Exact Evolution of Discrete Relativistic Cosmological Models

22 pages, 16 figures22 pages, 16 figuresWe study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions

Effects of boundary conditions on the dynamics of the solar convection zone

Recent analyses of the helioseismic data have produced evidence for a variety of interesting dynamical behaviour associated with torsional oscillations. What is not so far clear is whether these oscillations extend all the way to the bottom of the convection zone and, if so, whether the oscillatory behaviour at the top and the bottom of the convection zone is different. Attempts have been made to understand such modes of behaviour within the framework of nonlinear dynamo models which include the nonlinear action of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. One aspect of these models that remains uncertain is the nature of the boundary conditions on the magnetic field. Here by employing a range of physically plausible boundary conditions, we show that for near-critical and moderately supercritical dynamo regimes, the oscillations extend all the way down to the bottom of the convection zone. Thus, such penetration is an extremely robust feature of the models considered. We also find parameter ranges for which the supercritical models show spatiotemporal fragmentation for a range of choices of boundary conditions. Given their observational importance, we also make a comparative study of the amplitude of torsional oscillations as a function of the boundary conditions

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and

Optical response of supported gold nanodisks

It is shown that the ellipsometric spectra of short range ordered planar arrays of gold nanodisks supported on glass substrates can be described by modeling the nanostructured arrays as uniaxial homogeneous layers with dielectric functions of the Lorentz type. However, appreciable deviations from experimental data are observed in calculated spectra of irradiance measurements. A qualitative and quantitative description of all measured spectra is obtained with a uniaxial effective medium dielectric function in which the nanodisks are modeled as oblate spheroids. Dynamic depolarization factors in the long-wavelength approximation and interaction with the substrate are considered. Similar results are obtained calculating the optical spectra using the island-film theory. Nevertheless, a small in-plane anisotropy and quadrupolar coupling effects reveal a very complex optical response of the nanostructured arrays