One focus of research in cosmology regards the growth of structure in the universe: how we end up with stars, galaxies, galaxy clusters, and large scale structure in a universe that appears homogeneous and isotropic on large scales. Using cosmological perturbation theory, we investigate the evolution of density and velocity perturbations corresponding to a universe that is slowly contracting (Ijjas and Steinhardt), testing with and comparing different values for the equation-of-state parameter. This allows for the comparison of the growth of large scale structure in scenarios including a matter-dominated expanding universe, a dark energy-dominated expanding universe, and now, an ekpyrotic scalar field-dominated contracting universe. Further, we consider the timescales on which deviations from ΛCDM in favor of the model considered could become relevant.

Over the last 50 years significant advancements have been made in the southern yellow pine (SYP) forests in the U.S. south. Due to silvicultural changes and large scale reforestation efforts the US south has seen significant increases in standing volume (more than 120% over the period). Landowners that grow SYP plantations largely manage for trees that are harvested to produce dimensional lumber. With the changes in growth patterns it is of interest if there have been any changes in structural properties of the lumber that is produced from timber grown today. Landowners desire confirmation that what they are doing in terms of management is maintaining the quality and strength of lumber that the market demands. This information is critical because timberland owners’ plant and manage trees that will ultimately be brought to market at lumber 25-40 years into the future. In an effort to provide clarity to this topic this dissertation investigates: 1) The extent to which the specific gravity (SG), bending strength (modulus of rupture, MOR), and bending stiffness (modulus of elasticity, MOE) of small clear specimens of SYP have changed, particularly with respect to reduction(s), during the interval from approximately 1965 to 2015. 2) The extent to which the compression parallel to grain and perpendicular to grain strength of small clear specimens of SYP have changed, particularly with respect to reduction(s), during the interval from approximately 1965 to 2015. Use statistical analysis of variance to investigate potential differences among data from a historical 1966 data set, a 2014 in-grade data set, and a 2018 staircase material data set. 3) The nature of the relationship between and among SG, MOE, and MOR of small clear specimens of SYP and how these relationships may have changed, during the interval from approximately 1965 to 2015. Use statistical regression analysis to explore changes to the interrelationships of SG, MOE, and MOR among the three samples, with particular interest toward how these may impact or influence non-destructive evaluation. This work consists of 3 independent chapters using varying appropriate statistical methods and is accompanied by an introduction and conclusion.

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Stellar structure is investigated within the framework of scalar-tensor gravity. Novel perturbative analytical results are obtained for constant-density stars and for Newtonian polytropes in the quadratic model with coupling function A(Φ) = exp(αΦ+1/2βΦ^2). They are compared to full numerical calculations, and possible applications to main-sequence stars, white dwarfs, and the Chandrasekhar mass are indicated. It is found that Buchdahl's theorem is violated in Brans-Dicke theory for stars with exponentially-decaying density profiles. However, the mass-to-radius ratio M/R tends to the constant-density value in a certain limit. It is observed that for β < 0, there exists a maximum value of η = P0/ρo for constant-density stars, where P0 and ρ0 are the central pressure and density, respectively. It is conjectured that if such a maximum value also exists for other equations of state, and is less than the constant-density maximum value, then knowledge of P/ρ in the centre of a star can be used to constrain β. / Thesis / Master of Science (MSc)