The inclusion of electrostatic and dispersion interactions into potentials of mean torque for solutes dissolved in uniaxial liquid crystal solvents

A potential of mean torque is derived for a solute at infinite dilution in a uniaxial liquid crystal solvent, which contains terms originating from the dispersion interaction, and the electrostatic interaction between quadrupole moments on both molecules. It is shown that the electrostatic term is non-zero only if the solute-solvent vectors are distributed with lower than spherical symmetry. If this distribution has cylindrical symmetry then both the electrostatic and dispersion terms in the potential of mean torque are shown to depend on order parameters for the orientational distribution of the solute-solvent vectors, as well as on the order parameters of the solvent molecules.     

Growth and magnetic characterization of YBCO films

Summary Epitaxial films of YBa₂Cu₃O_7−x were depositedin situ on LaAlO₃ substrates using single-target 90° off-axis sputtering. The films were characterized by magnetization measurements (M vs. T, H), applying the field parallel toc-axis. The observed differences in theT _c andJ _c values are attributed to the different oxygen content in the superconducting films. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

All-fibre optical system for exciting and detecting the vibration of silicon microresonator sensors

An all-fibre optical system for optical interrogation and detection of the vibrations of a silicon microresonator is reported. Metal-coated silicon microresonators are excited by intensity modulated laser light delivered through an optical fibre, while the vibration of the resonators is detected by an optical fibre interferometer. Measurements have shown that an average optical power of 10 μW is sufficient to maintain the flexural vibration of the resonator. When the resonator is used as a pressure sensor, its resonant frequency changes from 62 kHz to 130 kHz as the pressure varies from -0°6 bar to 1 bar (gauge). A silicon resonator with 700 nm aluminium coating functions as a temperature sensor, showing a frequency shift from 262 kHz to 251 kHz when the temperature changes from 25 °C to 80 °C.     

Anomalous anisotropies and field dependencies of the muon Knight shift and the relaxation rate in monocrystalline Bi

The angular dependence of the muon Knight shift,K _μ, and the muon relaxation rate in Bi at 11 K were measured in external magnetic fields up to 1 T. BothK _μ and the second moment,M ₂, are field dependent and involveP ₄ ⁰(cos θ) andP ₄ ³(cos θ) terms in the angular dependence. The Knight shift behaviour is discussed in terms of the dipole-dipole interaction and the de Haas-van Alphen effect, a consistent interpretation was not achieved in either case. The field dependence ofM ₂ is in complete contrast to the second moment calculations and points to a field dependent redistribution of the charge distribution around the interstitial site.     

Pseudo-billiards

A new class of Hamiltonian dynamical systems with two degrees of freedom and kinetic energy of the form T = c₁|p₁| + c₂|p₂| (called “pseudo-billiards”) is studied. For any kind of interaction, the canonical equations can always be integrated on sequential time intervals; i.e. in principle all the trajectories can be found explicitly.

Depending on the potential, a dynamical system of this class can either be completely integrable or behave just as a usual non-integrable Hamiltonian system with two degrees of freedom: in its phase space there exist invariant tori, stochastic layers, domains of global chaos, etc. Pseudo-billiard models of both the types are considered.

If a potential of a pseudo-billiard system has critical points (equilibria), then trajectories close to these points (“loops”) can exist; they can be treated as images of self-localized objects with finite duration. Such a model (with quartic potential) is also studied.     

A demonstration of the diffusion of sodium in a glass-gas discharge system

A demonstration is proposed of the nonstationary diffusion of sodium from a melt of its salt in two-electrode light indicators of a discharge in the cases of electric fields accelerating and damping the motion of ions.Mordovinian Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–102, May, 1992.     

Algebraic composition operators

The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.