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Regge Calculus as a Numerical Approach to General RelativityKhavari, Parandis 17 January 2012 (has links)
A (3+1)-evolutionary method in the framework of Regge Calculus, known as "Parallelisable Implicit Evolutionary Scheme", is analysed and revised so that it accounts for causality. Furthermore, the ambiguities associated with the notion of time in this evolutionary scheme are addressed and a solution to resolving such ambiguities is presented. The revised algorithm is then numerically tested and shown to produce the desirable results and indeed to resolve a problem previously faced upon implementing this scheme.
An important issue that has been overlooked in "Parallelisable Implicit Evolutionary Scheme" was the restrictions on the choice of edge lengths used to build the space-time lattice as it evolves in time. It is essential to know what inequalities must hold between the edges of a 4-dimensional simplex, used to construct a space-time, so that the geometry inside the simplex is Minkowskian.
The only known inequality on the Minkowski plane is the "Reverse Triangle Inequality" which holds between the edges of a triangle constructed only from space-like edges. However, a triangle, on the Minkowski plane, can be built from a combination of time-like, space-like or null edges. Part of this thesis is concerned with deriving a number of inequalities that must hold between the edges of mixed triangles.
Finally, the Raychaudhuri equation is considered from the point of view of Regge Calculus. The Raychaudhuri equation plays an important role in many areas of relativistic Physics and Astrophysics, most importantly in the proof of singularity theorems. An analogue to the Raychaudhuri equation in the framework of Regge Calculus is derived. Both (2+1)-dimensional and (3+1)-dimensional cases are considered and analogues for average expansion and shear scalar are found.
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The Emergence of Cosserat-type Structures in Metal PlasticityLauteri, Gianluca 29 May 2017 (has links) (PDF)
We study an energy functional able to describe low energy configurations of a two dimensional lattice with dislocations in a nonlinear elasticity regime. The main result can be described as follows: configurations of energy comparable to the lattice spacing consist of piecewise constant microrotations with small angle grain boundaries between them. Moreover, we also give bounds to the energy of particular configurations describing a small angle symmetric tilt grain boundary.
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On the Stielitjes IntegralKeagy, Thomas A. 08 1900 (has links)
This paper is a study of the Stieltjes integral, a generalization of the Riemann integral normally studied in introductory calculus courses. The purpose of the paper is to investigate many of the basic manipulative properties of the integral.
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The relationship between grades in calculus and certain factors for college freshmanNewton, Andrea January 1966 (has links)
Thesis (Ed.M.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / 2031-01-01
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A Maple Package for the Variational CalculusHillyard, Cinnamon 01 May 1992 (has links)
The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete listing of the Maple code for HELMHOLTZ is found in an appendix.
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Partikulare Integrale des Problems der n KörperBrehm, Erich, January 1908 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1908. / Cover title. Vita.
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Analytical differentiation by a digital computerKahrimanian, Harry G. January 1953 (has links)
Thesis (M.A.)--Temple University. / Bibliography: leaf [49].
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Homogenization of an elastic-plastic problemOnofrei, Daniel T. January 2003 (has links)
Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: homogenization; calculus of variations. Includes bibliographical references (p. 21).
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On Cartan form and equivalence of variational problems黃志榮, Wong, Chi-wing. January 1997 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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ON THE NUMBER OF CRITICAL CONFIGURATIONS OF CHARGES ON AN M-TORUSBronder, Joseph Bertram, 1934- January 1965 (has links)
No description available.
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