The fastest,simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems

Nonlinear Dynamics - Classical method of Lyapunov exponents spectrum estimation for a n-th-order continuous-time, smooth dynamical system involves Gram–Schmidt orthonormalization and...     

Identification of the Isomeric Dideutero p-Benzoquinones by 13C-H and 13C-D Coupling Constants

2,5- and 2,6-dideuterobenzoquinone-1,4 were prepared by a direct catalytic (NaBD₄/PdCl₂) exchange of bromine in the corresponding dibromo derivatives and the subsequent oxidation with Ag₂O. The structure of the products was unambiguously established by proton-carbon and deuteron-carbon splitting pattern of their NMR spectra.     

Creation of nematic and reentrant nematic phases in bi- and multi-component smectic mixtures

Abstract

Experimental results referring to the transformation of smectic phases, mainly smectic A, into nematic and reentrant nematic phases are reviewed. A new explanation of some experimental results is proposed. Factors which are responsible for the depression of smectic phases in mixtures of polar mesogens are discussed and the possibility of forming mixtures with a broad temperature range of nematic phase from smectic compounds, which can be useful for liquid crystal displays (LCDs), is shown. A nematic gap observed in some cases between monolayer (S_A1) or monolayer and partially bilayer (S_Ad) smectics results from the differences in the organization of the molecules in the smectic layers. It is concluded that polar phase from smectic A₁ phases can be divided into two groups: (a) the first one is characteristic for compounds with the -NCS, -F, -CI, -I or ?COC _m H_{2m + 1} terminal group. The spacing of the smectic layer slowly expands with the increase in alkyl chain length and the structure of the smectic A₁ phase slowly changes to be more like the smectic A_d phase (d/1 > 1). It is proposed that such a smectic is called an enhanced monolayer smectic (S_A1e (b) the second one is typical for compounds with the -CN terminal group. This kind of smectic A₁ phase is rapidly transformed into the smectic A_d phase with increasing alkyl chain length. These latter monolayer mesogens easily form the reentrant nematic phase when they are mixed with other polar smectic mesogens.     

Energy–vector method in mechanical oscillations

The new conception of the space, and its construction are introduced. The space allows for a geometrical view on energy changes in mechanical vibrating systems. It posses all the possibilities of the system dynamics analysis that are used in the traditional phase space but it also shows an amount of the energy accumulated in the system, an energy changes, flow, dissipation, synchronization, an energy attractors. Thus it increases our knowledge and intuition on energy changes in vibrating systems. Dynamics of the chaotic system is studied using the energy space. New types of maps are introduced.     

Enhancement of electrical conductivity,director relaxation frequency and slope of electro-optical characteristics in the composites of single-walled carbon nanotubes and a strongly polar nematic liquid crystal

In the present work, single-walled carbon nanotubes (SWCNTs) were dispersed in a room temperature nematic liquid crystal 4-pentyl-4′-cyanobiphenyl at the concentration of 0.02 and 0.05 wt%. Differential scanning calorimetry and temperature-dependent dielectric studies suggest decrease in clearing temperature of the composite materials as compared to the pure material. Ionic conductivity increases by two orders of magnitude due to the dispersion of such a low concentration (0.05 wt%) of SWCNTs. Dielectric studies also show that the presence of the SWCNTs decreases the effective longitudinal as well as transverse components of the dielectric permittivity. For homeotropic aligned samples, a relaxation mechanism has been detected in the lower MHz region both for the pure as well as dispersed samples. Presence of SWCNTs increases the relaxation frequency corresponding to flip-flop motion of molecules around their short axes. From frequency-dependent dielectric studies, important dielectric parameters such as relaxation frequency, dielectric strength and distribution parameters have been determined. Electro-optical experiments show that the threshold voltage decreases and the steepness of the transmission voltage curve improves due to the dispersion of SWCNTs.     

On the origin of high optical director tilt in a partially fluorinated orthoconic antiferroelectric liquid crystal mixture

We have investigated the orthoconic antiferroelectric liquid crystal mixture W107 by means of optical, X-ray and calorimetry measurements in order to assess the origin of the unusally high tilt angle between the optic axis and the smectic layer normal in this material. The optical birefringence increases strongly below the transition to the tilted phases, showing that the onset of tilt is coupled with a considerable increase in orientational order. The layer spacing in the smectic A* (SmA*) phase is notably smaller than the extended length of the molecules constituting the mixture, and the shrinkage in smectic C* (SmC*) and smectic C_a* (SmC_a*) is much less than the optical tilt angle would predict. These observations indicate that the tilting transition in W107 to a large extent follows the asymmetric de Vries diffuse cone model. The molecules are on average considerably tilted with respect to the layer normal already in the SmA* phase but the tilting directions are there randomly distributed, giving the phase its uniaxial characteristics. At the transition to the SmC* phase, the distribution is biased such that the molecular tilt already present in SmA* now gives a contribution to the macroscopic tilt angle. In addition, there is a certain increase of the average tilt angle, leading to a slightly smaller layer thickness in the tilted phases. Analysis of the wide angle scattering data show that the molecular tilt in SmC_a* is about 20° larger than in SmA*. The large optical tilt (45°) in the SmC_a* phase thus results from a combination of an increased average molecule tilt and a biasing of tilt direction fluctuations.     

Electron beam irradiation induced changes in the dielectric and electro-optical properties of a room temperature nematic display material 4-(trans-4′-n-hexylcyclohexyl) isothiocyanatobenzoate (6CHBT)

Dielectric and electro-optical studies of a pure and electron beam irradiated liquid crystalline compound 4-(trans-4′-n-hexylcyclohexyl) isothiocyanatobenzoate have been carried out. Dielectric anisotropy, relaxation frequency, activation energy and distribution parameter of an observed non-collective mode corresponding to the molecular rotation about the short axes have been determined as a function of temperature and irradiation dose whereas threshold and switching voltages, splay elastic constant are determined as a function of irradiation dose. The relaxation frequencies initially decrease up to an irradiation dose of 40 kGy but thereafter increase due to irradiation. The activation energies are increased up to irradiation dose of 40 kGy but around 60 kGy dose of irradiation, we found decrease in the activation energy. Electro-optical measurements show the lowering of the threshold voltage with sufficient improvement in the steepness of the transmission voltage curves due to irradiation. The observed changes in the dielectric and electro-optical properties are related with the cis–trans isomerization due to electron beam irradiation.     

A note about proving non-Γ under a finite non-microstates free Fisher information assumption

We prove that if X₁,…,Xn (n>1) are self-adjoints in a W^∗-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W^∗(X₁,…,Xn) they generate doesn't have property Γ (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy.