A cosmological solution of Regge calculus

We revisit the Regge calculus model of the Kasner cosmology first considered by S. Lewis. One of the most highly symmetric applications of lattice gravity in the literature, Lewis' discrete model closely matched the degrees of freedom of the Kasner cosmology. As such, it was surprising that Lewis was unable to obtain the full set of Kasner-Einstein equations in the continuum limit. Indeed, an averaging procedure was required to ensure that the lattice equations were even consistent with the exact solution in this limit. We correct Lewis' calculations and show that the resulting Regge model converges quickly to the full set of Kasner-Einstein equations in the limit of very fine discretization. Numerical solutions to the discrete and continuous-time lattice equations are also considered.Comment: 12 pages, 3 figure

A parsimonious model for the proportional control valve

A generic non-linear dynamic model of a direct-acting electrohydraulic proportional solenoid valve is presented. The valve consists of two subsystems-s-a spool assembly and one or two unidirectional proportional solenoids. These two subsystems are modelled separately. The solenoid is modelled as a non-linear resistor-inductor combination, with inductance parameters that change with current. An innovative modelling method has been used to represent these components. The spool assembly is modelled as a mass-spring-damper system. The inertia and the damping effects of the solenoid armature are incorporated in the spool mode1. The model accurately and reliably predicts both the dynamic and steady state responses of the valve to voltage inputs. Simulated results are presented, which agree well with experimental results

Lifshitz entanglement entropy from holographic cMERA

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA). In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$. We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension. We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow. We focus on strip regions but also consider a disc in the undeformed theory.Comment: 17 pages, v2: references added and improved discussions, v3: published versio

Diagnostics for magnetically confined high-temperature plasmas

During the last 20 years, magnetically confined laboratory plasmas of steadily increasing temperatures and densities have been obtained, most notably in tokamak configurations, and now approach the conditions necessary to sustain a fusion reaction. Even more important to the goal of understanding the physics of such systems, remarkable advances in plasma diagnostics, the techniques for determining the properties of such plasmas, have accompanied these developments. More parameters can be determined with greater accuracy and finer spatial and temporal resolution. The magnetic configuration, the primary local thermodynamic quantities (density, temperature, and drift velocity), and other necessary quantities can now be measured with sufficient accuracy to determine particle and energy fluxes within the plasma and to characterize the basic transport processes. These plasmas are far from thermodynamic equilibrium. This deviation manifests itself in a variety of instabilities on several spatial and temporal scales, many of which are aptly described as turbulence. Many aspects of the turbulence can also be characterized. This article reviews the current state of diagnostics from an epistemoiogical perspective: the capabilities and limitations for measuring each important physical quantity are presented.Physic

On the convergence of Regge calculus to general relativity

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

A brief review of Regge calculus in classical numerical relativity

We briefly review past applications of Regge calculus in classical numerical relativity, and then outline a programme for the future development of the field. We briefly describe the success of lattice gravity in constructing initial data for the head-on collision of equal mass black holes, and discuss recent results on the efficacy of Regge calculus in the continuum limit.Comment: 2 pages, submitted to the Proceedings of the IX Marcel Grossmann Meeting, Rome, July 2-8, 200

The BSSN formulation is a partially constrained evolution system

Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the momentum constraints as first-order evolution equations, and show that the popular BSSN formulation of the Einstein equations explicitly uses the momentum constraints as evolution equations. We conjecture that this feature is a key reason for the relative success of the BSSN formulation in numerical relativity.Comment: 8 pages, minor grammatical correction

Holographic entanglement entropy of surface defects

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in ${\cal N}=4$ Super Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussedComment: 41 pages. pdflatex, 3 figures. v2: typos corrected, reference corrected, some comments on CFT interpretation added. v3: references added, some clarification