Upper-Branch Instability of Flow in Pipes of Large Aspect Ratio with Three-Dimensional Nonlinear Viscous Critical Layers

We consider the upper-branch neutral stability of flow in pipesof large aspect ratio, basically extending the work of F. T.Smith to the nonlinear regime. The inclusion of weak nonlinearityleads to an eigenproblem whose solution depends on the propertiesof three-dimensional nonlinear critical layers. Two specialcases are considered. The first is for very small amplitude perturbations, where R is a Reynolds numberbased on the height of the tube and which is assumed large.Then a fully analytical solution of the three-dimensional criticallayers is possible, from which the linear results of Smith maybe deduced. The second case studied is that of flow in a rectangularpipe, where a solution of the nonlinear critical layer problemcan be obtained. Further analysis of neutral modes in this lattercase suggests the possible existence, inter alia, of neutralmodes for finite aspect ratio tubes. These modes depend on thescaled amplitude and have O(1) wavespeeds.     

Structure of a nonequilibrium high-frequency discharge

The problem for a one-temperature plasma is considered with allowance for the finite ionization rate. It is shown that in the developed nonequilibrium case the leading effect of ambipolar electron diffusion and ionization lag lead to a qualitatively different picture as compared with the equilibrium case. In particular, the heat release zone covers only a relatively small leading part of the ionization zone with a relatively low (n_e n_ef) electron concentration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 161–169, May–June, 1989.The authors thank A. A. Barmin and A. G. Kulikovskii for useful discussions.     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

Impossibility of centrally symmetric shock waves in vacuum in the relativistic theory of gravitation

Burevestnik Scientific-Industrial Union, Leningrad. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 3, pp. 473–480, June, 1989.     

A modified Tolman mass-energy formula

A modified Tolman mass (energy) formula is derived for spherically symmetric, time-independent systems. In the absence of surfaces of discontinuity, the modified formula has, in contradistinction to the original formula, the following desirable properties: (i) it always gives the correct mass of the system as a whole; (ii) it always gives the correct mass of any portion of the system which is surrounded by vacuum; and (iii) it remains invariant under a rescaling of the time coordinate of the formt Ct, C=constant. In the presence of surfaces of discontinuity the Tolman mass formula is further modified by the addition of the Israel mass associated with each surface. The resulting formula also has the above three properties. A new exact solution of Einstein's equations which is well behaved everywhere and is, in a sense, a generalization of Florides' new interior Schwarzschild solution is also presented.This result explains why, takingT ₁ ¹ =[C] in Section 2, we were able to obtain a solution free of surfaces of discontinuity.     

Variation of the instability index on stationary curves of elliptic equations depending on a parameter

The set of solutions of the equation A(u, )=0 in the case of general position consists of smooth curves. Solutions of a quasilinear elliptic equation with large instability index are constructed and an estimate obtained for the number of turning points of the solution curves.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 12, pp. 47–58, 1987.     

Spectrum of the algebra of pseudodifferential operators in a halfspace

One considers C*-algebras, generated by pseudodifferential operators in a halfspace. The operators act in functional spaces with weighted norms. One describes the set of all classes of equivalent irreducible representations of algebras and reveals the topology on the spectrum. One investigates, in particular, the dependence of the spectrum on the choice of the weighted functional space.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 160–180, 1986.     

Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be anyons, i.e. particles with arbitrary real spin and intermediate () statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT _csuperconductors.     

Messung der Gewebetemperatur mit infrarotem Thermometer in einer Trockenanlage

Zusammenfassung Es wurde eine theoretische Analyse der kontaktlosen Temperaturmessung des an der Spann-, Trocken- und Fixiermaschine bearbeiteten Gewebes vorgenommen. Der Einfluß der Trocknerwand ist durch die Korrektive Funktion ausgedrückt, zu deren Festlegung ein allgemein anwendbares Diagramm zusammengestellt wurde. Dabei wird die Tatsache berücksichtigt, daß die Messung in einem beschränkten Teil des Spektrums durchgeführt wird, welcher außerhalb der Wasserdampfabsorptionsbänder liegt.

---

Measuring temperature of textiles in driers with infrared thermometer

The paper undertakes a theoretical analysis of contactless temperature measurement of textiles processed on a stretching, drying and fixation machine. The effect of the drier wall is expressed through a corrective function for whose determination a universal diagram has been established. The measurements have been performed in a narrow part of the spectrum lying outside the water vapour absorption bands.

---

Formelzeichen B W· m^–2 Effektive Wärmestromdichte durch Strahlung - K _i Radiationskoeffizient für Oberflächei - q W · m^–2 Wärmestromdichte durch Strahlung - T K Temperatur - t °C Temperatur - dtj Kroneckersches Symbol - Emissionsgrad der Oberfläche - m Wellenlänge - _ij Radiationskoeffizient - _T W·m ^–2 ·K ^–4 Koeffizient in der Gleichung (2) - Winkelkoeffizient für Strahlung zwischen Oberflächen 1, 2 - – Korrektionsfunktion - W·m ^–2 Wärmestromdichte des schwarzen Körpers Indizes c Gewebe - M Meßwert - w Trocknerwand     

Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

---

Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.