Dusty plasma induced by solar radiation under microgravitational conditions: An experiment on board the Mir orbiting space station

The dynamics of the formation of ordered structures of macroparticles charged by photoemission under the action of solar radiation under microgravitational conditions without the use of electrostatic traps to confine the particles is studied experimentally and theoretically. The working conditions needed for the formation of structures of charged macroparticles are chosen as a result of a numerical solution of the problem posed, the particle charges and the interparticle interaction parameter are determined, and the characteristic times specifying the dynamics of the formation of an ordered system of macroparticles are calculated. The behavior of an ensemble of macroparticles under the effect of solar radiation is observed experimentally on board the Mir space station. An analysis and comparison of the results of the experimental and theoretical investigations permit drawing a conclusion regarding the possibility of the existences of extended ordered formations of macroparticles charged by photoemission under microgravitational conditions. Zh. éksp. Teor. Fiz. 114, 2004–2021 (December 1998)     

Local strength of thin-walled structures

We suggest efficient methods for studying stress concentrations in thin-walled structural members. The advantages of these methods are determined by their essential distinguishing characteristics as compared with well-known methods. After the separation of variables, the solution of linear ordinary differential equations of shell strain mechanics is analytically determined in the form of a matrix Taylor series. The property of the solution to satisfy arbitrary initial conditions allows one simply to reduce the boundary conditions to the initial conditions prior to calculating. Another method for structures with arbitrary parameters of the shells permits one to transfer the boundary conditions by a multiplicative method to the stress concentration site and to use them as the initial conditions in studying the stress concentration. We present the results of investigations of the stress concentration in transport-launch containers of aircraft by various methods.     

Commutant lifting and factorization of reproducing kernels

A general version of the commutant lifting theorem for operators between different spaces is proved. It includes as special cases the lifting theorems of Ball-Trent-Vinnikov and Volberg-Treil. A multivariable variant of the Volberg-Treil theorem is obtained as a corollary. A certain factorization property of reproducing kernels is shown to be a sufficient condition for the lifting. Another factorization property is shown to be a necessary condition.     

Caractéristique directionnelle calculée et mesurée d'une sonde électrochimiqueCalculated and measured directional characteristic of an electrochemical probe

The present paper demonstrates how the directional characteristics of an actual three-segment electrodiffusional sensor can be calculated from the probe image. It was shown that utilization of ‘ideal’ directional characteristics lead to an important (up to 15^°) error in flow angle determination. The directional characteristics calculated from the probe image improve significantly (up to 50%) the accuracy of the flow angle measurements. To cite this article: F. Barbeu et al., C. R. Mecanique 330 (2002) 433–436.     

Electric fields in the rheology of disperse systems

In the present survey, the influence of electric fields on the structure and rheological properties of disperse systems as well as the effect of deformations on their electrical characteristics are discussed. The properties of these systems are considered in terms of the dielectric permittivity and electrification potential. The considerable thickness of the double electric layer around the disperse phase particles, which is characteristic of disperse systems with nonpolar hydrocarbon dispersion media, provides the possibility for strong electric fields to produce an electric nonuniformity on the surface of the disperse phase particles. The formation of hydrate layers on the particles creates the possibility of polarization of the disperse phase. In plastic disperse systems such as greases, a strong orientation effect is observed, which contributes to the creation of frozen flow patterns when the flow is suddenly stopped. The survey is concluded with a consideration of the process of formation of chain structures in the direction of the lines of force of the electric field whose orientation is normal to the direction of flow, which can lead to complete stoppage of the flow.     

The laminar flow of plastic disperse systems in circular tubes

Summary The present work offers an analysis of the regularities of the flow of plastic disperse systems (PDS) as applied to the Bulkley-Herschel three-constant rheological equation. Theoretical data on the velocity profile distribution have been confirmed by experiments on the device, in which the flow structure was studied by the method of the frozen flow. By introducing expressions for the generalized Bingham and Reynolds numbers for non-linear viscoplastic bodies, formulas have been obtained for the calculation of the resistance coefficient of a hydrodynamically stabilized flow; the formulas for power law liquids and the Schwedoff-Bingham model follow from it as special cases. The results of the calculations are in good accord with experimental data for various PDS. A nomogram is given for the determination of the resistance coefficient in engineering calculations.Finally the present work considers the flow in the initial hydrodynamic zone of the tube. An analysis is given of the existing methods used for the solution of the problems and it is shown that the method used in this work for numerical calculation of simplified equations of continuity and motion provides sufficient accuracy. The results of numerical calculations are compared with the literature data, and these results are used for the analysis of the development of the flow of nonlinearly viscoplastic bodies in the initial zone. Relations are given for the determination of the length of the initial zone and of the increase of the resistance to flow due to the formation of the velocity profile. With account taken of this resistance, formulas have been derived for the calculation of pressure losses during the flow of PDS in tubes, including the initial zone.

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Zusammenfassung Es wird die Rohrströmung plastischer disperser Systeme (PDS), welche mittels einer drei-konstantigen Stoffgleichung nachBulkley undHerschel beschrieben werden können, untersucht. Das theoretisch berechnete Strömungsprofil wird durch Experimente unter Verwendung von Strömungs-Sichtbarmachungs-Methoden bestätigt. Durch Einführung geeignet definierter verallgemeinerter Bingham- und Reynolds-Zahlen für nicht-linear viskoplastische Stoffe werden Formeln zur Berechnung des Widerstandsbeiwerts einer hydrodynamisch stabilisierten Strömung erhalten; die Formeln für Ostwald-de Waele-Flüssigkeiten und Schwedoff-Bingham-Körper sind als Spezialfälle darin enthalten. Die berechneten Ergebnisse stimmen gut mit den bei verschiedenen PDS erhaltenen experimentellen Daten überein. Für ingenieurmäßige Rechnungen wird ein Nomogramm zur Bestimmung des Widerstandsbeiwerts mitgeteilt.Schließlich wird noch die Strömung im Einlaufbereich des Rohrs betrachtet. Die für die Lösung dieses Problems bekannten Methoden werden analysiert, und es wird gezeigt, daß die hier verwendete numerische Methode unter Zugrundelegung von vereinfachten Gleichungen für Kontinuität und Bewegung eine hinreichende Genauigkeit liefert. Die Ergebnisse der numerischen Rechnung werden mit aus der Literatur bekannten Daten verglichen, und diese werden dann zur Analyse der Entwicklung der Strömung von nichtlinear-viskoplastischen Stoffen in der Einlaufzone herangezogen. Es werden Beziehungen zur Bestimmung der Länge der Einlaufzone und der Vergrößerung des Widerstands infolge der Abweichung des Profils von der stationären Form angegeben. Durch Einbeziehung des erhöhten Einlaufwiderstands werden Formeln abgeleitet, mit denen sich der Druckverlust beim Fließen von PDS in Rohren unter Berücksichtigung der Einlaufzone berechnen lassen.

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With 11 figures and 2 tables     

Circular consecutive choosability of k‐choosable graphs

Let S(r) denote a circle of circumference r. The circular consecutive choosability ch_cc(G) of a graph G is the least real number t such that for any r≥χ_c(G), if each vertex v is assigned a closed interval L(v) of length t on S(r), then there is a circular r‐coloring f of G such that f(v)∈L(v). We investigate, for a graph, the relations between its circular consecutive choosability and choosability. It is proved that for any positive integer k, if a graph G is k‐choosable, then ch_cc(G)?k + 1 ? 1/k; moreover, the bound is sharp for k≥3. For k = 2, it is proved that if G is 2‐choosable then ch_cc(G)?2, while the equality holds if and only if G contains a cycle. In addition, we prove that there exist circular consecutive 2‐choosable graphs which are not 2‐choosable. In particular, it is shown that ch_cc(G) = 2 holds for all cycles and for K_{2, n} with n≥2. On the other hand, we prove that ch_cc(G)>2 holds for many generalized theta graphs. © 2011 Wiley Periodicals, Inc. J Graph Theory 67: 178‐197, 2011     

Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples

We give explicit examples of unbounded Jacobi operators with a few gaps in their essential spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum fills any finite number of bounded intervals is considered. Their point spectrum accumulates to +?? and ???. The asymptotics of large eigenvalues is also found.