Numerical derivation of the generalized Ginzburg-Landau equations of wavy vortex flow

Starting from the Navier-Stokes equations we treat the onset of the wavy vortex flow of the Taylor problem in a fully nonlinear manner. To this end we first transform the original partial differential equations into a set of ordinary differential equations by means of a Galerkin method. By a specific choice of the basic functions the Galerkin coefficients acquire a very concise form. Since these functions fulfil the boundary conditions individually, there are no additional constraints on these coefficients, which usually stem from the boundary conditions. We then first calculate the Taylor vortex flow and perform a linear stability analysis of it. Finally we calculate the coefficients of the generalized Ginzburg-Landau equations in the vicinity of the second threshold and solve these equations.     

Galactic Rotational velocities and dark neutrino matter

It has been assumed that neutrinos with non-vanishing rest mass contribute the gravitational field of our Galaxy. This contribution can be studied empirically from the orbiting velocities of galactic objects. In this way hints for the neutrino rest mass can be obtained from the rotation curve of our Galaxy.     

Acoustic coupling between the loudspeaker and the resonator in a standing-wave thermoacoustic device

Thermoacoustic refrigerators work with high amplitude sound waves, which are often created using an acoustic source coupled to a resonator. This coupling can be calculated analytically using linear acoustic equations and a linear model of the loudspeaker. This paper makes a comparison between such a coupling and measurements obtained in a large-scale thermoacoustic resonator constructed at the University of Manchester. The resonator was driven from low to large pressure amplitudes, with drive ratios up to 10%. It is shown that a good agreement is obtained for small amplitudes and this progressively worsens as the amplitude is increased. In the absence of wave harmonics and loudspeaker nonlinearities, the increasing discrepancy is attributed to the presence of minor losses.     

Experimente mit thermisch getriebenen Gas-Flüssigkeits-Schwingungen

Zusammenfassung Bei thermisch angeregten Gas-Flüssigkeits-Schwingungen wurden die angefachten Druckschwingungen für verschiedene Temperaturverhältnisse direkt gemessen. Dies erlaubte die Ermittlung der Anfachung und einen Vergleich mit theoretischen Werten.Mit den Druckamplituden im stationären Zustand wurde der Charakter der nichtlinearen Dämpfung bestimmt.

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Summary Direct measurements of the amplified pressure oscillations in a thermally driven gas-liquid system have been made for several temperature ratios. The rates of amplification have been evaluated and compared with theoretical values.From the measured steady-state pressure amplitudes it has also been possible to determine the character of the nonlinear damping.

     

Regular incidence-polytopes with Euclidean or toroidal faces and vertex-figures

Regular incidence-polytopes are combinatorial generalizations of regular polyhedra. Certain group-theoretical constructions lead to many new regular incidence-polytopes whose faces and vertex-figures are combinatorially isomorphic to classical Euclideanly regular polytopes or regular maps on the torus.