Liquid crystal parameters through image analysis

A technique which combines image analysis and polarising optical microscope (POM) is a useful tool for the physical investigation of discotic liquid crystals, such as hexabutoxytriphenylene and hexahexyloxytriphenylene. This investigation includes the phase transitions, optical properties and order parameter as a function of temperature. Textures of discotic liquid crystals are captured as a function of temperature using POM. These microscopic textures are analysed using MATLAB software to compute statistical parameters, Legendre moments, optical parameters and order parameters of discotic liquid crystal samples. Compared with other techniques in the literature, the proposed methodology is a reliable and very simple technique for the physical investigation of liquid crystals.     

Optical properties of a mesogen by image analysis

An image analysis technique in conjunction with polarising optical microscopy (POM) is proposed for assessment of the thermo-optical properties of homogeneously aligned chiral ester liquid crystals of the type ((S)-(-)-2-methylbutyl 4′-(4″-n-alkanoyloxybenzoyloxy) biphenyl-4-carboxylates, where n?=?16 or 18. Chiral ester textures are recorded as a function of temperature using POM provided with a hot-stage and a high-resolution colour camera. Temperature-dependent optical parameters, or thermo-optical properties such as optical transmission, degree of polarisation, absorption coefficient and birefringence are computed for chiral esters by analysing the texture of samples using MATLAB software. This is a simple experimental technique for observing how the optical parameters of liquid crystals change with temperature.     

Maximum entropy-based variational multiscale element-free Galerkin methods for scalar advection–diffusion problems

Journal of Thermal Analysis and Calorimetry - This paper presents a new parameter-free stability term via Galerkin mesh-free scheme to solve the multiscale behavior of steady-state...     

Dielectric and Thermodynamic Studies on the Hydrogen Bonded Binary System of Isopropyl Alcohol and Aniline

The molecular interactions between the polar systems isopropyl alcohol (IPA) and aniline for various mole fractions at different temperatures were studied by determining the dielectric permittivity using an HP-LF impedance analyzer at radio frequencies, the plunger method in the microwave frequency range and Abbe’s refractometer in optical region. Kirkwood effective correlation factors, corrective Kirkwood correlation factors, excess permittivities, Bruggeman parameters, excess Helmholtz free energy, relaxation time, dipole moment and excessive dipole moment were calculated using the experimental data. Optimized geometries were calculated using Spartan Modeling software for both pure and equimolar systems of isopropyl alcohol and aniline for Hamiltonian quantum mechanical calculations. Conformational analysis of the formation of hydrogen bond between the two systems is supported by the FT-IR spectra.     

On certain self-decomposable distributions

Probability Theory and Related Fields -     

On the limiting behavior of randomly weighted partial sums

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form where {W_nj, 1jn, n1} and {X_nj, 1jn, n1} are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed.     

On sums of independent random variables whose distributions belong to the max domain of attraction of max stable laws

In this article we study the max domains of attraction of distributions of sums of independent random variables belonging to the max domains of attraction of max stable laws under linear normalization. These results lead to the study of the max domains of attraction of distributions of products of independent random variables belonging to the max domain of attraction of max stable laws under power normalization.     

Mesomorphic behavior of new benzothiazole liquid crystals having Schiff base linker and terminal methyl group

正A homologous series of heterocycles,6-methyl-2-(4-alkoxybenzylidenamino)benzothiazoles,were synthesized and characterized using FT-IR,~1H and ~(13)C NMR and mass spectrometric analysis.Enantiotropic nematic phase was observed for shorter members.Smectic A phase only emerged from octyloxy derivative onwards.The terminal methyl group at the benzothiazole fragment and the Schiff base linkage influenced the mesomorphic behavior of the present series.     

Synthesis and mesomorphic behaviours of a homologous series of 2-(4-alkyloxybenzylidenamino)benzothiazoles

The synthesis and characterisation of a series of new rod-shaped liquid crystal (LC), 2-(4-alkyloxybenzylidenamino)benzothiazoles possessing even number of carbon atoms at the alkyloxy chain (C_nH_2n?+?1O-, n = 2, 4, 6, 8, 10, 12, 14, 16, 18) are reported. The molecular structures of title compounds were elucidated using FTIR and nuclear magnetic resonance spectroscopic techniques. The phase behaviour of these new compounds was characterised and studied by differential scanning calorimetry and polarising optical microscopy. Lower members (n = 2, 4 and 6) did not exhibit mesophase. Octyloxy derivative was monotropic LC. Enantiotropic smectic A phase was observed from n-decyloxy derivatives onward to the last homologous synthesised.     

Phase transition behaviours of calamitic liquid crystals comprising phenylbenzothiazole core

A series of new calamitic liquid crystals 2-[4-(4-alkyloxybenzoyloxy)-phenyl]benzothiazoles comprising a benzothiazole core, terminal alkyl chain and an ester linkage were synthesised and characterised. This series consists of 13 members, wherein the members differ by the length of alkyloxy chain (C _n H_2n+1O^?, where n?=?2–10, 12, 14, 16, 18). Their mesomorphic properties were studied by using differential scanning calorimetry, optical polarising microscopy and powder X-ray diffraction techniques. Enantiotropic nematic phase was present throughout the series, i.e. from the lowest member (n?=?2) until the highest member (n?=?18) of the series. The smectic A phase emerged from the nonyloxy derivative onwards.