Influence of electrocaloric effect upon the dynamic susceptibility of multi-domain ferroelectric materials

In anti-parallel domains, the electrocaloric effect has opposite signs. At the dynamic measurement of susceptibility there exists a temperature field inside the crystal, which varies both in space and in time and which affects the measured susceptibility . The heat conduction results in dielectric losses , the maximum value of which almost equals one half of the difference of susceptibilities at constant temperature? _T and at constant entropy? _S . The frequency, at which these losses reach the maximum value, is given by the formula $$\omega _r = q \cdot \frac{{8\lambda }}{{\varrho c_E W^2 }}$$ whereq is a numerical factor, given by-the unequality 1·25<q<1·30,λ is the thermal conductivity,? the density,c _E is the specific heat, andW the width of the domains. In the vicinity of the frequencyω _r , the real component of the susceptibility mostly differs from the extreme values? _T and? _S .     

Recursion operator for the intrinsic generalized sine-Gordon equation

We find the inverse and direct recursion operator for the intrinsic generalized sine-Gordon equation in any number n > 2 of independent variables. Among the flows generated by the direct operator we identify a higher-dimensional analogue of the pmKdV equation. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 117–128, 2006.     

On the Horizontal Gauge Cohomology and Nonremovability of the Spectral Parameter

Given a zero-curvature representation , the horizontal gauge cohomology group H ¹ is shown to contain obstructions to removability of the 'spectral parameter' of . A method to compute H ¹ is suggested.     

Thermodynamic theory of finite ferroelectric crystals with surface energy

The phenomenological Landau theory of phase transition is generalized to finite ferroelectric crystals with surface energy. Restrictions of the expansion imposed by the symmetry of the surface are considered, and further analysis is devoted to a special case. The solution in the approximation of constant polarization is discussed. Single domain states of a plate are analysed in greater detail.The authors are very grateful to Dr. V.Janovec and Dr. J.Fousek of the Czechoslovak Academy of Sciences for helpful discussions. Thanks are due to Prof. L.Valenta for the valuable discussions dealing with the magnetical analogical problem.     

The theory of flexoelectric effect of polymer glasses

Electric polarization induced by a nonhomogenous deformation flied — flexo-electricity — has has been studied on a model of polymer in the glassy state. The results are expressed in terms of phenomenological coefficients, which are analogical to the electric polarizability. It is found that a gradient of the tensor of small rotation, and not just that of small deformation contributes to the polarization. Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

Differential invariants of generic hyperbolic Monge-Ampère equations

In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.      

The electric polarization induced by temperature gradient and associated thermoelectric effects

It is shown that the possible existence of a direct effect, which consists in the production of electric polarization in a temperature gradient, is connected with the existence of effects that are analogous to the known thermoelectric effects. The thermoelectric effects under study play a role in a periodic regime of temperature and electric current.The author expresses his thanks to Dr. V. Janovec, Ph. D., Dr. V. Dvoák, Ph. D., and Assoc. Prof. Dr. J. Kvasnica, Ph. D. for their valuable comments on this paper.     

Coverings and Integrability of the Gauss–Mainardi–Codazzi Equations

Using the covering theory approach (zero-curvature representations with the gauge group SL), we insert the spectral parameter into the Gauss–Mainardi–Codazzi equations in Chebyshev and geodesic coordinates. For each choice, four integrable systems are obtained.