On the dynamics of a quadratic scalar field potential

We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann-Robertson-Walker universe are written as an autonomous system of equations, and the solutions of physical interest appear as critical points. This new formalism is then applied to the study of inflation dynamics, in which we can go beyond the known slow-roll formalism of inflation.Comment: 14 pages, 6 eps figures, matches version to appear in IJMP

A Particle Image Velocimetry study of dual-rotor counter-rotating wind turbine near wake

This experimental work studied the flow characteristics in the near wake region behind dual-rotor wind turbines using two-dimensional particle image velocimetry. Two auxiliary rotors of 50% and 80% scale of the main rotor were installed upwind and operated in counter-rotating condition, which are compared to the conventional single rotor turbine. In all the three configurations, a constant Reynolds number 9.5×104 was applied and all the rotors operated at a fixed tip speed ratio of 3.46. The mean and phase averaged velocity fields were investigated together with the turbulence kinetic energy. It was found that the two auxiliary rotors do not result in a significantly different wake flow property. The configuration implementing the 50% auxiliary rotor sees a slightly better wake characteristics, in terms of weaker main rotor tip vortices and a counter-rotating swirling shear region at the mid-span behind the main rotor. The decay rates of the peak vorticity of the main rotor tip vortices and their circulation are found to follow an exponential manner

Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes

The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.Comment: 16 pages, some minor changes and clarifications; section 4 has been shortened as some unnecessary constructions have been remove

Visual cue training to improve walking and turning after stroke:a study protocol for a multi-centre, single blind randomised pilot trial

Visual information comprises one of the most salient sources of information used to control walking and the dependence on vision to maintain dynamic stability increases following a stroke. We hypothesize, therefore, that rehabilitation efforts incorporating visual cues may be effective in triggering recovery and adaptability of gait following stroke. This feasibility trial aims to estimate probable recruitment rate, effect size, treatment adherence and response to gait training with visual cues in contrast to conventional overground walking practice following stroke.Methods/design: A 3-arm, parallel group, multi-centre, single blind, randomised control feasibility trial will compare overground visual cue training (O-VCT), treadmill visual cue training (T-VCT), and usual care (UC). Participants (n = 60) will be randomly assigned to one of three treatments by a central randomisation centre using computer generated tables to allocate treatment groups. The research assessor will remain blind to allocation. Treatment, delivered by physiotherapists, will be twice weekly for 8 weeks at participating outpatient hospital sites for the O-VCT or UC and in a University setting for T-VCT participants.Individuals with gait impairment due to stroke, with restricted community ambulation (gait spee

Functional electrical stimulation versus ankle foot orthoses for foot-drop: a meta-analysis of orthotic effects

Objective: To compare the effects on walking of Functional Electrical Stimulation (FES) and Ankle Foot Orthoses (AFO) for foot-drop of central neurological origin, assessed in terms of unassisted walking behaviours compared with assisted walking following a period of use (combined-orthotic effects). Data Sources: MEDLINE, AMED, CINAHL, Cochrane Central Register of Controlled Trials, Scopus, REHABDATA, PEDro, NIHR Centre for Reviews and Dissemination and clinicaltrials.gov. plus reference list, journal, author and citation searches. Study Selection: English language comparative Randomised Controlled Trials (RCTs). Data Synthesis: Seven RCTs were eligible for inclusion. Two of these reported different results from the same trial and another two reported results from different follow up periods so were combined; resulting in five synthesised trials with 815 stroke participants. Meta-analyses of data from the final assessment in each study and three overlapping time-points showed comparable improvements in walking speed over ten metres (p=0.04-0.95), functional exercise capacity (p=0.10-0.31), timed up-and-go (p=0.812 and p=0.539) and perceived mobility (p=0.80) for both interventions. Conclusion: Data suggest that, in contrast to assumptions that predict FES superiority, AFOs have equally positive combined-orthotic effects as FES on key walking measures for foot-drop caused by stroke. However, further long-term, high-quality RCTs are required. These should focus on measuring the mechanisms-of-action; whether there is translation of improvements in impairment to function, plus detailed reporting of the devices used across diagnoses. Only then can robust clinical recommendations be made

Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.Comment: 34 page

Axiomatic quantum field theory in curved spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.Comment: Latex, 44 pages, 2 figure

Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime

We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the real free scalar field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same argument also works for anti-commutation relations and it can be generalised to vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a very weak form of the Jost-Schroer theorem. The original proofs of these results in the Wightman framework make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.Comment: 18 page