Inverse monodromy problems in mathematical physics

After a short introduction devoted to the origin of the problem considered from the physical problems of quantum field theory and statistical mechanics, the paper considers the mathematical aspects of the Knizhnik-Zamolodchikov equation theory associated with various root systems and the results connected with the inverse monodromy problem for them. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Charge injection in study of ferroelectric film properties

A model of a capacitor with a two-layer insulator has been considered. The current density exponentially depends on voltage in one of layers and is negligible in the other layer. The dependences of current on the time of voltage action and the charge-voltage characteristics of the two-layer capacitor have been calculated. The results obtained can be used to detect and study charge injection during polarization of ferroelectrics.     

Low-mode tomography of inhomogeneities in a shallow sea

Potentialities of observing spatially localized inhomogeneities by the low-frequency low-mode pulsed diffraction tomography in a shallow sea are analyzed. A numerically simulated model is used to study the procedure of reconstructing the parameters of inhomogeneities by coprocessing the signals of the tomographic projections formed at the multistatic excitation and reception of low-frequency low-mode acoustic pulses.     

Copolymers of acrylic acid with urea

Composition and rheological characteristics of aqueous solutions of acrylic acid/urea copolymers were studied, including the composition dependences of the equivalent conductivity and viscosity.     

Thermochemistry of potassium morpholinodithiocarbamate

Results of thermochemical studies of a new compound, potassium morpholinodithiocarbamate, are presented. The enthalpies of its solution in water at various dilutions and the specific heat at 173–348 K were examined by the experimental methods of isothermal and dynamic calorimetry.     

Electric field-induced birefringence, optical rotatory power and conoscopic measurements of a chiral antiferroelectric smectic liquid crystal

Using a photoelastic modulator-based novel set-up, the electric field-induced in-plane birefringence and the optical rotatory power (ORP) were measured of an antiferroelectric liquid crystalline compound (12OF1M7) in its various phases using 30 µm homeotropic cells. Some specific signatures of the in-plane birefringence and of the ORP for the various phases are being established. A relatively small threshold field is needed for the unwinding process of the antiferroelectric phase with a unit cell of four layers [SmC_A*(1/2)] compared with that for two layers [SmC_A*(0)]. On application of the electric field on the high temperature side of the SmC_A*(1/2) phase (80.1-81.5°C), a field-induced phase transition is shown to occur directly to the SmC* phase, whereas on the lower temperature side (79.4-80.1°C) the transition takes place to SmC* via the SmC_A*(1/3) phase. The in-plane birefringence exhibits a critical power law dependence for the SmC*-SmA transition. The ORP changes sign within the temperature range of the phase with a unit cell of three layers, reflecting a change in the handedness during this phase. Using tilted conoscopy, the results for the biaxiality and the apparent tilt angle for a smectic liquid crystal with a tilt angle greater than 18° in the ferroelectric phase are reported. The biaxiality implies the difference in the refractive indices between the two minor axes of the refractive index ellipsoid. The optical transmittance at visible and IR wavelengths for free-standing films reveal characteristic reflection bands for these phases. The modulated structures of the reflected bands appear just above the SmC_A* phase and below SmC_A*(1/3); these are possibly due to an easy deformation of the phase by the surfaces.