The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Integrable models for vicious and friendly walkers

We consider random walks of two essentially different classes of random walkers, namely, of vicious and friendly ones, on one-dimensional lattices with periodic boundary conditions. The walkers are called vicious since, arriving at a lattice site, they annihilate not only one another but all the remaining walkers as well. On the contrary, an arbitrary number of friendly walkers can share the same lattice sites. It is shown that a natural model describing the behavior of friendly walkers is an integrable model of the boson type. A representation of the generating function for the number of the lattice paths performed by a fixed number of friendly walkers for a certain number of steps is obtained. Bibliography: 22 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 59–74.     

New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.     

Inverse Problem with Free Boundary for Heat Equation

We establish conditions for the existence and uniqueness of a solution of the inverse problem for a one-dimensional heat equation with unknown time-dependent leading coefficient in the case where a part of the boundary of the domain is unknown.     

Formation of coherent spatial structures in the reaction-diffusion atmospheric system under the action of a planetary wave

On the example of the effect of an atmospheric wave with given amplitude on the density oscillations of minor gas constituents near the mesopause (at heights 80–90 km, we consider the influence of the quasi-resonant periodic spatial transport on a distributed system responding subharmonically to a periodic external action (diurnal sunlight variations). Numerical modeling revealed the formation of a coherent horizontal distribution of the dynamical variables (i.e., the concentrations of small constituents). Application of this effect to the mesopause conditions is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 9, pp. 739–752, September, 2004.     

Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow

Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.