Parity-locking effect in a strongly-correlated ring

Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder.     

Methods of constructing optimal stabilizers

The problem of transforming a linear dynamical system in the neighbourhood of a state of equilibrium [1,2] is solved using the special problem of the damping of the system by controls of minimum intensity after a finite time interval. The possibility of using other problems of optimal control is discussed. The main attention is devoted to constructing algorithms of the operation of a device (a stabilizer) which is able, in real time, to generate a stabilizing control circulating in the closed optimal system when unknown perturbations operate constantly [3, 4]. The proposed method is based on the constructive theory of optimal control [5, 6]. Another form of this theory for solving the problem of stabilization is presented in [7](see also [8]).     

2H NMR spectra of 2-(p-heptylbenzoyloxy)-5-(p-heptylbenzenazo)tropone. A new sigmatropic liquid crystal

Liquid crystals incorporating in their molecular framework a seven-membered ring are still relatively rare [1]. Recently the synthesis and thermal behaviour of a series of liquid crystal materials having a tropone moiety in their mesogenic core have been reported [2-4]. These mesogens, based on a 2-(acyloxy)tropone core structure, show intramolecular migration of the acyl substituents between the two oxygen atoms at C-1 and C-2, an effect already known for simple 2-(acyloxy)tropones in their isotropic solutions [5]. This migration involves a concerted [1, 9]-sigmatropic rearrangement [2]. This rearrangement could play a major role in determining the properties of the mesophases: it has been suggested in fact that, because of this rearrangement, the mesogenic molecules acquire a mean rod-like shape which can sustain the mesophase formation [2].     

Associators as measures of memory for media with optical memory and the optimization problem

The interference of light in a medium with optical memory is discussed within the framework of a nonassociative algebra. It is shown that it is possible to introduce an energy coefficient of useful action K_e, an information coefficient of useful action K_int, and a coefficient characterizing the size of the memory of the medium D. The problem of optimizing the process over these parameters is considered. Graphs are given for K_e, K_int, and D as functions of a free parameter β that accounts for experimental conditions. Tbilisi State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 29–32, August, 1997.     

Enumeration of Full Graphs: Onset of the Asymptotic Region

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.     

Quasiparticle bandstructures of covalent semiconductors and their surfaces

The exchange-correlation self-energies and quasiparticle shifts are calculated for band states of covalent materials (diamond, silicon) and their (001) 2×1 surface in order to solve the bulk and surface band-gap problem of the LDA. The screening properties are described by a model dielectric function taking into account the spatial nonlocality in the surface case assuming specular electron reflection. The wave functions are expanded in terms of localized orbitals. The quasiparticle bandstructures obtained are in reasonable agreement with experimental results.     

Dynamics of phase separation in mesomorphic mixtures

We describe the dynamics of phase separation and transition processes, in binary mesomorphic mixtures with the help of a system of two coupled partial derivative equations. We emphasize, both analytically and numerically, that, depending on the regions of the phase diagram, the dynamical behaviour may result either from a two step process (first the phase transition, then the phase separation) or from a process showing salient features of the Cahn-Hilliard spinodal decomposition (bicontinuous periodic networks in the transient stages). The dynamics of evolution of the domain patterns are illustrated with the help of numerical simulations in which homeotropic and planar anchorages are visualized.     

Rapid multielemental analysis of Chinese reference soils by laser ablation inductively coupled plasma-source mass spectrometry

Summary Laser ablation inductively coupled plasma-source mass spectrometry has been used to determine thirty elements (Na, Mg, Al, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, As, Rb, Sb, Cs, Ba, La, Ce, Nd, Sm, Eu, Dy, Ho, Yb, Hf, Ta, W, Th, U) in seven Chinese reference soils. The Surrey prototype spectrometer was employed with sample ablation by a free-running ruby laser. Concentrations in the soils (GSS-2 to GSS-8) were calculated from elemental responses and sensitivities derived from another soil in the series, namely GSS-1. Comparisons with previous neutron activation analyses are made. Rapid semiquantitative analyses are proved feasible. About eighty percent of the LA-ICP-MS determined concentrations were within a factor of two of the concentrations measured by INAA, and many were considerably closer than this. Precisions were typically in the range 2–10% RSD, but some were considerably poorer for elements present at trace levels.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.