Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4'-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

Study of the dissolution and growth of salt single crystals in inhomogeneous acoustic fields: I. A standing acoustic wave

The growth of the isolated (100) face of a KDP crystal at exposure of the phase boundary to the initial ultrasound field and a standing acoustic wave has been investigated. A significant growth response of this face, exposed to sound normally along the acoustic axis in the near zone of a piston-like half-wave vibrator with f = 20 kHz and tangentially in the pulsed two-frequency (f = 600 and 900 kHz) standing-wave mode, has been revealed. It is shown that the mechanisms of mass exchange enhancement in these acoustic modes are different. The results obtained show a fundamental possibility of controlling crystal growth and dissolution by varying the parameters of inhomogeneous acoustic field.     

Doping of KDP single crystals with cerium: Growth and optical properties

The features of doping of KDP crystals with cerium ions and organocerium complexes with alizarin complexon and arsenazo III have been investigated. It is established that “direct” doping by introducing cerium salts into the initial solution cannot be implemented. The effect of organometallic complexes of cerium on the crystal growth has been studied. Organocerium complexes predominantly enter the prismatic or pyramidal growth sectors. It is shown that the complex arsenazo III + Ce blocks the growth of the prismatic sector. Cerium-doped KDP crystals exhibit a photoluminescence band peaking at the wavelength λ_max= 350 nm.     

An analysis of migration paths of Li+ cations in ternary oxygen-containing compounds Li p X q O r

A new method was developed for studying voids and channels in crystal structures based on the Voronoi-Dirichlet partition of crystal space, and 822 structurally characterized ternary compounds Li ^p X ^q O ^r were analyzed for the first time. For these compounds, the dimensionality was determined and the migration patterns of channel systems capable of providing lithium-ion transport were constructed. The calculated coordinates of lithium atoms in the centers of the voids are consistent (within 0.4 ?) with the known structural data. Among these compounds, 113 compounds have infinite channel systems, 60 compounds (18 structural types, STs) have been described earlier in the literature as solid electrolytes, and 53 compounds (23 STs) can be considered as potential one-, two-, or three-dimensional ionic conductors (13, 3, and 7 STs, respectively). Original Russian Text ? N.A. Anurova, V.A. Blatov, G.D. Ilyushin, O.A. Blatova, A.K. Ivanov-Shitz, L.N. Dem’yanets, 2008, published in Kristallografiya, 2008, Vol. 53, No. 6, pp. 987–993.     

Effect of oxygen deficit and nonuniform distribution of technological impurities on the dielectric properties of Y3Fe5O12 crystals

The experimental and calculated values of the optical permittivity ε_∞ have been analyzed and generalized with allowance for the oxygen concentration and possible valences of Fe and O ions in YIG single crystals. It is shown that the deficit of oxygen ions in the samples is accompanied by a decrease in ε_∞. A decrease in the gradient of distribution of Ba ions over the sample thickness decreases the difference between the calculated and experimental values. It is revealed that the ratio of the number of valence electrons to the number of core electrons, with regard to their polarizabilities, is proportional to the ratio of the incoherent and coherent X-ray scattering intensities, nk/k.     

Accuracy analysis of airborne gravimeter calibration using repeated flight paths

Some possible errors in determining the gravity anomalies are discussed. Such errors may be caused by an inaccurate calibration of the gravimeter used in an airborne survey system. An approach based on wavelet decompositions is proposed for its additional calibration with the use of flight data obtained during repeated flights.     

Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.