The structure of flame filaments in chaotic flows

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents the effect of stirring as a convergent flow. The dependence of the steady solutions on the Damkohler number and Lewis number is treated in detail. It is found that, below a critical Damkohler number Da(crit), the flame is quenched by the flow. The quenching transition appears as a result of a saddle-node bifurcation where the stable steady filament solution collides with an unstable one. The shape of the steady solutions for the concentration and temperature profiles changes with the Lewis number and the value of Da(crit) increases monotonically with the Lewis number. Properties of the solutions are studied analytically in the limit of large Damkohler number and for small and large Lewis number.Comment: 17 pages, 13 figures, to be published in Physica

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

A Phenomenological Analysis of Gluon Mass Effects in Inclusive Radiative Decays of the J/ψ\rm{J/\psi} and $\Upsilon

The shapes of the inclusive photon spectra in the processes \Jp \to \gamma X and \Up \to \gamma X have been analysed using all available experimental data. Relativistic, higher order QCD and gluon mass corrections were taken into account in the fitted functions. Only on including the gluon mass corrections, were consistent and acceptable fits obtained. Values of $0.721^{+0.016}_{-0.068}$ GeV and $1.18^{+0.09}_{-0.29}$ GeV were found for the effective gluon masses (corresponding to Born level diagrams) for the \Jp and \Up respectively. The width ratios \Gamma(V \to {\rm hadrons})/\Gamma(V \to \gamma+ {\rm hadrons}) V=\Jp, \Up were used to determine $\alpha_s(1.5 {\rm GeV})$ and $\alpha_s(4.9 {\rm GeV})$. Values consistent with the current world average $\alpha_s$ were obtained only when gluon mass correction factors, calculated using the fitted values of the effective gluon mass, were applied. A gluon mass $\simeq 1$ GeV, as suggested with these results, is consistent with previous analytical theoretical calculations and independent phenomenological estimates, as well as with a recent, more accurate, lattice calculation of the gluon propagator in the infra-red region.Comment: 50 pages, 11 figures, 15 table

Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium

We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We discuss the interplay of the scales arising in the Soft-Collinear Effective Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2. For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for 1-z << alpha_s^2. The S- and P-wave octet shape functions are calculated. When they are included in the analysis of the photon spectrum of the Upsilon (1S) system, the agreement with data in the end-point region becomes excellent. The NRQCD matrix elements and are also obtained.Comment: Revtex, 11 pages, 6 figures. Minor improvements and references added. Journal versio

General Relativistic MHD Jets

Magnetic fields connecting the immediate environs of rotating black holes to large distances appear to be the most promising mechanism for launching relativistic jets, an idea first developed by Blandford and Znajek in the mid-1970s. To enable an understanding of this process, we provide a brief introduction to dynamics and electromagnetism in the spacetime near black holes. We then present a brief summary of the classical Blandford-Znajek mechanism and its conceptual foundations. Recently, it has become possible to study these effects in much greater detail using numerical simulation. After discussing which aspects of the problem can be handled well by numerical means and which aspects remain beyond the grasp of such methods, we summarize their results so far. Simulations have confirmed that processes akin to the classical Blandford-Znajek mechanism can launch powerful electromagnetically-dominated jets, and have shown how the jet luminosity can be related to black hole spin and concurrent accretion rate. However, they have also shown that the luminosity and variability of jets can depend strongly on magnetic field geometry. We close with a discussion of several important open questions.Comment: 21 pages, 2 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

Are schools drifting apart? Intake stratification in English secondary schools

The issue of social segregation in schools has seen a recent resurgence of interest – in the US, UK and internationally – as the debate rages on about whether policies that expand families’ freedom to choose amongst schools encourage divergence or convergence in the types of pupil different schools admit. Most attention has been focussed on segregation along lines of ethnic or social background. Yet, the real consideration that seems to be in the back of most people’s minds is the issue of segregation or stratification of schools along lines of pupil ability. We look explicitly at this issue using data on the population of pupils entering Secondary school in England from 1996 to 2002. Our study does highlight wide disparities between peer-group ability in different schools. But we also find that, contrary to popular opinion, almost nothing has changed over these years in terms of the way pupils of different age-11 abilities are sorted into different Secondary schools