Improved cubature formulae of high degrees of exactness for the square

AbstractThe method of constructing minimal cubature rules with high algebraic degrees of exactness is developed by adapting a powerful algorithm for solving the system of nonlinear equations. As a result, new cubature formulae of degrees 15, 17, 19, 21, and 23 are derived for the square. They lead to lower numbers of knots and/or to better quality with respect to those known previously. The formulae obtained should be considered as the most efficient for the calculation of two-dimensional integrals with a high precision

Dipole glass parameter behaviour for ferro-antiferroelectric solid mixtures

A new definition of a dipole glass parameter for ferro-antiferroelectric solid mixtures is suggested. It is constructed on the nearest neighbours pair correlation functions for interacting dipole momenta. The behaviour of the dipole glass parameter is calculated and discussed.Запропоновано нове означення параметра дипольного скла для сегнето-антисегнетоелектричних твердих сумiшей. Цей параметр будується на парних кореляцiйних функцiях взаємодiючих дипольних моментiв частинок найближчих сусiдiв. Розраховано та дослiджено поведiнку параметра дипольного скла, а також фiзичнi властивостi фази дипольного скла

Ferroelectric-antiferroelectric mixed systems. Equation of state, thermodynamic functions

The problem of equation of state for ferroelectric-antiferroelectric mixed systems in the whole region of a concentration change (06n61) is discussed. The main peculiarity of the presented model turns out to be the possibility for the site dipole momentum to be oriented ferroelectrically in z-direction and antiferroelectrically in x-direction. Such a situation takes place in mixed compounds of KDP type. The different phases (ferro-, antiferro-, paraelectric, dipole glass and some combinations of them) have been found and analyzed

On the problem of low-temperature ordering in ferro-antiferroelectric mixed compounds

The problem of microscopic description of low-temperature phases in ferro-antiferroelectric mixed compounds is discussed. Those phases (ferro-, antiferroelectric and dipole glass) are interpreted based on the specific distributions for single and pair correlation functions in a non-ergodic thermodynamic system. Phase diagram and dielectric susceptibility of a mixed system are obtained and analyzed