Abstract:
The Biot linearized theory for fluid saturated porous materials is used to study the plane strain deformation of an isotropic, homogeneous, poroelastPic half space in welded contact with a homogeneous, transversely isotropic, elastic half space caused by an inclined line-load in elastic half space. The integral expressions for the displacements and stresses in the two half spaces in welded contact are obtained from the corresponding expressions for an unbounded transversely isotropic elastic and poroelastic medium by applying boundary conditions at the interface. The integrals for the inclined line-load are solved analytically for the limiting casei.e. undrained conditions in high frequency limit. The undrained displacements, stresses and pore pressure are shown graphically. Expression for the pore pressure is also calculated for undrained conditions in the high frequency limit.

Abstract:
The general solution to the field equations in micropolar generalized thermodiffusive in the context of G-L theory is investigated by applying the Laplace and Fourier transform's as a result of various sources. An application of distributed normal forces or thermal sources or potential sources has been taken to show the utility of the problem. To get the solution in the physical form, a numerical inversion technique has been applied. The transformed components of stress, temperature distribution and chemical potential for G-L theory and CT theory has been depicted graphically and results are compared analytically to show the impact of diffusion, relaxation times and micropolarity on these quantities. Some special case of interest are also deduced from present investigation.

Abstract:
Apoyado en un marco analítico derivado tanto de la teoría institucional como de la teoría de la planeación urbana, este estudio examina los resultados de dos programas creados para restablecer el orden y la estabilidad después de una situación de crisis urbana. Estos son: el Programa de Renovación Habitacional Popular en la Ciudad de México, establecido luego del terremoto de 1985, y el Programa Ghost Town establecido en la ciudad de Los Angeles, California, después del terremoto de 1994. Ambos han sido encomiados por su accionar rápido, su financiamiento masivo, el mejoramiento de las condiciones preexistentes, la participación comunitaria, y la coordinación institucional. El argumento principal de este estudio es que las intituciones de planeación urbana en ambas ciudades fueron efectivas durante la crisis provocada por los sismos, principalmente porque se apoyaron en rutinas institucionales: un tipo de procedimiento que suele ser denostado o subestimado porque tiene la reputación de ser extremadamente burocrático. Las instituciones de planeación en la Ciudad de México y Los Angeles respondieron con efectividad porque fueron capaces de adaptar rutinas institucionales, en forma rápida y eficiente, a circunstancias imprevistas y dramáticas. Planteado como un estudio de caso, este análisis se propone clarificar y explicar la dinámica de la planeación urbana en un contexto de crisis de dos maneras: Primero, los estudios de caso demuestran que un análisis institucional explícito y sistemático ayuda a entender mejor qué elementos dan buenos resultados en materia de planeación urbana, y por qué. Segundo, el análisis institucional muestra bajo qué condiciones pueden servir las rutinas institucionales como herramientas poderosas y efectivas para resolver situaciones imprevistas sin importar el contexto sociopolítico dominante.

Abstract:
A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's Macroscopic Gravity and show that, after making some essential gauge choices, the Cosmological equations receive \emph{spacetime scalar} corrections which are therefore observable in principle, and further, that the broad structure of these corrections is \emph{identical} to those derived by Buchert.

Abstract:
This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working on the large scales appropriate for cosmology. It has been claimed in the literature that these terms may account for the phenomenon of dark energy which causes the late time universe to accelerate. We investigate the nature of these terms by using averaging schemes available in the literature and further developed to be applicable to the problem at hand. We show that the effect of these terms when calculated carefully, remains negligible and cannot explain the late time acceleration.

Abstract:
There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (``backreaction'') in cosmology. In particular, some simple models of structure formation studied in the literature seem to indicate that the backreaction can play a significant role at late times, and it has also been suggested that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we use Zalaletdinov's covariant averaging scheme (macroscopic gravity or MG) to show that as long as the metric of the Universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, we show that as long as matter velocities remain small (which is true in our model), the perturbed FLRW form of the metric can be explicitly recovered. Together, these results imply that the backreaction remains small even during nonlinear structure formation, and we confirm this within the toy model with a numerical calculation.

Abstract:
The problem of corrections to Einstein's equations arising from averaging of inhomogeneities ("backreaction") in the cosmological context, has gained considerable attention recently. We present results of analysing cosmological perturbation theory in the framework of Zalaletdinov's fully covariant Macroscopic Gravity. We show that this framework can be adapted to the setting of cosmological perturbations in a manner which is free from gauge related ambiguities. We derive expressions for the backreaction which can be readily applied in \emph{any} situation (not necessarily restricted to the linear perturbations considered here) where the \emph{metric} can be brought to the perturbed FLRW form. In particular these expressions can be employed in toy models studying nonlinear structure formation, and possibly also in N-body simulations. Additionally, we present results of example calculations which show that the backreaction remains negligible well into the matter dominated era.

Abstract:
We investigate potential systematic effects in constraining the amplitude of primordial fluctuations \sigma_8 arising from the choice of halo mass function in the likelihood analysis of current and upcoming galaxy cluster surveys. We study the widely used N-body simulation fit of Tinker et al. (T08) and, as an alternative, the recently proposed analytical model of Excursion Set Peaks (ESP). We first assess the relative bias between these prescriptions when constraining \sigma_8 by sampling the ESP mass function to generate mock catalogs and using the T08 fit to analyse them, for various choices of survey selection threshold, mass definition and statistical priors. To assess the level of absolute bias in each prescription, we then repeat the analysis on dark matter halo catalogs in N-body simulations designed to mimic the mass distribution in the current data release of Planck SZ clusters. This N-body analysis shows that using the T08 fit without accounting for the scatter introduced when converting between mass definitions (alternatively, the scatter induced by errors on the parameters of the fit) can systematically over-estimate the value of \sigma_8 by as much as 2\sigma\ for current data, while analyses that account for this scatter should be close to unbiased in \sigma_8. With an increased number of objects as expected in upcoming data releases, regardless of accounting for scatter, the T08 fit could over-estimate the value of \sigma_8 by ~1.5\sigma. The ESP mass function leads to systematically more biased but comparable results. A strength of the ESP model is its natural prediction of a weak non-universality in the mass function which closely tracks the one measured in simulations and described by the T08 fit. We suggest that it might now be prudent to build new unbiased ESP-based fitting functions for use with the larger datasets of the near future.

Abstract:
The effect of radiation on flow and heat transfer over a vertically oscillating porous flat plate embedded
in porous medium with oscillating surface temperature is investigated. The analytic solutions
of momentum and energy equations are obtained. The velocity and temperature profiles are
computed. The frictional force at the plate due to viscosity of fluid is estimated in terms of non dimensional
skin friction coefficient and heat convection at the plate is estimated in the form of
Nusselt number. The effects of physical parameters Prandtl number Pr, Grashof number Gr, Suction
parameter S and radiative parameter R on velocity and temperature profiles are analyzed
through graphs. The effects of oscillation on the velocity and temperature profiles are shown
through 3-D surface plot.