GaAs:Cr) were investigated by Raman measurements. It is shown that high‐energy Li³⁺ irradiation causes amorphization beyond a fluence of 3 × 10¹³ ions/cm² in undoped SI‐GaAs. Interestingly, the same fluence of ions does not seem to affect the crystallinity in GaAs:Cr appreciably. The effect of ion irradiation on the change in lattice ordering and anharmonicity of the phonon modes of undoped SI‐GaAs and GaAs:Cr is also compared. Copyright © 2011 John Wiley & Sons, Ltd.     

A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.