A theoretical model for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe

A theoretical model has been developed for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Special attention was paid to understanding how the buoyancy force on the core, resulting from any density difference between the oil and water, is counterbalanced. This problem was simplified by assuming the oil viscosity to be so high that any flow inside the core may be neglected and hence that there is no variation of the profile of the oil-water interface with time. In the model the core is assumed to be solid and the interface to be a solid/liquid interface.By means of the hydrodynamic lubrication theory it has been shown that the ripples on the interface moving with respect to the pipe wall can generate pressure variations in the annular layer. These result in a force acting perpendicularly on the core, which can counterbalance the buoyancy effect.To check the validity of the model, oil-water core-annular flow experiments have been carried out in a 5.08 cm and an 20.32-cm pipeline. Pressure drops measured have been compared with those calculated with the aid of the model. The agreement is satisfactory.     

Vibronic and spin-orbit splitting in spectra of systems exhibiting Jahn-Teller-Effect

Simple two- and three-dimensional models have been used to investigate the vibronic states of molecules exhibiting Jahn-Teller-Effect. According to the topology of the adiabatic potential surface, two cases have to be distinguished, which may (A) or may not (B) be treated in the Born-Oppenheimer approximation. In the latter case B strong Jahn-Teller coupling leads to a splitting of an A E absorption line into three peaks instead of the usual two ones. This additional splitting originates from transitions into the first and second metastable level of the upper potential well. However, the vibronic splitting will often be smeared out by coupling of the Jahn-Teller effect to a distortion of a Jahn-Teller inactive vibration. The effective spin-orbit splitting of an absorption band with unresolved vibrational structure is larger than in the case of vanishing Jahn-Teller coupling, contrary to the spin-orbit splitting of single vibronic levels. An experimental example of this effect is discussed. In Jahn-Teller case B it may be interpreted as a superposition of the vibronic and the spin-orbit splitting effects.

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Zusammenfassung Mittels einfacher zwei- und dreidimensionaler Modelle wurden die vibronischen Zustände von Molekülen untersucht, die einen Jahn-Teller-Effekt zeigen. Entsprechend der Topologie der adiabatischen Potentialfläche sind zwei Fälle A und B zu unterscheiden, die im Rahmen der Born-Oppenheimer-Näherung behandelt werden können bzw. wo dies nicht möglich ist. Im letzteren Falle B führt eine sehr starke Jahn-Teller-Kopplung zur Aufspaltung einer AE Absorptionslinie in drei statt wie üblich in zwei Peaks. Diese zusätzliche Aufspaltung rührt her von Übergängen in die ersten beiden metastabilen Resonanzzustände der oberen Potentialmulde. In vielen Fällen wird mit einer Jahn-Teller-Kopplung der asymmetrischen Schwingung eine Verschiebung der Gleichgewichtslage einer Jahn-Teller inaktiven Schwingung einherlaufen: Die vibronischen Aufspaltungen sollten daher durch Schwingungsverbreiterung teilweise verschmiert sein. Während die Spin-Bahn-Aufspaltung einzelner vibronischer Niveaus durch Jahn-Teller-Kopplung verringert wird, wird die effektive Spin-Bahn-Aufspaltung einer Absorptionslinie mit nichtaufgelöster Schwingungsstruktur vergrößert. Ein experimentelles Beispiel für diesen Effekt wird diskutiert. Im Jahn-Teller-Fall B kann er als Überlagerung der vibronischen und der Spin-Bahn-Aufspaltung interpretiert werden.

     

Nuclear magnetic resonance-compatible furnace for high temperature MR imaging and spectroscopy in situ

A high temperature magnetic resonance compatible furnace for real time in situ monitoring of materials, processes, and chemical reactions with magnetic resonance imaging and spectroscopy is described. Design issues are analyzed. Example applications are demonstrated with a time sequence of proton images of the binder burnout in a porous green ceramic cylinder containing polyethylene glycol binder at 200 degrees C, and 7Li images of the molten salt LiCl at 700 degrees C.     

Selecting distances in arrangements of hyperplanes spanned by points

In this paper we consider a problem of distance selection in the arrangement of hyperplanes induced by n given points. Given a set of n points in d-dimensional space and a number k, , determine the hyperplane that is spanned by d points and at distance ranked by k from the origin. For the planar case we present an O(nlog²n) runtime algorithm using parametric search partly different from the usual approach [N. Megiddo, J. ACM 30 (1983) 852]. We establish a connection between this problem in 3-d and the well-known 3SUM problem using an auxiliary problem of counting the number of vertices in the arrangement of n planes that lie between two sheets of a hyperboloid. We show that the 3-d problem is almost 3SUM-hard and solve it by an O(n²log²n) runtime algorithm. We generalize these results to the d-dimensional (d4) space and consider also a problem of enumerating distances.