Dielectric spectroscopy of a smectic liquid crystal

Complex dielectric spectroscopy (frequency range 5 Hz-13 MHz) has been used to analyse the frequency, temperature and bias-field dependences of the molecular dynamics of a very high-spontaneous-polarization ferroelectric liquid crystalline material exhibiting SmA, SmC* and unknown SmX smectic phases. Different smectic phase transition temperatures have been observed from the study of the temperature dependence of the dielectric strength and the relaxation frequency. The phase transition temperatures (crystalline to isotropic phases) have also been described very accurately from the temperature-dependent symmetric and asymmetric shape parameters of the relaxation function and also the dc conductivity. In a planar aligned cell, two symmetric modes (Goldstone mode and domain mode) have been observed in both the SmX and SmC* phases. One asymmetric mode (X-mode) observed in the SmC* and SmA phases could be related to the interaction of dipoles of the ferroelectric liquid crystals being affected by the surface of the cell. The soft mode, which usually appears very close to the SmC*-SmA phase transition was not observed until the bias field was applied. The second order nature of the SmC*-SmA phase transition was revealed.     

Non-negative Wigner functions in prime dimensions

According to a classical result due to Hudson, the Wigner function of a pure, continuous-variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [1]. For the case of systems of odd prime dimension, a different, greatly simplified method of proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods. PACS  03.65.Fd; 03.65.Sq; 03.67.-a     

Numerical and experimental investigation of burner device for anode gas reburning

A complex numerical and experimental investigation of burner devices for a reburning of the anode gas of aluminum production was carried out. The chosen mathematical model of the processes of aerodynamics, heat exchange, and gas burning was identified and adapted on the basis of data of real-scale measurements. Basing on computational experiments the optimization of the design of elements of the system for anode gas detoxication and transport was carried out. A new system was proposed and tested for reburning the anode gases of electrolysis production, which consists of an improved burner device and a dust-sedimenting chamber with a possibility of regulating the amount of gas suction.     

Chaotic buffering and its mathematical models

We propose a general idea of obtaining different chains of coupled oscillators with chaotic buffering. As examples, we consider chains of diffusively coupled generalized cubic Schrödinger equations and nonlinear telegraph equations. We also give examples of systems that have an infinite-dimensional chaotic attractor.     

On Ramsey numbers of uniform hypergraphs with given maximum degree

For every ?>0 and every positive integers Δ and r, there exists C=C(?,Δ,r) such that the Ramsey number, R(H,H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C|V(H)|^1+?.     

Volumetric and refractive properties of binary mixtures containing 1,3-dioxolane and isomeric chlorobutanes

The relation between refractive index deviations and excess volumes for binary mixtures formed by a cyclic ether and a haloalkane has been tested using several methods: refractive index mixing rules and equations of state. Refractive index deviations, excess volumes and molar refractions have been calculated from experimental data of refractive indices and densities at two temperatures 298.15 and 313.15 K. Results obtained have been discussed in terms of intermolecular interactions. Refractive indices were compared with those predicted by several mixing rules. Excess volumes have also been correlated using several cubic equations of state and finally a relation between parameter b from equations of state and molar refraction has been provided.     

Boric acid esters as thermal stabilizers and fungicidal additives for elastomers from natural rubber

New and previously synthesized boric acid esters were studied as thermal stabilizing and fungicidal additives to elastomers based on natural rubbers.     

Specific features of separate and joint mastication of natural and 1,4-cis-butadiene rubbers in the presence of dibenzoylaminodiphenyl disulfide

Variation of the molecular structure characteristics and properties of natural and 1,4-cis-polybutadiene rubbers (gel content, molecular weight, degree of branching of macromolecules, viscosity) in the course of their separate and joint mastication in the presence of dibenzoylaminodiphenyl sulfide as mastication accelerator or without it was studied.