Gasdynamische Untersuchung des Jouleschen Überströmversuches

Zusammenfassung Es wird die zeitabhängige Strömung beim Ausgleichsvorgang zwischen zwei endlichen Behältern untersucht. Den Überlegungen wird eine eindimensionale, reibungsfreie und quasistationäre Strömung zugrunde gelegt. Während bei überkritischer Strömung eine analytische Lösung möglich ist, wird das Problem bei unterkritischer Strömung numerisch gelöst.Dem Druckausgleich zwischen den beiden Behältern folgt ein isobarer Wärme- und Massenaustausch, bis sich das thermodynamische Gleichgewicht eingestellt hat.

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Gasdynamical investigation of Joule's overflow experiment

The time-dependent flow of an exchange process between two big insulated tanks is considered. The problem is treated on the basis of a one-dimensional, inviscid and quasi-steady flow. An analytical solution is obtained for supercritical flow, while for subcritical flow the problem is solved numerically.After the pressure-equilibrium between the two-tanks an isobar heat and mass exchange follows, until the thermodynamic equilibrium is reached.

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Formelzeichen a Schallgechwindigkeit - A engster Querschnitt - c Geschwindigkeit - c _p spezifische Wärme bei konstantem Druck - c _v spezifische Wärme bei konstantem Volumen - e innere Energie - i Enthalpie - m Masse - M Machzahl - p Druck - spezielle Gaskonstante - s Stromlinie, spezifische Entropie - t dimensionsbehaftete Zeit - T Temperatur - V Volumen - Konstante - Abkürzung - Volumenverhältnis - Verhältnis der spezifischen Wärmen - Dichte - dimensionslose Zeit Indizes 0 Zustand zur Zeitt=0 - 1 Zustand im Überdruckbehälter - 2 Zustand im Überströmbehälter - * Zustand im engsten Querschnitt - K kritisch - M Zustand bei Druckausgleich - E Endzustand bei Temperaturausgleich Herrn Prof. Dr. B. Schmidt in Dankbarkeit zum 60. Geburtstag gewidmet     

Forces of a fluid in a rotating straight pipe

The fluid flow through a rotating straight pipe is considered, the axis of rotation being perpendicular to the pipe axis. The flow of the fluid is taken as fully developed, i.e. the velocity field is assumed to be the same in all transverse cross sections of the pipe. The derivation presented applies to viscous and nonviscous incompressible fluids. For constant angular pipe velocity a simple and exact (Coriolis type) relationF=2Q(t) is derived between the forceF by which the fluid acts on the (unit length of the) pipe in the direction perpendicular to the two axes, the fluid mass flow rateQ(t) through the pipe, and the angular velocity. Variable angular velocities, i.e. , introduce an additional term into the expression for the inertial forceF, which depends only on and on known (constant) parameters; this term is known for given angular velocity(t). The flow configuration investigated here is an idealization of those appearing (over short space and time intervals) in the devices measuring mass flow rateQ(t) through the (Coriolis) forceF. Therefore the exact results derived here cast some light on the degree of precision one expects in these devices, where more complicated flow configurations are present than those looked at in this paper.     

Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

Radiative processes and non-equilibrium thermodynamics

With the assumption of an elementary physical concept meteorologically effective radiative processes (absorption-emission, scattering) can be included consistently in nonequilibrium thermodynamics of irreversible phenomena. Analogously to the usual Gibbs relations a fundamental equation was formulated for monochromatic light rays as the nucleus of the theory.Using the methods of classical irreversible theory, a complete entropy balance equation is derived in which the entropy variations of the mass as well as of the radiation field are explicitly represented. The resulting entropy source strength function through its analytical structure reveals the dynamical character of the irreversible variation terms. The-expression being positive according to the second law of thermodynamics is found to have a bilinear form as a function of the irreversible fluxes representing the entropy generating radiative processes and their conjugated thermodynamic forces. The mathematical structure and the positive sign of, following the usual line of reasoning, motivate the assumption of constitutive relations for the irreversible radiative processes. These equations developed from purely thermodynamical reasoning turn out to be equivalent to the usual radiative transfer equation which is founded on a very different theoretical concept. A very fundamental relationship can be deduced in this context from the entropy production function. It provides a direct thermodynamical proof that in nonscattering media the definition of a local temperature is necessarily accompanied by the validity of the Kirchhoff law.     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant     

Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

Excitation functions for some output channels following the p +55Mn interaction atE p=1·3–2·0 MeV

Excitation functions for the⁵⁵Mn(p, p )⁵⁵Mn,⁵⁵Mn(p, n )⁵⁵Fe and⁵⁵Mn(p, )⁵⁶Fe reactions are studied for proton beam energyE _p=1·3–2 MeV. The excitation functions are established from yield functions for -rays emitted from the first excited states of final nuclei. Many resonances are observed and competition of their decay into all three output channels is analysed. Spin-parity assignment for some resonant states in the⁵⁶Fe compound nucleus is deduced.Participated partly in the course of his work on a Thesis.The authors wish to thank the staff of the Van de Graaff accelerator at Charles University in Prague for the efficient operation of the machine and dr. I. Wilhelm for the valuable technical help in the early period of the experimental work. One of us (N. A. N.) acknowledges the staff of the Dept. of Nuclear Physics of Charles University in Prague for the excellent working conditions.     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

61Ni Mössbauer study of the surface hyperfine magnetic field in nickel

⁶¹Ni Mössbauer measurements have been performed at 4.2 K on spherical Ni particles with an average diameter of 100 and 30 Å, covered with a protective layer of SiO. Their spectra contain a surface component with a significantly reduced hyperfine magnetic field as compared with the field in the bulk. This result confirms recent theoretical predictions.