907 research outputs found

    Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities

    Get PDF
    Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can be expressed in a simple closed form in terms of certain special functions (Dawson's integral and parabolic cylinder functions), and there are qualitative differences depending on whether the number of moments available is even, odd or not an integer, and whether the distributions are symmetric or not. If the increments have an even number of moments, then additional logarithmic corrections must also be incorporated in the expansion parameter. An interesting feature of our correction terms for the CLT is that they become dominant outside the central region and blend naturally with known large-deviation asymptotics when these are applied formally to the spatial scales of the CLT

    Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation

    Full text link
    We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of Fiedler et al. [PRL 98, 114101 (2007)], who demonstrated that such feedback control can stabilize the UPO associated with a two-dimensional subcritical Hopf normal form. Pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization, as well as knowledge of the period of the targeted UPO. We apply feedback in the directions tangent to the two-dimensional center manifold. We parameterize the feedback gain by a modulus and a phase angle, and give explicit formulae for choosing these two parameters given the period of the UPO in a neighborhood of the bifurcation point. We show, first heuristically, and then rigorously by a center manifold reduction for delay differential equations, that the stabilization mechanism involves a highly degenerate Hopf bifurcation problem that is induced by the time-delayed feedback. When the feedback gain modulus reaches a threshold for stabilization, both of the genericity assumptions associated with a two-dimensional Hopf bifurcation are violated: the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied, and the real part of the cubic coefficient of the normal form vanishes. Our analysis of this degenerate bifurcation problem reveals two qualitatively distinct cases when unfolded in a two-parameter plane. In each case, Pyragas-type feedback successfully stabilizes the branch of small-amplitude UPOs in a neighborhood of the original bifurcation point, provided that the phase angle satisfies a certain restriction.Comment: 35 pages, 19 figure

    Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

    Full text link
    We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are τ\tau = 1.21(2) for the avalanche size distribution and DD = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of dBd_B = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent α=DdB\alpha = D - d_B = 0.41(3) and the dynamic exponent z=D(2τ)z = D(2 - \tau) = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields α\alpha = 0.42(3) and zz = 1.5(1) in excellent agreement with those obtained from the scaling relations.Comment: 7 pages, 8 figures, accepted for publication in PR

    Dilepton production in proton-nucleus and nucleus-nucleus collisions at SPS energies

    Get PDF
    Dilepton production in proton- and nucleus-induced reactions is studied in relativistic transport model using initial conditions determined by the string dynamics from RQMD. It is found that both the CERES and HELIOS-3 data for dilepton spectra in proton-nucleus reactions can be well described by the `conventional' mechanism of Dalitz decay and direct vector meson decay. However, to provide a quantitative explanation of the observed dilepton spectra in central S+Au and S+W collisions requires contributions other than these direct decays. Introducing a decrease of vector meson masses in hot and dense medium, we find that these heavy-ion data can also be satisfactorily explained. This agrees with our earlier conclusions based on a fire cylinder model. We also give predictions for Pb+Au collisions at 160 GeV/nucleon using current CERES mass resolution and acceptance.Comment: RevTeX, 45 pages, including 21 postscript figures, to be published in Nuclear Physics

    Meson Cloud of the Nucleon in Polarized Semi-Inclusive Deep-Inelastic Scattering

    Get PDF
    We investigate the possibility of identifying an explicit pionic component of the nucleon through measurements of polarized Δ++\Delta^{++} baryon fragments produced in deep-inelastic leptoproduction off polarized protons, which may help to identify the physical mechanism responsible for the breaking of the Gottfried sum rule. The pion-exchange model predicts highly correlated polarizations of the Δ++\Delta^{++} and target proton, in marked contrast with the competing diquark fragmentation process. Measurement of asymmetries in polarized Λ\Lambda production may also reveal the presence of a kaon cloud in the nucleon.Comment: 23 pages REVTeX, 7 uuencoded figures, accepted for publication in Zeit. Phys.

    Interstellar MHD Turbulence and Star Formation

    Full text link
    This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

    Grain Surface Models and Data for Astrochemistry

    Get PDF
    AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions

    Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

    Get PDF
    The B0B^0-Bˉ0\bar B^0 oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives Δmd=0.493±0.012(stat)±0.009(syst)\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)} ps1^{-1}.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

    Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya

    Get PDF
    Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization
    corecore