Covariant change of signature in classical relativity

This paper gives a covariant formalism enabling investigation of the possibility of change of signature in classical General Relativity, when the geometry is that of a Robertson-Walker universe. It is shown that such changes are compatible with the Einstein field equations, both in the case of a barotropic fluid and of a scalar field. A criterion is given for when such a change of signature should take place in the scalar field case. Some examples show the kind of resulting exact solutions of the field equations.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Two-dimensional on-line particle imaging velocimetry

A high-performance algorithm is described for the on-line computation of two-dimensional velocity maps using particle displacement imaging. It relies on the computation of direct correlations in a multiple-scale spatial hierarchy. Layered rejection criteria based on correlation quality and conditional averaging techniques are employed to achieve the robustness required for continuous, unsupervised operation. Implementations are described using a UNIX-based workstation and a DOS-based personal computer with a real-time image processing/correlator subsystem. The cooperation of the algorithm with other real-time visualization techniques is demonstrated using the example of colour-coded streak integration.The authors wish to thank Dr. Philippe Georis of the Université Libre de Bruxelles (ULB) for making available to us video sequences of his Marangoni convection experiment.     

Geochemical and physical analysis of the bedrock formations and lowest tills at the Wellsch Valley Site,Saskatchewan, Canada

Nine bedrock and two till samples were analyzed to determine whether their chemical and physical properties could be used to distinguish between bedrock units and to differentiate local bedrock from overlying tills. The bedrock samples came from The North Cliff subsite of the Wellsch Valley Site, and the till samples from Jaw Face subsite. Eight of the nine bedrock samples show great similarity. However, their geochemical differences from the overlying Quaternary tills establish that the tills contain much material entrained, during one or more early Quaternary glaciations, from older bedrock outcrops to the north and northeast. The glaciers that laid down the tills appear to have reworked and concentrated elements compatible with a dry climate, probably formed by weathering during long interglacial, and perhaps preglacial, intervals when the surface was undergoing slow degradation.     

The automatic conversion of spinor equations to dyad form in MAPLE

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

Microcomputers and the Preparation of Secondary Science Teachers: An Eight Year Follow-Up

Science teacher educators from 205 colleges/universities completed a questionnaire concerning the nature and extent of microcomputer offerings in their secondary science teacher preparation programs. These data are reported and compared to a similar sample surveyed in 1984. Seventy-seven percent of reporting institutions now require either a microcomputer course or completion of a microcomputer competency within their secondary science certification program. The most common applications in these courses are simulations, word processing, databases, and spreadsheet use. Chi-square analysis revealed that more institutions in 1992 were requiring a microcomputer course than in 1984. However, only 23.4% of the institutions offered a microcomputer course designed solely for secondary science majors, and 10.6% of the institutions offered such a course taught by a science teacher educator. Preservice science teachers were also more likely in 1992 than in 1984 to be using microcomputers in instruction during supervised field experiences in secondary schools. Finally, college/university science teacher educators perceived that microcomputer use in secondary science classrooms has increased during the past five years.