Highly ordered hexatic phases with large spontaneous polarization

In this article the physical properties of hexatic phases of three substances MHPNBC, FOOPP and FNHPP have been studied by differential scanning calorimetry, texture observation and dielectric spectroscopy. Experimental results are discussed from the point of view of existing theories. It is interesting that two of the substances studied, the FOOPP and FNHPP, exhibit enhanced spontaneous polarization in the highly ordered SmI* phase and show a jump of the spontaneous polarization in the vicinity of the SmC*–SmI* transition. In the SmI* phase of FOOPP a very high value of spontaneous polarization of the order of 530?nC?cm^?2 was found. Based on the results obtained the macroscopic and microscopic properties of the hexatic phases are discussed.     

Fracture mechanics analysis of a composite piezoelectric strip with an internal semi-infinite electrode

IA piezoelectric strip with semi-infinite electrode is investigated. Two combinations of mechanical–electrical loadings are considered. They consist of the anti-plane deformation with in-plane electrical field and the in-plane electroelastic field. Based on the Fourier transform and the Wiener–Hopf technique, the electroelastic local stress fields are found to exhibit the square root singularity near the electrode tip. The energy density factor criterion is applied to examine the fracture behavior near the electrode tip.     

Antiplane stress singularities in a bonded bimaterial piezoelectric wedge

Summary  In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically. Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones. Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated. It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case, C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is. Received 26 March 2002; accepted for publication 2 July 2002     

The Influence of the Dispersion and Vertical Divergence on the Reflection Curve of a Double-crystal Arrangement

The influence of the dispersion and vertical divergence on the half width of the reflection curves was investigated using a double-crystal arrangement where the second crystal could be rotated about an axis parallel to the beam reflected by the first crystal. The experimentally measured dependence of the half width of the reflection curves on the angle of rotation φ is accurately confirmed by geometrical considerations.     

Growth morphology of zinc tris(thiourea) sulphate crystals

The growth morphology of crystals of zinc tris(thiourea) sulphate (ZTS) is investigated experimentally, and computed using the Hartman-Perdok approach. Attachment energies of the observed habit faces are calculated for determining their relative morphological importance. A computer code is developed for carrying out these calculations. A special procedure is adopted for computing the cohesive energy of a slice of the structure parallel to any rational crystallographic plane. For estimating the cohesive energies, formal charges on the experimentally determined atomic positions in the molecules of ZTS are calculated by ab initio molecular-orbital computations, with wave functions obtained by the Hartree-Fock procedure. Fairly good agreement with the observed crystal morphology is obtained for a model of growth mechanism in which ZTS is assumed to exist in solution sa szinc tris(thiourea) ions and sulphate ions.     

A note on Keldysh's perturbation formalism

The expansion theorem of quantum field theoy relating Heisenberg operators to asymptotic free-field operators is rewritten by means of the time-path technique, originally due to Schwinger, which to date has only found application in statistical mechanics. The theorem is combined with Bogoliubov's initial condition of vanishing correlations in the infinite past to rederive Keldysh's perturbation scheme for non-equilibrium statistical Green's functions.     

Ion equilibria in THF solutions of models of “living” methacrylonitrile oligomers with Li+ counterion

The electro-chemical characteristics of isobutyronitrile lithium (P₁Li) and 2-lithio-4-cyano-2,4-dimethylpentanenitrile (P₂Li) are studied. The dissociation constants K of P₁Li and P₂Li are of the order of 10^?11M and show that in THF mainly contact ion pairs exist. The lower value of K for P²Li is an indication for intramolecular complexation between the counterion and the cyano group, next to the active center. Both compounds tend to form ion triples. The results obtained show that in THF the nitrile group of the second monomer unit participates both in intra- and intermolecular interactions with the counterion.     

Feedback Grid Generation via Monotone Discretization for Two-point Boundary-Value Problems

We describe a uniformly enclosing discretization technique formildly nonlinear boundary-value problems. This method allowsus to derive a grid generation principle, using the distancebetween the lower and upper solutions to control the grid-generationprocedure. The convergence of the proposed feedback gridgenerationmethod is proved.