Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda w_i(t)$ at the individual level with a global coupling through a constraint which does not allow the $w_i$'s to fall below a lower cutoff given by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a constant. The dynamic variables $w_i$ are found to exhibit a power-law distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$ is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor $\lambda$, but it is non-universal, and increases monotonically as a function of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$ for any finite $N$ while $\alpha(c,\infty) \ge 1$ (which is the common range in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}$ exhibits intermittent fluctuations parametrized by a (truncated) L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This non-trivial relation between the distribution of the $w_i$'s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed.Comment: 7 pages, 4 figure

Methane gas hydrate effect on sediment acoustic and strength properties

Author Posting. © The Author(s), 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Petroleum Science and Engineering 56 (2007): 127-135, doi:10.1016/j.petrol.2006.02.003.To improve our understanding of the interaction of methane gas hydrate with host sediment, we studied: (1) the effects of gas hydrate and ice on acoustic velocity in different sediment types, (2) effect of different hydrate formation mechanisms on measured acoustic properties (3) dependence of shear strength on pore space contents, and (4) pore-pressure effects during undrained shear. A wide range in acoustic p-wave velocities (Vp) were measured in coarse-grained sediment for different pore space occupants. Vp ranged from less than 1 km/s for gascharged sediment to 1.77 - 1.94 km/s for water-saturated sediment, 2.91 - 4.00 km/s for sediment with varying degrees of hydrate saturation, and 3.88 - 4.33 km/s for frozen sediment. Vp measured in fine-grained sediment containing gas hydrate was substantially lower (1.97 km/s). Acoustic models based on measured Vp indicate that hydrate which formed in high gas flux environments can cement coarse-grained sediment, whereas hydrate formed from methane dissolved in the pore fluid may not. The presence of gas hydrate and other solid pore-filling material, such as ice, increased the sediment shear strength. The magnitude of that increase is related to the amount of hydrate in the pore space and cementation characteristics between the hydrate and sediment grains. We have found, that for consolidation stresses associated with the upper several hundred meters of subbottom depth, pore pressures decreased during shear in coarse-grained sediment containing gas hydrate, whereas pore pressure in fine-grained sediment typically increased during shear. The presence of free gas in pore spaces damped pore pressure response during shear and reduced the strengthening effect of gas hydrate in sands.This work was supported by the Coastal and Marine Geology, and Energy Programs of the U.S. Geological Survey and funding was provided by the Gas Hydrate Program of the U.S. Department of Energy

Conceptualising sustainability in UK urban Regeneration: a discursive Formation

Despite the wide usage and popular appeal of the concept of sustainability in UK policy, it does not appear to have challenged the status quo in urban regeneration because policy is not leading in its conceptualisation and therefore implementation. This paper investigates how sustainability has been conceptualised in a case-based research study of the regeneration of Eastside in Birmingham, UK, through policy and other documents, and finds that conceptualisations of sustainability are fundamentally limited. The conceptualisation of sustainability operating within urban regeneration schemes should powerfully shape how they make manifest (or do not) the principles of sustainable development. Documents guide, but people implement regeneration—and the disparate conceptualisations of stakeholders demonstrate even less coherence than policy. The actions towards achieving sustainability have become a policy ‘fix’ in Eastside: a necessary feature of urban policy discourse that is limited to solutions within market-based constraints

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Inequality of opportunity in the land of opportunities : 1968-2001

We measure inequality of opportunity for earnings acquisition in the U.S. between 1968 and 2001. Following recent theories of social justice, earnings determinants are divided into two parts: Circumstances, which are characteristics outside individual control and effort representing factors impacting earnings but under individuals’ responsibility. Equality of opportunity requires that inequality of circumstances must be corrected while differences of effort must remain unaltered. Circumstances are represented by parental education and occupation, ethnic origin, place of birth and age. Effort is modeled with schooling choices and labour supply decisions. Using the PSID from 1968 to 2001, we provide two alternative assessments of inequality of opportunity using counterfactual distributions. The statistical framework is semi-parametric and builds on duration models. Finally, we conclude that inequality of opportunity represents between 20 and 43% of earnings inequality, but decreases all over the period reaching around 18% in 2001

Formation of Large-Scale Semi-Organized Structures in Turbulent Convection

A new mean-field theory of turbulent convection is developed. This theory predicts the convective wind instability in a shear-free turbulent convection which causes formation of large-scale semi-organized fluid motions in the form of cells or rolls. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection which results in generation of convective shear waves with a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed. This theory can be applied also for the describing a mesogranular turbulent convection in astrophysics.Comment: 16 pages, 10 figures, REVTEX4, PHYSICAL REVIEW E, v. 67, in press (2003

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Search for dark matter in events with heavy quarks and missing transverse momentum in pp collisions with the ATLAS detector

This article reports on a search for dark matterpair production in association with bottom or top quarks in20.3fb−1ofppcollisions collected at√s=8TeVbytheATLAS detector at the LHC. Events with large missing trans-verse momentum are selected when produced in associationwith high-momentum jets of which one or more are identifiedas jets containingb-quarks. Final states with top quarks areselected by requiring a high jet multiplicity and in some casesa single lepton. The data are found to be consistent with theStandard Model expectations and limits are set on the massscale of effective field theories that describe scalar and tensorinteractions between dark matter and Standard Model par-ticles. Limits on the dark-matter–nucleon cross-section forspin-independent and spin-dependent interactions are alsoprovided. These limits are particularly strong for low-massdark matter. Using a simplified model, constraints are set onthe mass of dark matter and of a coloured mediator suitableto explain a possible signal of annihilating dark matter