On inhibiting runaway in catalytic reactors

We consider the problem of heat and mass transfer in porous catalyst pellets. Both the steady and time dependent operating characteristics are studied. Accurate approximate equations are derived from the basic governing equations of motion. A nonlinear stability analysis is employed to account for the observation that under certain conditions reactions on catalyst pellets can pass transiently stably into a region which would correspond to instability in the steady state. One consequence of our analysis is a possible control mechanism which inhibits temperature runaway by extending the stable operating characteristics desirable in modern reactors

Neon, sulphur and argon abundances of planetary nebulae in the sub-solar metallicity Galactic anti-centre

Context: Spectra of planetary nebulae show numerous fine structure emission lines from ionic species, enabling us to study the overall abundances of the nebular material that is ejected into the interstellar medium. The abundances derived from planetary nebula emission show the presence of a metallicity gradient within the disk of the Milky Way up to Galactocentric distances of ∼ 10 kpc, which are consistent with findings from studies of different types of sources, including H II regions and young B-type stars. The radial dependence of these abundances further from the Galactic centre is in dispute. Aims: We aim to derive the abundances of neon, sulphur and argon from a sample of planetary nebulae towards the Galactic anti- centre, which represent the abundances of the clouds from which they were formed, as they remain unchanged throughout the course of stellar evolution. We then aim to compare these values with similarly analysed data from elsewhere in the Milky Way in order to observe whether the abundance gradient continues in the outskirts of our Galaxy. Methods: We have observed 23 planetary nebulae at Galactocentric distances of 8–21 kpc with Spitzer IRS. The abundances were calculated from infrared emission lines, for which we observed the main ionisation states of neon, sulphur, and argon, which are little affected by extinction and uncertainties in temperature measurements or fluctuations within the planetary nebula. We have complemented these observations with others from optical studies in the literature, in order to reduce or avoid the need for ionisation correction factors in abundance calculations. Results: The overall abundances of our sample of planetary nebulae in the Galactic anti-centre are lower than those in the solar neighbourhood. The abundances of neon, sulphur, and argon from these stars are consistent with a metallicity gradient from the solar neighbourhood up to Galactocentric distances of ∼ 20 kpc, albeit with varying degrees of dispersion within the data

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain `base points' of the Cauchy horizon, which are defined as `past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's `Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a `time machine'. Specifically, we prove: Theorem 1: There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2: The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in MXM) of (x,x). Theorem 2 implies quantities such as the renormalized expectation value of \phi^2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proofs rely on the `Propagation of Singularities' theorems of Duistermaat and H\"ormander.Comment: 37 pages, LaTeX, uses latexsym and amsbsy, no figures; updated version now published in Commun. Math. Phys.; no major revisions from original versio

The pion charge radius from charged pion electroproduction

We analyze a low-energy theorem of threshold pion electroproduction which allows one to determine the charge radius of the pion. We show that at the same order where the radius appears, pion loops induce a correction to the momentum dependence of the longitudinal dipole amplitude $L_{0+}^{(-)}$. This model-independent correction amounts to an increase of the pion charge radius squared from the electroproduction data by about 0.26~fm$^2$. It sheds light on the apparent discrepancy between the recent determination of the pion radius from electroproduction data and the one based on pion-electron scattering.Comment: 3 pp, REVTeX, uses eps

Lattice QCD at the end of 2003

I review recent developments in lattice QCD. I first give an overview of its formalism, and then discuss lattice discretizations of fermions. We then turn to a description of the quenched approximation and why it is disappearing as a vehicle for QCD phenomenology. I describe recent claims for progress in simulations which include dynamical fermions and the interesting theoretical problems they raise. I conclude with brief descriptions of the calculations of matrix elements in heavy flavor systems and for kaons.Comment: Review for Int J Mod Phys A. 58 pages, latex, WSPC macros,, 22 postscript figure

Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e. those in which the valence and sea quark masses, $m_V$ and $m_S$, are different. I point out that for lattice fermions which retain some chiral symmetry on the lattice, e.g. staggered fermions, the leading order prediction of the chiral expansion is that the mass of the pion depends only on $m_V$, and is independent of $m_S$. This surprising result is shown to receive corrections from loop effects which are of relative size $m_S \ln m_V$, and which thus diverge when the valence quark mass vanishes. Using partially quenched chiral perturbation theory, I calculate the full one-loop correction to the mass and decay constant of pions composed of two non-degenerate quarks, and suggest various combinations for which the prediction is independent of the unknown coefficients of the analytic terms in the chiral Lagrangian. These results can also be tested with Wilson fermions if one uses a non-perturbative definition of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected (alpha_4 is replaced by alpha_4/2

Staggered Chiral Perturbation Theory and the Fourth-Root Trick

Staggered chiral perturbation theory (schpt) takes into account the "fourth-root trick" for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, nF=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces nF=4 to nF=1. One can then treat nondegenerate quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of nF=3, 2, or 1. A apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular the restoration of taste symmetry, schpt then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a "mixed" theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of schpt, so that a variety of possible new routes for testing this validity are opened.Comment: 39 pages, 3 figures. v3: minor changes: improved explanations and less tentative discussion in several places; corresponds to published versio

LIDA: A Working Model of Cognition

In this paper we present the LIDA architecture as a working model of cognition. We argue that such working models are broad in scope and address real world problems in comparison to experimentally based models which focus on specific pieces of cognition. While experimentally based models are useful, we need a working model of cognition that integrates what we know from neuroscience, cognitive science and AI. The LIDA architecture provides such a working model. A LIDA based cognitive robot or software agent will be capable of multiple learning mechanisms. With artificial feelings and emotions as primary motivators and learning facilitators, such systems will ‘live’ through a developmental period during which they will learn in multiple ways to act in an effective, human-like manner in complex, dynamic, and unpredictable environments. We discuss the integration of the learning mechanisms into the existing IDA architecture as a working model of cognition

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.

Topics in Chiral Perturbation Theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.Comment: 30 pp, TeX, Review talk, Third Workshop on High Energy Particle Physics (WHEPP III), Madras, India, January 1994. 7 figures available upon request. CRN--94/0