On the energy-momentum tensor for a scalar field on manifolds with boundaries

We argue that already at classical level the energy-momentum tensor for a scalar field on manifolds with boundaries in addition to the bulk part contains a contribution located on the boundary. Using the standard variational procedure for the action with the boundary term, the expression for the surface energy-momentum tensor is derived for arbitrary bulk and boundary geometries. Integral conservation laws are investigated. The corresponding conserved charges are constructed and their relation to the proper densities is discussed. Further we study the vacuum expectation value of the energy-momentum tensor in the corresponding quantum field theory. It is shown that the surface term in the energy-momentum tensor is essential to obtain the equality between the vacuum energy, evaluated as the sum of the zero-point energies for each normal mode of frequency, and the energy derived by the integration of the corresponding vacuum energy density. As an application, by using the zeta function technique, we evaluate the surface energy for a quantum scalar field confined inside a spherical shell.Comment: 25 pages, 2 figures, section and appendix on the surface energy for a spherical shell are added, references added, accepted for publication in Phys. Rev.

Effect of methane on the conversion of HFC-134a in a dielectric barrier discharge non-equilibrium plasma reactor

The effect of methane on the conversion of HFC-134a (CF3CH2F) in a dielectric barrier discharge non-equilibrium plasma reactor was examined. Reactions were conducted in an argon bath gas and in the absence of oxygen and nitrogen. The products of the reaction include H2, HF, CHF3, CH2F2, C2H6, C3H8, C2H3F, CHF2CHF2, C2H4F2, C3H7F as well as a polymeric solid deposit. The polymeric materials are predominantly fluorine containing random copolymers, which can be categorised as fluoropolymers, constituted from various functional groups including CF3, CF2, CHF, CHF2, CH2F, CH2 and CH3. While the presence of methane in the feed stream reduces the conversion level of CF3CH2F, it also modifies the polymer architecture. The addition of 1.25% methane with 12.5% CF3CH2F in an argon bath gas at 100cm3min-1 feed rate reduces the conversion of CF3CH2F from 74.5% to 46.8% and increases the formation of HF from 1500μmolh-1 to 2640μmolh-1. The effect of methane addition on the electrical discharge and the reaction pathways are discussed

Comparative study of the decomposition of CH4 in a nonequilibrium plasma and under high temperature pyrolytic conditions

In this study, the decomposition of methane in a nonequilibrium plasma, where nitrogen and oxygen were excluded from the feed mixture, was investigated. The major product species formed under conditions where the conversion level of methane was relatively high (up to 50 %) were determined. Hydrogen, acetylene, ethylene, ethane and propane were the primary gaseous species identified, and a liquid fraction was detected, which was characterised by 1 H NMR and gel permeation chromatography. The product spectrum formed in the nonequilibrium plasma is compared to the species profile predicted from methane pyrolysis, where the feed composition, residence time and methane conversion levels used in the high temperature pyrolysis simulation matched those in the nonequilibrium plasma experimental reactor

Learning and Designing Stochastic Processes from Logical Constraints

Continuous time Markov Chains (CTMCs) are a convenient mathematical model for a broad range of natural and computer systems. As a result, they have received considerable attention in the theoretical computer science community, with many important techniques such as model checking being now mainstream. However, most methodologies start with an assumption of complete specification of the CTMC, in terms of both initial conditions and parameters. While this may be plausible in some cases (e.g. small scale engineered systems) it is certainly not valid nor desirable in many cases (e.g. biological systems), and it does not lead to a constructive approach to rational design of systems based on specific requirements. Here we consider the problems of learning and designing CTMCs from observations/ requirements formulated in terms of satisfaction of temporal logic formulae. We recast the problem in terms of learning and maximising an unknown function (the likelihood of the parameters) which can be numerically estimated at any value of the parameter space (at a non-negligible computational cost). We adapt a recently proposed, provably convergent global optimisation algorithm developed in the machine learning community, and demonstrate its efficacy on a number of non-trivial test cases

Calculating Casimir Energies in Renormalizable Quantum Field Theory

Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been studied by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$ not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for $D\ne1$. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in $D$ and three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B and Appendix, and other minor correction

Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co

Modulatory effects of oleanolic acid on cardiac anti-oxidant status and inflammatory response in high fructose-fed neonatal Sprague-Dawley rats

This present study investigated the antioxidant and inflammatory properties of oleanolic acid (OA) on neonatal rats administered with high fructose diet (HFD). Neonatal rats (24) were assigned at random to four (4) groups namely: Group A (control) which had distilled water only; Group B was administered with OA only; Group C was administered with HFD; Group D received HFD and OA. Animals were administered orally using orogastric gavage at a dosage of 10 ml/kg for 7 days (postnatal day 7-14. The antioxidant status of the hearts such as TEAC, Ferric Reducing Anti-oxidant Power, FRAP, Trolox Equivalence Antioxidant Capacity and oxidative stress biomarkers (MDA, Malondialdehyde and GSH, Glutathione) were evaluated using standard procedures. The levels of inflammatory cytokines in the hearts were determined using magnetic bead-based assays procedure. The TEAC values were significantly decreased in HFD+OA treatment (p < 0.05) in comparison with HFD group. Glutathione concentration in the HFD group had significant increase (p < 0.05) following treatment with oleanolic acid. FRAP values and MDA level were significantly (p < 0.01) elevated post exposure to HFD and treatment with oleanolic acid insignificantly decreased MDA level when compared with HFD group. The pro-inflammatory cytokines (IL-1β, IL-6, IL-12, IFN-γ, TNF-a and MCP-1) were significantly (p < 0.05) increased HFD group when compared to the control. Oleanolic acid administration significantly reduced inflammation in postexposure to HFD. Neonatal intake of oleanolic acid may help to prevent inflammation and oxidative damage in the progression of cardiovascular related diseases.https://www.tjnpr.orgam2023Physiolog

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated