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.     

Nonlinear vibrations of a charged drop due to the initial excitation of neighboring modes

The asymptotic analysis of the nonlinear vibrations of a charged drop that are induced by a multi-mode initial deformation of its equilibrium shape is performed. It is shown that when two, three, or several neighboring modes are present in the initial deformation spectrum, the mode with the number one (translational mode) appears in the second-order mode spectrum. The excitation of the translational mode follows from the requirement of center-of-mass immobility and causes the dipole components (which are absent in the linear analysis) to appear in the spectra of the acoustic and electromagnetic radiation of the charged drop.     

Multi-layer structure in the strongly coupled 5D abelian Higgs model

We explore the phase diagram of the five-dimensional anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four-dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order, and that each layer moves into the Higgs phase independently of the others (decoupling of layers). As the Higgs couplings vary, we find, using mean field techniques, that this transition may probably become second order. Received: 21 December 2001 / Published online: 12 April 2002     

Entangled state generation and modulation of vacuum squeezing by classical optical fields in birefringent fiber

Evolution of the vacuum fluctuations in the two-wave mixing of the optical fields propagating in a birefringent fiber is studied. The two-wave mixing in the birefringent fiber was suggested as a possible scheme for the entangled-state generation. Our treatment in studying the entangled-state generation uses depleted pump approximation and enables one to trace the influence of the input conditions of classical optical fields on the evolution of vacuum squeezing. We report the periodical modulation of the vacuum squeezing when the input relative phase of coherent waves varies. The measure of nonclassical correlations imposed on the generated light is calculated.