On a generalization of Pólya’s theorem

We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points.     

Dimensional variation in production of high-aspect-ratio micro-pillars array by micro powder injection molding

Micro powder injection molding (μPIM) is one of the potential processes for the mass production of metallic microstructures and micro components. Here, μPIM is the miniaturization of conventional PIM, which involves four processing steps: mixing, injection molding, debinding and sintering. This paper looks into the feasibility and effectiveness of μPIM as a key mass production process for the fabrication of metallic micro components. For it to be an effective re-production process, it is imperative to examine how well parts can be duplicated/fabricated from a master mold. In this work, the dimensional variation of high-aspect-ratio micro-pillars arrays, in particular the dimensional shrinkage, global warpage, and surface roughness at each stage of the μPIM process for a range of molding pressures, are quantified and compared in detail. The sensitivity of the dimensional variation of the microstructures to the packing pressure is reported. The mechanism behind the dimensional variation is analyzed. PACS 81.20.Ev; 81.20.Hy; 81.70.Fy; 07.60.Ly; 81.05.-t     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

Synthesis of water-soluble fullerene-containing vinyl polymers by low-temperature radiation-induced living polymerization

Water-soluble polymers of acrylamide and acrylic acid that contain fullerene (more than 90% C₆₀) have been prepared by the low-temperature radiation-induced living polymerization. In the absorption spectra of these polymers, a monotonically decaying absorption typical of the covalently bound fullerene or its associates is observed in the range 240–700 nm. The radiation initiation of the process allows preparation of high-purity polymers useful for designing medicinal preparations.     

Radio-frequency controllable quantum interference in Mössbauer spectroscopy

The role of quantum interference (QI) in spectra of the resonant Mössbauer scattering is investigated. As a mechanism ensuring the QI conditions, the radio-frequency (RF) mixing of the spin sublevels of the excited nuclear state is considered. It is shown that QI leads to a significant intensity redistribution of the elastic and Raman scattering.     

Simulation of structure formation in disperse systems

The main rules governing the redistribution of microparticles in disperse systems were revealed by computer simulation. These rules predetermine the character and properties of the structure being formed, which opens up the possibility to control the properties of disperse materials, including sorbents and catalysts based on high-dispersity solid phases.     

Pressure recovery system for a high-power HF/DF laser: implementation practice

The matter of development of a high-performance pressure recovery system (PRS) for a high-power HF/DF laser is discussed. A sequence of design steps is proposed, which involves estimation of basic characteristics of PRS components with the help of one-dimensional integral and semi-empirical procedures; simulation, to be performed using three-dimensional non-stationary Navier — Stokes equations; experimental modelling aimed at verification of the calculation procedures and at refinement of obtained parameters; and a fullscale experiment. An ejector-type system providing for recovery of pressure from 12 Torr to atmospheric pressure in the gas-dynamic system of an HF/DF laser of several-tens-kilowatt power is developed. Matching conditions for parameters of individual PRS components as well as joint functioning of the PRS with a continuous chemical laser in an integral complex are analysed. Conditions for minimization of mass-dimensional characteristics of the laser-PRS complex necessary for the development of ground-based mobile systems are identified.     

Dynamical state reconstruction and guaranteeing control for a system of parabolic equations

A problem of guaranteeing control for a system of parabolic equations is considered. A solving algorithm based on the combination of real time reconstruction processes and feedback control is designed.