TR-LII for sizing of carbon particles forming at room temperature

Time-resolved laser-induced incandescence (TR-LII) was applied for the determination of particle sizes during carbon-particle formation from supersaturated atomic carbon vapor that was generated by laser photolysis of carbon suboxide (C₃O₂) at room temperature. Thus, the solid carbon particles were formed under hydrogen-free conditions. The TR-LII technique was used for in situ size measurement of growing carbon particles and samples of final particles were analyzed by transmission electron microscopy (TEM). It was found that the particles grow to a final size of 4–12 nm within 0.02–1 ms. The properties of the obtained particles depend on the initial conditions in the reaction volume, i.e. concentration of carbon suboxide, pressure and type of gas diluter, photolysis wavelength, and laser pulse energy. The comparison of TR-LII and TEM particle sizing results yields information about the effective thermal energy accommodation coefficients for He, Ar, CO, and C₃O₂ molecules on carbon particles. PACS 61.46.Df; 07.60.-j; 78.70.-g     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

Electroless deposition of open-end Cu nanotube arrays

Cu nanotube arrays were fabricated by electroless deposition using porous anodic aluminium oxide membranes as templates. This was accomplished by a four-step procedure, i.e. pore-wall modification, polishing treatment, sensitization-activation and electroless deposition. The as-synthesized Cu nanotubes possess controllable inner diameter and open ends.     

Low-Frequency Parasitic Space-Charge Oscillations in the Helical Electron Beam of a Gyrotron

We developed a medium-power pulsed gyrotron equipped with diagnostic systems for studying low-frequency parasitic space-charge oscillations in the helical electron beam and the energy spectrum of electrons in the collector region. Methods for suppressing parasitic oscillations are proposed and tested. An explanation of the mechanism of suppression of these oscillations is given.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

Evaluation of the probability of bankruptcy for a model of insurance company

We study the problem of evaluation of the probability of ruin of an insurance company for infinitely many steps in the case where the company can invest its capital to bank deposits at any time. As a distribution of the amounts of claims to the insurance company, we use the gamma-distribution with the parameters n and α. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 447–457, April, 2007.     

Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures.