Quadrupolar forces and aggregation of nematic droplets

The electrostatic quadrupolar interaction between spherical nematic droplets in an isotropic (and nonconducting) liquid is calculated. It is found to have an anisotropic form U _q ∝1/R ⁵, where R is the distance between droplets, with repulsion for droplets having parallel orientation of the quadrupole moments and attraction at oblique angles around the orthogonal orientation. In an external magnetic field aligning the orientations of the quadrupole moments, a competition of the quadrupolar repulsion and van der Waals attraction (U _vdW∝ 1/R ⁶) leads to a specific spatial organization of droplets which is in fact often reported in experimental observations (see the monograph by P. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore (1995) and references cited therein). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 747–752 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Disintegration of Cnoidal Waves over Smooth Topography

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg–de Vries equation and the generalized Zakharov's system. It is shown that the cnoidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate depth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.     

Photocatalytic oxidation of cyclohexane by atmospheric oxygen in CH2Cl2 in the presence of an oxometallate-tetraalkylammonium system

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2390–2391, October, 1989.     

Application of cluster expansions to the computation of phase equilibria in solid solutions

In the framework of the method of cluster fields, exact solutions and rapidly converging decompositions are obtained for the variational parameters of the theory. The capabilities of cluster expansions are illustrated by computating the critical point of the disintegration of an Ising ferromagnet in a null field on a square lattice.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 5–9, December, 1990.     

Possible use of a gas-discharge plasma in an oscillating field to modulate electromagnetic radiation

The conditions for resonance and signal cutoff are determined from the dispersion relation for the complex refractive index for a plane electromagnetic wave propagating in a gas-discharge plasma when a magnetic field H = H₀ + H₁e^jt is imposed on the plasma. The refractive index and absorption are calculated for circularly polarized waves as functions of the alternating magnetic field with _p, _b, andv as parameters. Possible observation of modulation of the transmitted signal is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 94–99, April, 1971.     

Chain structures and clusters of particles with the mixed dipole–quadrupole interaction in smectic freely suspended nanofilms

The formation of unusual chain structures and clusters of particles with the mixed dipole–quadrupole interaction has been found in smectic nanofilms. Unlike topological dipoles and quadrupoles, the interaction between which leads to the formation of structures with finite interparticle distances, the particles with the mixed interaction touch each other and form stable chains and two-dimensional clusters. The orientation of particles in chains is intermediate between dipole and quadrupole chains. The variation of the interparticle distance and orientation of chains is explained qualitatively on the basis of the calculation of the с-director (field lines) near particles and the mutual arrangement of particles providing the minimum distortion of field lines.