Orientational changes in the nematic liquid crystal structure on a polymer surface induced by phase separation in a magnetic field

The change in the domain texture of the 5CB nematic liquid crystal on the surface of a polyvinyl butyral gelatinous polymer solution cured in a magnetic field is studied optically. The alignment of the nematic is described by the effective order parameter S* of the polydomain cells. The anchoring energy of a liquid crystal with gelatinous polymer W _ϕ = 1 × 10⁻³ erg/cm₂ is determined.     

Theory of sparse random matrices and vibrational spectra of amorphous solids

The random matrix theory has been used for analyzing vibrational spectra of amorphous solids. The random dynamical matrix M = AA ^T with nonnegative eigenvalues ɛ = ω² has been investigated. The matrix A is an arbitrary square (N-by-N) real sparse random matrix with n nonzero elements in each row, mean values 〈A _ij 〉 = 0, and finite variance 〈A _ij ²〉 = V ². It has been demonstrated that the density of vibrational states g(ω) of this matrix at N, n ≫ 1 is described by the Wigner quarter-circle law with the radius independent of N. For n ≪ N, this representation of the dynamical matrix M = AA ^T makes it possible in a number of cases to adequately describe the interaction of atoms in amorphous solids. The statistics of levels (eigenfrequencies) of the matrix M is adequately described by the Wigner surmise formula and indicates the repulsion of vibrational terms. The participation ratio of the vibrational modes is approximately equal to 0.2–0.3 almost over the entire range of frequencies. The conclusions are in qualitative and, frequently, quantitative agreement with the results of numerical calculations performed by molecular dynamics methods for real amorphous systems.     

Atomic Dynamics of Diamond at a “Negative” Pressure

JETP Letters - Changes in the structure and atomic dynamics of diamond irradiated by fast neutrons have been studied. It has been shown that a sample irradiated to a fluence of 1021 cm−2...     

Analytic Solution of the Problem of Additive Formation of an Inhomogeneous Elastic Spherical Body in an Arbitrary Nonstationary Central Force Field

We study the processes of additive formation of spherically shaped rigid bodies due to the uniform accretion of additional matter to their surface in an arbitrary centrally symmetric force field. A special case of such a field can be the gravitational or electrostatic force field. We consider the elastic deformation of the formed body. The body is assumed to be isotropic with elasticmoduli arbitrarily varying along the radial coordinate.We assume that arbitrary initial circular stresses can arise in the additional material added to the body in the process of its formation. In the framework of linear mechanics of growing bodies, the mathematical model of the processes under study is constructed in the quasistatic approximation. The boundary value problems describing the development of stress–strain state of the object under study before the beginning of the process and during the entire process of its formation are posed. The closed analytic solutions of the posed problems are constructed by quadratures for some general types of material inhomogeneity. Important typical characteristics of the mechanical behavior of spherical bodies additively formed in the central force field are revealed. These characteristics substantially distinguish such bodies from the already completely composed bodies similar in dimensions and properties which are placed in the force field and are described by problems of mechanics of deformable solids in the classical statement disregarding the mechanical aspects of additive processes.     

Temperature dependence of the effective anchoring energy for a nematic-ferroelectric interface

Specific features of the anisotropic interaction between a nematic mixture and a polar surface of a ferroelectric triglycine sulfate crystal have been studied over a wide temperature range including the substrate's Curie point T_c. The mixture was composed of two nematic liquid crystals, 60% of p-methoxybenzylidene-p-n-butylaniline (MBBA) and 40% of p-ethoxybenzylidene-p-n-butylaniline (EBBA), and doped with a small amount of a dichroic dye. The temperature dependence of the polarized components of optical density D_j of the dye absorption band for the nematic and isotropic phases of the MBBA+EBBA mixture has been obtained using polarization optic techniques. The temperature-induced structural changes in the nematic layer near T_c were found to be related to the changes in the orientational part of the tensor order parameter Q_ik. The experimental data have been interpreted using the model, in which the dispersive van der Waals forces of the substrate stabilize the planar orientation of the nematic in the bulk competing with the short-range anchoring forces in the vicinity of T_c. At the same time, the anisotropic part of the surface energy has two terms with the orthogonal easy axes. The nature of the surface electric field and its effect on the director alignment at the interface have been clarified. Taking into account the known relation between anchoring strength and the nematic order parameter, the effective anchoring energy w_eff for the studied system has been determined as a function of temperature.     

Bipolar-homogeneous structural phase transition in nematic droplets formed in the polymer matrix in a magnetic field

The phase transition from the bipolar structure to the homogeneous structure in droplets formed from the nematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl in poly(vinyl butyral) in the presence of a magnetic field has been investigated. The phase transition is associated with the expansion of the regions with a tilted orientation of the director in the vicinity of defects (the disappearance of boojums) and with the alignment of the nematic director lines in the bulk of the droplet in the direction of the magnetic field. In the temperature range T = 24−34°C, cyclic mutual transformations between the bipolar configuration of the nematic director and the homogeneous structure, which have a period of ∼0.5–3.5 s and result from thermal fluctuations of the order parameter, are observed in droplets 3–15 μm in size after the forming field is switched off.     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

The different and discriminant of regular mappings

The different of morphisms of surfaces onto curves is studied. A relationship is established between the discriminant and Euler characteristics of degenerate layers for morphisms without multiple components.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 519–524, November, 1968.