Electrical conductivity and dielectric relaxation processes of the ceramic system Y2O3-ZrO2-SrTiO3-BiScO3

The ceramic system Y2O3-ZrO2-SrTiO3-BiScO3 was synthesized by the reaction method in the solid phase. The frequency and temperature dependences of the electrical conductivity of Y2O3-ZrO2-SrTiO3-BiScO3 ceramics are obtained. At a temperature above 500 K, the dielectric relaxation of the Y2O3-ZrO2-SrTiO3-BiScO3 ceramic system was detected, the activation energy of the relaxation process was 1.25 e

Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $\epsilon$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.Comment: 4 pages (including 5 figures) LaTeX file. Submitted to Phys. Rev. Let

Optical determination of flexoelectric coefficients and surface polarization in a hybrid aligned nematic cell

A. Mazzulla, F. Ciuchi, and J. Roy Sambles, Physical Review E, Vol. 64, article 021708 (2001). "Copyright © 2001 by the American Physical Society."We present an optical study of the influence of both the flexoelectric effect and surface polarization on a hybrid-aligned nematic cell using the half-leaky guided mode technique. Tilt angle profiles, obtained from fits of experimental data (reflectivity curves) taken under applied voltages, are compared with the ones derived by a complete theoretical model. Measurements with an applied alternating voltage allow the evaluation of the anchoring energy by solving the torque balance equation at the planar surface. From measurements with static fields, the sum of flexoelectric coefficients and the surface polarization are determined by numerical solution of Euler-Lagrange equations

Ferroelectric ordering in chiral smectic C^* liquid crystals determined by nonchiral intermolecular interactions

General microscopic mechanism of ferroelectric ordering in chiral smectic C* liquid crystals is considered. It is shown that if the mesogenic molecules have a sufficiently low symmetry, the spontaneous polarization is proportional to one of the biaxial vector order parameters of the smectic C phase. This order parameter may be determined by intermolecular interactions which are not sensitive to molecular chirality. At the same time, the polarization is also proportional to a pseudoscalar parameter which vanishes if the molecules are nonchiral. The general statistical theory of ferroelectric ordering is illustrated by two particular models. The first model is based on electrostatic quadrupole-quadrupole interactions, and it enables one to obtain explicit analytical expressions for the spontaneous polarization. In the second model, the molecular chirality and polarity are determined by a pair of off-center nonparallel dipoles. For this case, the spontaneous polarization is calculated numerically as a function of temperature. The theory provides a more general interpretation of the previous approaches including the classical Boulder model

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface

A mathematical model and a computational method for studying the influence of the particle diffusion on equilibrium shapes of a magnetic liquid is developed. It is then applied on the ferrohydrostatic problem of doubly connected equilibrium shapes of a magnetic fluid located on a horizontal plate around a vertical cylindrical conductor with a direct current. Numerical simulations show the limits of the uniform concentration approximatio