29 research outputs found
Conditions for spontaneous homogenization of the Universe
The present-day Universe appears to be homogeneous on very large scales. Yet
when the casual structure of the early Universe is considered, it becomes
apparent that the early Universe must have been highly inhomogeneous. The
current paradigm attempts to answer this problem by postulating the inflation
mechanism However, inflation in order to start requires a homogeneous patch of
at least the horizon size. This paper examines if dynamical processes of the
early Universe could lead to homogenization. In the past similar studies seem
to imply that the set of initial conditions that leads to homogenization is of
measure zero. This essay proves contrary: a set of initial conditions for
spontaneous homogenization of cosmological models can form a set of non-zero
measure.Comment: 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay
competitio
The Similarity Hypothesis in General Relativity
Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
Spherically symmetric dissipative anisotropic fluids: A general study
The full set of equations governing the evolution of self--gravitating
spherically symmetric dissipative fluids with anisotropic stresses is deployed
and used to carry out a general study on the behaviour of such systems, in the
context of general relativity. Emphasis is given to the link between the Weyl
tensor, the shear tensor, the anisotropy of the pressure and the density
inhomogeneity. In particular we provide the general, necessary and sufficient,
condition for the vanishing of the spatial gradients of energy density, which
in turn suggests a possible definition of a gravitational arrow of time. Some
solutions are also exhibited to illustrate the discussion.Comment: 28 pages Latex. To appear in Phys.Rev.
Knowledge modeling in prior art search
This study explores the benefits of integrating knowledge representations in prior art patent retrieval. Key to the introduced approach is the utilization of human judgment available in the form of classifications assigned to patent documents. The paper first outlines in detail how a methodology for the extraction of knowledge from such an hierarchical classification system can be established. Further potential ways of integrating this knowledge with existing Information Retrieval paradigms in a scalable and flexible manner are investigated. Finally based on these integration strategies the effectiveness in terms of recall and precision is evaluated in the context of a prior art search task for European patents. As a result of this evaluation it can be established that in general the proposed knowledge expansion techniques are particularly beneficial to recall and, with respect to optimizing field retrieval settings, further result in significant precision gains