Applied electric field effect on light-scattering birefringence of dye-doped liquid crystal molecule and consistent neural network empirical physical formula construction for scattering intensities

In this paper, we realized two objectives. Firstly, birefringence of azo and anthraquinone dye-doped nematic liquid crystal (NLC) molecules was investigated by applied electric field dependent laser scattering intensities. The birefringence was essentially calculated from ordinary and extraordinary ray phase difference, which is determined from the measured intensities corresponding to parallel and perpendicular orientations of analyzer to polarizer. The birefringence was found to be dependent on both applied voltage and the kind of the doping dye. As the second objective, by nonlinear universal function approximator layered feedforward neural network (LFNN), we constructed explicit form of empirical physical formulas (EPFs) for experimentally measured dye-doped NLC nonlinear scattering intensities. Excellent LFNN test set predictions over yet-to-be measured experimental data proved that the constructed LFNN-EPFs estimated the measured intensities consistently. The correlation coefficients assessing the goodness of predictions were about r = 0.998for all cases. The LFNN-EPFs also extracted the intensity dependency on the kind of dye used. When theoretical and LFNN-EPFs intensities are compared, we conclude that given certain experimental conditions, theoretical and LFNN-EPFs predictions are in excellent agreement. In this sense, we can say that the physical laws embedded in the birefringence scattering data can be consistently extracted by LFNN. Therefore, judging from the consistent extraction of the molecular dependencies of pure and doped NLC intensities, we predict that the LFNN-EPFs can help to identify unknown molecular structural parameters in liquid crystal extracts. More concretely, by suitable mathematical operations such as differentiation, integration, minimization on these intensity LFNN-EPFs, some useful information into the charge distributions of the LC molecules can be gained.     

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

In this paper, the FEM modelling of the time-harmonic dynamical stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation is developed. The mathematical formulation of the considered problem is made by the use of the equations and relations of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The proposed modelling is tested on the concrete problems as an example. The numerical results testing the validity of the developed FEM modelling are presented. Moreover, the numerical results attained for the various values of the problem parameters are also presented.     

Cyclic codes over <Emphasis Type="Italic">R</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>

Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2 ^k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over R _k via this map.     

Scattering of sound waves by a turbulent wake

In this investigation, the Doppler shifted power spectrum of the scattering cross-section is obtained for plane acoustic waves scattered by fluid flow fluctuations appropriate to a turbulent wake. The wake considered in this paper is assumed almost homogeneous and isotropic and of low Reynolds number.It is shown that the evaluation of the Doppler scattering cross-section essentially reduces to the calculation of the wave number converted and frequency shifted energy spectrum function of the turbulent flow fluctuations. In prescribing the low Reynolds number turbulence spectrum, inertial forces are assumed negligible. Convective effects of the macro-eddies, which cause a Doppler shift in the scattered waves, are considered using a Lagrangian-type of space-time velocity correlation.After finding the spectrum of turbulent fluctuations, the Doppler shifted power spectrum of the scattering cross-section, which characterizes the scattered waves, is obtained explicitly for the far field approximation.     

A coupled WC-TL SPH method for simulation of hydroelastic problems

A coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.     

Conjugation of arginine–glycine–aspartic acid peptides to thermoreversible N‐isopropylacrylamide polymers

Thermoreversible polymeric biomaterials are finding increased acceptance in tissue engineering applications. One drawback of the polymers is their synthetic nature, which does not allow direct interaction of mammalian cells with the polymers. This limitation may be alleviated by grafting arginine–glycine–aspartic acid (RGD) containing peptides onto the polymer backbone to facilitate interactions with cell‐surface integrins. Toward this goal, N‐isopropylacrylamide (NiPAM)‐based thermoreversible polymers containing amine‐reactive N‐acryloxysuccinimide (NASI) groups were synthesized. Conjugation of RGD‐containing peptides to polymers was demonstrated with ¹H NMR spectroscopy and reverse‐phase high‐pressure liquid chromatography. The conjugation reaction was optimal at 4 °C and pH of 8.0, and increased with the increasing NASI content of polymers. With a peptide grafting ratio of 0.25 mol %, there was no significant change in the lower critical solution temperature of the polymers. Finally, the NASI‐containing polymers, cast as films, on tissue culture polystyrene, were shown to conjugate to RGD‐containing peptides and support C2C12 cell attachment. We conclude that NASI‐containing thermoreversible polymers are amenable for grafting biomimetic peptides to impart cell adhesiveness to the polymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3989–4000, 2003     

Studies on the synthesis of the azocino[4,3‐b]indole framework and related compounds

An efficient method for the synthesis of C‐4 position alkylated azocino[4,3‐b]indole 13 and 18 is described. Reduction of compounds 5, 6, 7 and 8 yielded the corresponding alcohols. Compounds 5, 6, 7 and 8 were synthesized through several steps starting from 1 . The resulting alcohols underwent acid catalyzed ring closure to give tetracyclic azocino[4,3‐b]indole 9, 10, 11 and 12 . Finally, compounds 9 and 17 were alkylated at C‐4 position to the corresponding products 13 and 18 . The structure of the compounds 13 and 18 has been confirmed by X‐ray single crystal analysis.