Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

Calibration and use of the Epprecht Rheomat

Summary This paper deals with the calibration and use of an Epprecht Rheomat with particular reference to non Newtonian liquids. A method of calculating accurate rates of shear for non-Newtonian flow is derived using theEuler-Maclaurin sum formula. Some examples are given of the calculation of shear of poly vinyl chlorideplasticiser suspensions.

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Zusammenfassung Die vorliegende Abhandlung befaßt sich mit der Eichung und dem Gebrauch eines Epprecht-Rheomats mit besonderer Hinsicht auf nicht-Newtonische Flüssigkeiten.Ein Verfahren zur exakten Berechnung von Scherwerten für nicht-Newtonische Flüssigkeiten läßt sich aus derEuler-Maclaurinschen Summenformel ableiten.Einige Beispiele zur Berechnung von Scherwerten für Weichmacher von Polyvinylchlorid sind beigefügt.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

Covalent ladder formation becomes kinetically trapped beyond four rungs

Scrambling experiments suggest that the self-assembly of 2D ladders via imine metathesis is kinetically trapped at four or more rungs. Consequently, ladders containing five or more rungs cannot be synthesized in high yield under the conditions used, as misaligned out-of-register byproducts cannot self-correct.     

The Simulation of Some Simple Control Policies for a Signalized Intersection

The authors present the results of some simulation studies concerned with the computer control of signalized intersections. The simplest model considered is that of two competing random streams. The transient response and delay/flow characteristics of some simple control procedures are investigated. These are based on the Dunne-Potts policy in which the traffic light is switched when the queue of the road with right of way has been dispersed.The model is then developed to consider four competing streams and the control policies are modified accordingly. Similar results to the two-stream case are presented. In the final section turning vehicles are considered by including eight competing streams in the intersection model.     

High-K quasiparticle structures in 159Er and 160Er

A series of new strongly coupled high-K, multi-quasiparticle structures have been observed in the light erbium transitional nuclei, ¹⁵⁹Er and ¹⁶⁰Er. The interpretation of these bands is discussed within the framework of the cranked shell model. These sequences, when taken together with the existing quasiparticle excitations, form a near complete set of low-lying, multi-quasiparticle structures on which a coherent series of aligned angular momentum, band crossing and blocking arguments can be based. The measured B(M1)/B(E2) ratios are compared with geometrical calculations to test the proposed configuration assignments. Received: 19 November 1997     

A Case Study on the Development of the Home Defence Training Game HOT SEAT

Home defence is concerned with enhancing the prospects for survival and recovery of this country in the eventuality of nuclear war. Contingency plans exist for the creation of a system of wartime regional government which includes elements from peacetime local and central governments. Senior officers in local government with designated wartime roles receive training at the Home Defence College. The Home Office decided that a crisis management game should form part of their overall programme of indoctrination. The resulting game, which is known as HOT SEAT, has been successfully implemented and is now in regular use at the College. This paper describes how the need for the game arose, the structure of the resulting game, the problems that arose during its development, and should be of interest to those concerned with the development of management and crisis games.     

Beziehung zwischen den freien Sulfhydrylgruppen und ehromatographischer Heterogenität und Polymerisation des Rinderserumalbumins

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