Nonstandard cosmological models of two broad classes are examined: those in which there are more than four spacetime dimensions, and those in which there is a variable cosmological “constant” Λ. We test claims that a number of higher-dimensional models give rise to inflation. New constraints are placed on such models, and a number of them are ruled out. We then investigate the potential of variable-Λ theories to address the problem of the initial singularity. We consider a number of different phenomenological representations for this parameter, assessing their implications for the evolution of the cosmological scale factor as well as a range of observational data. In several cases we find nonsingular models which are compatible with observation. / Graduate

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 79-81). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 94-96).

by Lai Chi Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves [104]-107). / Text in English; abstract also in Chinese. / by Lai Chi Wai. / Abstract --- p.i / Acknowledgment --- p.iv / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction to Numerical Relativity --- p.1 / Chapter 1.1 --- The need for numerical approach --- p.2 / Chapter 1.2 --- A brief history of numerical relativity --- p.3 / Chapter 1.3 --- What this thesis concern --- p.4 / Chapter 2 --- Mathematical Formulation --- p.6 / Chapter 2.1 --- The initial value problem --- p.6 / Chapter 2.2 --- The space-plus-time (3+1) formalism --- p.8 / Chapter 3 --- Methods in Numerical Relativity --- p.17 / Chapter 3.1 --- General numerical methods --- p.17 / Chapter 3.2 --- Consistency and stability --- p.18 / Chapter 3.3 --- Difficulties and limitations --- p.20 / Chapter 3.4 --- Strategies specific to numerical relativity --- p.21 / Chapter 3.5 --- Boundary conditions --- p.27 / Chapter 4 --- Detweiler's Scheme --- p.29 / Chapter 4.1 --- Constrainted evolution in numerical relativity --- p.29 / Chapter 4.2 --- Detweiler's Scheme --- p.31 / Chapter 5 --- Constraint Enforcement in Plane Waves --- p.36 / Chapter 5.1 --- General solution for a linearized plane wave --- p.36 / Chapter 5.2 --- Code test --- p.40 / Chapter 5.3 --- Comparison of results with and without Detweiler's scheme --- p.41 / Chapter 5.4 --- Stability of evolution --- p.46 / Chapter 5.5 --- Comparison of Detweiler's scheme and simple diffusion method --- p.50 / Chapter 5.6 --- Two parameter extension of Detweiler's scheme --- p.55 / Chapter 5.7 --- Long time behavior --- p.59 / Chapter 5.8 --- Comparison of Hamiltonian and momentum constraint --- p.63 / Chapter 5.9 --- Indicator of Detweiler's scheme --- p.67 / Chapter 5.10 --- The maximal slicing condition --- p.70 / Chapter 5.11 --- The leaking problem --- p.73 / Chapter 5.12 --- The near-linear plane waves --- p.75 / Chapter 6 --- Constraint Enforcement in MTW Waves --- p.83 / Chapter 6.1 --- MTW waves --- p.83 / Chapter 6.2 --- Linear regime --- p.85 / Chapter 6.3 --- Comparison of results with and without Detweiler's scheme --- p.85 / Chapter 6.4 --- The indicator --- p.90 / Chapter 6.5 --- A comparison of simple diffusion method and Detweiler's scheme with a large amplitude wave --- p.92 / Chapter 7 --- Summary and Conclusion --- p.97 / Chapter A --- The Numerical Scheme of the Code --- p.98 / Chapter B --- Convergence Test --- p.100 / Chapter B.1 --- Plane wave --- p.100 / Chapter B.2 --- MTW wave --- p.102 / Bibliography --- p.104

No description available.

Thesis (Ph. D.)--School of Aerospace Engineering, Georgia Institute of Technology, 2004. Directed by Dewey H. Hodges. / Vita. Includes bibliographical references (leaves 162-176).

Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2007. / Bauchau, Olivier, Committee Member ; Hodges, Dewey, Committee Chair ; Singhose, William, Committee Member ; Costello, Mark, Committee Member ; Flannery, Raymond, Committee Member.

In this thesis constraint solving/satisfaction is presented as a model of computation. Advantages of using constraints as a paradigm of programming are presented. A semantic schema for constraint based computations is given, following a brief survey of the more important systems based on constraints. These systems range from particular algorithms to problem solvers to constraint based general purpose programming languages. Finally, constraint satisfaction is applied to logic programming and theorem proving. It is shown that incorporating constraint solving in definite clause programs enhances their expressive power. Also, an alternative semantics - based on constraint satisfaction - is given for theorem proving. / Master of Science

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 90-94).

A nonlinear mixed finite element formulation based on the Hellinger-Reissner variational principle is developed for planar contact stress analysis. The formulation is based on the updated Lagrangian approach and accounts for geometric nonlinearity. In the mixed model, both displacements and stresses are approximated independently and this approach has in general been found to be more accurate than the displacement finite element model, especially for contact problems since it avoids the extrapolation of stresses computed at the Gauss points to the boundary nodes. An algorithm based on the penalty technique for equality constraints has been developed to handle the interface boundary conditions arising in a contact problem. The algorithm automatically tracks potential contact nodes, detects overlap during any load step and iteratively restores geometric compatibility at the contact surface. The classical Hertz contact problem is solved to validate the algorithm. The mixed formulation algorithm in cylindrical coordinates is applied in conjunction with the penalty based algorithm to solve the contact problem in layered cylindrical bodies. Static condensation techniques are used to condense out the discontinuous components of stresses at the element level. The contact stress distribution and variation of contact area with load is computed for different loading situations. Furthermore, the effect of the difference in the relative magnitudes of the moduli of the layers on the stability of the contact algorithm is investigated. / Master of Science