312,640 research outputs found
Invariance of the distributional curvature of the cone under smooth diffeomorphisms
No full textAn explicit calculation is carried out to show that the distributional curvature of a 2-cone, calculated by Clarke et al (Clarke C J S, Vickers J A and Wilson J P 1996 Class. Quantum Grav. 13 2485-98), using Colombeau's new generalized functions is invariant under nonlinear Coo coordinate transformations
On the Geroch-Traschen class of metrics
No full textWe compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
Integration using invariant operators: conformally flat radiation metrics
No full textA new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalization of those of Geroch, Held and Penrose) which are invariant under null rotations and rescalings. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of this class of metrics
A nonlinear theory of distributional geometry
No full textThis paper builds on the theory of nonlinear generalized functions begun in Nigsch & Vickers (Nigsch, Vickers 2021 Proc. R. Soc. A 20200640(doi:10.1098/rspa.2020.0640)) and extends this to a diffeomorphism-invariant nonlinear theory of generalized tensor fields with the sheaf property. Thegeneralized Lie derivative is introduced and shown to commute with the embedding of distributional tensor fields and the generalized covariant derivative commutes with the embedding at the level of association. The concept of a generalized metric is introduced and used to develop a non-smooththeory of differential geometry. It is shown that the embedding of a continuous metric results in a generalized metric with well-defined connection andcurvature and that for C2 metrics the embedding preserves the curvature at the level of association. Finally, we consider an example of a conical metric outside the Geroch–Traschen class and show that the curvature is associated to a delta function
A Work Approach to Determine Vickers Indentation Fracture Toughness
No full textAccording to the comparison of Vickers microindentation tests and Vickers macroindentation tests on several brittle materials, it is found that the ratio of hardness (H) to elastic modulus (E) is sensitive to well-developed radial cracks, but the ratio of unloading work (W(u)) to total loading work (W(t)) is not. Based on this finding together with the approximate linear relationship between the ratio of H to reduced modulus (E(r)) and W(u)/W(t), a new approach taking W(u)/W(t) instead of H/E as the input parameter to determine Vickers indentation fracture toughness is proposed. For this proposed approach, all input parameters can be obtained in one single instrumented indentation test for fracture toughness, thus the test procedure can be simplified significantly. The formula of the newly proposed approach is calibrated by the macroindentation tests on several brittle materials. The validity of the new approach is investigated by comparing its estimation with the old one's
Sheaves of nonlinear generalized functions and manifold-valued distributions
No full textThis paper is part of an ongoing program to develop a theory of generalized differential geometry. We consider the space G[X,Y] of Colombeau generalized functions defined on a manifold X and taking values in a manifold Y. This space is essential in order to study concepts such as flows of generalized vector fields or geodesics of generalized metrics. We introduce an embedding of the space of continuous mappings C(X,Y) into G[X,Y] and study the sheaf properties of
G[X,Y]. Similar results are obtained for spaces of generalized vector bundle homomorphisms. Based on these constructions we propose the definition of a space D'[X,Y] of distributions on X taking values in Y. D'[X,Y] is realized as a quotient of a certain subspace of G[X,Y
A global theory of algebras of generalized functions II: tensor distributions
No full textWe extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical embedding of distributional tensor fields also commutes with the Lie derivative. This construction provides the basis for applications of algebras of generalized functions in nonlinear distributional geometry and, in particular, to the study of spacetimes of low differentiability in general relativity
Vickers, E H, 403153
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/423060Surname: VICKERS. Given Name(s) or Initials: E H. Military Service Number or Last Known Location: 403153. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 40655.249575
Item: [2016.0049.55321] "Vickers, E H, 403153
Vickers-Bush, Oswald E, VX61090
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/423064Surname: VICKERS-BUSH. Given Name(s) or Initials: OSWALD E. Military Service Number or Last Known Location: VX61090. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 19936.249579
Item: [2016.0049.55325] "Vickers-Bush, Oswald E, VX61090
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