Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Error analysis: a tool for selecting travel demand models

In developing travel demand models it is generally assumed that the base-year data used in developing the parameters, as well as the forecasted data to be used as independent variables for the design year, are of acceptable quality. The purpose of this paper is to present the application of error propagation theory in assesing the predictive quality of one type of travel demand forecasting model (multinomial logit models) and to demonstrate how error considerations can be used as a tool for identifying the optimal model. The general conclusions of this study are that: (1) it is indeed possible to quantify errors in dependent variables in logit models as a consequence of errors in independent variables; and (2) error consideration can be used as a tool for identifying the optimal model from a set of candidate models. Further research is recommended to develop better insights into the phenomenon of error propagation so that the consideration of errors can be a factor in decisions on model selection.     

Correlations between dynamical properties and features of potential energy surfaces for the light atom transfer reactions O+HCl→OH+Cl AND Cl+HCl→ClH+Cl

A three-dimensional quasiclassical trajectory study of the dynamics of the light atom transfer reaction O(³P) + HCl(ν=0)→ OH + Cl was carried out employing two LEPS potential energy surfaces (I and II). Attention was focused mainly on three-dynamical properties; the oscillatory behavior of partial cross sections as a function of collision energy; the rotational excitation of the products; and the influence of reagent rotation on reactivity. Distinct differences were found between surfaces I and II with respect to these properties. The examination of individual trajectories indicated that there is a significant difference in the nature of these surfaces. While surface I is governed by weak repulsive forces, surface II is governed by strong attractive forces which tend to direct the reactants toward a collinear geometry. The present results confirm conclusions reached from an earlier study of the reaction Cl+HCl→ClH+Cl concerning correlations between dynamical properties and features of potential energy surfaces. For surfaces of the type that we termed HREP, since they are of repulsive nature and they lead to highly rotationally excited products, no significant oscillations of partial cross sections are obtained and reagent rotation promotes the reaction. On the other hand, for surfaces of the type that we termed COLD (collinearly directing), since they tend to direct the reactants toward a collinear geometry and form rotationally “cold” products, significant oscillations of partial cross sections are obtained and reagent rotation causes a decline in reactivity.     

The Barnett approximation in the theory of hydrodynamic fluctuations

The Langevin dynamics and fluctuational-dissipative relationships for the hydrodynamic fluctuations for systems which are described in the third Barnett order with respect to the gradients of the hydrodynamic variables are generalized on the basis of a kinetic approach.     

Automatic error correction in inflected languages

Systems for automatic detection and correction of spelling errors in natural language texts are considered. The development of such systems for both English and Russian (and for inflected languages in general, including all Slavic languages) is discussed. An approach associated with morphological analysis of the wordforms in the given text is described. The topics considered in the paper include the main methods of automatic spelling correction, levels of automation of the spelling error correction process, the effect of the type of computer used, the use of spelling error correctors in a stand-alone mode and in combination with word-processing software, and the maintenance of auxiliary dictionaries.Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 28, pp. 111–139, 1988.     

EXPRESSIONS FOR PREDICTING FUNDAMENTAL NATURAL FREQUENCIES OF NON-CYLINDRICAL HELICAL SPRINGS

Numerical and analytical studies are performed for the free vibration analysis of non-cylindrical (conical, barrel and hyperboloidal types) helical springs. The stiffness matrix method is used in the numerical analysis. A total of 12 degrees of freedom (six displacements and six rotations) is described for an element. The exact element stiffness matrix and the exact concentrated element inertia matrix are used in the formulation. The rotary inertia, the shear and extensional deformation effects are considered in the analysis. Comparison of the numerical results with the reported results obtained numerically and experimentally gives satisfactory values. After verification of the numerical frequencies, the non-dimensional fundamental frequencies of fixed-fixed non-cylindrical helical springs with circular section are expressed in a simple formula with a maximum absolute relative error of 5% using those numerical values for the constant helix pitch angles (5°, 10°, and 15°). These expressions restricted to the fundamental frequencies are also verified with ANSYS results.     

Navier-Stokes approximation and problems of the Chapman-Enskog projection for kinetic equations

The purpose of this paper is to investigate problems of the Navier-Stokes approximation to kinetic equations in terms of the so-called Chapman-Enskog projection. One considers properties of the Chapman-Enskog projection for the Cauchy problem for moment approximations of the kinetic equation and primarily the Chapman-Enskog projection for the Boltzmann-Peierls kinetic equation. The existence of the Chapman-Enskog projection for the Cauchy problem is proved for the phase space of conservative variables (phenomena of nonlinear diffusion) and for the phase space of physical variables (the second sound projection). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 184–225, 2005.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006