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Thesis (M.S.)--Boston Universit

Effective action approach to cosmological perturbations in dark energy and modified gravity

In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, {\delta}G_{\mu\nu} = 8{\pi}G{\delta}T_{\mu\nu} + {\delta}U_{\mu\nu} for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of {\delta}U_{\mu\nu} for two explicit generic examples: (i) the dark sector does not contain extra fields, L = L(g_{\mu\nu}) and (ii) the dark sector contains a scalar field and its first derivative L = L(g_{\mu\nu}, {\phi}, \nabla_{\mu}{\phi}). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.Comment: Version accepted by JCAP. Typos corrected. Covariant decoupling conditions adde

Documents of the JPL Photovoltaics Program Analysis and Integration Center: An annotated bibliography

A bibliography of internal and external documents produced by the Jet Propulsion Laboratory, based on the work performed by the Photovoltaics Program Analysis and Integration Center, is presented with annotations. As shown in the Table of Contents, the bibliography is divided into three subject areas: (1) Assessments, (2) Methdological Studies, and (3) Supporting Studies. Annotated abstracts are presented for 20 papers

The 5C 6 and 5C 7 surveys of radio sources

5C 6 and 5C 7 continue the series of deep surveys made at 408 and 1407 MHz with the One-Mile telescope at Cambridge. They were intended (1) to provide a sample of faint radio sources suitable for further study; (2) to improve the statistics of source counts N(S) and spectral-index distributions at low flux densities; (3) to study the isotropy of the distribution of faint sources. Each observed field is about 4° in diameter at 408 MHz and 1° in diameter at 1407 MHz, and the field-centres are a α = 02ʰ14ᵐ, δ = 32° (5C 6) and α = 08ᵏ17ᵐ, δ = 27° (5C 7). The synthesized beamwidths (FWHM) are 80 arcsec (408 MHz) and 23 arcsec (1407 MHz). The techniques of observation and data-analysis followed closely those used for 5C 5 (Pearson, T. J., 1975. Mon. Not. R. astr. Soc., 171, 475), with some minor variations which are noted in Section 2

A New Approximation of the Schur Complement in Preconditioners for PDE Constrained Optimization

Saddle point systems arise widely in optimization problems with constraints. The utility of Schur complement approximation is now broadly appreciated in the context of solving such saddle point systems by iteration. In this short manuscript, we present a new Schur complement approximation for PDE constrained optimization, an important class of these problems. Block diagonal and block triangular preconditioners have previously been designed to be used to solve such problems along with MINRES and non-standard Conjugate Gradients respectively; with appropriate approximation blocks these can be optimal in the sense that the time required for solution scales linearly with the problem size, however small the mesh size we use. In this paper, we extend this work to designing such preconditioners for which this optimality property holds independently of both the mesh size and of the Tikhonov regularization parameter \beta that is used. This also leads to an effective symmetric indefinite preconditioner that exhibits mesh and \beta-independence. We motivate the choice of these preconditioners based on observations about approximating the Schur complement obtained from the matrix system, derive eigenvalue bounds which verify the effectiveness of the approximation, and present numerical results which show that these new preconditioners work well in practice