Method of fictitious regions for second-order quasilinear elliptical equations

We consider the application of the fictitious region method to solve the first and second boundary-value problems for a second-order quasilinear elliptical equation. Rate of convergence bounds are obtained for two versions of the fictitious region method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 7–14, 1985     

Dimensionally and thermally stable polymer,containing disordered graphitic structure and adamantane

In an attempt to develop a low‐k interlayer dielectric, adamantane‐diphenyldiethynyl moiety containing oligomer is prepared. Oligomerization of 1,3,5,7‐tetrakis[3/4‐ethynylphenyl]adamantane ( 4 ) is accomplished by a Glaser–Hay oxidative coupling with 1,3,5‐triethynylbenzene and phenylacetylene end‐capping agent. The CHCl₃ soluble oligomer is then thermally treated by step‐curing at 200, 300, 380, and 450 °C for 30 min at each temperature under nitrogen flow to render a shiny void‐free black polymer. TGA analysis indicates that the polymer is stable under nitrogen up to 500 °C with a marginal decomposition up to 800 °C. Solid‐state ¹³C NMR, Raman scattering, and FTIR are used to characterize the structure of the polymer. The polymer consists of amorphous carbon networks with the adamantane moieties and nanosized graphitic regions (clusters), which are generated from the thermal crosslinking of the diphenyldiethynyl units. It shows a remarkably low linear coefficient of thermal expansion (～25 ppm/°C), presumably due to the presence of the disordered graphitic structure. Its high density (～1.21 g/cm³), refractive index (～1.80 at 632 nm), and Young's modulus (～17.0 GPa) are also consistent with the interpretation. This study reveals important details about the effect of microscopic structure on the macroscopic properties of the highly crosslinked polymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6909–6925, 2006     

Role of orientation in kinetics of nucleation and growth of crystals in polymers

A theoretical framework is provided for generalizing the inferences drawn from the results of earlier experimental studies of kinetics of crystallization in oriented poly(ethylene terephthalate). The framework is obtained by combining extensions of classical nucleation theories in polymers^3,4 and a theory of crystal growth with anisotropic incorporation of segments into growing crystals.¹⁵ It is shown that, while a very strong dependence of rate of primary nucleation on orientation does exist, there is a only a much weaker dependence of rate of crystal growth on the orientation of the crystallizing polymer. The theoretical formulation provided here would allow qualitative estimates for comparison with experiments.     

Numerical method for problems of diffraction on semi-infinite structures

We propose a method which transforms homogeneous integral equations into inhomogeneous ones for problems of diffraction by semi-infinite structures. New integral equations and the corresponding stationary functionals dependent on the desired scattering parameters are obtained. The consideration is performed for the open-end diffraction problem of a parallel-plate waveguide which has a rigorous solution, but the method has sufficient generality to use it for two-dimensional surface integral equations describing planar and nonplanar structures as well as for an arbitrary structure of waveguide transformer type, the solution for which can be sought in the finite domain. The method is based on field representation at the infinity as incident and scattered waves. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 235–245, March 2006.