The Hamiltonian Canonical Form for Euler-Lagrange Equations

Based on the theory of calculus of variation, some suffcient conditions are given for some Euler-Lagrangcequations to be equivalently represented by finite or even infinite many Hamiltonian canonical equations. Meanwhile,some further applications for equations such as the KdV equation, MKdV equation, the general linear Euler Lagrangeequation and the cylindric shell equations are given.     

Phasing of three vircators simulated in terms of coupled van der Pol oscillators

Phase synchronization in a system of three virtual-cathode microwave oscillators (vircators) simulated by coupled van der Pol oscillators is studied. The phasing dynamics of the vircators is visualized with the phase portraits of the system in the triangular coordinates. Different phasing conditions are found.     

Fundamental aspects of initiated oxidation of tridecane and polyethylene in solutions

Specific features of the initiated oxidation of polyethylene and its low-molecular-weight analogue tridecane, associated with the occurrence of the process in the short-chain mode, were studied.     

Cosmic γ-ray bursts: Observations and modeling

It is now commonly accepted that cosmic γ-ray bursts (GRBs) are of cosmological origin. This conclusion is based on the statistical analysis of GRBs and the measurements of line redshifts in GRB optical afterglows, i.e., in the so-called long GRBs. In this review, the models of radiation and models of GRB sources are considered. In most of these models, if not in all of them, the isotropic radiation cannot provide the energy release necessary for the appearance of a cosmological GRB. No correlation is noted between the redshift, the GRB-spectrum shape, and the total detected energy. The comparison between data obtained in the Soviet experiment KONUS and the American experiment BATSE shows that they substantially differ in statistical properties and the detection of hard x-ray lines. The investigation of hard gamma (0.1–10 GeV) afterglows, the measurement of prompt optical spectra during the GRB detection, and the further investigation of hard x-ray lines is of obvious importance for gaining insight into the GRB origin. Observations of two bright optical GRB afterglows point to the fact that an initially bright optical flare is directly related to the GRB itself, and the subsequent weak and much more continuous optical radiation is of a different nature. The results of observations of optical GRB afterglows are discussed. They point to the fact that the GRBs originate in distant galaxies with a high matter density, where intense star formation takes place. The interaction of the cosmological GRB radiation with a dense surrounding molecular cloud results in the appearance of long-duration (up to 10 years) weak optical afterglows associated with the heating and reradiation of gas. Results of 2D numerical simulation of the heating and reradiation of gas in various variants of the relative disposition of GRB and molecular clouds are presented. In conclusion, the possible relation between the so-called short GRBs and recurrent sources of soft γ rays in our Galaxy, the so-called “soft gamma repeaters,” is discussed.     

Elektrische Charakterisierung von Hochfrequenz-Niederdruck-Gasentladungen

In recent years there has emerged significant interest in low pressure radio frequency (rf) glow discharges which are used widely particulary in IC fabrication. Various parameters of the rf glow discharge have been found to be useful for its electrical characterization; however, there is no uniformity and agreement. Extensive experimental investigations on various discharge systems have shown, that the self-bias on the rf driven electrode, the complex conductivity and the breakdown characteristic are preferable parameters of rf discharges. Advantageously the self-bias and the complex conductivity should be presented in dependence on the pressure and the applied rf voltage. The discharge current cannot be measured quite accurately due to currents via leaky capacitors and the deviations from a sinusoidal form of the current due to nonlinearities.     

Coagulation in lipid- and protein-containing systems

The behavior of real disperse systems with organic impurities was examined under conditions of destabilization by inorganic coagulants. A number of physicochemical methods of analysis and a simulation method were used to identify the character and type of the complexes formed and to calculate their stability constants.     

Latex particles bearing hydrophilic grafted hairs with controlled chain length and functionality synthesized by reversible addition–fragmentation chain transfer

A method is described for synthesizing latex particles with anchored hairs by the grafting of hydrophilic chains, synthesized by reversible addition–fragmentation chain transfer, onto functionalized latex particles. These have the potential to bind biologically active species. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1188–1195, 2003     

Dispersion and distribution of organically modified montmorillonite in nylon‐66 matrix

Nylon‐66 nanocomposites were prepared by melt‐compounding nylon‐66 with an alkyl ammonium surfactant pretreated montmorillonite (MMT). The thermal stability of the organic MMT powders was measured by thermogravimetric analysis. The decomposition of the surfactant on the MMT occurred from 200 to 500 °C. The low onset decomposition temperature of the organic MMT is one shortcoming when it is used to prepare polymer nanocomposites at high melt‐compounding temperatures. To provide greater property enhancement and better thermal stability of the polymer/MMT nanocomposites, it is necessary to develop MMT modified with more thermally stable surfactants. The dispersion and spatial distribution of the organic MMT layers in the nylon‐66 matrix were characterized by X‐ray diffraction. The organic MMT layers were exfoliated but not randomly dispersed in the nylon‐66 matrix. A model was proposed to describe the spatial distribution of the organic MMT layers in an injection‐molded rectangular bar of nylon‐66/organic MMT nanocomposites. Most organic MMT layers were oriented in the injection‐molding direction. Layers near the four surfaces of the bar were parallel to their corresponding surfaces; whereas those in the bulk differed from the near‐surface layers and rotated themselves about the injection‐molding direction. The influence of the spatial distribution of the organic MMT on crystallization of nylon‐66 was also investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1234–1243, 2003