Gottfried Köthe, 1905-1989 / neu hrsg. von Gabriele Dörflinger, Universitätsbibliothek Heidelberg

Leben und Werk des Mathematikers Gottfried Köthe, der von 1957 bis 1965 in Heidelberg lehrte. Der Beitrag enthält auch ein Verzeichnis der Schriften Gottfried Köthes

On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator

The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order ordinary differential equations. We establish global estimates for the eigenvalues of this system in terms of the turbulence function alpha and its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a non-oscillation theorem. The conditions of these theorems, which again involve alpha and alpha', must be violated in order to reach supercritical or oscillatory regimes.Comment: 35 pages, 4 figures, to be published in SIAM J. Math. Anal

Urwaldrelikt-Arten - Xylobionte Käfer als Indikatoren für Strukturqualität und Habitattradition

On the basis of the list of saproxylic beetles of Germany, the authors present a definition and list of “Urwald relict species”, comprising 115 beetles that are considered to be associated with primeval forest (“Urwald”) structures and features. We use the term “habitat tradition” to describe a continuity in supply of old growth dead wood and forest structures. The selection of species is made on behalf of the following criteria: relict records in Central Europe; attachment to continuity of deadwood resources and habitat tradition; continuity of old growth stand features like tree and deadwood maturity and di-versity; absence from cultivated Central European forest.Urwaldrelikt-Arten - Xylobionte Käfer als Indikatoren für Strukturqualität und Habitattradition Auf der Basis der Liste xylobionter Käfer Deutschlands legen die Autoren eine Definition und Liste von 115 Käferarten vor, die in Deutschland als Urwaldreliktarten bezeichnet werden können. Wir definieren die Kontinuität eines Bestandes hinsichtlich Totholzangebot und Bestandsstruktur als „Habitattradition“. Die Auswahl der Arten erfolgt anhand folgender Kriterien: Reliktäres Vorkommen in Mitteleuropa; Bindung an Strukturkontinuität bzw. Habitattradition sowie Kontinuität der Alters- und Zerfallsphase; hohe Ansprüche an Totholzqualitäten und –quantitäten; aus den kultivierten Wäldern Mitteleuropas verschwindend oder schon verschwunden

Application of the Christiansen-Shelyubskii method to determine homogeneity and refractive index of industrial glasses

The Christiansen-Shelyubskii method has been applied to determine the homogeneity of both colorless and colored technical glasses. It could be confirmed that this method is sufficiently sensitive to changes by the melting process of flat, container and special glasses. The homogeneity factor, which essentially is the standard deviation of the refractive index, can be obtained with a precision of about ±5 %. The measurement simultaneously delivers the mean refractive index with high accuracy. This property possibly could be used to substitute density measurements to control the constancy of glass composition. The Christiansen-Shelyubskii method can be standardized and highly automated. About 15 samples can be measured per day. Thus it shows all features of a method to be used for industrial quality control

Laboratory trials to incorporate sulphur in the vitrification of filter ashes from incineration plants and hydrolytic investigation of the melt products

Incineration of refuse in incineration plants produces toxic dusts in the waste gas filters which have to be disposed of Vitrification is one possibility of immobilization of such dusts which are contaminated by heavy metals, sulphates and Chlorides. Under oxidizing melting conditions, alkaline sulphates a n d Chlorides would volatilize and would have to be precipitated again. Therefore, in this work reducing melts were used. Thus, it was possible to reduce the sulphate to sulphide and to incorporate the latter in the glass matrix to an efficiency of up to 100%. This is experimentally proved by melting batch compositions of a filter ash from a refuse incineration plant with glass forming additives as well as model glasses. The reduction of CaSO₄ and formation of sulphides is induced by means of suitable additions of the Clements carbon, iron, zinc, titanium, manganese, Silicon, and aluminium, separately and in combination. The sulphides CaS, FeS, ZnS, MnS and AI₂S₃ are present in the melt product mainly in giassy form and only for a small part in a crystalline phase. The melts with additions of manganese and Silicon show the best properties with respect tc vitrification, incorporation of the sulphur and hydrolytic resistance of the product. By means of leaching tests using the Soxhlet equipment, products of great hydrolitic resistance are proved falling under the hydrolytic class III at least

Influence of small additions of Li₂O raw materials on glass melting

For a container glass composition up to 1 mol% of the alkali oxide was substituted by Li₂O in steps of ≈0.2 %. The lithia was added as Li₂CO₃ and as spodumene, respectively. As shown earlier Li₂O reduces the viscosity of the melts considerably, irrespective of the Li₂O source. However, melt formation, carbonate decomposidon, silicate and silicate melt formation processes during raw materials reactions are considerably accelerated by Li₂CO₃ addition only, whereas Li₂O in the spodumene silicate does not enhance these reactions. The fining of the melt and the corrosion behavior of refractories are strongly influenced also by the lower viscosity melts. Thus, the corrosion rate may be diminished by temperature reduction at constant viscosity. For technical purposes the glasses are very stable against crystallization, however, thermal analysis shows that the higher the Li₂O content is, the faster the crystal growth proceeds. The surface tension of the glass melts decreases and the water leach resistance of the solid glasses is enhanced with increasing Li₂O content. The Li⁺ ions are less polarizable and, due to their high Dietzel field strength, the glass structure is dghtened compared with that of Li₂O-free glass. In conclusion, the substitution of small amounts of Li₂O instead of Na₂O and/or K₂O shows several advantages. At low temperatures different raw materials reactions are accelerated and at high temperature the decrease in melt viscosity is decisive

Homogenization of glass melts by bubbling on a laboratory scale

In a typical melter, the molten glass tends to be inhomogeneous due to the heterogeneity of the raw materials. One means of yielding more homogeneous glass is bubbling air through the glass melt through nozzles at the base of the melter. The induced fluid flow dissolves cords and homogenizes the glass melt. This bubbling process was investigated on a laboratory scale both from an experimental and a theoretical point of view. A standard soda-lime-silica glass was bubbled with argon in a platinum crucible at 1400 C. The samples treated were tested with regard to their optical homogeneity, using an improved version of the Christiansen-Shelyubskii method. The corresponding fluid flow phenomena were simulated by a suitable mathematical model. Due to the axial symmetry of the bubbling equipment and the high viscosity of the glass melt (creeping flow), the problem can be reduced to the solution of a differential equation of the fourth order with the stream function as independent variable. The numerical treatment superposes Gegenbauer functions matching the given boundary values for the velocity and tension, respectively. The homogeneity strongly increased with bubbling time and its local variation showed good correlation with the calculated flow pattern in the crucible

Influence of different Al2O3-containing batch materials on melting, fining and properties of soda-lime-silica glass

Proceeding from the composition (in wt% ) : 72.5 SiO2, 1.5 AI2O3, 10.5 CaO, 2.5 MgO, 12.5 Na2O, and 0.5 K2O the batch raw materials calcined and hydrated alumina, nepheline syenite, Calumite, and Ecomelt, respectively, were employed in order to introduce aluminum oxide to the glass. Batch calculations assured constant chemical composition, sand/sulfate ratios, sulfate/carbon ratios, redox numbers, and total sulfur contents. The glasses and melts obtained were investigated with respect to different properties, e. g. viscosity, homogeneity, optical transmission, and residual sulfur content. The results display similarities, however, partly also significant differences with respect to the AI2O3 source used. Thus especially the glasses containing the blast furnace slags revealed distinct characteristics compared to glasses with nepheline syenite and hydrated alumina. With increasing melting time the differences are reduced