Nonlinear travelling waves in φ6 polarizable model

We present a complete theoretical analysis of the periodic and non-periodic travelling waves in a diatomic chain model, in the continuum limit by incorporating nonlinear sixth order polarization potential (φ⁶) at the anion site. We have formulated a nonlinear lattice dynamical theory in which various energy curves are obtained for different types and magnitudes of the core-shell force constants. For periodic solutions, we have obtained two types of commensurate wave amplitudes which propagate in the opposite direction with respect to each other. For nonperiodic solutions, we have obtained various travelling excitations such as kink, antikink, excitons etc. for different values of the mass ratio and velocity parameter. The dipole moment per unit charge for SrTiO₃ has been calculated and it is found that the nonlinear excitations in this model carry large amount of energy as compared to those obtained from harmonic and anharmonic optical phonons in the φ⁴-polarizable model.     

Mass spectrometric investigation of polyfluorinated C60. Evidence for the existence of C60F2n (n = 0–30)

Electron-capture negative ion chemical ionization (EC-NICI) and field desorption (FD) mass spectrometric techniques were utilized to examine polyfluorinated C₆₀. Two different samples from the same preparation, one prior to sublimation and the other sublimed material, were investigated. From the raw non-sublimed product in EC-NCI six series of ions corresponding to different numbers of attached oxygen atoms were obtained, which are represented by the formula [C₆₀F_2nO_m]^?, where n ranged from 0 to 30 and m from 0 to 5. The sublimed material in EC-NICI produced the same six series of ions with up to 48 fluorine atoms attached to C₆₀. The field desorption of the same sample produced similar results, but the signal-to-noise ratios of the spectra were low. Both samples, in the two different techniques examined, yielded C₆₀F₆₀ ions with only an even number of fluorine atoms attached. The present investigation, for the first time, provides direct experimental evidence for the existence of higher fluorinated C₆₀ up to C₆₀F₆₀ and multiple oxides of polyfluoro-C₆₀ with up to five oxygen atoms attached.     

Phonons and periodons in IV–VI semiconductor superlattices

We have calculated the phonon and periodon dispersion relations in IV–VI semi-conducting bulk PbTe and SnTe and their superlattice structure. The model used here is a one-dimensional lattice which includes harmonic interactions up to second neighbours as well as on-site nonlinear electron-ion interactions at the anion site. We calculate the phonon and periodon dispersion relations in bulk and PbTe-SnTe superlattice for the transverse optic and acoustic modes using the transfer matrix method. Our analysis has predicted correct nature of the folding of acoustic and confinement of optical phonons at various frequency intervals corresponding to pass and stop bands of the superlattices.     

Analysis of Low-energy α-4He Elastic Scattering Process in Direct Channel Regge-Pole Formalism

The elastic scattering of low-energy α-particles by a ⁴He target has been analysed within the frame-work of a modified Regge-Pole model which reproduces the partial wave phaseshifts in an elegant and simple way and describes all other relevant features of the scattering phenomena.     

Loop Algebra of Lie symmetries for a short-wave equation

It is demonstrated that Lie point symmetries associated with a nonlinear equation for short waves in three dimensions generate an infinite-dimensional Lie algebra—a loop Algebra. Classification of the independent sets of the subalgebra is done through the adjoint action of the corresponding generators. Different forms of similarity solutions are discussed.     

Painleve Analysis and the Yang-Mills Equation in Two Specific Cases

Two important configurations of Yang-Mills fields are discussed applying to them the Painleve test of Ablowitz. The case with a constant electric E-field does not admit an exact solution while the cylindrically symmetric self-dual system admits an inverse scattering approach for instanton solution.     

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.     

Representation of supercharges over the scattering data for super-sine-Gordon system

We determine the form of the superchargesQ ₁ andQ ₂ in terms of the scattering data for the super-sine-Gordon equation. The technique is to ascertain the effect of supertranslation on the scattering data used in the inverse scattering transform. The same result was obtained by Kulish and Tsypleyv from the Riccatti equation by expanding in A.