Microwave reflection properties of grooved metallic mirrors

Maxwell's equations are solved using finite difference equations to obtain the near and the far field distribution of electromagnetic waves in front of corrugated mirrors. We treat the case of perpendicular incidence to obtain both the phaseshift between TE- and TM-modes in polarisation twisters and mode converters as well as the amplitude of the electromagnetic field.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

An experiment to measure collisionless radial transport ofenergetic electrons confined by a dipole magnetic field

A new laboratory terrella has been constructed in order to study collisionless radial diffusion of particles trapped within a dipole magnetic field. Columbia's collisionless terrella experiment (CTX) aims to reproduce the process of wave-induced radial transport and does not try to simulate magnetospheric structure. The first experiment planned for CTX is the direct measurement of stochastic radial diffusion induced from wave-particle drift resonances. The motivation for the CTX experiment is described, and the procedures to be used to measure the intensity and spectrum of fluctuations generating chaos, the rate of radial transport, and the evolution of the density and pressure profiles are illustrated. Because of the success of similar experiments conducted earlier in a long thin magnetic mirror, these dipole experiments can be performed with a high degree of confidence. An example from these earlier experiments is presented     

Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Synthesis of polysiltrimethylenes with trimethylsilyl groups in the branch of the main chain

The thermally initiated and platinum-catalyzed polymerization of 1-silacyclobutanes with substitutents containing a trimethylsilyl group was carried out. Soluble, high-molecular-weight, heterochain siltrimethylene polymers were obtained, containing trimethylsilyl groups removed from the main chain by various bridges.A. V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 117912 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 223–225, January, 1992.     

Coulomb blockade electrometer with a high-T c island

We report on a successful attempt to fabricate a Coulomb blockade electrometer consisting of an ultrasmall YBa₂Cu₃O_7−δ (YBCO) island coupled to two gold electrodes through a high-resistance native surface tunnel barrier. A third electrode placed near the island was used as an electrostatic gate. Spectra typical for tunneling into the YBCO superconductor were reproducibly measured. At temperatures below 0.5 K the low-bias conductance was suppressed by the Coulomb blockade. The blockade could be periodically varied by the gate potential. An external magnetic field of up to 5 T strongly influenced the transport via the island but without any change in the period of the Coulomb oscillations. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 112–117 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.