Classical theory of radiating strings

The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities

Integration of Batch-to-Batch and Within Batch Control Techniques: Application to a Simulated Nylon-6,6Process

Using a simulated nylon-6,6 batch process, this work presents three batch control schemes, 1) within batch, 2) batch-to-batch, and 3) integrated batch-to-batch and within batch, as improvements over fixed-recipe operation alone for disturbance rejection. The control schemes were developed using process understanding gained through analysis of a historical database of easily measured batch profiles. Various concerns regarding development and implementation of each strategy were discussed. The strengths and weaknesses of each controller\u27s performance were discussed as well. The analysis method used focused on separating batch measurement variability into time-axis and magnitude-axis components. Partitioning the data in this way generated time and magnitude scale parameters that described the normal variability in the process. These scale parameters provided improved process understanding and formed the basis for the improved control schemes developed in this work. The within batch controller was a feedforward strategy that made mid-course recipe adjustments based on predicted deviation from target quality. The batch-to-batch controller utilized quality measurements to provide feedback adjustments to subsequent batches. The integrated control scheme utilized the predictive feedforward performance of the within batch controller tempered by the off-line feedback of the batch-to-batch controller in a cascade arrangement. The three control schemes were compared to fixed-recipe operation. All three provided significant improvement in quality control. The within batch controller resulted in a 91% reduction in mean squared target error (MSE) over fixed recipe operation. The batch-to-batch controller provided an 87% reduction in MSE. The integrated control scheme was found to be the most effective providing a 99% reduction in MSE over fixed-recipe operation

Kinky Brane Worlds

We present a toy model for five-dimensional heterotic M-theory where bulk three-branes, originating in 11 dimensions from M five-branes, are modelled as kink solutions of a bulk scalar field theory. It is shown that the vacua of this defect model correspond to a class of topologically distinct M-theory compactifications. Topology change can then be analysed by studying the time evolution of the defect model. In the context of a four-dimensional effective theory, we study in detail the simplest such process, that is the time evolution of a kink and its collision with a boundary. We find that the kink is generically absorbed by the boundary thereby changing the boundary charge. This opens up the possibility of exploring the relation between more complicated defect configurations and the topology of brane-world models.Comment: 31 pages, Latex, 6 eps-figure

Correlations in Cosmic String Networks

We investigate scaling and correlations of the energy and momentum in an evolving network of cosmic strings in Minkowski space. These quantities are of great interest, as they must be understood before accurate predictions for the power spectra of the perturbations in the matter and radiation in the early Universe can be made. We argue that Minkowski space provides a reasonable approximation to a Friedmann background for string dynamics and we use our results to construct a simple model of the network, in which it is considered to consist of randomly placed segments moving with random velocities. This model works well in accounting for features of the two-time correlation functions, and even better for the power spectra.Comment: 20pp Plain LaTeX, 11 EPS figures, uses epsf.st

WIMP Dark Matter and the QCD Equation of State

Weakly Interacting Massive Particles (WIMPs) of mass m freeze out at a temperature T_f ~ m/25, i.e. in the range 400 MeV -- 40 GeV for a particle in the typical mass range 10 -- 1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at T_f, may be measured to better than 1% by Planck, warranting comparable theoretical precision. Recent theoretical and experimental advances in the understanding of high temperature QCD show that the quark gluon plasma departs significantly from ideal behaviour up to temperatures of several GeV, necessitating an improvement of the cosmological equation of state over those currently used. We discuss how this increases the relic density by approximately 1.5 -- 3.5% in benchmark mSUGRA models, with an uncertainly in the QCD corrections of 0.5 -- 1 %. We point out what further work is required to achieve a theoretical accuracy comparable with the expected observational precision, and speculate that the effective number of degrees of freedom at T_f may become measurable in the foreseeable future.Comment: 4pp, 2figs. More info including Matlab scripts used to generate equation of state curves at http://www.pact.cpes.sussex.ac.uk/arXiv/hep-ph/0501232

Scaling in a SU(2)/Z_3 model of cosmic superstring networks

Motivated by recent developments in superstring theory in the cosmological context, we examine a field theory which contains string networks with 3-way junctions. We perform numerical simulations of this model, identify the length scales of the network that forms, and provide evidence that the length scales tend towards a scaling regime, growing in proportion to time. We infer that the presence of junctions does not in itself cause a superstring network to dominate the energy density of the early Universe.Comment: 12pp, 3 fig

Gravitational waves from the sound of a first order phase transition

We report on the first three-dimensional numerical simulations of first-order phase transitions in the early Universe to include the cosmic fluid as well as the scalar field order parameter. We calculate the gravitational wave (GW) spectrum resulting from the nucleation, expansion, and collision of bubbles of the low-temperature phase, for phase transition strengths and bubble wall velocities covering many cases of interest. We find that the compression waves in the fluid continue to be a source of GWs long after the bubbles have merged, a new effect not taken properly into account in previous modeling of the GW source. For a wide range of models, the main source of the GWs produced by a phase transition is, therefore, the sound the bubbles make

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)