795 research outputs found
A simplified structure for the second order cosmological perturbation equations
Increasingly accurate observations of the cosmic microwave background and the
large scale distribution of galaxies necessitate the study of nonlinear
perturbations of Friedmann-Lemaitre cosmologies, whose equations are
notoriously complicated. In this paper we present a new derivation of the
governing equations for second order perturbations within the framework of the
metric-based approach that is minimal, as regards amount of calculation and
length of expressions, and flexible, as regards choice of gauge and
stress-energy tensor. Because of their generality and the simplicity of their
structure our equations provide a convenient starting point for determining the
behaviour of nonlinear perturbations of FL cosmologies with any given
stress-energy content, using either the Poisson gauge or the uniform curvature
gauge.Comment: 30 pages, no figures. Changed title to the one in published version
and some minor changes and addition
The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models
The purpose of this paper is to further investigate the solution space of
self-similar spherically symmetric perfect-fluid models and gain deeper
understanding of the physical aspects of these solutions. We achieve this by
combining the state space description of the homothetic approach with the use
of the physically interesting quantities arising in the comoving approach. We
focus on three types of models. First, we consider models that are natural
inhomogeneous generalizations of the Friedmann Universe; such models are
asymptotically Friedmann in their past and evolve fluctuations in the energy
density at later times. Second, we consider so-called quasi-static models. This
class includes models that undergo self-similar gravitational collapse and is
important for studying the formation of naked singularities. If naked
singularities do form, they have profound implications for the predictability
of general relativity as a theory. Third, we consider a new class of
asymptotically Minkowski self-similar spacetimes, emphasizing that some of them
are associated with the self-similar solutions associated with the critical
behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure
Способ обработки крупногабаритных деталей
В данной статье приведены результаты исследования проблем обработки крупногабаритных деталей в условиях машиностроительных заводов Республики Казахстан. Исследования показали, что при обработке крупногабаритных деталей из труднообрабатываемых материалов возникают осевые и поперечные колебания, которые отрицательно сказываются на точности обработки и на стойкости режущего инструмента. Кроме этого существует проблема обработки крупногабаритных деталей с функционально связанными поверхностями. Для решения данных проблем предлагаются комбинированные способы обработки.This article presents the results of a study of the state of the problem of processing largesized parts in the conditions of machine-building plants of the Republic of Kazakhstan (RK). Studies have shown that when machining large parts from hard-to-digest materials, axial and lateral vibrations arise, which adversely affect machining accuracy and the resistance of the cutting tool. In addition, there is the problem of processing large parts with functionally connected surfaces. To solve these problems, combined treatment methods are proposed
Homothetic perfect fluid space-times
A brief summary of results on homotheties in General Relativity is given,
including general information about space-times admitting an r-parameter group
of homothetic transformations for r>2, as well as some specific results on
perfect fluids. Attention is then focussed on inhomogeneous models, in
particular on those with a homothetic group (acting multiply
transitively) and . A classification of all possible Lie algebra
structures along with (local) coordinate expressions for the metric and
homothetic vectors is then provided (irrespectively of the matter content), and
some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra
Linearization of homogeneous, nearly-isotropic cosmological models
Homogeneous, nearly-isotropic Bianchi cosmological models are considered.
Their time evolution is expressed as a complete set of non-interacting linear
modes on top of a Friedmann-Robertson-Walker background model. This connects
the extensive literature on Bianchi models with the more commonly-adopted
perturbation approach to general relativistic cosmological evolution.
Expressions for the relevant metric perturbations in familiar coordinate
systems can be extracted straightforwardly. Amongst other possibilities, this
allows for future analysis of anisotropic matter sources in a more general
geometry than usually attempted.
We discuss the geometric mechanisms by which maximal symmetry is broken in
the context of these models, shedding light on the origin of different Bianchi
types. When all relevant length-scales are super-horizon, the simplest Bianchi
I models emerge (in which anisotropic quantities appear parallel transported).
Finally we highlight the existence of arbitrarily long near-isotropic epochs
in models of general Bianchi type (including those without an exact isotropic
limit).Comment: 31 pages, 2 figures. Submitted to CQ
Closed cosmologies with a perfect fluid and a scalar field
Closed, spatially homogeneous cosmological models with a perfect fluid and a
scalar field with exponential potential are investigated, using dynamical
systems methods. First, we consider the closed Friedmann-Robertson-Walker
models, discussing the global dynamics in detail. Next, we investigate
Kantowski-Sachs models, for which the future and past attractors are
determined. The global asymptotic behaviour of both the
Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either
expand from an initial singularity, reach a maximum expansion and thereafter
recollapse to a final singularity (for all values of the potential parameter
kappa), or else they expand forever towards a flat power-law inflationary
solution (when kappa^2<2). As an illustration of the intermediate dynamical
behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic
fluid, and of a massless scalar field in detail. We also briefly discuss
Bianchi type IX models.Comment: 15 pages, 10 figure
Cosmological dynamics of R^n gravity
A detailed analysis of dynamics of cosmological models based on
gravity is presented. We show that the cosmological equations can be written as
a first order autonomous system and analyzed using the standard techniques of
dynamical system theory. In absence of perfect fluid matter, we find exact
solutions whose behavior and stability are analyzed in terms of the values of
the parameter . When matter is introduced, the nature of the (non-minimal)
coupling between matter and higher order gravity induces restrictions on the
allowed values of . Selecting such intervals of values and following the
same procedure used in the vacuum case, we present exact solutions and analyze
their stability for a generic value of the parameter . From this analysis
emerges the result that for a large set of initial conditions an accelerated
expansion is an attractor for the evolution of the cosmology. When matter
is present a transient almost-Friedman phase can also be present before the
transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which
are not included and can be found at http://www.mth.uct.ac.za/~peter/R
Qualitative Analysis of String Cosmologies
A qualitative analysis is presented for spatially flat, isotropic and
homogeneous cosmologies derived from the string effective action when the
combined effects of a dilaton, modulus, two-form potential and central charge
deficit are included. The latter has significant effects on the qualitative
dynamics. The analysis is also directly applicable to the anisotropic Bianchi
type I cosmology.Comment: 13 pages, 4 postscript figures, accepted to Physical Review
Stable Exact Solutions in Cosmological Models with Two Scalar Fields
The stability of isotropic cosmological solutions for two-field models in the
Bianchi I metric is considered. We prove that the sufficient conditions for the
Lyapunov stability in the Friedmann-Robertson-Walker metric provide the
stability with respect to anisotropic perturbations in the Bianchi I metric and
with respect to the cold dark matter energy density fluctuations. Sufficient
conditions for the Lyapunov stability of the isotropic fixed points of the
system of the Einstein equations have been found. We use the superpotential
method to construct stable kink-type solutions and obtain sufficient conditions
on the superpotential for the Lyapunov stability of the corresponding exact
solutions. We analyze the stability of isotropic kink-type solutions for string
field theory inspired cosmological models.Comment: 23 pages, v3:typos corrected, references adde
Thinking beyond the hybrid:“actually-existing” cities “after neoliberalism” in Boyle <i>et al.</i>
In their article, ‘The spatialities of actually existing neoliberalism in Glasgow, 1977 to present’, Mark Boyle, Christopher McWilliams and Gareth Rice (2008) usefully problematise our current understanding of neoliberal urbanism. Our response is aimed at developing a sympathetic but critical approach to Boyle et al's understanding of neoliberal urbanism as illustrated by the Glasgow example. In particular, the counterposing by Boyle et al of a 'hybrid, mutant' model to a 'pure' model of neoliberalism for us misrepresents existing models of neoliberalism as a perfectly finished object rather than a roughly mottled process. That they do not identify any ‘pure’ model leads them to create a straw construct against which they can claim a more sophisticated, refined approach to the messiness of neoliberal urbanism. In contrast, we view neoliberalism as a contested and unstable response to accumulation crises at various scales of analysis
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