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Creator:: Hellaby, Charles and Dray, Tevian
Abstract:: We contrast the two approaches to ‘‘classical’’ signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward’s distributional approach is based on a postulated modified form of the field equations. We make an...
Resource Type:: Article
Full Text:: approaches to classical signature change Charles Hellaby* Department of Applied Mathematics, University of

Creator:: Hellaby, Charles and Dray, Tevian
Abstract:: The divergence theorem as usually stated cannot be applied across a change of signature unless it is reexpressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be ‘‘modified,’’ and therefore insistence on conservation of matter across such a surface cannot...
Resource Type:: Article
Full Text:: conservation laws at a classical change of signature Charles Hellaby' Department of App/ied Mathematics

Creator:: Dray, Tevian and Hellaby, Charles
Abstract:: The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
Resource Type:: Article
Full Text:: Mathematics, Oregon State University, Corvallis, Oregon 97331 Charles Hellabyb) Department of Applied

Creator:: Schray, Jörg, Dray, Tevian, Manogue, Corinne A., Tucker, Robin W., and Wang, Charles
Abstract:: We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex...
Resource Type:: Article
Full Text:: degenerate metrics J6rg Schray,a) Tevian Dray,b) Corinne A. Manogue,c) Robin W. Tucker,d) and Charles Wang,e

Creator:: Dray, Tevian
Abstract:: We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no...
Resource Type:: Article
Full Text:: -compatible connection 1-formsv6 a b onM 6 satisfy dgab5v m agmb1v m bgma , ~7! and have torsion

Creator:: Dray, Tevian, Manogue, Corinne A., and Tucker, Robin W.
Abstract:: We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
Resource Type:: Article
Full Text:: manifold M with a non-degenerate metric may be written (15) +d4 = e sgn(h) —8 4 /~hundt . (24)~ ( B@dx

Creator:: Kustusch, Mary Bridget, Roundy, David, Dray, Tevian, and Manogue, Corinne A.
Abstract:: Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task...
Resource Type:: Article
Full Text:: . B., Roundy, D., Dray, T., & Manogue, C. A. (2014). Partial derivative games in thermodynamics: A

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