Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

ON GROUP VELOCITY OF ELASTIC WAVES, IN AN ANISOTROPIC PLATE

A proof is offered for the equivalence of the group velocity and the energy velocity for elastic waves in a free anisotropic homogenous plate. The proof is valid in the case where the group velocity may be negative while the wave number is positive.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.     

Algebraic methods in quantum mechanics: from molecules to polymers

We present a brief review of algebraic techniques developed and applied in molecular spectroscopy in the last five years. We also outline perspectives for new applications of the Lie algebraic method in the first decade of the new century. Received 21 November 2001     

Studies on antiatherosclerotic agents. Synthesis of 5-substituted derivatives of 7-ethoxycarbonyl-6,8-dimethyl-1(2H)-phthalazinone.off.

Several 5-substituted derivatives of 7-ethoxycarbonyl-6,8-dimethyl-1(2H)- phthalazinone were prepared by means of nitration, reductive amination, and diazonium decomposition. The substituents introduced included NO2, NH2, F, Cl, CN. Among the derivatives, the fluorine compound was obtained only in poor yield because intramolecular cyclization occurred predominantly.     

Purification and some properties of squalene-2,3-epoxide: lanosterol cyclase from rat liver

Squalene-2,3-epoxide: lanosterol cyclase was purified from rat liver in five steps as a soluble and homogeneous protein. The purified enzyme showed a single band on SDS-polyacrylamide gel electrophoresis with a molecular weight of 75 kD. In its native state it behaved as a homo-dimer. The isoelectric point of 5.5 and the apparent Km value for (3S)-squalene-epoxide of 55 microM were estimated for the cyclase.     

Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

Diffraction in a nonlinear defocusing medium

Diffraction by a semitransparent screen is considered in the framework of the nonlinear Schrödinger equation. The case of a defocusing medium is investigated. The method used represents a synthesis of the method of Riemann's matrix problem and the technique of Whitham's deformations of spectral curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 23–31, 1989.     

The measurement of subcritical electroconvection

Under idealized conditions, electroconvection in a nematic liquid crystal sets in at a well-defined threshold of the driving ac voltage. Fluctuating convection rolls of a small amplitude below that threshold have been observed recently. The measurement of the amplitude of these fluctuations is described in detail in this paper. It is based on averaging the light intensity signals using the structure function and a quantitative analysis of the light deflection.