The Energetic Implications of Using Deforming Reference Descriptions to Simulate the Motion of Incompressible, Newtonian Fluids

In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming reference descriptions is resolved. These properties are intrinsic to real flows and the conventional Navier-Stokes equations. A completely general reference description of an incompressible, Newtonian fluid, which reconciles the differences between opposing schools of thought in the literature is derived for the purposes of this investigation. The work subsequently focusses on establishing a class of time discretisations which inherit these self-same energetic properties, irrespective of the time increment employed. The findings of this analysis have profound consequences for the use of certain classes of finite difference schemes in the context of deforming references. It is significant that many algorithms presently in use do not automatically inherit the fundamental qualitative features of the dynamics. An `updated' approach as a means of avoiding ever burgeoning deformation gradients and a still further simplified implementation are further topics explored.Comment: 26 pages, 2 figures, lemma 2 proof correcte

Phase measurements with weak reference pulses

Quantum state discrimination for two coherent states with opposite phases as measured relative to a reference pulse is analyzed as functions of the intensities of both the signal states and of the reference pulse. This problem is relevant for Quantum Key Distribution with phase encoding. We consider both the optimum measurements and simple measurements that require only beamsplitters and photodetectors.Comment: 5 pages, 5 figures. I apologize for this boring pape

Gravitational waves from self-ordering scalar fields

Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as $\Omega_{\rm GW}(f) \propto f^3$ with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon ($k\eta_* \ll 1$), enters the horizon, for $k\eta \gtrsim 1$, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information.Comment: 21 pages, 2 figures, added discussion about numerical integration and a new figure to illustrate the scale-invariance of the GW power spectrum, conclusions unchange

A nonperturbative calculation of the electron's magnetic moment

In principle, the complete spectrum and bound-state wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its light-cone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using light-cone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the light-cone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing light-cone-quantized gauge theories in Feynman and light-cone gauges: (1) the introduction of a spectrum of Pauli-Villars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gauge-theory Lagrangian with higher derivatives. In the latter case, which is applicable to light-cone gauge (A^+ = 0), the A^- component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finite-mass Pauli-Villars regulators can also be used to compensate for neglected higher Fock states. As a test case, we apply these regularization procedures to an approximate nonperturbative computation of the anomalous magnetic moment of the electron in QED as a first attempt to meet Feynman's famous challenge.Comment: 35 pages, elsart.cls, 3 figure

Effects of landscape metrics and land-use variables on macroinvertebrate communities and habitat characteristics

ABSTRACT: The growing number of studies establishing links between stream biota, environmental factors and river classification has contributed to a better understanding of fluvial ecosystem function. Environmental factors influencing river systems are distributed over hierarchically organised spatial scales. We used a nested hierarchical sampling design across four catchments to assess how benthic macroinvertebrate community composition and lower spatial scale habitat descriptors were shaped by landscape and land-use patterns. We found that benthic macroinvertebrate community structure and composition varied significantly from catchment to habitat level. We assessed and identified fractal metrics of landscape descriptors capable of explaining compositional and functional change in the benthic faunal indicators and compared them with the traditional variables describing land use and reach level habitat descriptors within a 1 km radius of each sampling site. We found that fractal landscape metrics were the best predictor variables for benthic macroinvertebrate community composition, function, instream habitat and river corridor characteristics

The evolution of RNAi as a defence against viruses and transposable elements

RNA interference (RNAi) is an important defence against viruses and transposable elements (TEs). RNAi not only protects against viruses by degrading viral RNA, but hosts and viruses can also use RNAi to manipulate each other's gene expression, and hosts can encode microRNAs that target viral sequences. In response, viruses have evolved a myriad of adaptations to suppress and evade RNAi. RNAi can also protect cells against TEs, both by degrading TE transcripts and by preventing TE expression through heterochromatin formation. The aim of our review is to summarize and evaluate the current data on the evolution of these RNAi defence mechanisms. To this end, we also extend a previous analysis of the evolution of genes of the RNAi pathways. Strikingly, we find that antiviral RNAi genes, anti-TE RNAi genes and viral suppressors of RNAi all evolve rapidly, suggestive of an evolutionary arms race between hosts and parasites. Over longer time scales, key RNAi genes are repeatedly duplicated or lost across the metazoan phylogeny, with important implications for RNAi as an immune defence