WorldWideScience

Sample records for low-mach number diffusion-controlled

  1. Axisymmetric vortex method for low-Mach number, diffusion-controlled combustion

    CERN Document Server

    Lakkis, I

    2003-01-01

    A grid-free, Lagrangian method for the accurate simulation of low-Mach number, variable-density, diffusion-controlled reacting flow is presented. A fast-chemistry model in which the conversion rate of reactants to products is limited by the local mixing rate is assumed in order to reduce the combustion problem to the solution of a convection-diffusion-generation equation with volumetric expansion and vorticity generation at the reaction fronts. The solutions of the continuity and vorticity equations, and the equations governing the transport of species and energy, are obtained using a formulation in which particles transport conserved quantities by convection and diffusion. The dynamic impact of exothermic combustion is captured through accurate integration of source terms in the vorticity transport equations at the location of the particles, and the extra velocity field associated with volumetric expansion at low Mach number computed to enforced mass conservation. The formulation is obtained for an axisymmet...

  2. Improving Euler computations at low Mach numbers

    NARCIS (Netherlands)

    Koren, B.; Leer, van B.; Deconinck, H.; Koren, B.

    1997-01-01

    The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of

  3. Improving Euler computations at low Mach numbers

    NARCIS (Netherlands)

    Koren, B.

    1996-01-01

    This paper consists of two parts, both dealing with conditioning techniques for low-Mach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized linearized 1-D Euler equations, the smoothing behavior of

  4. Aeroacoustic computation of low Mach number flow

    Energy Technology Data Exchange (ETDEWEB)

    Dahl, K.S.

    1996-12-01

    This thesis explores the possibilities of applying a recently developed numerical technique to predict aerodynamically generated sound from wind turbines. The technique is a perturbation technique that has the advantage that the underlying flow field and the sound field are computed separately. Solution of the incompressible, time dependent flow field yields a hydrodynamic density correction to the incompressible constant density. The sound field is calculated from a set of equations governing the inviscid perturbations about the corrected flow field. Here, the emphasis is placed on the computation of the sound field. The nonlinear partial differential equations governing the sound field are solved numerically using an explicit MacCormack scheme. Two types of non-reflecting boundary conditions are applied; one based on the asymptotic solution of the governing equations and the other based on a characteristic analysis of the governing equations. The former condition is easy to use and it performs slightly better than the characteristic based condition. The technique is applied to the problems of the sound generation of a pulsating sphere, which is a monopole; a co-rotating vortex pair, which is a quadrupole, and the viscous flow over a circular cylinder, which is a dipole. The governing equations are written and solved for spherical, Cartesian, and cylindrical coordinates, respectively, thus, representing three common orthogonal coordinate systems. Numerical results agree very well with the analytical solutions for the problems of the pulsating sphere and the co-rotating vortex pair. Numerical results for the viscous flow over a cylinder are presented and evaluated qualitatively. The technique has potential for applications to airfoil flows as they are on a wind turbine blade, as well as for other low Mach number flows. (au) 2 tabs., 33 ills., 48 refs.

  5. Mathematical and numerical aspects of low mach number flows

    Energy Technology Data Exchange (ETDEWEB)

    Schochet, St.; Bresch, D.; Grenier, E.; Alazard, T.; Gordner, A.; Sankaran, V.; Massot, M.; Sery, R.; Pebay, P.; Lunch, O.; Mazhorova, O.; Turkel, O.E.; Faille, I.; Danchin, R.; Allain, O.; Birken, P.; Lafitte, O.; Kloczko, T.; Frick, W.; Bui, T.; Dellacherie, S.; Klein, R.; Roe, Ph.; Accary, G.; Braack, M.; Picano, F.; Cadiou, A.; Dinescu, C.; Lesage, A.C.; Wesseling, P.; Heuveline, V.; Jobelin, M.; Weisman, C.; Merkle, C.

    2004-07-01

    Low Mach number flows represent a significant part of the various flows encountered in geophysics, industry or every day life. Paradoxically, the mathematical analysis of the equations governing these flows is difficult and on the practical side, the research of numerical algorithms valid for all flow speeds is continuing to be a challenge. However, in the last decade, both from the theoretical and the numerical sides, significant progresses were made in the understanding and analysis of the equations governing these flows. This conference intends to provide an up-to-date inventory of recent mathematical and numerical results in the analysis of these flows by bringing together both mathematicians and numericists active in this area. In the framework of the conference, a numerical workshop is organized which proposes to compute several challenging low Mach number flows: liquid flow around non-cavitating and cavitating NACA0015 hydrofoil, natural convection with large temperature differences, free convection, free surface flow, vessel pressurization. This document brings together the descriptions of the test cases of the numerical workshop and the abstracts of the conference papers: A 3D high order finite volume method for the prediction of near-critical fluid flows (G. ACCARY, I. RASPO, P. BONTOUX, B. ZAPPOLI); low Mach number limit of the non-isentropic Navier-Stokes equations (T. ALAZARD); simulation of cavitation rolls past a forward step with a bubble model (O. ALLAIN, N. BLASKA, C. LECA); flux preconditioning methods and fire events (P. BIRKEN, A. MEISTER); an adaptive finite element solver for compressible flows: application to heat-driven cavity benchmarks in 2D and 3D (M. BRAACK); comparison of various implicit, explicit, centered and upwind schemes for the simulation of compressed flows on moving mesh (A. CADIOU, M. BUFFAT, L. Le PENVEN, C. Le RIBAULT); low Mach number limit for viscous compressible flows (R. DANCHIN); some Properties of the low Mach number

  6. Physical and numerical modelling of low mach number compressible flows

    International Nuclear Information System (INIS)

    Paillerre, H.; Clerc, S.; Dabbene, F.; Cueto, O.

    1999-01-01

    This article reviews various physical models that may be used to describe compressible flow at low Mach numbers, as well as the numerical methods developed at DRN to discretize the different systems of equations. A selection of thermal-hydraulic applications illustrate the need to take into account compressibility and multidimensional effects as well as variable flow properties. (authors)

  7. Low-Mach number simulations of transcritical flows

    KAUST Repository

    Lapenna, Pasquale E.

    2018-01-08

    A numerical framework for the direct simulation, in the low-Mach number limit, of reacting and non-reacting transcritical flows is presented. The key feature are an efficient and detailed representation of the real fluid properties and an high-order spatial discretization. The latter is of fundamental importance to correctly resolve the largely non-linear behavior of the fluid in the proximity of the pseudo-boiling. The validity of the low-Mach number assumptions is assessed for a previously developed non-reacting DNS database of transcritical and supercritical mixing. Fully resolved DNS data employing high-fidelity thermodynamical models are also used to investigate the spectral characteristic as well as the differences between transcritical and supercritical jets.

  8. Low Mach number asymptotics for reacting compressible fluid flows

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Petzeltová, Hana

    2010-01-01

    Roč. 26, č. 2 (2010), s. 455-480 ISSN 1078-0947 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : low Mach number * Navier-Stokes-Fourier system * reacting fluids Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4660

  9. Low Mach number limits of compressible rotating fluids

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2012-01-01

    Roč. 14, č. 1 (2012), s. 61-78 ISSN 1422-6928 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : low Mach number limit * rotating fluid * compressible fluid Subject RIV: BA - General Mathematics Impact factor: 1.415, year: 2012 http://www.springerlink.com/content/635r1116j40t6428/

  10. Numerical simulation of low Mach number reacting flows

    International Nuclear Information System (INIS)

    Bell, J B; Aspden, A J; Day, M S; Lijewski, M J

    2007-01-01

    Using examples from active research areas in combustion and astrophysics, we demonstrate a computationally efficient numerical approach for simulating multiscale low Mach number reacting flows. The method enables simulations that incorporate an unprecedented range of temporal and spatial scales, while at the same time, allows an extremely high degree of reaction fidelity. Sample applications demonstrate the efficiency of the approach with respect to a traditional time-explicit integration method, and the utility of the methodology for studying the interaction of turbulence with terrestrial and astrophysical flame structures

  11. Derivation of the low Mach number diphasic system. Numerical simulation in mono-dimensional geometry

    International Nuclear Information System (INIS)

    Dellacherie, St.

    2004-01-01

    This work deals with the derivation of a diphasic low Mach number model obtained through a Mach number asymptotic expansion applied to the compressible diphasic Navier Stokes system, expansion which filters out the acoustic waves. This approach is inspired from the work of Andrew Majda giving the equations of low Mach number combustion for thin flame and for perfect gases. When the equations of state verify some thermodynamic hypothesis, we show that the low Mach number diphasic system predicts in a good way the dilatation or the compression of a bubble and has equilibrium convergence properties. Then, we propose an entropic and convergent Lagrangian scheme in mono-dimensional geometry when the fluids are perfect gases and we propose a first approach in Eulerian variables where the interface between the two fluids is captured with a level set technique. (author)

  12. Applicability of higher-order TVD method to low mach number compressible flows

    International Nuclear Information System (INIS)

    Akamatsu, Mikio

    1995-01-01

    Steep gradients of fluid density are the influential factor of spurious oscillation in numerical solutions of low Mach number (M<<1) compressible flows. The total variation diminishing (TVD) scheme is a promising remedy to overcome this problem and obtain accurate solutions. TVD schemes for high-speed flows are, however, not compatible with commonly used methods in low Mach number flows using pressure-based formulation. In the present study a higher-order TVD scheme is constructed on a modified form of each individual scalar equation of primitive variables. It is thus clarified that the concept of TVD is applicable to low Mach number flows within the framework of the existing numerical method. Results of test problems of the moving interface of two-component gases with the density ratio ≥ 4, demonstrate the accurate and robust (wiggle-free) profile of the scheme. (author)

  13. Numerical simulation of unsteady compressible low Mach number flow in a channel

    Czech Academy of Sciences Publication Activity Database

    Punčochářová-Pořízková, P.; Kozel, Karel; Horáček, Jaromír; Fürst, J.

    2010-01-01

    Roč. 17, č. 2 (2010), s. 83-97 ISSN 1802-1484 R&D Projects: GA MŠk OC09019 Institutional research plan: CEZ:AV0Z20760514 Keywords : CFD * finite volume method * unsteady flow * low Mach number Subject RIV: BI - Acoustics

  14. Background-oriented schlieren imaging of flow around a circular cylinder at low Mach numbers

    Science.gov (United States)

    Stadler, Hannes; Bauknecht, André; Siegrist, Silvan; Flesch, Robert; Wolf, C. Christian; van Hinsberg, Nils; Jacobs, Markus

    2017-09-01

    The background-oriented schlieren (BOS) imaging method has, for the first time, been applied in the investigation of the flow around a circular cylinder at low Mach numbers (Msuccessive imaging at incremental angular positions around the cylinder. This density distribution has been found to agree well with the pressure measurements and with potential theory where appropriate.

  15. Study and discretization of kinetic models and fluid models at low Mach number

    International Nuclear Information System (INIS)

    Dellacherie, Stephane

    2011-01-01

    This thesis summarizes our work between 1995 and 2010. It concerns the analysis and the discretization of Fokker-Planck or semi-classical Boltzmann kinetic models and of Euler or Navier-Stokes fluid models at low Mach number. The studied Fokker-Planck equation models the collisions between ions and electrons in a hot plasma, and is here applied to the inertial confinement fusion. The studied semi-classical Boltzmann equations are of two types. The first one models the thermonuclear reaction between a deuterium ion and a tritium ion producing an α particle and a neutron particle, and is also in our case used to describe inertial confinement fusion. The second one (known as the Wang-Chang and Uhlenbeck equations) models the transitions between electronic quantified energy levels of uranium and iron atoms in the AVLIS isotopic separation process. The basic properties of these two Boltzmann equations are studied, and, for the Wang-Chang and Uhlenbeck equations, a kinetic-fluid coupling algorithm is proposed. This kinetic-fluid coupling algorithm incited us to study the relaxation concept for gas and immiscible fluids mixtures, and to underline connections with classical kinetic theory. Then, a diphasic low Mach number model without acoustic waves is proposed to model the deformation of the interface between two immiscible fluids induced by high heat transfers at low Mach number. In order to increase the accuracy of the results without increasing computational cost, an AMR algorithm is studied on a simplified interface deformation model. These low Mach number studies also incited us to analyse on cartesian meshes the inaccuracy at low Mach number of Godunov schemes. Finally, the LBM algorithm applied to the heat equation is justified

  16. Turbulent mixing of a slightly supercritical van der Waals fluid at low-Mach number

    International Nuclear Information System (INIS)

    Battista, F.; Casciola, C. M.; Picano, F.

    2014-01-01

    Supercritical fluids near the critical point are characterized by liquid-like densities and gas-like transport properties. These features are purposely exploited in different contexts ranging from natural products extraction/fractionation to aerospace propulsion. Large part of studies concerns this last context, focusing on the dynamics of supercritical fluids at high Mach number where compressibility and thermodynamics strictly interact. Despite the widespread use also at low Mach number, the turbulent mixing properties of slightly supercritical fluids have still not investigated in detail in this regime. This topic is addressed here by dealing with Direct Numerical Simulations of a coaxial jet of a slightly supercritical van der Waals fluid. Since acoustic effects are irrelevant in the low Mach number conditions found in many industrial applications, the numerical model is based on a suitable low-Mach number expansion of the governing equation. According to experimental observations, the weakly supercritical regime is characterized by the formation of finger-like structures – the so-called ligaments – in the shear layers separating the two streams. The mechanism of ligament formation at vanishing Mach number is extracted from the simulations and a detailed statistical characterization is provided. Ligaments always form whenever a high density contrast occurs, independently of real or perfect gas behaviors. The difference between real and perfect gas conditions is found in the ligament small-scale structure. More intense density gradients and thinner interfaces characterize the near critical fluid in comparison with the smoother behavior of the perfect gas. A phenomenological interpretation is here provided on the basis of the real gas thermodynamics properties

  17. Turbulent mixing of a slightly supercritical van der Waals fluid at low-Mach number

    Energy Technology Data Exchange (ETDEWEB)

    Battista, F.; Casciola, C. M. [Department of Mechanical and Aerospace Engineering, Sapienza University, via Eudossiana 18, 00184 Rome (Italy); Picano, F. [Department of Industrial Engineering, University of Padova, via Venezia 1, 35131 Padova (Italy)

    2014-05-15

    Supercritical fluids near the critical point are characterized by liquid-like densities and gas-like transport properties. These features are purposely exploited in different contexts ranging from natural products extraction/fractionation to aerospace propulsion. Large part of studies concerns this last context, focusing on the dynamics of supercritical fluids at high Mach number where compressibility and thermodynamics strictly interact. Despite the widespread use also at low Mach number, the turbulent mixing properties of slightly supercritical fluids have still not investigated in detail in this regime. This topic is addressed here by dealing with Direct Numerical Simulations of a coaxial jet of a slightly supercritical van der Waals fluid. Since acoustic effects are irrelevant in the low Mach number conditions found in many industrial applications, the numerical model is based on a suitable low-Mach number expansion of the governing equation. According to experimental observations, the weakly supercritical regime is characterized by the formation of finger-like structures – the so-called ligaments – in the shear layers separating the two streams. The mechanism of ligament formation at vanishing Mach number is extracted from the simulations and a detailed statistical characterization is provided. Ligaments always form whenever a high density contrast occurs, independently of real or perfect gas behaviors. The difference between real and perfect gas conditions is found in the ligament small-scale structure. More intense density gradients and thinner interfaces characterize the near critical fluid in comparison with the smoother behavior of the perfect gas. A phenomenological interpretation is here provided on the basis of the real gas thermodynamics properties.

  18. Acoustic-hydrodynamic-flame coupling—A new perspective for zero and low Mach number flows

    Science.gov (United States)

    Pulikkottil, V. V.; Sujith, R. I.

    2017-04-01

    A combustion chamber has a hydrodynamic field that convects the incoming fuel and oxidizer into the chamber, thereby causing the mixture to react and produce heat energy. This heat energy can, in turn, modify the hydrodynamic and acoustic fields by acting as a source and thereby, establish a positive feedback loop. Subsequent growth in the amplitude of the acoustic field variables and their eventual saturation to a limit cycle is generally known as thermo-acoustic instability. Mathematical representation of these phenomena, by a set of equations, is the subject of this paper. In contrast to the ad hoc models, an explanation of the flame-acoustic-hydrodynamic coupling, based on fundamental laws of conservation of mass, momentum, and energy, is presented in this paper. In this paper, we use a convection reaction diffusion equation, which, in turn, is derived from the fundamental laws of conservation to explain the flame-acoustic coupling. The advantage of this approach is that the physical variables such as hydrodynamic velocity and heat release rate are coupled based on the conservation of energy and not based on an ad hoc model. Our approach shows that the acoustic-hydrodynamic interaction arises from the convection of acoustic velocity fluctuations by the hydrodynamic field and vice versa. This is a linear mechanism, mathematically represented as a convection operator. This mechanism resembles the non-normal mechanism studied in hydrodynamic theory. We propose that this mechanism could relate the instability mechanisms of hydrodynamic and thermo-acoustic systems. Furthermore, the acoustic-hydrodynamic interaction is shown to be responsible for the convection of entropy disturbances from the inlet of the chamber. The theory proposed in this paper also unifies the observations in the fields of low Mach number flows and zero Mach number flows. In contrast to the previous findings, where compressibility is shown to be causing different physics for zero and low Mach

  19. Low Mach-number collisionless electrostatic shocks and associated ion acceleration

    Science.gov (United States)

    Pusztai, I.; TenBarge, J. M.; Csapó, A. N.; Juno, J.; Hakim, A.; Yi, L.; Fülöp, T.

    2018-03-01

    The existence and properties of low Mach-number (M≳ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model, we study the effect of the electron-to-ion temperature ratio and the presence of impurities on both the maximum shock potential and the Mach number. We find that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.

  20. Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Ke; Naguib, Ahmed M. [Michigan State University, East Lansing, MI (United States)

    2011-11-15

    The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity's side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity. (orig.)

  1. Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers

    Science.gov (United States)

    Grabbe, Crockett L.; Cairns, Iver H.

    1995-01-01

    A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a

  2. Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations

    International Nuclear Information System (INIS)

    Xu Kun; He Xiaoyi

    2003-01-01

    Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented

  3. Numerical resolution of the Navier-Stokes equations for a low Mach number by a spectral method

    International Nuclear Information System (INIS)

    Frohlich, Jochen

    1990-01-01

    The low Mach number approximation of the Navier-Stokes equations, also called isobar, is an approximation which is less restrictive than the one due to Boussinesq. It permits strong density variations while neglecting acoustic phenomena. We present a numerical method to solve these equations in the unsteady, two dimensional case with one direction of periodicity. The discretization uses a semi-implicit finite difference scheme in time and a Fourier-Chebycheff pseudo-spectral method in space. The solution of the equations of motion is based on an iterative algorithm of Uzawa type. In the Boussinesq limit we obtain a direct method. A first application is concerned with natural convection in the Rayleigh-Benard setting. We compare the results of the low Mach number equations with the ones in the Boussinesq case and consider the influence of variable fluid properties. A linear stability analysis based on a Chebychev-Tau method completes the study. The second application that we treat is a case of isobaric combustion in an open domain. We communicate results for the hydrodynamic Darrieus-Landau instability of a plane laminar flame front. [fr

  4. Impact of Shock Front Rippling and Self-reformation on the Electron Dynamics at Low-Mach-number Shocks

    Science.gov (United States)

    Yang, Zhongwei; Lu, Quanming; Liu, Ying D.; Wang, Rui

    2018-04-01

    Electron dynamics at low-Mach-number collisionless shocks are investigated by using two-dimensional electromagnetic particle-in-cell simulations with various shock normal angles. We found: (1) The reflected ions and incident electrons at the shock front provide an effective mechanism for the quasi-electrostatic wave generation due to the charge-separation. A fraction of incident electrons can be effectively trapped and accelerated at the leading edge of the shock foot. (2) At quasi-perpendicular shocks, the electron trapping and reflection is nonuniform due to the shock rippling along the shock surface and is more likely to take place at some locations accompanied by intense reflected ion-beams. The electron trapping process has a periodical evolution over time due to the shock front self-reformation, which is controlled by ion dynamics. Thus, this is a cross-scale coupling phenomenon. (3) At quasi-parallel shocks, reflected ions can travel far back upstream. Consequently, quasi-electrostatic waves can be excited in the shock transition and the foreshock region. The electron trajectory analysis shows these waves can trap electrons at the foot region and reflect a fraction of them far back upstream. Simulation runs in this paper indicate that the micro-turbulence at the shock foot can provide a possible scenario for producing the reflected electron beam, which is a basic condition for the type II radio burst emission at low-Mach-number interplanetary shocks driven by Coronal Mass Ejections (CMEs).

  5. A combined volume-of-fluid method and low-Mach-number approach for DNS of evaporating droplets in turbulence

    Science.gov (United States)

    Dodd, Michael; Ferrante, Antonino

    2017-11-01

    Our objective is to perform DNS of finite-size droplets that are evaporating in isotropic turbulence. This requires fully resolving the process of momentum, heat, and mass transfer between the droplets and surrounding gas. We developed a combined volume-of-fluid (VOF) method and low-Mach-number approach to simulate this flow. The two main novelties of the method are: (i) the VOF algorithm captures the motion of the liquid gas interface in the presence of mass transfer due to evaporation and condensation without requiring a projection step for the liquid velocity, and (ii) the low-Mach-number approach allows for local volume changes caused by phase change while the total volume of the liquid-gas system is constant. The method is verified against an analytical solution for a Stefan flow problem, and the D2 law is verified for a single droplet in quiescent gas. We also demonstrate the schemes robustness when performing DNS of an evaporating droplet in forced isotropic turbulence.

  6. Derivation of the low Mach number diphasic system. Numerical simulation in mono-dimensional geometry; Derivation du systeme diphasique bas Mach. Simulation numerique en geometrie monodimensionnelle

    Energy Technology Data Exchange (ETDEWEB)

    Dellacherie, St

    2004-07-01

    This work deals with the derivation of a diphasic low Mach number model obtained through a Mach number asymptotic expansion applied to the compressible diphasic Navier Stokes system, expansion which filters out the acoustic waves. This approach is inspired from the work of Andrew Majda giving the equations of low Mach number combustion for thin flame and for perfect gases. When the equations of state verify some thermodynamic hypothesis, we show that the low Mach number diphasic system predicts in a good way the dilatation or the compression of a bubble and has equilibrium convergence properties. Then, we propose an entropic and convergent Lagrangian scheme in mono-dimensional geometry when the fluids are perfect gases and we propose a first approach in Eulerian variables where the interface between the two fluids is captured with a level set technique. (author)

  7. Low Mach and Peclet number limit for a model of stellar tachocline and upper radiative zones

    Directory of Open Access Journals (Sweden)

    Donatella Donatelli

    2016-09-01

    Full Text Available We study a hydrodynamical model describing the motion of internal stellar layers based on compressible Navier-Stokes-Fourier-Poisson system. We suppose that the medium is electrically charged, we include energy exchanges through radiative transfer and we assume that the system is rotating. We analyze the singular limit of this system when the Mach number, the Alfven number, the Peclet number and the Froude number approache zero in a certain way and prove convergence to a 3D incompressible MHD system with a stationary linear transport equation for transport of radiation intensity. Finally, we show that the energy equation reduces to a steady equation for the temperature corrector.

  8. Practical computational aeroacoustics for compact surfaces in low mach number flows

    DEFF Research Database (Denmark)

    Pradera-Mallabiabarrena, Ainara; Keith, Graeme; Jacobsen, Finn

    2011-01-01

    compared to the wavelength of interest. This makes it possible to focus on the surface source term of the Ffowcs Williams-Hawkings equation. In this paper, in order to illustrate the basic method for storing and utilizing data from the CFD analysis, the flow past a circular cylinder at a Reynolds number...

  9. Low Mach number analysis of idealized thermoacoustic engines with numerical solution.

    Science.gov (United States)

    Hireche, Omar; Weisman, Catherine; Baltean-Carlès, Diana; Le Quéré, Patrick; Bauwens, Luc

    2010-12-01

    A model of an idealized thermoacoustic engine is formulated, coupling nonlinear flow and heat exchange in the heat exchangers and stack with a simple linear acoustic model of the resonator and load. Correct coupling results in an asymptotically consistent global model, in the small Mach number approximation. A well-resolved numerical solution is obtained for two-dimensional heat exchangers and stack. The model assumes that the heat exchangers and stack are shorter than the overall length by a factor of the order of a representative Mach number. The model is well-suited for simulation of the entire startup process, whereby as a result of some excitation, an initially specified temperature profile in the stack evolves toward a near-steady profile, eventually reaching stationary operation. A validation analysis is presented, together with results showing the early amplitude growth and approach of a stationary regime. Two types of initial excitation are used: Random noise and a small periodic wave. The set of assumptions made leads to a heat-exchanger section that acts as a source of volume but is transparent to pressure and to a local heat-exchanger model characterized by a dynamically incompressible flow to which a locally spatially uniform acoustic pressure fluctuation is superimposed.

  10. Plasma wave profiles of Earth's bow shock at low Mach number: ISEE 3 observations on the far flank

    International Nuclear Information System (INIS)

    Greenstadt, E.W.; Coroniti, F.V.; Moses, S.L.; Smith, E.J.

    1992-01-01

    The Earth's bow shock is weak along its distant flanks where the projected component of solar wind velocity normal to the hyperboloidal surface is only a fraction of the total free stream velocity, severely reducing the local Mach number. The authors present a survey of selected crossings far downstream from the subsolar shock, delineating the overall plasma wave (pw) behavior of a selected set of nearly perpendicular crossings and another set of limited Mach number but broad geometry; they include their immediate upstream regions. The result is a generalizable pw signature, or signatures, of low Mach number shocks and some likely implications of those signatures for the weak shock's plasma physical processes on the flank. They find the data consistent with the presence of ion beam interactions producing noise ahead of the shock in the ion acoustic frequency range. One subcritical case was found whose pw noise was presumably related to a reflected ion population just as in stronger events. The presence or absence, and the amplitudes, of pw activity are explainable by the presence or absence of a population of upstream ions controlled by the component of interplanetary magnetic field normal to the solar wind flow

  11. Measurement and analysis of the noise radiated by low Mach numbers centrifugal blowers

    Science.gov (United States)

    Yeager, D. M.; Lauchle, G. C.

    1987-11-01

    The broad band, aerodynamically generated noise in low tip-speed Mach number, centrifugal air moving devices is investigated. An interdisciplinary approach was taken which involved investigation of the aerodynamic and acoustic fields, and their mutual relationship. The noise generation process was studied using two experimental vehicles: (1) a scale model of a homologous family of centrifugal blowers typical of those used to cool computer and business equipment, and (2) a single blade from a centrifugal blower impeller which was placed in a known, controllable flow field. The radiation characteristics of the model blower were investigated by measuring the acoustic intensity distribution near the blower inlet and comparing it with the intensity near the inlet to an axial flow fan. Aerodynamic studies of the flow field in the inlet and at the discharge to the rotating impeller were used to assess the mean flow distribution through the impeller blade channels and to identify regions of excessive turbulence near the rotating blade row. New frequency-domain expressions for the correlation area and dipole source strength per unit area on a surface immersed in turbulence were developed which can be used to characterize the noise generation process over a rigid surface immersed in turbulence. An investigation of the noise radiated from the single, isolated airfoil (impeller blade) was performed using modern correlation and spectral analysis techniques.

  12. Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

    Science.gov (United States)

    Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

    2008-02-01

    We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald

  13. Measurement and Analysis of the Noise Radiated by Low Mach Number Centrifugal Blowers.

    Science.gov (United States)

    Yeager, David Marvin

    An investigation was performed of the broad band, aerodynamically generated noise in low tip-speed Mach number, centrifugal air moving devices. An interdisciplinary experimental approach was taken which involved investigation of the aerodynamic and acoustic fields, and their mutual relationship. The noise generation process was studied using two experimental vehicles: (1) a scale model of a homologous family of centrifugal blowers typical of those used to cool computer and business equipment, and (2) a single blade from a centrifugal blower impeller placed in a known, controllable flow field. The radiation characteristics of the model blower were investigated by measuring the acoustic intensity distribution near the blower inlet and comparing it with the intensity near the inlet to an axial flow fan. Results showed that the centrifugal blower is a distributed, random noise source, unlike an axial fan which exhibited the effects of a coherent, interacting source distribution. Aerodynamic studies of the flow field in the inlet and at the discharge to the rotating impeller were used to assess the mean flow distribution through the impeller blade channels and to identify regions of excessive turbulence near the rotating blade row. Both circumferential and spanwise mean flow nonuniformities were identified along with a region of increased turbulence just downstream of the scroll cutoff. The fluid incidence angle, normally taken as an indicator of blower performance, was estimated from mean flow data as deviating considerably from an ideal impeller design. An investigation of the noise radiated from the single, isolated airfoil was performed using modern correlation and spectral analysis techniques. Radiation from the single blade in flow was characterized using newly developed expressions for the correlation area and the dipole source strength per unit area, and from the relationship between the blade surface pressure and the incident turbulent flow field. Results

  14. A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

    Science.gov (United States)

    Nonaka, Andrew; Day, Marcus S.; Bell, John B.

    2018-01-01

    We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

  15. Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

    Science.gov (United States)

    MacArt, Jonathan F.; Mueller, Michael E.

    2016-12-01

    Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

  16. CFD simulation with Code-Saturne of the light gas stratification erosion by a vertical air gas injection using a Low Mach number algorithm

    International Nuclear Information System (INIS)

    Hou Bingxu; Yu Jiyang; Senechal, Dorothee; Mechitoua, Namane; Min Jiesheng; Chen Guofei

    2015-01-01

    During CFD simulations of the flows at low Mach number regime, the classical assumption which neglects the dilatable effect of gas is no longer applicable when the temperature variation or the concentration variation of the mixture's components is too large in the fluid domain. To be able to correctly predict the flow at such a regime, some authors have recourse to a Low Mach number algorithm. This algorithm is based on the well-known pressure-based algorithm or elliptic solver for incompressible flows, SIMPLE, with a modification for the treatment of the pressure which is split into two parts (the hydrodynamic pressure and the thermodynamic pressure) and a dilatable term added in the mass equation. This algorithm has been implemented in the CFD code, Code_—Saturne, developed by EDF R and D, and applied for the CFD simulations of the erosion phenomena of light gas stratification by air injection. This paper is devoted to the analytical work with the Low Mach number algorithm based on the ST1 series of the SETH-2 campaign provided by the OECD project on the PANDA test facility of PSI. The first part is focused on a mesh sensitivity analysis, which is a common procedure for CFD codes validation. The second part of the paper presents a comparison between the CFD results obtained with the standard algorithms used for incompressible flows and the Low Mach number algorithm. The third part is an analysis of the CFD results obtained on the reference mesh with both different Froude numbers corresponding to the tests ST1_—7 (Fr=6.04) and ST1_—10 (Fr=7.95) from the ST1 series. In the last part the authors perform the knowledge of the initial light gas distribution effect on the stratification erosion and the capability of the CFD codes to predict this phenomenon with an area governed by diffusion regime (at the top of the vessel) and another one by forced convection near the injection. (author)

  17. Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Xinyi; Narayan, Ramesh [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Sironi, Lorenzo [NASA Einstein Postdoctoral Fellow. (United States)

    2014-12-10

    Electron acceleration to non-thermal energies is known to occur in low Mach number (M{sub s} ≲ 5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M{sub s} = 3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (≳ 20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

  18. LOW MACH NUMBER MODELING OF CONVECTION IN HELIUM SHELLS ON SUB-CHANDRASEKHAR WHITE DWARFS. II. BULK PROPERTIES OF SIMPLE MODELS

    Energy Technology Data Exchange (ETDEWEB)

    Jacobs, A. M.; Zingale, M. [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Nonaka, A.; Almgren, A. S.; Bell, J. B. [Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)

    2016-08-10

    The dynamics of helium shell convection driven by nuclear burning establish the conditions for runaway in the sub-Chandrasekhar-mass, double-detonation model for SNe Ia, as well as for a variety of other explosive phenomena. We explore these convection dynamics for a range of white dwarf core and helium shell masses in three dimensions using the low Mach number hydrodynamics code MAESTRO. We present calculations of the bulk properties of this evolution, including time-series evolution of global diagnostics, lateral averages of the 3D state, and the global 3D state. We find a variety of outcomes, including quasi-equilibrium, localized runaway, and convective runaway. Our results suggest that the double-detonation progenitor model is promising and that 3D dynamic convection plays a key role.

  19. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

    International Nuclear Information System (INIS)

    Ansanay-Alex, G.

    2009-01-01

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  20. An improved method to experimentally determine temperature and pressure behind laser-induced shock waves at low Mach numbers

    International Nuclear Information System (INIS)

    Hendijanifard, Mohammad; Willis, David A

    2011-01-01

    Laser-matter interactions are frequently studied by measuring the propagation of shock waves caused by the rapid laser-induced material removal. An improved method for calculating the thermo-fluid parameters behind shock waves is introduced in this work. Shock waves in ambient air, induced by pulsed Nd : YAG laser ablation of aluminium films, are measured using a shadowgraph apparatus. Normal shock solutions are applied to experimental data for shock wave positions and used to calculate pressure, temperature, and velocity behind the shock wave. Non-dimensionalizing the pressure and temperature with respect to the ambient values, the dimensionless pressure and temperature are estimated to be as high as 90 and 16, respectively, at a time of 10 ns after the ablation pulse for a laser fluence of F = 14.5 J cm -2 . The results of the normal shock solution and the Taylor-Sedov similarity solution are compared to show that the Taylor-Sedov solution under-predicts pressure when the Mach number of the shock wave is small. At a fluence of 3.1 J cm -2 , the shock wave Mach number is less than 3, and the Taylor-Sedov solution under-predicts the non-dimensional pressure by as much as 45%.

  1. Aeroacoustic computation of low mach number flow

    Energy Technology Data Exchange (ETDEWEB)

    Skriver Dahl, K. [Risoe National Laboratory, Roskilde (Denmark)

    1997-12-31

    The possibilities of applying a recently developed numerical technique to predict aerodynamically generated sound from wind turbines is explored. The technique is a perturbation technique that has the advantage that the underlying flow field and the sound field are computed separately. Solution of the incompressible, time dependent flow field yields a hydrodynamic density correction to the incompressible constant density. The sound field is calculated from a set of equations governing the inviscid perturbations about the corrected flow field. Here, the emphasis is placed on the computation of the sound field. The nonlinear partial differential equations governing the sound fields are solved numerically using an explicit MacCormack scheme. Two types of non-reflecting boundary conditions are applied; one based on the asymptotic solution of the governing equations and the other based on a characteristic analysis of the governing equations. The former condition is easy to use and it performs slightly better than the charcteristic based condition. The technique is applied to the problems of the sound generation of a co-rotating vortex pair, which is a quadrupole, and the viscous flow over a circular cylinder, which is a dipole. Numerical results agree very well with the analytical solution for the problem of the co-rotating vortex pair. Numerical results for the viscous flow over a cylinder are presented and evaluated qualitatively. (au)

  2. Adaptive multilevel mesh refinement method for the solution of low Mach number reactive flows; Methode adaptative de raffinement local multi-niveaux pour le calcul d'ecoulements reactifs a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Core, X.

    2002-02-01

    The isobar approximation for the system of the balance equations of mass, momentum, energy and chemical species is a suitable approximation to represent low Mach number reactive flows. In this approximation, which neglects acoustics phenomena, the mixture is hydrodynamically incompressible and the thermodynamic effects lead to an uniform compression of the system. We present a novel numerical scheme for this approximation. An incremental projection method, which uses the original form of mass balance equation, discretizes in time the Navier-Stokes equations. Spatial discretization is achieved through a finite volume approach on MAC-type staggered mesh. A higher order de-centered scheme is used to compute the convective fluxes. We associate to this discretization a local mesh refinement method, based on Flux Interface Correction technique. A first application concerns a forced flow with variable density which mimics a combustion problem. The second application is natural convection with first small temperature variations and then beyond the limit of validity of the Boussinesq approximation. Finally, we treat a third application which is a laminar diffusion flame. For each of these test problems, we demonstrate the robustness of the proposed numerical scheme, notably for the density spatial variations. We analyze the gain in accuracy obtained with the local mesh refinement method. (author)

  3. High-resolution flow field measurements in the rotor passage of a low-mach number turbine for different tip geometries; Hochaufgeloeste Stroemungsfeldvermessungen in der Rotorpassage einer Niedermachzahlturbine fuer verschiedene Schaufelspitzengeometrien

    Energy Technology Data Exchange (ETDEWEB)

    Kegalj, Martin

    2013-11-01

    In axial turbines tip leakage forms a large portion of the overall losses. Applying a shroud is very aerodynamically useful, but the higher mechanical loads of the revolving rotor blading exposed to a high thermal load and the higher costs suggest a shroudless configuration is better. The main parameter in the tip leakage loss is the tip gap height, which cannot be reduced arbitrarily as a running gap is necessary due to thermal expansion and vibration of the jet engine. The pressure ratio between pressure and suction of the rotor blade forces the fluid over the blade tip and leads to the formation of the tip leakage vortex. Reduced turning and losses caused by vortices and subsequent mixing are responsible for the reduced efficiency. Using a squealer cavity on the flat blade tip is a feasible way to reduce the aerodynamic losses. A portion of the kinetic energy of the tip leakage flow is dissipated while entering the cavity; the flow exiting the cavity enters the passage with reduced momentum and reduced tip gap mass flow. A 1(1)/(2) stage low mach number turbine was used to investigate the influence of tip geometry. Aerodynamic measurements, performed with five-hole probes, two-component hot-wire anemometer, unsteady wall pressure sensors, stereo and borescopic particle-image-velocimetry setups and oil and dye flow visualization, found small differences in the flow velocities and angles between the flat and squealer tip configuration in the measurement planes downstream of the rotor. The measurement uncertainty proves the difficulty of determining the influence of the squealer cavity on the blade row outflow with global measurement data. To gather information on the flow close to the casing inside the rotor passage is only possible with non-intrusive laser measurement techniques. Comparison of the different tip geometries is still difficult due to the small differences in the absolute flow data. The use of the {lambda}{sub 2} vortex criterion enables an objective

  4. Entropy-based viscous regularization for the multi-dimensional Euler equations in low-Mach and transonic flows

    Energy Technology Data Exchange (ETDEWEB)

    Marc O Delchini; Jean E. Ragusa; Ray A. Berry

    2015-07-01

    We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging–diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.

  5. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Ansanay-Alex, G.

    2009-06-17

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  6. Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes

    Science.gov (United States)

    Zhang, Yong; Green, Christopher T.; Tick, Geoffrey R.

    2015-01-01

    This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer–aquitard complexes.

  7. Low Mach number limit for a model of accretion disk

    Czech Academy of Sciences Publication Activity Database

    Donatelli, D.; Ducomet, B.; Nečasová, Šárka

    2018-01-01

    Roč. 38, č. 7 (2018), s. 3239-3268 ISSN 1078-0947 R&D Projects: GA ČR GA13-00522S; GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier-Poisson system * magnetohydrodynamics * radiating transfer Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.099, year: 2016 http://aimsciences.org/article/doi/10.3934/dcds.2018141

  8. Low Mach number limit for a model of accretion disk

    Czech Academy of Sciences Publication Activity Database

    Donatelli, D.; Ducomet, B.; Nečasová, Šárka

    2018-01-01

    Roč. 38, č. 7 (2018), s. 3239-3268 ISSN 1078-0947 R&D Projects: GA ČR GA13-00522S; GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier-Poisson system * magnetohydrodynamics * radiating transfer Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.099, year: 2016 http://aimsciences.org/ article /doi/10.3934/dcds.2018141

  9. Miscellaneous: Various Low-Mach-Number Fluid Problems and Motions

    Science.gov (United States)

    Zeytounian, Radyadour Kh.

    In this last chapter, we consider, first, in Sect. 7.1, mainly the asymptotic derivation of the KZK equation of nonlinear acoustics, which generalizes the well-known Burgers' unsteady one-dimensional dissipative model equation (Burgers 1948) to an equation with a diffraction and parabolic effect.

  10. Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

    Science.gov (United States)

    Liu, Yechi

    2018-06-01

    The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier-Stokes system also has the same phenomenon when Mach number is suitably small.

  11. An implicit turbulence model for low-Mach Roe scheme using truncated Navier-Stokes equations

    Science.gov (United States)

    Li, Chung-Gang; Tsubokura, Makoto

    2017-09-01

    The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Reτ = 180 show that, with the 'low-Mach-fix for Roe' (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263-5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier-Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor-Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Reτ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Reτ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor-Green vortex at Re = 3000, the kinetic energy is consistent with the power law of decaying turbulence with -1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

  12. A finite element method with a high order L{sup 2} decomposition devoted to the simulation of diphasic low Mach number flows; Une methode elements finis a decomposition L{sup 2} d'ordre eleve motivee par la simulation d'ecoulement diphasique bas mach

    Energy Technology Data Exchange (ETDEWEB)

    Fortin, T

    2006-05-15

    This work deals with the discretization of Navier-Stokes equations using different finite element methods adapted to the problem of two-phase flows. These methods must be of high order to limit the presence of spurious flows (which contradict the establishment of a physical equilibrium) and to verify energy conservation properties. Several solutions are proposed which seem to fulfill these expectations. A reformulation of the six-equation system adapted to low Mach two-phase flows has been also proposed. These methods have been implemented into the Trio-U code of CEA Grenoble, but have been tested only on simple 'academic' configurations. (J.S.)

  13. Calibration of the 7—Equation Transition Model for High Reynolds Flows at Low Mach

    Science.gov (United States)

    Colonia, S.; Leble, V.; Steijl, R.; Barakos, G.

    2016-09-01

    The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients that need tuning. In this paper, the γ—equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. An aerofoil is used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solutions for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected.

  14. Stability with respect to domain of the low Mach number limit of compressible viscous fluids

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Karper, T.; Kreml, Ondřej; Stebel, Jan

    2013-01-01

    Roč. 23, č. 13 (2013), s. 2465-2493 ISSN 0218-2025 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : incompressible limit * domain dependence * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.351, year: 2013 http://www.worldscientific.com/doi/abs/10.1142/S0218202513500371

  15. On the low Mach number limit of compressible flows in exterior moving domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Kreml, Ondřej; Mácha, Václav; Nečasová, Šárka

    2016-01-01

    Roč. 16, č. 3 (2016), s. 705-722 ISSN 1424-3199 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * incompressible limit * moving domain Subject RIV: BA - General Mathematics Impact factor: 1.038, year: 2016 http://link.springer.com/article/10.1007%2Fs00028-016-0338-2

  16. Practical computational aeroacoustics for complex confined scattering geometries in low mach number flows

    DEFF Research Database (Denmark)

    Pradera-Mallabiabarrena, Ainara; Jacobsen, Finn; Svendsen, Christian

    2013-01-01

    -compact surfaces are involved. Here the generation of noise is dominated by the interaction of the flow with a surface whose maximum dimension is shorter than the wavelength of interest. The analysis is based on the surface-source term of the Ffowcs Williams-Hawkings equation. The acoustic source data of the flow...

  17. Measurement and Analysis of the Noise Radiated by Low Mach Numbers Centrifugal Blowers

    Science.gov (United States)

    1987-11-01

    Lang, V Manager of the IBM Poughkeepsie Acoustics Laboratory, for his understanding and support. I would also like to express my gratitude to the IBM...ficl.l. Knowlede p of these quantities provides important information on the relative strength of thL :cro- a dynamic noise sources on the blade... manageability . The model blower design was thus determined by scaling all of the linear dimensions of the reference device by 2.0 and by maintaining • all of

  18. Low Mach and Peclet number limit for a model of stellar tachocline and upper radiative zones

    Czech Academy of Sciences Publication Activity Database

    Donatelli, D.; Ducomet, B.; Kobera, M.; Nečasová, Šárka

    2016-01-01

    Roč. 2016, Č. 245 (2016), s. 1-31 ISSN 1072-6691 R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier-Poisson system * radiation transfer * compressible magnetohydrodynamics Subject RIV: BA - General Math ematics Impact factor: 0.954, year: 2016 http://ejde. math .txstate.edu/Volumes/2016/245/abstr.html

  19. SIERRA Low Mach Module: Fuego Theory Manual Version 4.44

    Energy Technology Data Exchange (ETDEWEB)

    Sierra Thermal/Fluid Team

    2017-04-01

    The SIERRA Low Mach Module: Fuego along with the SIERRA Participating Media Radiation Module: Syrinx, henceforth referred to as Fuego and Syrinx, respectively, are the key elements of the ASCI fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Syrinx represents the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

  20. SIERRA Low Mach Module: Fuego Theory Manual Version 4.46.

    Energy Technology Data Exchange (ETDEWEB)

    Sierra Thermal/Fluid Team

    2017-09-01

    The SIERRA Low Mach Module: Fuego along with the SIERRA Participating Media Radiation Module: Syrinx, henceforth referred to as Fuego and Syrinx, respectively, are the key elements of the ASCI fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Syrinx represents the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

  1. SIERRA Low Mach Module: Fuego User Manual Version 4.44

    Energy Technology Data Exchange (ETDEWEB)

    Sierra Thermal/Fluid Team

    2017-04-01

    The SIERRA Low Mach Module: Fuego along with the SIERRA Participating Media Radiation Module: Syrinx, henceforth referred to as Fuego and Syrinx, respectively, are the key elements of the ASCI fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Syrinx represents the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

  2. SIERRA Low Mach Module: Fuego User Manual Version 4.46.

    Energy Technology Data Exchange (ETDEWEB)

    Sierra Thermal/Fluid Team

    2017-09-01

    The SIERRA Low Mach Module: Fuego along with the SIERRA Participating Media Radiation Module: Syrinx, henceforth referred to as Fuego and Syrinx, respectively, are the key elements of the ASCI fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Syrinx represents the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

  3. Asymptotic preserving and all-regime Lagrange-Projection like numerical schemes: application to two-phase flows in low mach regime

    International Nuclear Information System (INIS)

    Girardin, Mathieu

    2014-01-01

    Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr

  4. Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei

    2018-01-01

    Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233

  5. Combustion-Powered Actuation for Dynamic Stall Suppression - Simulations and Low-Mach Experiments

    Science.gov (United States)

    Matalanis, Claude G.; Min, Byung-Young; Bowles, Patrick O.; Jee, Solkeun; Wake, Brian E.; Crittenden, Tom; Woo, George; Glezer, Ari

    2014-01-01

    An investigation on dynamic-stall suppression capabilities of combustion-powered actuation (COMPACT) applied to a tabbed VR-12 airfoil is presented. In the first section, results from computational fluid dynamics (CFD) simulations carried out at Mach numbers from 0.3 to 0.5 are presented. Several geometric parameters are varied including the slot chordwise location and angle. Actuation pulse amplitude, frequency, and timing are also varied. The simulations suggest that cycle-averaged lift increases of approximately 4% and 8% with respect to the baseline airfoil are possible at Mach numbers of 0.4 and 0.3 for deep and near-deep dynamic-stall conditions. In the second section, static-stall results from low-speed wind-tunnel experiments are presented. Low-speed experiments and high-speed CFD suggest that slots oriented tangential to the airfoil surface produce stronger benefits than slots oriented normal to the chordline. Low-speed experiments confirm that chordwise slot locations suitable for Mach 0.3-0.4 stall suppression (based on CFD) will also be effective at lower Mach numbers.

  6. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach

    Science.gov (United States)

    Domino, Stefan P.

    2018-04-01

    A hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P, promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy. Significant accuracy gains in manufactured solution error norms are noted even with modest promotion of the underlying polynomial order. The paper also demonstrates the CVFEM/DG methodology on two production-like simulation cases that include an inner block subjected to solid rotation, i.e., each of the simulations include a sliding mesh, non-conformal interface. The first production case presented is a turbulent flow past a high-rate-of-rotation cube (Re, 4000; RPM, 3600) on like and mixed-order polynomial interfaces. The final simulation case is a full-scale Vestas V27 225 kW wind turbine (tower and nacelle omitted) in which a hybrid topology, low-order mesh is used. Both production simulations

  7. Implantation of algorithms of diffuse control in DSPS

    International Nuclear Information System (INIS)

    Perez C, B.

    2003-01-01

    language assembler of the algorithm of diffuse control for the regulation of power of the TRIGA reactor presented in the chapter five. The chapter 3 treats the pattern of the punctual kinetics of a TRIGA Mark III reactor. Also they are defined basic concepts of the fission reactors. Due to the reaches of this thesis, the equations presented in this chapter are not used in the development of the controller since these they will cover in the master thesis where intends to simulate the dynamic behavior of the reactor in a Pc, but carrying out the power control functions in the system Dsp here developed. The chapter 4 explains the programming in C++ language of the diffuse controller for the regulation of power. This program is based on an algorithm developed with priority in ambient Mat lab. The program generated in C++ is used as pattern of reference to be able to evaluate the obtained results with the algorithm implanted in the Dsp. In the chapter 5 the numeric modifications carried out are explained to be able to manipulate the notation of floating point with operations among whole numbers. It is also described step to step the development of the program in the language assembler of the diffuse controller for the regulation of power of the TRIGA reactor. In the chapter 6 the obtained results there are shown with the control algorithm implanted in the Dsp. The program in C++ is used described in the chapter four for to be able to carry out the comparison of results generated exclusively by the stages that they conform the diffuse controller. As already was mentioned, later will be integrated this controller to a Pc which will simulate the behavior of the reactor. (Author)

  8. Accelerated diffusion controlled creep of polycrystalline materials. Communication 1. Model of diffusion controlled creep acceleration

    International Nuclear Information System (INIS)

    Smirnova, E.S.; Chuvil'deev, V.N.

    1998-01-01

    The model is suggested which describes the influence of large-angle grain boundary migration on a diffusion controlled creep rate in polycrystalline materials (Coble creep). The model is based on the concept about changing the value of migrating boundary free volume when introducing dislocations distributed over the grain bulk into this boundary. Expressions are obtained to calculate the grain boundary diffusion coefficient under conditions of boundary migration and the parameter, which characterized the value of Coble creep acceleration. A comparison is made between calculated and experimental data for Cd, Co and Fe

  9. Application of Powell's analogy for the prediction of vortex-pairing sound in a low-Mach number jet based on time-resolved planar and tomographic PIV

    NARCIS (Netherlands)

    Violato, D.; Bryon, K.; Moore, P.; Scarano, F.

    2010-01-01

    This paper describes an experimental investigation by time-resolved planar and tomographic PIV on the sound production mechanism of vortex pairing of a transitional water-jet flow at Re=5000. The shear layer is characterized by axisymmetric vortex rings which undergo pairing with a varicose mode.

  10. Modelling of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers. Part. 1 reference solutions

    International Nuclear Information System (INIS)

    Le Quere, P.; Weisman, C.; Paillere, H.; Vierendeels, J.; Dick, E.; Becker, R.; Braack, M.; Locke, J.

    2005-01-01

    Heat transfer by natural convection and conduction in enclosures occurs in numerous practical situations including the cooling of nuclear reactors. For large temperature difference, the flow becomes compressible with a strong coupling between the continuity, the momentum and the energy equations through the equation of state, and its properties (viscosity, heat conductivity) also vary with the temperature, making the Boussinesq flow approximation inappropriate and inaccurate. There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra 10 6 (constant property and variable property cases) and Ra = 10 7 (variable property case). These reference solutions were produced after a first international workshop organized by Cea and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established. (authors)

  11. Predictability of solute transport in diffusion-controlled hydrogeologic regimes

    International Nuclear Information System (INIS)

    Gillham, R.W.; Cherry, J.A.

    1983-01-01

    Hydrogeologic regimes that are favourable for the subsurface management of low-level radioactive wastes must have transport properties that will limit the migration velocity of contaminants to some acceptably low value. Of equal importance, for the purpose of impact assessment and licensing, is the need to be able to predict, with a reasonable degree of certainty and over long time periods, what the migration velocity of the various contaminants of interest will be. This paper presents arguments to show that in addition to having favourable velocity characteristics, transport in saturated, diffusion-controlled hydrogeologic regimes is considerably more predictable than in the most common alternatives. The classical transport models for unsaturated, saturated-advection-controlled and saturated-diffusion-controlled environments are compared, with particular consideration being given to the difficulties associated with the characterization of the respective transport parameters. Results are presented which show that the diffusion of non-reactive solutes and solutes that react according to a constant partitioning ratio (K/sub d/) are highly predictable under laboratory conditions and that the diffusion coefficients for the reactive solutes can be determined with a reasonable degree of accuracy from independent measurements of bulk density, porosity, distribution coefficient and tortuosity. Field evidence is presented which shows that the distribution of environmental isotopes and chloride in thick clayey deposits is consistent with a diffusion-type transport process in these media. These results are particularly important in that they not only demonstrate the occurrence of diffusion-controlled hydrogeologic regimes, but they also demonstrate the predictability of the migration characteristics over very long time periods

  12. Kinetics of diffusion-controlled and ballistically-controlled reactions

    International Nuclear Information System (INIS)

    Redner, S.

    1995-01-01

    The kinetics of diffusion-controlled two-species annihilation, A+B → O and single-species ballistically-controlled annihilation, A+A → O are investigated. For two-species annihilation, we describe the basic mechanism that leads to the formation of a coarsening mosaic of A- and B-domains. The implications of this picture on the distribution of reactants is discussed. For ballistic annihilation, dimensional analysis shows that the concentration and rms velocity decay as c∼t -α and v∼t -β , respectively, with α+β = 1 in any spatial dimension. Analysis of the Boltzmann equation for the evolution of the velocity distribution yields accurate predictions for the kinetics. New phenomena associated with discrete initial velocity distributions and with mixed ballistic and diffusive reactant motion are also discussed. (author)

  13. Diffusion in Solids Fundamentals, Methods, Materials, Diffusion-Controlled Processes

    CERN Document Server

    Mehrer, Helmut

    2007-01-01

    Diffusion is a vital topic in solid-state physics and chemistry, physical metallurgy and materials science. Diffusion processes are ubiquitous in solids at elevated temperatures. A thorough understanding of diffusion in materials is crucial for materials development and engineering. This book first gives an account of the central aspects of diffusion in solids, for which the necessary background is a course in solid state physics. It then provides easy access to important information about diffuson in metals, alloys, semiconductors, ion-conducting materials, glasses and nanomaterials. Several diffusion-controlled phenomena, including ionic conduction, grain-boundary and dislocation pipe diffusion, are considered as well. Graduate students in solid-state physics, physical metallurgy, materials science, physical and inorganic chemistry or geophysics will benefit from this book as will physicists, chemists, metallurgists, materials engineers in academic and industrial research laboratories.

  14. Implantation of algorithms of diffuse control in DSPS; Implantacion de algoritmos de control difuso en DSPS

    Energy Technology Data Exchange (ETDEWEB)

    Perez C, B

    2003-07-01

    language assembler of the algorithm of diffuse control for the regulation of power of the TRIGA reactor presented in the chapter five. The chapter 3 treats the pattern of the punctual kinetics of a TRIGA Mark III reactor. Also they are defined basic concepts of the fission reactors. Due to the reaches of this thesis, the equations presented in this chapter are not used in the development of the controller since these they will cover in the master thesis where intends to simulate the dynamic behavior of the reactor in a Pc, but carrying out the power control functions in the system Dsp here developed. The chapter 4 explains the programming in C++ language of the diffuse controller for the regulation of power. This program is based on an algorithm developed with priority in ambient Mat lab. The program generated in C++ is used as pattern of reference to be able to evaluate the obtained results with the algorithm implanted in the Dsp. In the chapter 5 the numeric modifications carried out are explained to be able to manipulate the notation of floating point with operations among whole numbers. It is also described step to step the development of the program in the language assembler of the diffuse controller for the regulation of power of the TRIGA reactor. In the chapter 6 the obtained results there are shown with the control algorithm implanted in the Dsp. The program in C++ is used described in the chapter four for to be able to carry out the comparison of results generated exclusively by the stages that they conform the diffuse controller. As already was mentioned, later will be integrated this controller to a Pc which will simulate the behavior of the reactor. (Author)

  15. Implantation of algorithms of diffuse control in DSPS; Implantacion de algoritmos de control difuso en DSPS

    Energy Technology Data Exchange (ETDEWEB)

    Perez C, B

    2003-07-01

    in language assembler of the algorithm of diffuse control for the regulation of power of the TRIGA reactor presented in the chapter five. The chapter 3 treats the pattern of the punctual kinetics of a TRIGA Mark III reactor. Also they are defined basic concepts of the fission reactors. Due to the reaches of this thesis, the equations presented in this chapter are not used in the development of the controller since these they will cover in the master thesis where intends to simulate the dynamic behavior of the reactor in a Pc, but carrying out the power control functions in the system Dsp here developed. The chapter 4 explains the programming in C++ language of the diffuse controller for the regulation of power. This program is based on an algorithm developed with priority in ambient Mat lab. The program generated in C++ is used as pattern of reference to be able to evaluate the obtained results with the algorithm implanted in the Dsp. In the chapter 5 the numeric modifications carried out are explained to be able to manipulate the notation of floating point with operations among whole numbers. It is also described step to step the development of the program in the language assembler of the diffuse controller for the regulation of power of the TRIGA reactor. In the chapter 6 the obtained results there are shown with the control algorithm implanted in the Dsp. The program in C++ is used described in the chapter four for to be able to carry out the comparison of results generated exclusively by the stages that they conform the diffuse controller. As already was mentioned, later will be integrated this controller to a Pc which will simulate the behavior of the reactor. (Author)

  16. Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.

    Science.gov (United States)

    Ji, Xinglong; Song, Li; He, Wei; Huang, Kejie; Yan, Zhiyuan; Zhong, Shuai; Zhang, Yishu; Zhao, Rong

    2018-03-28

    Selector elements with high nonlinearity are an indispensable part in constructing high density, large-scale, 3D stackable emerging nonvolatile memory and neuromorphic network. Although significant efforts have been devoted to developing novel thin-film selectors, it remains a great challenge in achieving good switching performance in the selectors to satisfy the stringent electrical criteria of diverse memory elements. In this work, we utilized high-defect-density chalcogenide glass (Ge 2 Sb 2 Te 5 ) in conjunction with high mobility Ag element (Ag-GST) to achieve a super nonlinear selective switching. A novel electrodeposition-diffusion dynamic selector based on Ag-GST exhibits superior selecting performance including excellent nonlinearity (<5 mV/dev), ultra-low leakage (<10 fA), and bidirectional operation. With the solid microstructure evidence and dynamic analyses, we attributed the selective switching to the competition between the electrodeposition and diffusion of Ag atoms in the glassy GST matrix under electric field. A switching model is proposed, and the in-depth understanding of the selective switching mechanism offers an insight of switching dynamics for the electrodeposition-diffusion-controlled thin-film selector. This work opens a new direction of selector designs by combining high mobility elements and high-defect-density chalcogenide glasses, which can be extended to other materials with similar properties.

  17. Diffusion-controlled reactions modeling in Geant4-DNA

    Energy Technology Data Exchange (ETDEWEB)

    Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)

    2014-10-01

    Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The

  18. Solid-state diffusion-controlled growth of the phases in the Au-Sn system

    Science.gov (United States)

    Baheti, Varun A.; Kashyap, Sanjay; Kumar, Praveen; Chattopadhyay, Kamanio; Paul, Aloke

    2018-01-01

    The solid state diffusion-controlled growth of the phases is studied for the Au-Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn4 phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn4 phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.

  19. From conservative to reactive transport under diffusion-controlled conditions

    Science.gov (United States)

    Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.

    2016-05-01

    We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.

  20. Organic influences on inorganic patterns of diffusion-controlled precipitation in gels

    Science.gov (United States)

    Barge, Laura M.; Nealson, Kenneth H.; Petruska, John

    2010-06-01

    The well-known AgNO 3/K 2CrO 4 reaction-diffusion system produces periodic bands of silver chromate precipitate in gelatin, but only randomly oriented crystals in agarose gel. We show that comparable bands can be produced in agarose gel by adding small amounts of simple organic acids (e.g., acetic acid, N-acetyl glycine, and N-acetyl alanine) that suppress crystal growth and promote formation of rounded particles of precipitate. These results indicate that α-carboxyl groups of amino acids or short peptides in gelatin under mildly acidic conditions can induce periodic band patterns in diffusion-controlled silver chromate precipitates.

  1. Design of an analytical aggregation of rules of a diffuse controller and its application in the model of a nuclear research reactor

    International Nuclear Information System (INIS)

    Najera H, M.C.

    2003-01-01

    As they have gone being managed complex systems that fulfill tasks inside industrial or nuclear processes, it becomes necessary the development of technical novel of control, in which can incorporate heuristic knowledge of operation without to necessarily use the theories of classic control based mainly in mathematical models. One of the control techniques that allows to carry out this is the control based on diffuse logic. For the case of a model of the nuclear research reactor Triga Mark III of the National Institute of Nuclear Research have been developed diverse algorithms of diffuse control that have as objective the regulation of the neutron power in the nucleus. The aggregation stages and desdifussification in these algorithms discretize the universe of values of the control variable, being required a high number of operations for their execution. With the purpose of reducing this number of operations and to obtain results more exact in the generation of the aggregated group in each cycle of control and in the determination of the center of gravity of this added group, it is presented the development of an analytical method for these calculations. The main objectives outlined in this entitled thesis D esign of an analytical aggregate of a diffuse controller rules and their application in the pattern of a nuclear research reactor , they are: to improve the behavior of control systems in closed knot based on diffuse logic by means of the development of an analytical method that determines an aggregated group resultant of the activation of rules in the diffuse controller and the obtaining of the exit variable using an exact solution of the technique of the center of gravity; and to compare the operation of these methods with those traditionally used ones that consider the discretization of the universe of the exit variable so much for the aggregation like for the desdiffusification. The chapters 1 and 2 present an introduction at two fundamental themes of the

  2. MODELING OF SUPERCRITICAL FLUID EXTRACTION KINETIC OF FLAXSEED OIL BY DIFFUSION CONTROL METHOD

    Directory of Open Access Journals (Sweden)

    Emir Zafer HOŞGÜN

    2013-06-01

    Full Text Available In this study, Flaxseed oil was extracted by Supercritical Carbondioxide Extraction, and extractionkinetics was modelled using diffusion controlled method.The effect of process parameters, such as pressure (20, 35, 55 MPa, temperature (323 and 343 K, and CO2 flow rate (1 and 3 L CO2 /min on the extraction yield and effective diffusivity (De was investigated. The effective diffusion coefficient varied between 2.4 x10-12 and 10.8 x10-12 m2s-1 for the entire range of experiments and increased with the pressure and flow rate. The model fitted well theexperimental data (ADD varied between 2.35 and 7.48%.

  3. Diffusion-controlled regime of surface-wave-produced plasmas in helium gas

    International Nuclear Information System (INIS)

    Berndt, J; Makasheva, K; Schlueter, H; Shivarova, A

    2002-01-01

    The study presents a numerical fluid-plasma model of diffusion-controlled surface-wave-sustained discharges in helium gas. The self-consistent behaviour of the discharge based on the interrelation between plasma density and Θ, the power absorbed on average by one electron, is described. The nonlinear process of step ionization in the charged particle balance equation is the main factor, which ensures the self-consistency. However, it is shown that in helium discharges, the ionization frequencies enter the dependence of Θ on the plasma density also through the ambipolar-diffusion coefficient. Results at two different values of the gas pressure and of the wave frequency are discussed. The lower value of the gas pressure is chosen according to the condition to have a pure diffusion-controlled regime without interference with a transition to the free-fall regime. The boundary condition for the ion flux at the wall sheath is used for determination of the value of μ, the quantity denoting the degree of the radial plasma-density inhomogeneity which, together with the electron-neutral elastic collision frequency, influences the wave propagation characteristics. The two values of the wave frequency chosen provide descriptions of high-frequency and microwave discharges. The model results in the self-consistent structure of the discharge: interrelated variations along the discharge length of wavenumber, space damping rate, Θ, plasma density and electron temperature. The power necessary for sustaining discharges of a given length is also calculated. Comparisons with argon discharges are shown

  4. Continuous and discreet methods in the aggregation and des fuzzy stages of a diffuse controller of neutron power

    International Nuclear Information System (INIS)

    Najera H, M.C.; Benitez R, J.S.

    2003-01-01

    The results of a comparative study are presented of: to) A denominated diffuse controller 'exact', designed by means of an innovative method that determines analytically so much the group of exit resultant in the aggregation stage like the de fuzzy process, and b) a diffuse controller denominated 'discreet' based on the discretization of the variable of having left as much for the aggregation as for the de fuzzy. These stages incorporated to the control algorithms whose objective is the ascent and regulation of the neutron power, carrying out an analysis of its performance. (Author)

  5. Investigations on diffusion-controlled transformations in creep resistant steels and graded cemented carbides

    International Nuclear Information System (INIS)

    Prat Borquez, Orlando

    2011-01-01

    The objective of this work was to simulate diffusion-controlled transformations on engineering alloys designed by the author and his colleagues. The main challenge of the work is to adapt the existing DICTRA models to the experimental processing and working conditions investigated, as well as to find the adequate boundary conditions for the description of the diffusion-controlled transformations governing the microstructure formation and evolution, in order to obtain reliable simulation results. The simulations were compared with experimental results of the microstructure evolution by scanning electron microscopy and scanning transmission electron microscopy (STEM). Two groups of materials were investigated. The first group was 9-12% Cr heat resistant alloys. These alloys are particularly interesting because the microstructure evolves during working conditions. Different compositions were designed in order to form different kinds and amounts of precipitates. For the designed 9-12% Cr creep steels the coarsening of MX and M 23 C 6 particles was modeled by applying the coarsening model implemented in DICTRA. The cell method of DICTRA was applied to investigate the kinetics of the Laves phase growth on 9-12% Cr alloys. The particular objectives of these investigations were: a) to determine the coarsening rate of precipitates, b) to investigate the influence of alloying element on the growth rate of the Laves phase, c) to determine the influence of the M 23 C 6 formation on the growth kinetics of the Laves phase, d) to determine the growth mechanism at the interface of the Laves phase (i.e. up-hill diffusion), e) to investigate the effect of the cell size on the simulation kinetics of Laves phase. The second group of materials was cemented carbides. They are used as cutting tools or wear parts in the automotive, aircraft and mining industry among others. The wear performance of cemented carbides (hardmetals and cermets) can be largely improved by applying wear

  6. Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

    Science.gov (United States)

    Everaers, Ralf; Rosa, Angelo

    2012-01-07

    The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

  7. Random-walk simulation of diffusion-controlled processes among static traps

    International Nuclear Information System (INIS)

    Lee, S.B.; Kim, I.C.; Miller, C.A.; Torquato, S.; Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910)

    1989-01-01

    We present computer-simulation results for the trapping rate (rate constant) k associated with diffusion-controlled reactions among identical, static spherical traps distributed with an arbitrary degree of impenetrability using a Pearson random-walk algorithm. We specifically consider the penetrable-concentric-shell model in which each trap of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable shell of thickness (1-λ)σ/2: λ=0 corresponding to randomly centered or ''fully penetrable'' traps and λ=1 corresponding to totally impenetrable traps. Trapping rates are calculated accurately from the random-walk algorithm at the extreme limits of λ (λ=0 and 1) and at an intermediate value (λ=0.8), for a wide range of trap densities. Our simulation procedure has a relatively fast execution time. It is found that k increases with increasing impenetrability at fixed trap concentration. These ''exact'' data are compared with previous theories for the trapping rate. Although a good approximate theory exists for the fully-penetrable-trap case, there are no currently available theories that can provide good estimates of the trapping rate for a moderate to high density of traps with nonzero hard cores (λ>0)

  8. Diffusion-controlled cementation experiments in porous rock analogues using potash alum and halite

    Energy Technology Data Exchange (ETDEWEB)

    Hufe, A.; Hilgers, C. [RWTH Aachen Univ. (Germany). Inst. of Reservoir-Petrology; Stanjek, H. [RWTH Aachen Univ. (Germany). Inst. of Interface and Clay Mineralogy

    2013-08-01

    A good understanding of cementation is critical for reservoir quality predictions. However, studies of core material have shown that cementation may be driven by variations in pore size of the host rock. To better understand the underlying process, we developed a transparent microreactor for diffusion-controlled cementation experiments under the microscope. We studied the effect of different pore sizes and surface charges of solid material at different pH, using rock analogs. High-resolution videos allowed to analyze the nucleation from solution, pore cementation and growth rates of cements. Diffusion - considered the major mass transport during burial diagenesis - was driven along a temperature gradient across the microreactor. Pores were cemented with salt, which is well known to form pore-size dependent seals in silicilastic reservoirs. While halite precipitated primarily in pores bigger than 200 {mu}m, alum nucleated in smaller pores. The growth rate of alum (10{sup -5} mm/s) was one order of magnitude higher than that of halite. However, the dissolution rates of both minerals was similar at about 10{sup -6} mm/s. Authigenic euhdral halite migrated against the bulk diffusion transport and towards the higher-temperature reservoir. Halite growth rates increased by one order of magnitude to 1.8 x 10{sup -5} mm/s, if the phase boundary was vapor-liquid. A comparison nucleation in a 2-phase porous rock analog showed no difference in cementation pattern at a pH 7. However, at a pH of 10.5 the surface energies of the two different solids are altered, and porosity was reduced 60% more by cements in the phase-1 porous layers. Our experiments showed that pore size dependent nucleation and cementation is a process, which may also take place in complex reservoirs. With the successful pore clogging of halite we can now bring our experimental setup to reservoir conditions and establish the processes at elevated p-T conditions. (orig.)

  9. The mean first passage time in an energy-diffusion controlled regime with power-law distributions

    International Nuclear Information System (INIS)

    Zhou, Yanjun; Du, Jiulin

    2013-01-01

    Based on the mean first passage time (MFPT) theory, we derive an expression of the MFPT in an energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. the thermal energy k B T is not small with respect to the potential barrier E b ) and compare it with Kramers’ infinite barrier result both in a power-law distribution and in a Maxwell–Boltzmann distribution. It is shown that the MFPT with a power-law distribution extends Kramers’ low-damping result to a relatively low barrier. We pay attention to the energy-diffusion controlled regime, which is of great interest in the context of Josephson junctions, and study how the power-law parameter κ affects the current distribution function in experiments with Josephson junctions. (paper)

  10. Solid diffusion control of the adsorption of basic dyes onto granular activated carbon and natural zeolite in fixed bed columns

    Directory of Open Access Journals (Sweden)

    M. MARINKOVSKI

    2001-07-01

    Full Text Available The adsorption of basic dyes from aqueous solutions onto granular activated carbon and natural zeolite was studied using a fixed bed column. The design procedures for fixed bed adsorption columns were investigated for two basic dyes Maxilon Goldgelb GL EC 400 % (MG-400 and Maxilon Schwarz FBL-01 300 % (MS-300. A computer program based on the solid diffusion control model has been developed. The model parameters: solid diffusion coefficient, DS, axial dispersion coefficient, DL and external mass transfer coefficient, kf for all the investigated systems were estimated by means of a best fit approach.

  11. Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

    International Nuclear Information System (INIS)

    Imre, K.; Odian, G.

    1979-01-01

    The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problems can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the upsilon power of the monomer concentration respectively, and, in which the proportionality constant a = k/sub p/R/sub i//sup w//k/sub t//sup z/, where k/sub p/ and k/sub t/ are the propagation and termination rate constants, respectively, and R/sub i/ is the initiation rate. The values of upsilon, w, and z depend on the particular reaction system. The results of earlier work were generalized by allowing a non-Fickian diffusion rate which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D 0 [exp(deltaC/M)], where M is the saturation concentration. A reaction system is characterized by the three dimensionless parameters, upsilon, delta, and A = (L/2)[aM/sup (upsilon--1)//D 0 ]/sup 1/2/, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of delta and ν cause a reaction system to behave closer to the diffusion-free regime. Transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, upsilon order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. Dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system. 11 figures, 4 tables

  12. Low Mach Scramjet Cavity Flameholder Stabilization, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — This proposal addresses a NASA solicitation topic A2.06 need for propulsion system flow control. A dual mode ram/scram engine is the most likely cycle for the...

  13. Modeling the Influence of Diffusion-Controlled Reactions and Residual Termination and Deactivation on the Rate and Control of Bulk ATRP at High Conversions

    Directory of Open Access Journals (Sweden)

    Ali Mohammad Rabea

    2015-04-01

    Full Text Available In high-conversion atom transfer radical polymerization (ATRP, all the reactions, such as radical termination, radical deactivation, dormant chain activation, monomer propagation, etc. could become diffusion controlled sooner or later, depending on relative diffusivities of the involved reacting species. These diffusion-controlled reactions directly affect the rate of polymerization and the control of polymer molecular weight. A model is developed to investigate the influence of diffusion-controlled reactions on the high conversion ATRP kinetics. Model simulation reveals that diffusion-controlled termination slightly increases the rate, but it is the diffusion-controlled deactivation that causes auto-acceleration in the rate (“gel effect” and loss of control. At high conversions, radical chains are “trapped” because of high molecular weight. However, radical centers can still migrate through (1 radical deactivation–activation cycles and (2 monomer propagation, which introduce “residual termination” reactions. It is found that the “residual termination” does not have much influence on the polymerization kinetics. The migration of radical centers through propagation can however facilitate catalytic deactivation of radicals, which improves the control of polymer molecular weight to some extent. Dormant chain activation and monomer propagation also become diffusion controlled and finally stop the polymerization when the system approaches its glass state.

  14. Numerical solutions of unsteady flows with low inlet Mach numbers

    Czech Academy of Sciences Publication Activity Database

    Punčochářová, Petra; Furst, Jiří; Horáček, Jaromír; Kozel, Karel

    2010-01-01

    Roč. 80, č. 8 (2010), s. 1795-1805 ISSN 0378-4754 R&D Projects: GA AV ČR IAA200760613 Institutional research plan: CEZ:AV0Z20760514 Keywords : finite volume method * unsteady flow * low Mach number * viscous compressible fluid Subject RIV: BI - Acoustics Impact factor: 0.812, year: 2010 http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0T-4Y0D67D-1-R&_cdi=5655&_user=640952&_pii=S0378475409003607&_origin=search&_coverDate=04%2F30%2F2010&_sk=999199991&view=c&wchp=dGLbVlb-zSkzk&md5=ed6eaf0a050968ee978714fd54e7f131&ie=/sdarticle.pdf

  15. Formulation and analyses of vaporization and diffusion-controlled combustion of fuel sprays

    OpenAIRE

    Arrieta Sanagustín, Jorge

    2012-01-01

    This dissertation focuses on the modelling of vaporization and combustion of sprays. A general two-continua formulation is given for the numerical computation of spray flows, including the treatment of the droplets as homogenized sources. Group combustion is considered, with the reaction between the fuel coming from the vaporizing droplets and the oxygen of the air modeled in the Burke-Schumann limit of infinitely fast chemical reaction, with nonunity Lewis numbers allowed for the different r...

  16. Viscous organic aerosol particles in the upper troposphere: diffusivity-controlled water uptake and ice nucleation?

    Directory of Open Access Journals (Sweden)

    D. M. Lienhard

    2015-12-01

    secondary organic aerosol (SOA material produced by oxidation of α-pinene and in a number of organic/inorganic model mixtures (3-methylbutane-1,2,3-tricarboxylic acid (3-MBTCA, levoglucosan, levoglucosan/NH4HSO4, raffinose are presented. These indicate that water diffusion coefficients are determined by several properties of the aerosol substance and cannot be inferred from the glass transition temperature or bouncing properties. Our results suggest that water diffusion in SOA particles is faster than often assumed and imposes no significant kinetic limitation on water uptake and release at temperatures above 220 K. The fast diffusion of water suggests that heterogeneous ice nucleation on a glassy core is very unlikely in these systems. At temperatures below 220 K, model simulations of SOA particles suggest that heterogeneous ice nucleation may occur in the immersion mode on glassy cores which remain embedded in a liquid shell when experiencing fast updraft velocities. The particles absorb significant quantities of water during these updrafts which plasticize their outer layers such that these layers equilibrate readily with the gas phase humidity before the homogeneous ice nucleation threshold is reached. Glass formation is thus unlikely to restrict homogeneous ice nucleation. Only under most extreme conditions near the very high tropical tropopause may the homogeneous ice nucleation rate coefficient be reduced as a consequence of slow condensed-phase water diffusion. Since the differences between the behavior limited or non limited by diffusion are small even at the very high tropical tropopause, condensed-phase water diffusivity is unlikely to have significant consequences on the direct climatic effects of SOA particles under tropospheric conditions.

  17. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    International Nuclear Information System (INIS)

    Plante, Ianik; Devroye, Luc

    2015-01-01

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well

  18. Ultrafast Excited-State Dynamics of Diketopyrrolopyrrole (DPP)-Based Materials: Static versus Diffusion-Controlled Electron Transfer Process

    KAUST Repository

    Alsulami, Qana

    2015-06-25

    Singlet-to-triplet intersystem crossing (ISC) and photoinduced electron transfer (PET) of platinum(II) containing diketopyrrolopyrrole (DPP) oligomer in the absence and presence of strong electron-acceptor tetracyanoethylene (TCNE) were investigated using femtosecond and nanosecond transient absorption spectroscopy with broadband capabilities. The role of platinum(II) incorporation in those photophysical properties was evaluated by comparing the excited-state dynamics of DPP with and without the metal centers. The steady-state measurements reveal that platinum(II) incorporation facilitates dramatically the interactions between DPP-Pt(acac) and TCNE, resulting in charge transfer (CT) complex formation. The transient absorption spectra in the absence of TCNE reveal ultrafast ISC of DPP-Pt(acac) followed by their long-lived triplet state. In the presence of TCNE, PET from the excited DPP-Pt(acac) and DPP to TCNE, forming the radical ion pairs. The ultrafast PET which occurs statically from DPP-Pt(acac) to TCNE in picosecond regime, is much faster than that from DPP to TCNE (nanosecond time scale) which is diffusion-controlled process, providing clear evidence that PET rate is eventually controlled by the platinum(II) incorporation.

  19. Diffusion-controlled oxygen reduction on multi-copper oxidase-adsorbed carbon aerogel electrodes without mediator

    Energy Technology Data Exchange (ETDEWEB)

    Tsujimura, S.; Kamitaka, Y.; Kano, K. [Division of Applied Life Sciences, Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto (Japan)

    2007-12-15

    Bioelectrocatalytic reduction of O{sub 2} into water was archived at diffusion-controlled rate by using enzymes (laccase from Trametes sp. and bilirubin oxidase from Myrothecium verrucaria, which belong to the family of multi-copper oxidase) adsorbed on mesoporous carbon aerogel particle without a mediator. The current density was predominantly controlled by the diffusion of dissolved O{sub 2} in rotating-disk electrode experiments, and reached a value as large as 10 mA cm{sup -2} at 1 atm O{sub 2}, 25 C, and 8,000 rpm on the laccase-adsorbed electrode. The overpotential of the bioelectrocatalytic reduction of O{sub 2} was 0.4-0.55 V smaller than that observed on a Pt disk electrode. Without any optimization, the laccase-adsorbed biocathode showed stable current intensity of the O{sub 2} reduction in an air-saturated buffer at least for 10 days under continuous flow system. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  20. Ultrafast Excited-State Dynamics of Diketopyrrolopyrrole (DPP)-Based Materials: Static versus Diffusion-Controlled Electron Transfer Process

    KAUST Repository

    Alsulami, Qana; Aly, Shawkat Mohammede; Goswami, Subhadip; Alarousu, Erkki; Usman, Anwar; Schanze, Kirk S.; Mohammed, Omar F.

    2015-01-01

    Singlet-to-triplet intersystem crossing (ISC) and photoinduced electron transfer (PET) of platinum(II) containing diketopyrrolopyrrole (DPP) oligomer in the absence and presence of strong electron-acceptor tetracyanoethylene (TCNE) were investigated using femtosecond and nanosecond transient absorption spectroscopy with broadband capabilities. The role of platinum(II) incorporation in those photophysical properties was evaluated by comparing the excited-state dynamics of DPP with and without the metal centers. The steady-state measurements reveal that platinum(II) incorporation facilitates dramatically the interactions between DPP-Pt(acac) and TCNE, resulting in charge transfer (CT) complex formation. The transient absorption spectra in the absence of TCNE reveal ultrafast ISC of DPP-Pt(acac) followed by their long-lived triplet state. In the presence of TCNE, PET from the excited DPP-Pt(acac) and DPP to TCNE, forming the radical ion pairs. The ultrafast PET which occurs statically from DPP-Pt(acac) to TCNE in picosecond regime, is much faster than that from DPP to TCNE (nanosecond time scale) which is diffusion-controlled process, providing clear evidence that PET rate is eventually controlled by the platinum(II) incorporation.

  1. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    Energy Technology Data Exchange (ETDEWEB)

    Plante, Ianik, E-mail: ianik.plante-1@nasa.gov [Wyle Science, Technology & Engineering, 1290 Hercules, Houston, TX 77058 (United States); Devroye, Luc, E-mail: lucdevroye@gmail.com [School of Computer Science, McGill University, 3480 University Street, Montreal H3A 0E9 (Canada)

    2015-09-15

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

  2. Hupa Numbers.

    Science.gov (United States)

    Bennett, Ruth, Ed.; And Others

    An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…

  3. Triangular Numbers

    Indian Academy of Sciences (India)

    Admin

    Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.

  4. Proth Numbers

    Directory of Open Access Journals (Sweden)

    Schwarzweller Christoph

    2015-02-01

    Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.

  5. Sagan numbers

    OpenAIRE

    Mendonça, J. Ricardo G.

    2012-01-01

    We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.

  6. Eulerian numbers

    CERN Document Server

    Petersen, T Kyle

    2015-01-01

    This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...

  7. Transfinite Numbers

    Indian Academy of Sciences (India)

    Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.

  8. Chocolate Numbers

    OpenAIRE

    Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela

    2015-01-01

    In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...

  9. Number theory

    CERN Document Server

    Andrews, George E

    1994-01-01

    Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl

  10. Nice numbers

    CERN Document Server

    Barnes, John

    2016-01-01

    In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...

  11. Design of an analytical aggregation of rules of a diffuse controller and its application in the model of a nuclear research reactor; Diseno de una agregacion analitica de reglas de un controlador difuso y su aplicacion en el modelo de un reactor nuclear de investigacion

    Energy Technology Data Exchange (ETDEWEB)

    Najera H, M.C

    2003-07-01

    As they have gone being managed complex systems that fulfill tasks inside industrial or nuclear processes, it becomes necessary the development of technical novel of control, in which can incorporate heuristic knowledge of operation without to necessarily use the theories of classic control based mainly in mathematical models. One of the control techniques that allows to carry out this is the control based on diffuse logic. For the case of a model of the nuclear research reactor Triga Mark III of the National Institute of Nuclear Research have been developed diverse algorithms of diffuse control that have as objective the regulation of the neutron power in the nucleus. The aggregation stages and desdifussification in these algorithms discretize the universe of values of the control variable, being required a high number of operations for their execution. With the purpose of reducing this number of operations and to obtain results more exact in the generation of the aggregated group in each cycle of control and in the determination of the center of gravity of this added group, it is presented the development of an analytical method for these calculations. The main objectives outlined in this entitled thesis {sup D}esign of an analytical aggregate of a diffuse controller rules and their application in the pattern of a nuclear research reactor{sup ,} they are: to improve the behavior of control systems in closed knot based on diffuse logic by means of the development of an analytical method that determines an aggregated group resultant of the activation of rules in the diffuse controller and the obtaining of the exit variable using an exact solution of the technique of the center of gravity; and to compare the operation of these methods with those traditionally used ones that consider the discretization of the universe of the exit variable so much for the aggregation like for the desdiffusification. The chapters 1 and 2 present an introduction at two fundamental

  12. Number names and number understanding

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    2014-01-01

    This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....

  13. Funny Numbers

    Directory of Open Access Journals (Sweden)

    Theodore M. Porter

    2012-12-01

    Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.

  14. Transcendental numbers

    CERN Document Server

    Murty, M Ram

    2014-01-01

    This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

  15. Transfinite Numbers

    Indian Academy of Sciences (India)

    this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...

  16. Continuous and discreet methods in the aggregation and des fuzzy stages of a diffuse controller of neutron power; Metodos continuo y discreto en las etapas de agregacion y desdifusificacion de un controlador disfuso de potencia neutronica

    Energy Technology Data Exchange (ETDEWEB)

    Najera H, M.C.; Benitez R, J.S. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)

    2003-07-01

    The results of a comparative study are presented of: to) A denominated diffuse controller 'exact', designed by means of an innovative method that determines analytically so much the group of exit resultant in the aggregation stage like the de fuzzy process, and b) a diffuse controller denominated 'discreet' based on the discretization of the variable of having left as much for the aggregation as for the de fuzzy. These stages incorporated to the control algorithms whose objective is the ascent and regulation of the neutron power, carrying out an analysis of its performance. (Author)

  17. Characterization of Secondary Mineral Grain Coatings and their Role as Diffusion-controlled Sinks and Sources for Metal Contaminants

    Science.gov (United States)

    Davis, J. A.; Guo, H.; Lai, B.; Kemner, K. M.; Ercius, P.; Fox, P. M.; Singer, D. M.; Minor, A.; Waychunas, G.

    2012-12-01

    ) tomography, it can be seen that there are large numbers of pore throat sizes less than 10 nm within the coatings. We hypothesize that diffusion through these pores, which likely have electrically charged surfaces, controls the observed macroscopic rates of U(VI) sorption in batch experiments with sand grains. Evidence to support this hypothesis was observed by studying U and Fe fluorescence spatial variation within FIB samples (1 micron thick) at 200 nm spatial resolution. With this greater spatial resolution, it is possible to see U concentration variations within the coatings that are dependent on the time of sorption reaction, and illustrates how the coating environment constitutes a diffusion constraint to achieve adsorptive equilibrium between an aqueous phase and the mineral surfaces. Including this diffusion constraint within conceptual models for reactive contaminant transport may be significant at the field scale, because secondary mineral coatings are potentially both sinks and sources of contaminants depending on the history of a contaminated site. This is important in resolving long-term transport predictions at DOE sites, such as Hanford and Savannah River, where equilibrium versus kinetic reactive transport models are being evaluated.

  18. The evolution of the flame surface in turbulent premixed jet flames at high Reynolds number

    Science.gov (United States)

    Luca, Stefano; Attili, Antonio; Bisetti, Fabrizio

    2017-11-01

    A set of direct numerical simulations of turbulent premixed flames in a spatially developing turbulent slot burner at four Reynolds number is presented. This configuration is of interest since it displays turbulent production by mean shear as in real combustion devices. The gas phase hydrodynamics are modeled with the reactive, unsteady Navier-Stokes equations in the low Mach number limit, with finite-rate chemistry consisting of 16 species and 73 reactions. For the highest jet Reynolds number of 22 ×103, 22 Billion grid points are employed. The jet consists of a lean methane/air mixture at 4 atm and preheated to 800 K. The analysis of stretch statistics shows that the mean total stretch is close to zero. Mean stretch decreases moving downstream from positive to negative values, suggesting a formation of surface area in the near field and destruction at the tip of the flame; the mean contribution of the tangential strain term is positive, while the mean contribution of the propagative term is always negative. Positive values of stretch are due to the tangential strain rate term, while large negative values are associated with the propagative term. Increasing Reynolds number is found to decrease the correlation between stretch and the single contributions.

  19. Diffuse control of gas turbines in power stations of combined cycle; Contral difuso de turbinas de gas en centrales de ciclo combinado

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez P, Marino; Garduno R, Raul; De Lara J, Salvadror; Castelo C, Luis [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)

    2001-07-01

    In this article the application of the technology of the fuzzy logic to the control of gas turbines is presented in order to evaluate it in one of the most difficult processes and with stricter control requirements that exist in the electrical generation industry. For being important for the generation electrical sector, given their use in Comision Federal de Electricidad (CFE), the first selected prototype was the gas turbines model W501 of Westinghouse, installed in the of combined cycle power stations of Dos Bocas, Veracruz, Gomez Palacio, Durango and Tula, Hidalgo, Mexico. The second selected prototype was the one of the turbo gas units type 5001 (that applies to the GE 5001 models and Westinghouse of series 191 and 251). Based on the analysis of the performance of the system of conventional control previously made, the controllers of speed and generation of electrical power were selected to be replaced by diffuse controllers. [Spanish] En este articulo se presenta la aplicacion de la tecnologia de la logica difusa al control de turbinas de gas con el proposito de evaluarla en uno de los procesos mas dificiles y con requerimientos mas estrictos de control que existen en la industria de generacion electrica. Por ser importantes para el sector electrico de generacion, dada su utilizacion en Comision Federal de Electricidad (CFE), el primer prototipo seleccionado fueron las turbinas de gas modelo W501 de Westinghouse, instaladas en la central de ciclo combinado de Dos Bocas, Veracruz, Gomez Palacio, Durango y Tula, Hidalgo, Mexico. El segundo prototipo seleccionado fue el de unidades turbogas tipo 5001 (que aplica a los modelos GE 5001 y Westinghouse de la serie 191 y 251). Basados en el analisis del desempeno del sistema de control convencional realizado previamente, los controladores de velocidad y de generacion de potencia electrica fueron seleccionados para ser sustituidos por controladores difusos.

  20. Number Sense on the Number Line

    Science.gov (United States)

    Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni

    2018-01-01

    A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

  1. The Super Patalan Numbers

    OpenAIRE

    Richardson, Thomas M.

    2014-01-01

    We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.

  2. Number words and number symbols a cultural history of numbers

    CERN Document Server

    Menninger, Karl

    1992-01-01

    Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.

  3. Diamond Fuzzy Number

    Directory of Open Access Journals (Sweden)

    T. Pathinathan

    2015-01-01

    Full Text Available In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above mentioned types of Diamond Fuzzy Numbers.

  4. Those fascinating numbers

    CERN Document Server

    Koninck, Jean-Marie De

    2009-01-01

    Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new n

  5. Building Numbers from Primes

    Science.gov (United States)

    Burkhart, Jerry

    2009-01-01

    Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

  6. Introduction to number theory

    CERN Document Server

    Vazzana, Anthony; Garth, David

    2007-01-01

    One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

  7. On the number of special numbers

    Indian Academy of Sciences (India)

    without loss of any generality to be the first k primes), then the equation a + b = c has .... This is an elementary exercise in partial summation (see [12]). Thus ... This is easily done by inserting a stronger form of the prime number theorem into the.

  8. p-adic numbers

    OpenAIRE

    Grešak, Rozalija

    2015-01-01

    The field of real numbers is usually constructed using Dedekind cuts. In these thesis we focus on the construction of the field of real numbers using metric completion of rational numbers using Cauchy sequences. In a similar manner we construct the field of p-adic numbers, describe some of their basic and topological properties. We follow by a construction of complex p-adic numbers and we compare them with the ordinary complex numbers. We conclude the thesis by giving a motivation for the int...

  9. On the number of special numbers

    Indian Academy of Sciences (India)

    We now apply the theory of the Thue equation to obtain an effective bound on m. Indeed, by Lemma 3.2, we can write m2 = ba3 and m2 − 4 = cd3 with b, c cubefree. By the above, both b, c are bounded since they are cubefree and all their prime factors are less than e63727. Now we have a finite number of. Thue equations:.

  10. Number projection method

    International Nuclear Information System (INIS)

    Kaneko, K.

    1987-01-01

    A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states

  11. Numbers and brains.

    Science.gov (United States)

    Gallistel, C R

    2017-12-01

    The representation of discrete and continuous quantities appears to be ancient and pervasive in animal brains. Because numbers are the natural carriers of these representations, we may discover that in brains, it's numbers all the way down.

  12. Number in Dinka

    DEFF Research Database (Denmark)

    Andersen, Torben

    2014-01-01

    had a marked singular and an unmarked plural. Synchronically, however, the singular is arguably the basic member of the number category as revealed by the use of the two numbers. In addition, some nouns have a collective form, which is grammatically singular. Number also plays a role...

  13. Safety-in-numbers

    DEFF Research Database (Denmark)

    Elvik, Rune; Bjørnskau, Torkel

    2017-01-01

    Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known....

  14. Discovery: Prime Numbers

    Science.gov (United States)

    de Mestre, Neville

    2008-01-01

    Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

  15. Asymptotic numbers: Pt.1

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1980-01-01

    The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

  16. Applied number theory

    CERN Document Server

    Niederreiter, Harald

    2015-01-01

    This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.  Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.  Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...

  17. Predicting Lotto Numbers

    DEFF Research Database (Denmark)

    Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert

    numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....

  18. Invitation to number theory

    CERN Document Server

    Ore, Oystein

    2017-01-01

    Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  19. The adventure of numbers

    CERN Document Server

    Godefroy, Gilles

    2004-01-01

    Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind. The development of mathematics has been punctuated by a n

  20. Predicting Lotto Numbers

    DEFF Research Database (Denmark)

    Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl

    2016-01-01

    We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...... as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’....

  1. Beurling generalized numbers

    CERN Document Server

    Diamond, Harold G; Cheung, Man Ping

    2016-01-01

    "Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...

  2. Intuitive numbers guide decisions

    Directory of Open Access Journals (Sweden)

    Ellen Peters

    2008-12-01

    Full Text Available Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a perceived differences between numbers, b the extent to which proportional differences are weighed in decisions, and, ultimately, c the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

  3. Numbers, sequences and series

    CERN Document Server

    Hirst, Keith

    1994-01-01

    Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc

  4. Diffusion-controlled melting in granitic systems at 800-900degC and 100-200 MPa. Temperature and pressure dependence of the minimum diffusivity in granitic melts

    International Nuclear Information System (INIS)

    Yuguchi, Takashi; Yamaguchi, Takashi; Iwamoto, Manji-rou; Eguchi, Hibiki; Isobe, Hiroshi; Nishiyama, Tadao

    2012-01-01

    This paper presents the temperature and pressure dependence of the minimum binary diffusivity in granitic melts. The minimum diffusivities are determined by monitoring the temporal development of the diffusion-controlled melt layer(DCM) in granitic systems (albite (Ab)-quartz (Qtz)-H 2 O and orthoclase (Or)-Qtz-H 2 O) gathered during 31 melting experiments under conditions of 800-900degC and 100-200 MPa for durations of 19-72 h. The DCM is formed between single crystals (Ab or Or crystals) and powdered quartz in all runs and is characterized by a distinct concentration gradient. The maximum thickness of the DCM increases systematically with temperature, pressure, and run duration. Temporal development of the DCM obeys the parabolic growth rate law, using which the diffusivity can be estimated. Plots of concentrations along the diffusion paths in ternary diagrams (Na 2 O-Al 2 O 3 -SiO 2 diagram for the Ab-Qtz-H 2 O system and K 2 O-Al 2 O 3 -SiO 2 diagram for the Or-Qtz-H 2 O system) show linear trends rather than S-shaped trends, indicating that binary nature of diffusion occurs in these systems. Therefore, the diffusive component can be interpreted as an albite component or orthoclase and quartz components (SiO 2 ) rather than an oxide or a cation. (author)

  5. Templates, Numbers & Watercolors.

    Science.gov (United States)

    Clemesha, David J.

    1990-01-01

    Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)

  6. Random number generation

    International Nuclear Information System (INIS)

    Coveyou, R.R.

    1974-01-01

    The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)

  7. Algebraic number theory

    CERN Document Server

    Weiss, Edwin

    1998-01-01

    Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

  8. Advanced number theory

    CERN Document Server

    Cohn, Harvey

    1980-01-01

    ""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts

  9. The emergence of number

    CERN Document Server

    Crossley, John N

    1987-01-01

    This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the deve

  10. Professor Stewart's incredible numbers

    CERN Document Server

    Stewart, Ian

    2015-01-01

    Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,

  11. Fundamentals of number theory

    CERN Document Server

    LeVeque, William J

    1996-01-01

    This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha

  12. Numbers and computers

    CERN Document Server

    Kneusel, Ronald T

    2015-01-01

    This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb

  13. Elementary theory of numbers

    CERN Document Server

    Sierpinski, Waclaw

    1988-01-01

    Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian

  14. On powerful numbers

    Directory of Open Access Journals (Sweden)

    R. A. Mollin

    1986-01-01

    Full Text Available A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25,27 is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance's result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n=p1−p2 where p1 and p2 are powerful numbers with g.c.d. (p1,p2=1. Golomb (op.cit. conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non-zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel's proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel's result as well as an effective algorithm (in the proof for explicitly determining infinitely many such representations. However, in both our proof and McDaniel's proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4. We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in

  15. Brief history of numbers

    CERN Document Server

    Corry, Leo

    2015-01-01

    The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the

  16. Elementary number theory

    CERN Document Server

    Dudley, Underwood

    2008-01-01

    Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta

  17. Volume 9 Number 1

    African Journals Online (AJOL)

    OLUWOLE

    Agro-Science Journal of Tropical Agriculture, Food, Environment and Extension. Volume 9 Number 1 ... of persistent dumping of cheap subsidized food imports from developed ... independence of the inefficiency effects in the two estimation ...

  18. High Reynolds Number Turbulence

    National Research Council Canada - National Science Library

    Smits, Alexander J

    2007-01-01

    The objectives of the grant were to provide a systematic study to fill the gap between existing research on low Reynolds number turbulent flows to the kinds of turbulent flows encountered on full-scale vehicles...

  19. Crunching the Numbers

    International Development Research Centre (IDRC) Digital Library (Canada)

    Operating a Demographic Surveillance System (DSS) like this one requires a blend of high-tech number-crunching ability and .... views follow a standardized format that takes several ... general levels of health and to the use of health services.

  20. Quantum random number generator

    Science.gov (United States)

    Pooser, Raphael C.

    2016-05-10

    A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.

  1. Solar Indices - Sunspot Numbers

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of indices related to solar activity contributed by a number of national and private solar observatories located worldwide. This...

  2. Really big numbers

    CERN Document Server

    Schwartz, Richard Evan

    2014-01-01

    In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual i...

  3. The Congruent Number Problem

    Indian Academy of Sciences (India)

    One could endlessly churn out congruent numbers following the method in Box 1 without being certain when a given number n (or n x m 2, for some integer m) will ap- pear on the list. Continuing in this way ·would exhaust one's computing resources, not to mention one's patience! Also, this procedure is of no avail if n is not ...

  4. The Brothel Phone Number

    DEFF Research Database (Denmark)

    Korsby, Trine Mygind

    2017-01-01

    Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro-infrastructure in......Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro...... in turn cultivate and maximize uncertainty about themselves in others. When making the move to go abroad into unknown terrains, accessing the infrastructure generated by the phone number can provide certainty and consolidate one’s position within criminal networks abroad. However, at the same time......, mishandling the phone number can be dangerous and in that sense produce new doubts and uncertainties....

  5. Report number codes

    Energy Technology Data Exchange (ETDEWEB)

    Nelson, R.N. (ed.)

    1985-05-01

    This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.

  6. Report number codes

    International Nuclear Information System (INIS)

    Nelson, R.N.

    1985-05-01

    This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name

  7. A Numbers Game

    DEFF Research Database (Denmark)

    Levin, Bruce R; McCall, Ingrid C.; Perrot, Veronique

    2017-01-01

    We postulate that the inhibition of growth and low rates of mortality of bacteria exposed to ribosome-binding antibiotics deemed bacteriostatic can be attributed almost uniquely to these drugs reducing the number of ribosomes contributing to protein synthesis, i.e., the number of effective......-targeting bacteriostatic antibiotics, the time before these bacteria start to grow again when the drugs are removed, referred to as the post-antibiotic effect (PAE), is markedly greater for constructs with fewer rrn operons than for those with more rrn operons. We interpret the results of these other experiments reported...... here as support for the hypothesis that the reduction in the effective number of ribosomes due to binding to these structures provides a sufficient explanation for the action of bacteriostatic antibiotics that target these structures....

  8. Quantum random number generator

    Science.gov (United States)

    Soubusta, Jan; Haderka, Ondrej; Hendrych, Martin

    2001-03-01

    Since reflection or transmission of a quantum particle on a beamsplitter is inherently random quantum process, a device built on this principle does not suffer from drawbacks of neither pseudo-random computer generators or classical noise sources. Nevertheless, a number of physical conditions necessary for high quality random numbers generation must be satisfied. Luckily, in quantum optics realization they can be well controlled. We present an easy random number generator based on the division of weak light pulses on a beamsplitter. The randomness of the generated bit stream is supported by passing the data through series of 15 statistical test. The device generates at a rate of 109.7 kbit/s.

  9. The LHC in numbers

    CERN Multimedia

    Alizée Dauvergne

    2010-01-01

    What makes the LHC the biggest particle accelerator in the world? Here are some of the numbers that characterise the LHC, and their equivalents in terms that are easier for us to imagine.   Feature Number Equivalent Circumference ~ 27 km   Distance covered by beam in 10 hours ~ 10 billion km a round trip to Neptune Number of times a single proton travels around the ring each second 11 245   Speed of protons first entering the LHC 299 732 500 m/s 99.9998 % of the speed of light Speed of protons when they collide 299 789 760 m/s 99.9999991 % of the speed of light Collision temperature ~ 1016 °C ove...

  10. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  11. Analytic number theory

    CERN Document Server

    Iwaniec, Henryk

    2004-01-01

    Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis

  12. CONFUSION WITH TELEPHONE NUMBERS

    CERN Multimedia

    Telecom Service

    2002-01-01

    he area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service

  13. CONFUSION WITH TELEPHONE NUMBERS

    CERN Multimedia

    Telecom Service

    2002-01-01

    The area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service  

  14. Earthquake number forecasts testing

    Science.gov (United States)

    Kagan, Yan Y.

    2017-10-01

    We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness

  15. Colour by Numbers

    Science.gov (United States)

    Wetherell, Chris

    2017-01-01

    This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

  16. The magic of numbers

    CERN Document Server

    Bell, Eric Temple

    1991-01-01

    From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how ""number magic"" has influenced religion, philosophy, science, and mathematics

  17. ALARA notes, Number 8

    International Nuclear Information System (INIS)

    Khan, T.A.; Baum, J.W.; Beckman, M.C.

    1993-10-01

    This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the 'tyranny' of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment

  18. Uniform random number generators

    Science.gov (United States)

    Farr, W. R.

    1971-01-01

    Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.

  19. Key numbers: Energy

    International Nuclear Information System (INIS)

    1994-01-01

    The key numbers of energy give statistical data related to production, consumption, and to foreign trade of each energy in the World and in France. A chapter is dedicated to environment and brings quantitative elements on pollutant emissions connected to energy uses

  20. The numbers game

    Directory of Open Access Journals (Sweden)

    Oli Brown

    2008-10-01

    Full Text Available Estimates of the potential number of ‘climate changemigrants’ vary hugely. In order to persuade policymakers ofthe need to act and to provide a sound basis for appropriateresponses, there is an urgent need for better analysis, betterdata and better predictions.

  1. Introducing Complex Numbers

    Science.gov (United States)

    Trudgian, Timothy

    2009-01-01

    One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

  2. Typical Complexity Numbers

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Typical Complexity Numbers. Say. 1000 tones,; 100 Users,; Transmission every 10 msec. Full Crosstalk cancellation would require. Full cancellation requires a matrix multiplication of order 100*100 for all the tones. 1000*100*100*100 operations every second for the ...

  3. Littlewood and Number Theory

    Indian Academy of Sciences (India)

    IAS Admin

    improved by Selberg [4] in 1941 who showed that a pos- ... be seen by entries of his first letter to G H Hardy in ... tary in the technical sense of the word, employed com- ..... III: On the expression of a number as a sum of primes, Acta Math.,.

  4. Low Reynolds Number Vehicles

    Science.gov (United States)

    1985-02-01

    of the blade. The Darrieus VAWT has more complex aerodynamics. This type of wind turbine produces power as a result of the tangential thrust as...Horizontal Axis Propeller-Type b) Verticle Axis Darrieus -Type Figure 78. Wind Turbine Configurations 0 6 Q K [_ 2 -, C 4 UJ UJ...Sailplanes 23 5.2 Wind Turbines 23 6. CONCLUDING REMARKS 24 7. RECOMMENDATIONS FOR FUTURE RESEARCH 24 REFERENCES 25 FIGURES 32 yv/ LOW REYNOLDS NUMBER

  5. Topics in number theory

    CERN Document Server

    LeVeque, William J

    2002-01-01

    Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symb

  6. Drawing a random number

    DEFF Research Database (Denmark)

    Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik

    2006-01-01

    Random numbers are used for a great variety of applications in almost any field of computer and economic sciences today. Examples ranges from stock market forecasting in economics, through stochastic traffic modelling in operations research to photon and ray tracing in graphics. The construction...... distributions into others with most of the required characteristics. In essence, a uniform sequence which is transformed into a new sequence with the required distribution. The subject of this article is to consider the well known highly uniform Halton sequence and modifications to it. The intent is to generate...

  7. [The power of numbers].

    Science.gov (United States)

    van Gijn, J

    2000-01-01

    The round figure for the current year has stirred people's minds in anticipation. Numbers have acquired great significance also in today's medical science. The Paris physician Pierre Charles Alexandre Louis (1787-1872) is considered the founding father of the numerical method in medicine. At first the principle of aggregating data from different individuals aroused much resistance and even disgust: Claude Bernard was a leading figure among those who warned that one will never find a mean in nature, and that grouping findings together obscures the true relationship between biological phenomena. True enough, statistical significance is not a characteristic of nature itself. Significant differences or risk reductions do not necessarily imply clinical relevance, and results obtained in a group of patients are rarely applicable to an individual patient in the consultation room. Likewise, the health of a human being cannot be captured in biochemical, radiological or other technical measures, nor in disease-specific scales that reduce well-being to one or two digits. The editors of this journal will remain keen on publishing numerical studies that contribute to evidence-based medicine, but at the same time they will continue to foster the art of reporting illness from the point of view of the sick person.

  8. Lepton family number violation

    International Nuclear Information System (INIS)

    Herczeg, P.

    1999-01-01

    At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the τ, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author's conclusions

  9. Straight flavor of Binary Number in Decimal Number System

    OpenAIRE

    MD. Abdul Awal Ansary; Sushanta Acharjee

    2012-01-01

    Different number systems are available on the basis of their base numbers. For instance, decimal number system is of base 10, hexadecimal number system which base is 16 and, Binary number system which base is 2 etc. Some numbers systems are easy to understand by the human being and some are easy to understand by electronics machine for instance digital computers. Computers only can understand data and instructions that are stored in binary form, though we input the data and instruction in dec...

  10. Neutrino number of the universe

    International Nuclear Information System (INIS)

    Kolb, E.W.

    1981-01-01

    The influence of grand unified theories on the lepton number of the universe is reviewed. A scenario is presented for the generation of a large (>> 1) lepton number and a small (<< 1) baryon number. 15 references

  11. [Intel random number generator-based true random number generator].

    Science.gov (United States)

    Huang, Feng; Shen, Hong

    2004-09-01

    To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.

  12. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...

  13. Cosmic numbers the numbers that define our universe

    CERN Document Server

    Stein, James D

    2011-01-01

    Our fascination with numbers begins when we are children and continues throughout our lives. We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers , mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers lik

  14. Fermion number in supersymmetric models

    International Nuclear Information System (INIS)

    Mainland, G.B.; Tanaka, K.

    1975-01-01

    The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)

  15. The Mental Number Line in Dyscalculia: Impaired Number Sense or Access from Symbolic Numbers?

    Science.gov (United States)

    Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël

    2017-01-01

    Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…

  16. THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how th......, a second, regular set of number names is introduced in primary school. The study’s findings suggest that the regularity of number names influences the development of number concepts and creates a positive impact on the understanding of the base-10 system....

  17. The theory of algebraic numbers

    CERN Document Server

    Pollard, Harry

    1998-01-01

    An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

  18. Elementary number theory with programming

    CERN Document Server

    Lewinter, Marty

    2015-01-01

    A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con

  19. Distribution theory of algebraic numbers

    CERN Document Server

    Yang, Chung-Chun

    2008-01-01

    The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

  20. Random Numbers and Quantum Computers

    Science.gov (United States)

    McCartney, Mark; Glass, David

    2002-01-01

    The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

  1. Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

    International Nuclear Information System (INIS)

    Ônishi, Yoshihiro

    2011-01-01

    The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.

  2. 2016 Gainesville Number Theory Conference

    CERN Document Server

    Garvan, Frank

    2017-01-01

    Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find th...

  3. Photon number projection using non-number-resolving detectors

    International Nuclear Information System (INIS)

    Rohde, Peter P; Webb, James G; Huntington, Elanor H; Ralph, Timothy C

    2007-01-01

    Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters

  4. Bernoulli numbers and zeta functions

    CERN Document Server

    Arakawa, Tsuneo; Kaneko, Masanobu

    2014-01-01

    Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

  5. Compendium of Experimental Cetane Numbers

    Energy Technology Data Exchange (ETDEWEB)

    Yanowitz, Janet [Ecoengineering, Sharonville, OH (United States); Ratcliff, Matthew A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); McCormick, Robert L. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Taylor, J. D. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Murphy, M. J. [Battelle, Columbus, OH (United States)

    2017-02-22

    This report is an updated version of the 2014 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single-compound cetane number data found in the scientific literature up until December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTM Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines. It is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant-volume combustion chamber. Values in the previous compendium derived from octane numbers have been removed and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.

  6. Dynamic Virtual Credit Card Numbers

    Science.gov (United States)

    Molloy, Ian; Li, Jiangtao; Li, Ninghui

    Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.

  7. Number-unconstrained quantum sensing

    Science.gov (United States)

    Mitchell, Morgan W.

    2017-12-01

    Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.

  8. Schmidt number for quantum operations

    International Nuclear Information System (INIS)

    Huang Siendong

    2006-01-01

    To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided

  9. Random number generation and creativity.

    Science.gov (United States)

    Bains, William

    2008-01-01

    A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers and a deficit of repeats of the same number, in line with previous literature. However, the previous literature suggests that humans generate random numbers with substantial conscious effort, and distractions which reduce that effort reduce the randomness of the numbers. I reduced my subjects' concentration by asking them to call out in another language, and with alcohol - neither affected the randomness of their responses. This suggests that the ability to generate random numbers is a 'basic' function of the human mind, even if those numbers are not mathematically 'random'. I hypothesise that there is a 'creativity' mechanism, while not truly random, provides novelty as part of the mind's defence against closed programming loops, and that testing for the effects seen here in people more or less familiar with numbers or with spontaneous creativity could identify more features of this process. It is possible that training to perform better at simple random generation tasks could help to increase creativity, through training people to reduce the conscious mind's suppression of the 'spontaneous', creative response to new questions.

  10. Unsolved problems in number theory

    CERN Document Server

    Guy, Richard K

    1994-01-01

    Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.

  11. Complex numbers in n dimensions

    CERN Document Server

    Olariu, Silviu

    2002-01-01

    Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbe...

  12. A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

    Directory of Open Access Journals (Sweden)

    J. Y. Kang

    2013-01-01

    Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.

  13. BKP and projective Hurwitz numbers

    Science.gov (United States)

    Natanzon, Sergey M.; Orlov, Aleksandr Yu.

    2017-06-01

    We consider d-fold branched coverings of the projective plane RP^2 and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for weighted sums of the related Hurwitz numbers. In particular, we get the RP^2 analogues of the CP^1 generating functions proposed by Okounkov and by Goulden and Jackson. Other examples are Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials. We also consider integrals of tau functions which generate Hurwitz numbers related to base surfaces with arbitrary Euler characteristics sc {e}, in particular projective Hurwitz numbers sc {e}=1.

  14. Prandtl number of toroidal plasmas

    International Nuclear Information System (INIS)

    Itoh, K.; Itoh, S.; Fukuyama, A.; Yagi, M.; Azumi, M.

    1993-06-01

    Theory of the L-mode confinement in toroidal plasmas is developed. The Prandtl number, the ratio between the ion viscosity and the thermal conductivity is obtained for the anomalous transport process which is caused by the self-sustained turbulence in the toroidal plasma. It is found that the Prandtl number is of order unity both for the ballooning mode turbulence in tokamaks and for the interchange mode turbulence in helical system. The influence on the anomalous transport and fluctuation level is evaluated. Hartmann number and magnetic Prandtl number are also discussed. (author)

  15. Generalized r-Lah numbers

    Indian Academy of Sciences (India)

    016-0309-0. Generalized r-Lah numbers. MARK SHATTUCK. Department of ...... of Dowling lattices, Discrete Math. 312. (2012) 2337–2348. [7] Hsu L C and Shiue P J-S, A unified approach to generalized Stirling numbers, Adv. Appl. Math.

  16. Number theory and its history

    CERN Document Server

    Ore, Oystein

    1988-01-01

    A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.

  17. Investigating the Randomness of Numbers

    Science.gov (United States)

    Pendleton, Kenn L.

    2009-01-01

    The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…

  18. Fractions, Number Lines, Third Graders

    Science.gov (United States)

    Cramer, Kathleen; Ahrendt, Sue; Monson, Debra; Wyberg, Terry; Colum, Karen

    2017-01-01

    The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…

  19. Pseudo-Random Number Generators

    Science.gov (United States)

    Howell, L. W.; Rheinfurth, M. H.

    1984-01-01

    Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.

  20. On Counting the Rational Numbers

    Science.gov (United States)

    Almada, Carlos

    2010-01-01

    In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…

  1. Core Knowledge, Language, and Number

    Science.gov (United States)

    Spelke, Elizabeth S.

    2017-01-01

    The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

  2. The Algebra of Complex Numbers.

    Science.gov (United States)

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  3. Path-fan Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    2003-01-01

    For two given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest positive integer $p$ such that for every graph $F$ on $p$ vertices the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  4. Path-fan Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  5. Path-kipas Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    2007-01-01

    For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  6. From natural numbers to quaternions

    CERN Document Server

    Kramer, Jürg

    2017-01-01

    This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

  7. Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

    Energy Technology Data Exchange (ETDEWEB)

    Onishi, Yoshihiro [Faculty of Education Human Sciences, University of Yamanashi, Takeda, Kofu (Japan)

    2011-10-31

    The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.

  8. Low energy fermion number violation

    International Nuclear Information System (INIS)

    Peccei, R.D.

    1989-01-01

    After a brief aside on charge quantization in the standard electroweak theory, I concentrate on various aspects of anomaly induced fermion number violation in the standard model. A critical analysis of the role of sphalerons for the universe's baryon asymmetry is presented and the importance of calculating directly fermion number violating Green's functions is stressed. A physical interpretation of the recent observation of Ringwald, that coherent effects in the electroweak theory lead to catastrophic fermion number violation at 100 TeV, is discussed. Possible quantum effects which might spoil this semi-classical picture are examined

  9. Finding numbers in the brain.

    Science.gov (United States)

    Gallistel, C R

    2017-02-19

    After listing functional constraints on what numbers in the brain must do, I sketch the two's complement fixed-point representation of numbers because it has stood the test of time and because it illustrates the non-obvious ways in which an effective coding scheme may operate. I briefly consider its neurobiological implementation. It is easier to imagine its implementation at the cell-intrinsic molecular level, with thermodynamically stable, volumetrically minimal polynucleotides encoding the remembered numbers, than at the circuit level, with plastic synapses encoding them.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

  10. Fundamental number theory with applications

    CERN Document Server

    Mollin, Richard A

    2008-01-01

    An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition           Removal of all advanced material to be even more accessible in scope           New fundamental material, including partition theory, generating functions, and combinatorial number theory           Expa

  11. Classical theory of algebraic numbers

    CERN Document Server

    Ribenboim, Paulo

    2001-01-01

    Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

  12. Microcomputer Unit: Generating Random Numbers.

    Science.gov (United States)

    Haigh, William E.

    1986-01-01

    Presents an activity, suitable for students in grades 6-12, on generating random numbers. Objectives, equipment needed, list of prerequisite experiences, instructional strategies, and ready-to-copy student worksheets are included. (JN)

  13. Number theory via Representation theory

    Indian Academy of Sciences (India)

    2014-11-09

    Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.

  14. SEVIS By the Numbers 2014

    Data.gov (United States)

    Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...

  15. SEVIS By the Numbers 2016

    Data.gov (United States)

    Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...

  16. Additive theory of prime numbers

    CERN Document Server

    Hua, L K

    2009-01-01

    Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial x^k is replaced by an arbitrary polynomial of degree k. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.

  17. Advanced number theory with applications

    CERN Document Server

    Mollin, Richard A

    2009-01-01

    Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

  18. Integral Presentations of Catalan Numbers

    Science.gov (United States)

    Dana-Picard, Thierry

    2010-01-01

    We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

  19. Numbers their history and meaning

    CERN Document Server

    Flegg, Graham

    2003-01-01

    Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." - Choice.

  20. Poison control center - emergency number

    Science.gov (United States)

    For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...

  1. Women In Numbers - Europe workshop

    CERN Document Server

    Bucur, Alina; Feigon, Brooke; Schneps, Leila

    2015-01-01

    Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.

  2. Digital random-number generator

    Science.gov (United States)

    Brocker, D. H.

    1973-01-01

    For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

  3. Random numbers from vacuum fluctuations

    International Nuclear Information System (INIS)

    Shi, Yicheng; Kurtsiefer, Christian; Chng, Brenda

    2016-01-01

    We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.

  4. Numbers for reducible cubic scrolls

    Directory of Open Access Journals (Sweden)

    Israel Vainsencher

    2004-12-01

    Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.

  5. Random numbers from vacuum fluctuations

    Energy Technology Data Exchange (ETDEWEB)

    Shi, Yicheng; Kurtsiefer, Christian, E-mail: christian.kurtsiefer@gmail.com [Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Center for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Chng, Brenda [Center for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)

    2016-07-25

    We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.

  6. Banner prints social security numbers

    OpenAIRE

    Robbins RA

    2014-01-01

    No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1). The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pion...

  7. Higher-order Nielsen numbers

    Directory of Open Access Journals (Sweden)

    Saveliev Peter

    2005-01-01

    Full Text Available Suppose , are manifolds, are maps. The well-known coincidence problem studies the coincidence set . The number is called the codimension of the problem. More general is the preimage problem. For a map and a submanifold of , it studies the preimage set , and the codimension is . In case of codimension , the classical Nielsen number is a lower estimate of the number of points in changing under homotopies of , and for an arbitrary codimension, of the number of components of . We extend this theory to take into account other topological characteristics of . The goal is to find a "lower estimate" of the bordism group of . The answer is the Nielsen group defined as follows. In the classical definition, the Nielsen equivalence of points of based on paths is replaced with an equivalence of singular submanifolds of based on bordisms. We let , then the Nielsen group of order is the part of preserved under homotopies of . The Nielsen number of order is the rank of this group (then . These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.

  8. Dimensionless numbers in additive manufacturing

    Science.gov (United States)

    Mukherjee, T.; Manvatkar, V.; De, A.; DebRoy, T.

    2017-02-01

    The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.

  9. Grammatical typology and frequency analysis: number availability and number use

    Directory of Open Access Journals (Sweden)

    Dunstan Brown

    2013-12-01

    Full Text Available The Smith-Stark hierarchy, a version of the Animacy Hierarchy, offers a typology of the cross-linguistic availability of number. The hierarchy predicts that the availability of number is not arbitrary. For any language, if the expression of plural is available to a noun, it is available to any noun of a semantic category further to the left of the hierarchy. In this article we move one step further by showing that the structure of the hierarchy can be observed in a statistical model of number use in Russian. We also investigate three co-variates: plural preference, pluralia tantum and irregularity effects; these account for an item's behaviour being different than that solely expected from its animacy position.

  10. From Natural Numbers to Numbers and Curves in Nature - II

    Indian Academy of Sciences (India)

    line grows from C towards both left and right. Suppose ... Let there be n steps of growth to the left, and n-l to the right. Then n .... right-hand spirals is 8 and that of left-hand .... [4] I Stewart, Nature's Numbers - Discovering Order and Pattern in the.

  11. Number Meaning and Number Grammar in English and Spanish

    Science.gov (United States)

    Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique

    2012-01-01

    Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…

  12. The MIXMAX random number generator

    Science.gov (United States)

    Savvidy, Konstantin G.

    2015-11-01

    In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.

  13. Experimental determination of Ramsey numbers.

    Science.gov (United States)

    Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank

    2013-09-27

    Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.

  14. Stream ciphers and number theory

    CERN Document Server

    Cusick, Thomas W; Renvall, Ari R

    2004-01-01

    This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.

  15. Sequences, groups, and number theory

    CERN Document Server

    Rigo, Michel

    2018-01-01

    This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups.  This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

  16. Negative numbers and antimatter particles

    International Nuclear Information System (INIS)

    Tsan, Ung Chan

    2012-01-01

    Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter

  17. Generation of photon number states

    International Nuclear Information System (INIS)

    Waks, Edo; Diamanti, Eleni; Yamamoto, Yoshihisa

    2006-01-01

    The visible light photon counter (VLPC) has the capability to discriminate photon number states, in contrast to conventional photon counters which can only detect the presence or absence of photons. We use this capability, along with the process of parametric down-conversion, to generate photon number states. We experimentally demonstrate generation of states containing 1, 2, 3 and 4 photons with high fidelity. We then explore the effect the detection efficiency of the VLPC has on the generation rate and fidelity of the created states

  18. World Epidemiology Review, Number 105.

    Science.gov (United States)

    1978-09-13

    respectively last year. Not Siberian The official stated that the Soviet virus is not related to the famous pathogenic agent which appeared in the Siberian...numbers of aphids are due to appear on the alfalfa in the near future. The infestation has approached and even exceeded the extent at which serious

  19. Counting problems for number rings

    NARCIS (Netherlands)

    Brakenhoff, Johannes Franciscus

    2009-01-01

    In this thesis we look at three counting problems connected to orders in number fields. First we study the probability that for a random polynomial f in Z[X] the ring Z[X]/f is the maximal order in Q[X]/f. Connected to this is the probability that a random polynomial has a squarefree

  20. Linking numbers and variational method

    International Nuclear Information System (INIS)

    Oda, I.; Yahikozawa, S.

    1989-09-01

    The ordinary and generalized linking numbers for two surfaces of dimension p and n-p-1 in an n dimensional manifold are derived. We use a variational method based on the properties of topological quantum field theory in order to derive them. (author). 13 refs, 2 figs

  1. From Calculus to Number Theory

    Indian Academy of Sciences (India)

    A. Raghuram

    2016-11-04

    Nov 4, 2016 ... diverges to infinity. This means given any number M, however large, we can add sufficiently many terms in the above series to make the sum larger than M. This was first proved by Nicole Oresme (1323-1382), a brilliant. French philosopher of his times.

  2. RELATIONSHIP BETWEEN SLUDGE DEWATERABILITY NUMBER ...

    African Journals Online (AJOL)

    A representative of a sludge sample collected from the same source was filtered under the same environmental condition and the result analysed with two different concepts. One method of analysis uses Sludge Dewaterability Number, while the second employed the Carman's Specific resistance concept in sludge ...

  3. Materiales. Numbers 17-20.

    Science.gov (United States)

    Materiales, 1995

    1995-01-01

    Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2)…

  4. Materiales. Numbers 21-23.

    Science.gov (United States)

    Materiales, 1997

    1997-01-01

    These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…

  5. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  6. Models for Rational Number Bases

    Science.gov (United States)

    Pedersen, Jean J.; Armbruster, Frank O.

    1975-01-01

    This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

  7. Residual number processing in dyscalculia.

    Science.gov (United States)

    Cappelletti, Marinella; Price, Cathy J

    2014-01-01

    Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.

  8. Residual number processing in dyscalculia

    Directory of Open Access Journals (Sweden)

    Marinella Cappelletti

    2014-01-01

    Full Text Available Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.

  9. Residual number processing in dyscalculia☆

    Science.gov (United States)

    Cappelletti, Marinella; Price, Cathy J.

    2013-01-01

    Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008

  10. Learning Potentials in Number Blocks

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Misfeldt, Morten; Nielsen, Jacob

    2012-01-01

    This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher....

  11. An introduction to Catalan numbers

    CERN Document Server

    Roman, Steven

    2015-01-01

    This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics.  Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics.  Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more.  Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material.  The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones.  He has made an excellent choice o...

  12. Strouhal number for free swimming

    Science.gov (United States)

    Saadat, Mehdi; van Buren, Tyler; Floryan, Daniel; Smits, Alexander; Haj-Hariri, Hossein

    2015-11-01

    In this work, we present experimental results to explore the implications of free swimming for Strouhal number (as an outcome) in the context of a simple model for a fish that consists of a 2D virtual body (source of drag) and a 2D pitching foil (source of thrust) representing cruising with thunniform locomotion. The results validate the findings of Saadat and Haj-Hariri (2012): for pitching foils thrust coefficient is a function of Strouhal number for all gaits having amplitude less than a certain critical value. Equivalently, given the balance of thrust and drag forces at cruise, Strouhal number is only a function of the shape, i.e. drag coefficient and area, and essentially a constant for high enough swimming speeds for which the mild dependence of drag coefficient on the speed vanishes. Furthermore, a dimensional analysis generalizes the findings. A scaling analysis shows that the variation of Strouhal number with cruising speed is functionally related to the variation of body drag coefficient with speed. Supported by ONR MURI Grant N00014-14-1-0533.

  13. Higher-order Nielsen numbers

    Directory of Open Access Journals (Sweden)

    Peter Saveliev

    2005-04-01

    Full Text Available Suppose X, Y are manifolds, f,g:X→Y are maps. The well-known coincidence problem studies the coincidence set C={x:f(x=g(x}. The number m=dim X−dim Y is called the codimension of the problem. More general is the preimage problem. For a map f:X→Z and a submanifold Y of Z, it studies the preimage set C={x:f(x∈Y}, and the codimension is m=dim X+dim Y−dim Z. In case of codimension 0, the classical Nielsen number N(f,Y is a lower estimate of the number of points in C changing under homotopies of f, and for an arbitrary codimension, of the number of components of C. We extend this theory to take into account other topological characteristics of C. The goal is to find a “lower estimate” of the bordism group Ωp(C of C. The answer is the Nielsen group Sp(f,Y defined as follows. In the classical definition, the Nielsen equivalence of points of C based on paths is replaced with an equivalence of singular submanifolds of C based on bordisms. We let Sp'(f,Y=Ωp(C/∼N, then the Nielsen group of order p is the part of Sp'(f,Y preserved under homotopies of f. The Nielsen number Np(F,Y of order p is the rank of this group (then N(f,Y=N0(f,Y. These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.

  14. Gaussian distribution of LMOV numbers

    Directory of Open Access Journals (Sweden)

    A. Mironov

    2017-11-01

    Full Text Available Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri–Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (! and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.

  15. Number-theory dark matter

    Energy Technology Data Exchange (ETDEWEB)

    Nakayama, Kazunori [Theory Center, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Takahashi, Fuminobu, E-mail: fumi@tuhep.phys.tohoku.ac.jp [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Yanagida, Tsutomu T. [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)

    2011-05-23

    We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1){sub B-L} gauge symmetry, Z{sub 2}(B-L). We introduce a set of chiral fermions charged under the U(1){sub B-L} in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1){sub B-L} gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z{sub 2}(B-L).

  16. Number-theory dark matter

    International Nuclear Information System (INIS)

    Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.

    2011-01-01

    We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1) B-L gauge symmetry, Z 2 (B-L). We introduce a set of chiral fermions charged under the U(1) B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1) B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z 2 (B-L).

  17. More Sets, Graphs and Numbers

    CERN Document Server

    Gyori, Ervin; Lovasz, Laszlo

    2006-01-01

    This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.

  18. Large number discrimination by mosquitofish.

    Directory of Open Access Journals (Sweden)

    Christian Agrillo

    Full Text Available BACKGROUND: Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4 were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. METHODOLOGY/PRINCIPAL FINDINGS: Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance. Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1:2 or 2:3 but not when the ratio was 3:4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. CONCLUSIONS/SIGNIFICANCE: Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all

  19. DISCRETE MATHEMATICS/NUMBER THEORY

    OpenAIRE

    Mrs. Manju Devi*

    2017-01-01

    Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

  20. Number systems and combinatorial problems

    OpenAIRE

    Yordzhev, Krasimir

    2014-01-01

    The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in combinatorial analysis and most of all when proving some combinatorial identities. To demonstrate discussed in this article method we have chosen several suitable mathematical tasks.

  1. World Epidemiology Review, Number 109.

    Science.gov (United States)

    1978-10-11

    infantilism, "lung color," monale, followed by cardiac deficiency, cyanosis, intestinal stenosis ; glomerulonephritis and neurological symptoms. Many...Bursa were infected by rabid dogs and cats. The following breakdown was given for the number of persons infected during the succeeding 7 months of...area it is much more difficult to save his life. One of the six dogs taken into custody under the suspicion of being rabid during the past 8 months

  2. Number theory meets Higgs physics

    CERN Multimedia

    CERN. Geneva

    2014-01-01

    Inspired by results from modern number theory and algebraic geometry, a lot of progress has recently been made regarding the computation of multi-loop integrals and scattering amplitudes. I will discuss various new approaches to the computation of loop integrals, and illustrate them on the first computation of a quantity at N3LO in perturbative QCD, the soft-virtual part of the inclusive Higgs-boson cross section in gluon fusion at N3LO.

  3. Residual number processing in dyscalculia ?

    OpenAIRE

    Cappelletti, Marinella; Price, Cathy J.

    2013-01-01

    Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and ca...

  4. Secular Love number of Phobos

    International Nuclear Information System (INIS)

    Bursa, M.

    1988-01-01

    The secular Love number of Phobos was estimated k s =10.4. It only deviates by one order of magnitude from that corresponding to the ideal equilibrium state. It is not in contradiction with the theory of the origin of Phobos as a result of the accretion around Mars. In its early history, the rotation period of Phobos had been estimated to be approx. 2.4 hours. (author). 1 tab., 4 refs

  5. When a number is not only a number

    DEFF Research Database (Denmark)

    Christensen, Ken Ramshøj; Roepstorff, Andreas; Saddy, Douglas

    at. 1999, 2004). Furthermore, lesions studies have shown that damage to the posterior inferior parietal cortex leads to severe difficulties with performing simple calculation, such as stepwise computation (Joseph 2000: 463). The same frontal-parietal network is also involved in working memory (WM......MRI study which involves numerical processing as well as WM and error detection. Three types of stimuli: (a) repeated chunks (x, y, z, x, y, z…), (b) smaller structured chunks requiring minimal calculation (x, x+1, y, y+1, z, z+1…), and (c) strings with an increased calculation requirement (x = x+3......). The control condition consists of simple x = x+1 strings (e.g. 1, 2, 3, 4, 5, 6…). The subjects have to press a button when they detect error to the general patterns, i.e., when a number does not conform to the numerical string. Using a block design to investigate the numerical processing, all three...

  6. Propulsion at low Reynolds number

    International Nuclear Information System (INIS)

    Najafi, Ali; Golestanian, Ramin

    2005-01-01

    We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium

  7. Propulsion at low Reynolds number

    Energy Technology Data Exchange (ETDEWEB)

    Najafi, Ali [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of); Faculty of Science, Zanjan University, Zanjan 313 (Iran, Islamic Republic of); Golestanian, Ramin [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of)

    2005-04-13

    We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.

  8. Fedosov differentials and Catalan numbers

    Energy Technology Data Exchange (ETDEWEB)

    Loeffler, Johannes, E-mail: j.j.loeffler@web.d [Muehlgasse 19, 78549 Spaichingen (Germany)

    2010-06-11

    The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced.

  9. Fedosov differentials and Catalan numbers

    Science.gov (United States)

    Löffler, Johannes

    2010-06-01

    The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced. Dedicated to the memory of Nikolai Neumaier.

  10. Phalanx. Volume 47, Number 4

    Science.gov (United States)

    2014-12-01

    at $23,200 an hour. So that’s another $1.2M a day. Pete: Don’t they shoot at you? Joe: Well, we usually wire together a bunch of microwave ovens we...Officer, to break his vow never to sail on a “ bird farm.” MORS welcomes Kevin Williams as the new AF sponsor. He became the Director of...person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number

  11. Random Generators and Normal Numbers

    OpenAIRE

    Bailey, David H.; Crandall, Richard E.

    2002-01-01

    Pursuant to the authors' previous chaotic-dynamical model for random digits of fundamental constants, we investigate a complementary, statistical picture in which pseudorandom number generators (PRNGs) are central. Some rigorous results are achieved: We establish b-normality for constants of the form $\\sum_i 1/(b^{m_i} c^{n_i})$ for certain sequences $(m_i), (n_i)$ of integers. This work unifies and extends previously known classes of explicit normals. We prove that for coprime $b,c>1$ the...

  12. On the intriguing number 1001

    DEFF Research Database (Denmark)

    Krarup, Jakob

    2016-01-01

    Born in 1936 I was a schoolboy on the threshold of the secondary school when a knapsack-type game was played with a class mate around 1946–1947. To play the game well and fascinated by numbers in general since my early childhood, however, I realized soon the usefulness of knowing that 1001 = 7 × 11...... × 13. Today, about 70 years later, the game has been passed to some of my grandchildren who also should convince themselves that simple, arithmetic calculations do not necessarily require a pocket computer. As a side effect of the recent revival of the game I felt motivated to seek more insight...

  13. Nielsen number and differential equations

    Directory of Open Access Journals (Sweden)

    Andres Jan

    2005-01-01

    Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.

  14. Cryptography and computational number theory

    CERN Document Server

    Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99

    2001-01-01

    This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...

  15. Signals of lepton number violation

    CERN Document Server

    Panella, O; Srivastava, Y N

    1999-01-01

    The production of like-sign-dileptons (LSD), in the high energy lepton number violating ( Delta L=+2) reaction, pp to 2jets+l/sup +/l /sup +/, (l=e, mu , tau ), of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is reported, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the standard model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 700 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ( beta beta /sub 0 nu /) experiment, GENIUS, and i...

  16. Number theory III Diophantine geometry

    CERN Document Server

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  17. Banner prints social security numbers

    Directory of Open Access Journals (Sweden)

    Robbins RA

    2014-02-01

    Full Text Available No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1. The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pioneer Accountable Care Organization, a government health-care plan that Banner serves. Banner generated its mailing list from information it received from the U.S. Centers for Medicare & Medicaid Services, which is an agency within the U.S. Department of Health & Human Services (HHS responsible for administration of several federal health-care programs. Although medical information has been protected by the Health Insurance Portability and Accountability Act (HIPAA since 1996, penalties were recently increased. Civil monetary penalties were increased from a maximum of $100 ...

  18. Intersection numbers of spectral curves

    CERN Document Server

    Eynard, B.

    2011-01-01

    We compute the symplectic invariants of an arbitrary spectral curve with only 1 branchpoint in terms of integrals of characteristic classes in the moduli space of curves. Our formula associates to any spectral curve, a characteristic class, which is determined by the laplace transform of the spectral curve. This is a hint to the key role of Laplace transform in mirror symmetry. When the spectral curve is y=\\sqrt{x}, the formula gives Kontsevich--Witten intersection numbers, when the spectral curve is chosen to be the Lambert function \\exp{x}=y\\exp{-y}, the formula gives the ELSV formula for Hurwitz numbers, and when one chooses the mirror of C^3 with framing f, i.e. \\exp{-x}=\\exp{-yf}(1-\\exp{-y}), the formula gives the Marino-Vafa formula, i.e. the generating function of Gromov-Witten invariants of C^3. In some sense this formula generalizes ELSV, Marino-Vafa formula, and Mumford formula.

  19. Topics in Number Theory Conference

    CERN Document Server

    Andrews, George; Ono, Ken

    1999-01-01

    From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci­ ence Foundation, The Penn State Conference Center and the Penn State Depart­ ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. ...

  20. Use of number by fish.

    Directory of Open Access Journals (Sweden)

    Christian Agrillo

    Full Text Available BACKGROUND: Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. METHODOLOGY/PRINCIPAL FINDINGS: Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. CONCLUSIONS/SIGNIFICANCE: Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a 'last resort' strategy in fish, when no other

  1. Galaxy number counts: Pt. 2

    International Nuclear Information System (INIS)

    Metcalfe, N.; Shanks, T.; Fong, R.; Jones, L.R.

    1991-01-01

    Using the Prime Focus CCD Camera at the Isaac Newton Telescope we have determined the form of the B and R galaxy number-magnitude count relations in 12 independent fields for 21 m ccd m and 19 m ccd m 5. The average galaxy count relations lie in the middle of the wide range previously encompassed by photographic data. The field-to-field variation of the counts is small enough to define the faint (B m 5) galaxy count to ±10 per cent and this variation is consistent with that expected from galaxy clustering considerations. Our new data confirm that the B, and also the R, galaxy counts show evidence for strong galaxy luminosity evolution, and that the majority of the evolving galaxies are of moderately blue colour. (author)

  2. Polynomials formalism of quantum numbers

    International Nuclear Information System (INIS)

    Kazakov, K.V.

    2005-01-01

    Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

  3. A weakly compressible formulation for modelling liquid-gas sloshing

    CSIR Research Space (South Africa)

    Heyns, Johan A

    2012-09-01

    Full Text Available This study presents the development and extension of free-surface modelling techniques with the purpose of improving the modelling accuracy for liquid-gas sloshing. Considering high density ratio fluids under low Mach number conditions...

  4. Effect of Stoichiometry and Strain Rate on Transient Flame Response

    National Research Council Canada - National Science Library

    Knio, Omar M; Najm, Habib N

    2000-01-01

    The interaction of a premixed methane/air flame with a counter-rotating vortex pair is analyzed using a parallel low-Mach-number computational model that is based on a detailed C1C2 chemical mechanism...

  5. Diffusion-controlled reactions modeling in Geant4-DNA

    Czech Academy of Sciences Publication Activity Database

    Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davídková, Marie; Francis, Z.; Friedland, W.; Ivanchenko, A.; Ivanchenko, V.; Mantero, A.; Nieminen, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.

    2014-01-01

    Roč. 274, OCT (2014), s. 841-882 ISSN 0021-9991 Institutional support: RVO:61389005 Keywords : chemical kinetics simulation * radiation chemistry * Fokker-Planck equation * Smoluchowski diffusion equation * Brownian bridge * dynamical time steps * k-d tree * radiolysis * radiobiology * Geant4-DNA * Brownian dynamics Subject RIV: BO - Biophysics Impact factor: 2.434, year: 2014

  6. A MODEL FOR DIFFUSION CONTROLLED BIOAVAILABILITY OF CRUDE OIL COMPONENTS

    Science.gov (United States)

    Crude oil is a complex mixture of several different structural classes of compounds including alkanes, aromatics, heterocyclic polar compounds, and asphaltenes. The rate and extent of microbial degradation of crude oil depends on the interaction between the physical and biochemi...

  7. Reaction-diffusion controlled growth of complex structures

    Science.gov (United States)

    Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna

    2013-03-01

    Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support

  8. Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics.

    Science.gov (United States)

    Lee, Sangyun; Kim, Ji-Hyun; Lee, Sangyoub

    2012-02-14

    Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit. Our estimate of the overall bimolecular reaction rate constant for the enzyme is in good agreement with the experimental data. In addition, the present calculation provides a reasonable explanation for the effects of the ionic strength of solution and the mutation of surface residues of the enzyme. The study suggests that internal diffusion of the substrate could be a key factor in understanding the kinetics of enzymes of similar characteristics.

  9. Permeability, storage and hydraulic diffusivity controlled by earthquakes

    Science.gov (United States)

    Brodsky, E. E.; Fulton, P. M.; Xue, L.

    2016-12-01

    Earthquakes can increase permeability in fractured rocks. In the farfield, such permeability increases are attributed to seismic waves and can last for months after the initial earthquake. Laboratory studies suggest that unclogging of fractures by the transient flow driven by seismic waves is a viable mechanism. These dynamic permeability increases may contribute to permeability enhancement in the seismic clouds accompanying hydraulic fracking. Permeability enhancement by seismic waves could potentially be engineered and the experiments suggest the process will be most effective at a preferred frequency. We have recently observed similar processes inside active fault zones after major earthquakes. A borehole observatory in the fault that generated the M9.0 2011 Tohoku earthquake reveals a sequence of temperature pulses during the secondary aftershock sequence of an M7.3 aftershock. The pulses are attributed to fluid advection by a flow through a zone of transiently increased permeability. Directly after the M7.3 earthquake, the newly damaged fault zone is highly susceptible to further permeability enhancement, but ultimately heals within a month and becomes no longer as sensitive. The observation suggests that the newly damaged fault zone is more prone to fluid pulsing than would be expected based on the long-term permeability structure. Even longer term healing is seen inside the fault zone of the 2008 M7.9 Wenchuan earthquake. The competition between damage and healing (or clogging and unclogging) results in dynamically controlled permeability, storage and hydraulic diffusivity. Recent measurements of in situ fault zone architecture at the 1-10 meter scale suggest that active fault zones often have hydraulic diffusivities near 10-2 m2/s. This uniformity is true even within the damage zone of the San Andreas fault where permeability and storage increases balance each other to achieve this value of diffusivity over a 400 m wide region. We speculate that fault zones may evolve to a preferred diffusivity in a dynamic equilibrium.

  10. The european emergency number 112 - the questionnaire

    Directory of Open Access Journals (Sweden)

    Krzysztof Goniewicz

    2017-07-01

    Conclusions. Most of the respondents (92% identify the 112 number as an emergency number that allows them to connect to emergency services from anywhere in the European Union. A significant number of respondents (47% identify the 112 number as an emergency number in Poland. One in three respondents will use the 999 number to contact the emergency services as a witness to an emergency in Poland. Non-medical university students more often (63% will use the 112 emergency number than medical college students (41%. Respondents (98% confirmed the usefulness of a unified emergency number throughout Europe, but decided that they were not sufficiently informed about 112 as the European emergency number.

  11. Essays on the theory of numbers

    CERN Document Server

    Dedekind, Richard

    1963-01-01

    Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.

  12. How to be Brilliant at Numbers

    CERN Document Server

    Webber, Beryl

    2010-01-01

    How to be Brilliant at Numbers will help students to develop an understanding of numbers, place value, fractions and decimals. They will develop the language of number, and of the relationships between numbers. They will also use mathematics to solve problems and will develop mathematical reasoning. Using the worksheets in this book, pupils will learn about: ancient Greek numbers; coins; digits; consecutive numbers; magic ladders; fractions; matching pairs; multiples of 10; rounding; decimal un

  13. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  14. Visuospatial Priming of the Mental Number Line

    Science.gov (United States)

    Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco

    2008-01-01

    It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…

  15. Fast integration using quasi-random numbers

    International Nuclear Information System (INIS)

    Bossert, J.; Feindt, M.; Kerzel, U.

    2006-01-01

    Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples

  16. Fast integration using quasi-random numbers

    Science.gov (United States)

    Bossert, J.; Feindt, M.; Kerzel, U.

    2006-04-01

    Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples.

  17. On domination multisubdivision number of unicyclic graphs

    Directory of Open Access Journals (Sweden)

    Joanna Raczek

    2018-01-01

    Full Text Available The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009, 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.

  18. The magic of a number system

    DEFF Research Database (Denmark)

    Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki

    2010-01-01

    We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit i...... is 2 i-1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored....

  19. Observing Optional Number in DDC Edition 23

    Directory of Open Access Journals (Sweden)

    Rotmianto Mohamad

    2018-01-01

    Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially for a librarian as classifier. This paper is a literature study about Dewey Decimal Classification Edition 23, to describe about optional numbers, particularly the number in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.

  20. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Moreover, we will also study some stability problems of those equations. ... Wisconsin in which he discussed a number of important unsolved problems [18]. ... According to a well-known theorem in number theory, a positive integer of the form.

  1. Nielsen number of a covering map

    Directory of Open Access Journals (Sweden)

    Jezierski Jerzy

    2006-01-01

    Full Text Available We consider a finite regular covering over a compact polyhedron and a map admitting a lift . We show some formulae expressing the Nielsen number as a linear combination of the Nielsen numbers of its lifts.

  2. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... Bell number determinant; product; inequality; generating function; derivative; absolutely monotonic function; completely monotonic func- tion; logarithmically absolutely monotonic function; logarithmically completely monotonic function; Stirling number of the second kind; induction; Faà di Bruno formula;.

  3. A new definition of Bejan number

    Directory of Open Access Journals (Sweden)

    Awad Mohamed M.

    2012-01-01

    Full Text Available A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1, both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion.

  4. Hyperreal Numbers for Infinite Divergent Series

    OpenAIRE

    Bartlett, Jonathan

    2018-01-01

    Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent serie...

  5. 49 CFR 230.47 - Boiler number.

    Science.gov (United States)

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall...

  6. Developmental Changes in the Whole Number Bias

    Science.gov (United States)

    Braithwaite, David W.; Siegler, Robert S.

    2018-01-01

    Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…

  7. Altermatic number of categorical product of graphs

    DEFF Research Database (Denmark)

    Alishahi, Meysam; Hajiabolhassan, Hossein

    2018-01-01

    In this paper, we prove some relaxations of Hedetniemi's conjecture in terms of altermatic number and strong altermatic number of graphs, two combinatorial parameters introduced by the present authors Alishahi and Hajiabolhassan (2015) providing two sharp lower bounds for the chromatic number of ...

  8. Thermal convection for large Prandtl numbers

    NARCIS (Netherlands)

    Grossmann, Siegfried; Lohse, Detlef

    2001-01-01

    The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer

  9. Graphing Powers and Roots of Complex Numbers.

    Science.gov (United States)

    Embse, Charles Vonder

    1993-01-01

    Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)

  10. Combinatorial Interpretation of General Eulerian Numbers

    OpenAIRE

    Tingyao Xiong; Jonathan I. Hall; Hung-Ping Tsao

    2014-01-01

    Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions { a, a+d, a+2d,...}.

  11. Number to finger mapping is topological.

    NARCIS (Netherlands)

    Plaisier, M.A.; Smeets, J.B.J.

    2011-01-01

    It has been shown that humans associate fingers with numbers because finger counting strategies interact with numerical judgements. At the same time, there is evidence that there is a relation between number magnitude and space as small to large numbers seem to be represented from left to right. In

  12. 20 CFR 404.1220 - Identification numbers.

    Science.gov (United States)

    2010-04-01

    .... The special number will also be assigned to an interstate instrumentality if pre-1987 coverage is obtained and SSA will send a Form SSA-214-CD to the interstate instrumentality to notify it of the number.... SSA will send the State a Form SSA-214-CD, “Notice of Identifying Number,” to inform the State of the...

  13. 46 CFR Sec. 2 - Voyage numbers.

    Science.gov (United States)

    2010-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...

  14. An adventurer's guide to number theory

    CERN Document Server

    Friedberg, Richard

    1995-01-01

    In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes

  15. Fibonacci and Catalan Numbers An Introduction

    CERN Document Server

    Grimaldi, Ralph

    2012-01-01

    In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers

  16. Defense Horizons. Number 79, April 2015

    Science.gov (United States)

    2015-04-01

    law , no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB...79, April 2015 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT...aggression. Even more issues emerged following the downing of Malaysian Airlines Flight 17 over Ukraine in July 2014, and cross-border ar- tillery renewed

  17. What Do Numbers Do in Transnational Governance?

    DEFF Research Database (Denmark)

    Krause Hansen, Hans; Porter, Tony

    2012-01-01

    processes. Numbers have properties that differ from words, and shifts from one to the other in governance, for instance in the displacement of laws or norms with risk models or rankings based on numbers, have particular effects, including political effects on states, firms, individuals, and other actors......This study examines how numbers in transnational governance constitute actors, objects, and relationships, including relationships of power. We review the existing literatures on numbers for insights relevant to their role in transnational governance, including the ontology of numbers, the history...

  18. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    OpenAIRE

    Bugeaud, Yann; Evertse, Jan-Hendrik

    2007-01-01

    We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

  19. RELATIONSHIP BETWEEN MOBILE NUMBER PORTABILITY AND CONSUMER CHOICE OF ACTIVE MULTIPLE MOBILE PHONE NUMBERS IN GHANA

    OpenAIRE

    Solomon A. Keelson; Addo J. Odei

    2014-01-01

    The use of multiple mobile phone numbers in Ghana has become a dominate phenomenon in recent years. The introduction of mobile number portability (MNP) makes it possible for a subscriber to conveniently switch from one mobile network to another without losing his or her number. Because of mobile number portability, we expected that use of multiple numbers would become less attractive. This study examines how mobile number portability has affected the use of multiple phone numbers. We use top,...

  20. Fibonacci number of the tadpole graph

    Directory of Open Access Journals (Sweden)

    Joe DeMaio

    2014-10-01

    Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

  1. Certain number-theoretic episodes in algebra

    CERN Document Server

    Sivaramakrishnan, R

    2006-01-01

    Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

  2. On the binary expansions of algebraic numbers

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl

    2003-07-01

    Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.

  3. Interaction of Number Magnitude and Auditory Localization.

    Science.gov (United States)

    Golob, Edward J; Lewald, Jörg; Jungilligens, Johannes; Getzmann, Stephan

    2016-01-01

    The interplay of perception and memory is very evident when we perceive and then recognize familiar stimuli. Conversely, information in long-term memory may also influence how a stimulus is perceived. Prior work on number cognition in the visual modality has shown that in Western number systems long-term memory for the magnitude of smaller numbers can influence performance involving the left side of space, while larger numbers have an influence toward the right. Here, we investigated in the auditory modality whether a related effect may bias the perception of sound location. Subjects (n = 28) used a swivel pointer to localize noise bursts presented from various azimuth positions. The noise bursts were preceded by a spoken number (1-9) or, as a nonsemantic control condition, numbers that were played in reverse. The relative constant error in noise localization (forward minus reversed speech) indicated a systematic shift in localization toward more central locations when the number was smaller and toward more peripheral positions when the preceding number magnitude was larger. These findings do not support the traditional left-right number mapping. Instead, the results may reflect an overlap between codes for number magnitude and codes for sound location as implemented by two channel models of sound localization, or possibly a categorical mapping stage of small versus large magnitudes. © The Author(s) 2015.

  4. CT number of the fatty liver

    International Nuclear Information System (INIS)

    Maeda, Hiroko; Kawai, Takeshi; Kanasaki, Yoshiki; Akagi, Hiroaki

    1981-01-01

    This report is studied on CT number and CT images of the eight cases with fatty liver. Five of these cases showed the reversal of densities of the liver and vessels. In these cases, the diagnoses of the fatty liver were easible. In other cases, the diagnoses were possible only by comparison of the CT number of the liver and spleen because the CT number of normal liver were higher than those of the spleen. In the results which we examined the correlation of the CT number and specific gravities of the blood, normal saline, distilled water, mayonnaise, eatable iol, ethyl alcohol and lard, we observed the linear relationship between CT number and specific gravities. And so, we think that the diagnosis of the fatty liver and the degree of fatty infiltration can be guessed by the CT number of the liver and spleen. (author)

  5. Observing Optional Number in DDC Edition 23

    Directory of Open Access Journals (Sweden)

    Mohamad Rotmianto

    2015-04-01

    Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially  for  a  librarian  as  classifier.  This  paper  is  a  literature  study  about  Dewey  Decimal Classification  Edition  23,  to  describe  about  optional  numbers,  particularly  the  number  in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.

  6. Self-correcting random number generator

    Science.gov (United States)

    Humble, Travis S.; Pooser, Raphael C.

    2016-09-06

    A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.

  7. Relativistic theory of tidal Love numbers

    International Nuclear Information System (INIS)

    Binnington, Taylor; Poisson, Eric

    2009-01-01

    In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

  8. Cortical areas involved in Arabic number reading.

    Science.gov (United States)

    Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F

    2008-01-15

    Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p area (Brodmann area 37; p areas.

  9. Neocortical glial cell numbers in human brains

    DEFF Research Database (Denmark)

    Pelvig, D.P.; Pakkenberg, H.; Stark, A.K.

    2008-01-01

    Stereological cell counting was applied to post-mortem neocortices of human brains from 31 normal individuals, age 18-93 years, 18 females (average age 65 years, range 18-93) and 13 males (average age 57 years, range 19-87). The cells were differentiated in astrocytes, oligodendrocytes, microglia...... while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males...... and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons...

  10. THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY

    OpenAIRE

    Reluga, Timothy C.; Medlock, Jan; Galvani, Alison

    2009-01-01

    The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measur...

  11. Analysis of android random number generator

    OpenAIRE

    Sarıtaş, Serkan

    2013-01-01

    Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013. Thesis (Master's) -- Bilkent University, 2013. Includes bibliographical references leaves 61-65. Randomness is a crucial resource for cryptography, and random number generators are critical building blocks of almost all cryptographic systems. Therefore, random number generation is one of the key parts of secure communication. Random number generatio...

  12. Quality pseudo-random number generator

    International Nuclear Information System (INIS)

    Tarasiuk, J.

    1996-01-01

    The pseudo-random number generator (RNG) was written to match needs of nuclear and high-energy physics computation which in some cases require very long and independent random number sequences. In this random number generator the repetition period is about 10 36 what should be sufficient for all computers in the world. In this article the test results of RNG correlation, speed and identity of computations for PC, Sun4 and VAX computer tests are presented

  13. Number conserving approach in quasiparticle representation

    International Nuclear Information System (INIS)

    Oudih, M.R.; Fellah, M.; Allal, N.H.

    2003-01-01

    An exact number conserving approach is formulated in the quasiparticle representation to show the effect of the particle-number projection on the ground and the first 0+ excited states. It is applied to the two-level pairing model, which allows an exact solution and a comparison to other approaches. The present method has proved to be an advantageous alternative as compared to the BCS and to the usual methods used to restore the particle number symmetry. (author)

  14. Random walk of the baryon number

    International Nuclear Information System (INIS)

    Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.

    1989-01-01

    A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated

  15. Trading volume and the number of trades

    OpenAIRE

    Marwan Izzeldin

    2007-01-01

    Trading volume and the number of trades are both used as proxies for market activity, with disagreement as to which is the better proxy for market activity. This paper investigates this issue using high frequency data for Cisco and Intel in 1997. A number of econometric methods are used, including GARCH augmented with lagged trading volume and number of trades, tests based on moment restrictions, regression analysis of volatility on volume and trades, normality of returns when standardized by...

  16. Conferences on Combinatorial and Additive Number Theory

    CERN Document Server

    2014-01-01

    This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.

  17. Asymptotics of quantum weighted Hurwitz numbers

    Science.gov (United States)

    Harnad, J.; Ortmann, Janosch

    2018-06-01

    This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

  18. Unique Physician Identification Number (UPIN) Directory

    Data.gov (United States)

    U.S. Department of Health & Human Services — The Unique Physician Identification Number (UPIN) Directory contains selected information on physicians, doctors of Osteopathy, limited licensed practitioners and...

  19. Total dominator chromatic number of a graph

    Directory of Open Access Journals (Sweden)

    Adel P. Kazemi

    2015-06-01

    Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.

  20. Numbers and other math ideas come alive

    CERN Document Server

    Pappas, Theoni

    2012-01-01

    Most people don't think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive. Pappas explores mathematical ideas by looking behind the scenes of what numbers, points, lines, and other concepts are saying and thinking. In each story, properties and characteristics of math ideas are entertainingly uncovered and explained through the dialogues and actions of its math

  1. Asymptotic numbers, asymptotic functions and distributions

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1979-07-01

    The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)

  2. Continental anthropogenic primary particle number emissions

    Science.gov (United States)

    Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus

    2016-06-01

    Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening

  3. Continental anthropogenic primary particle number emissions

    Directory of Open Access Journals (Sweden)

    P. Paasonen

    2016-06-01

    Full Text Available Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas–Air Pollution Interactions and Synergies model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa, coke production (Russia and China, and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol–cloud interactions as well as particle number related adverse health effects, e.g. in response

  4. Analytic number theory an introductory course

    CERN Document Server

    Bateman, Paul T

    2004-01-01

    This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed.

  5. Hello, I am not an NHS number.

    Science.gov (United States)

    Bates, Jane

    2016-09-14

    I was handed a request to return a patient's call and given a name, signs and symptoms and a number with ten digits, starting with a seven. There was no preceding zero, and assuming it must be a mistake I stuck one on, and dialled. The number was unobtainable.

  6. Nonclassicality in phase-number uncertainty relations

    International Nuclear Information System (INIS)

    Matia-Hernando, Paloma; Luis, Alfredo

    2011-01-01

    We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.

  7. Nonclassicality in phase-number uncertainty relations

    Energy Technology Data Exchange (ETDEWEB)

    Matia-Hernando, Paloma; Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)

    2011-12-15

    We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.

  8. Savaaksrat Kisitchisit (Numbers 1-10).

    Science.gov (United States)

    Pulu, Tupou L.; And Others

    This first grade workbook is designed for children in bilingual Inupiat-English programs in the Alaskan villages of Ambler, Kiana, Kobuk, Noorvik, Selawik, and Shungnak. Each page has a particular number, a corresponding picture with an appropriate caption, and lines for the child to use in writing the number. (CFM)

  9. Hacking DNA copy number for circuit engineering.

    Science.gov (United States)

    Wu, Feilun; You, Lingchong

    2017-07-27

    DNA copy number represents an essential parameter in the dynamics of synthetic gene circuits but typically is not explicitly considered. A new study demonstrates how dynamic control of DNA copy number can serve as an effective strategy to program robust oscillations in gene expression circuits.

  10. 7 CFR 46.20 - Lot numbers.

    Science.gov (United States)

    2010-01-01

    ... and entered on all sales tickets identifying and segregating the sales from the various shipments on hand. The lot number shall be entered on the sales tickets by the salesmen at the time of sale or by the produce dispatcher, and not by bookkeepers or others after the sales have been made. No lot number...

  11. Search for lepton-family-number nonconservation

    International Nuclear Information System (INIS)

    Hoffman, C.M.

    1986-01-01

    A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given

  12. On contact numbers in random rod packings

    NARCIS (Netherlands)

    Wouterse, A.; Luding, Stefan; Philipse, A.P.

    2009-01-01

    Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well

  13. Families of Linear Recurrences for Catalan Numbers

    Science.gov (United States)

    Gauthier, N.

    2011-01-01

    Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…

  14. 41 CFR 105-1.109 - Numbering.

    Science.gov (United States)

    2010-07-01

    ... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering. ...

  15. Game chromatic number of lexicographic product graphs

    Directory of Open Access Journals (Sweden)

    R. Alagammai

    2015-11-01

    Full Text Available In this paper, we determine the exact values of the game chromatic number of lexicographic product of path P2 with path Pn, star K1,n and wheel Wn. Also we give an upper bound for the game chromatic number of lexicographic product of any two simple graphs G and H.

  16. Teach Kids about Numbers All around Us

    Science.gov (United States)

    Hudson, Hannah Trierweiler

    2011-01-01

    Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers…

  17. The Power of Numbers in Global Governance

    DEFF Research Database (Denmark)

    Krause Hansen, Hans; Mühlen-Schulte, Arthur

    2012-01-01

    of the historical and contemporary role of numbers in different governance settings. It includes a discussion of the capacity of numbers to foster social identities, relations and truths across national boundaries, to construct issue areas and to enable various modes of surveillance, communication and action...... and relations, as well as in relation to processes of politicisation and de-politicisation that transcend national spaces....

  18. Lepton number violation searches at the LHC

    CERN Document Server

    Salvucci, Antonio; The ATLAS collaboration

    2017-01-01

    Lepton number is conserved in the Standard Model, therefore, any evidence for its violation would indicate the existence of new physics. This talk presents a review of the latest searches performed at the LHC concerning Lepton Number Violation (LNV) processes in the context of Left-Right Symmetric theory and Seesaw mechanism.

  19. Cellular Automata Rules and Linear Numbers

    OpenAIRE

    Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika

    2012-01-01

    In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.

  20. On the Concept Image of Complex Numbers

    Science.gov (United States)

    Nordlander, Maria Cortas; Nordlander, Edvard

    2012-01-01

    A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…

  1. Fourier analysis in combinatorial number theory

    International Nuclear Information System (INIS)

    Shkredov, Il'ya D

    2010-01-01

    In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

  2. Fourier analysis in combinatorial number theory

    Energy Technology Data Exchange (ETDEWEB)

    Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2010-09-16

    In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

  3. Atomic Fisher information versus atomic number

    International Nuclear Information System (INIS)

    Nagy, A.; Sen, K.D.

    2006-01-01

    It is shown that the Thomas-Fermi Fisher information is negative. A slightly more sophisticated model proposed by Gaspar provides a qualitatively correct expression for the Fisher information: Gaspar's Fisher information is proportional to the two-third power of the atomic number. Accurate numerical calculations show an almost linear dependence on the atomic number

  4. The Ramsey Numbers of Paths Versus Fans

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.; Faigle, U.; Hurink, Johann L.; Pickl, Stefan; Woeginger, Gerhard

    2003-01-01

    For two given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Fm), where Pn is

  5. The prime numbers and their distribution

    CERN Document Server

    Tenenbaum, Gerald

    2000-01-01

    One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

  6. Complex numbers from A to Z

    CERN Document Server

    Andreescu, Titu

    2014-01-01

    It is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics. The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them. The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. The book reflects the unique experience of the authors. It distills a vast mathematical literature, most ...

  7. On the nullity number of graphs

    Directory of Open Access Journals (Sweden)

    Mustapha Aouchiche

    2017-10-01

    Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

  8. Ramsey numbers and adiabatic quantum computing.

    Science.gov (United States)

    Gaitan, Frank; Clark, Lane

    2012-01-06

    The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

  9. Topics from the theory of numbers

    CERN Document Server

    Grosswald, Emil

    1984-01-01

    Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: * divisibility * congruences * the Riemann zeta function * Diophantine equations and Fermat’s conjecture * the theory of partitions Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at...

  10. A conversational introduction to algebraic number theory

    CERN Document Server

    Pollack, Paul

    2017-01-01

    Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \\mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise w...

  11. Relativistic theory of surficial Love numbers

    Science.gov (United States)

    Landry, Philippe; Poisson, Eric

    2014-06-01

    A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

  12. Random numbers spring from alpha decay

    International Nuclear Information System (INIS)

    Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.

    1980-05-01

    Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a 235 U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables

  13. Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

    Science.gov (United States)

    Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter

    2004-01-01

    Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…

  14. Alternative analysis: the prime numbers theory and an extension of the real numbers set

    OpenAIRE

    Sukhotin A.; Zvyagin M.

    2016-01-01

    Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) applicatio...

  15. Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers

    OpenAIRE

    Kaneko, Hajime; Komatsu, Takao

    2017-01-01

    Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of Stirling-Carlitz numbers and give some general formulae, including Bernoulli and Cauchy numbers in formal power series with complex coefficients, and Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields. We also give some applications of Hasse-Teichm...

  16. Neocortical glial cell numbers in human brains.

    Science.gov (United States)

    Pelvig, D P; Pakkenberg, H; Stark, A K; Pakkenberg, B

    2008-11-01

    Stereological cell counting was applied to post-mortem neocortices of human brains from 31 normal individuals, age 18-93 years, 18 females (average age 65 years, range 18-93) and 13 males (average age 57 years, range 19-87). The cells were differentiated in astrocytes, oligodendrocytes, microglia and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males, a difference of 24% with a high biological variance. These numbers can serve as reference values in quantitative studies of the human neocortex.

  17. Theory of analogous force on number sets

    Energy Technology Data Exchange (ETDEWEB)

    Canessa, Enrique [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)

    2003-08-01

    A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions p{sub x} for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering p{sub x} to describe complex phenomena, the theory leads to derive a distinct analogous force f{sub x} on number sets proportional to ({partial_derivative}p{sub x}/{partial_derivative}x){sub T} at an analogous system temperature T. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed. (author)

  18. Language and number: a bilingual training study.

    Science.gov (United States)

    Spelke, E S; Tsivkin, S

    2001-01-01

    Three experiments investigated the role of a specific language in human representations of number. Russian-English bilingual college students were taught new numerical operations (Experiment 1), new arithmetic equations (Experiments 1 and 2), or new geographical or historical facts involving numerical or non-numerical information (Experiment 3). After learning a set of items in each of their two languages, subjects were tested for knowledge of those items, and new items, in both languages. In all the studies, subjects retrieved information about exact numbers more effectively in the language of training, and they solved trained problems more effectively than untrained problems. In contrast, subjects retrieved information about approximate numbers and non-numerical facts with equal efficiency in their two languages, and their training on approximate number facts generalized to new facts of the same type. These findings suggest that a specific, natural language contributes to the representation of large, exact numbers but not to the approximate number representations that humans share with other mammals. Language appears to play a role in learning about exact numbers in a variety of contexts, a finding with implications for practice in bilingual education. The findings prompt more general speculations about the role of language in the development of specifically human cognitive abilities.

  19. Limits on hypothesizing new quantum numbers

    International Nuclear Information System (INIS)

    Goldstein, G.R.; Moravcsik, M.J.

    1986-01-01

    According to a recent theorem, for a general quantum-mechanical system undergoing a process, one can tell from measurements on this system whether or not it is characterized by a quantum number, the existence of which is unknown to the observer, even though the detecting equipment used by the observer is unable to distinguish among the various possible values of the ''secret'' quantum number and hence always averages over them. The present paper deals with situations in which this averaging is avoided and hence the ''secret'' quantum number remains ''secret.'' This occurs when a new quantum number is hypothesized in such a way that all the past measurements pertain to the system with one and the same value of the ''secret'' quantum number, or when the new quantum number is related to the old ones by a specific dynamical model providing a one-to-one correspondence. In the first of these cases, however, the one and the same state of the ''secret'' quantum number needs to be a nondegenerate one. If it is degenerate, the theorem can again be applied. This last feature provides a tool for experimentally testing symmetry breaking and the reestablishment of symmetries in asymptotic regions. The situation is illustrated on historical examples like isospin and strangeness, as well as on some contemporary schemes involving spaces of higher dimensionality

  20. Low Nephron Number and Its Clinical Consequences

    Directory of Open Access Journals (Sweden)

    Valerie A. Luyckx

    2011-10-01

    Full Text Available decades ago, that developmental programming of the kidney impacts an individual’s risk for hypertension and renal disease in later life. Low birth weight is the strongest current clinical surrogate marker for an adverse intrauterine environment and, based on animal and human studies, is associated with a low nephron number. Other clinical correlates of low nephron number include female gender, short adult stature, small kidney size, and prematurity. Low nephron number in Caucasian and Australian Aboriginal subjects has been shown to be associated with higher blood pressures, and, conversely, hypertension is less prevalent in individuals with higher nephron numbers. In addition to nephron number, other programmed factors associated with the increased risk of hypertension include salt sensitivity, altered expression of renal sodium transporters, altered vascular reactivity, and sympathetic nervous system overactivity. Glomerular volume is universally found to vary inversely with nephron number, suggesting a degree of compensatory hypertrophy and hyperfunction in the setting of a low nephron number. This adaptation may become overwhelmed in the setting of superimposed renal insults, e.g. diabetes mellitus or rapid catch-up growth, leading to the vicious cycle of on-going hyperfiltration, proteinuria, nephron loss and progressive renal functional decline. Many millions of babies are born with low birth weight every year, and hypertension and renal disease prevalences are increasing around the globe. At present, little can be done clinically to augment nephron number; therefore adequate prenatal care and careful postnatal nutrition are crucial to optimize an individual’s nephron number during development and potentially to stem the tide of the growing cardiovascular and renal disease epidemics worldwide.

  1. Standard random number generation for MBASIC

    Science.gov (United States)

    Tausworthe, R. C.

    1976-01-01

    A machine-independent algorithm is presented and analyzed for generating pseudorandom numbers suitable for the standard MBASIC system. The algorithm used is the polynomial congruential or linear recurrence modulo 2 method. Numbers, formed as nonoverlapping adjacent 28-bit words taken from the bit stream produced by the formula a sub m + 532 = a sub m + 37 + a sub m (modulo 2), do not repeat within the projected age of the solar system, show no ensemble correlation, exhibit uniform distribution of adjacent numbers up to 19 dimensions, and do not deviate from random runs-up and runs-down behavior.

  2. Baryon number violation and string topologies

    International Nuclear Information System (INIS)

    Sjoestrand, T.; Skands, P.Z.

    2003-01-01

    In supersymmetric scenarios with broken R-parity, baryon number violating sparticle decays become possible. In order to search for such decays, a good understanding of expected event properties is essential. We here develop a complete framework that allows detailed studies. Special attention is given to the hadronization phase, wherein the baryon number violating vertex is associated with the appearance of a junction in the colour confinement field. This allows us to tell where to look for the extra (anti)baryon directly associated with the baryon number violating decay

  3. The generative basis of natural number concepts.

    Science.gov (United States)

    Leslie, Alan M; Gelman, Rochel; Gallistel, C R

    2008-06-01

    Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.

  4. Algebraic Geometry and Number Theory Summer School

    CERN Document Server

    Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

    2017-01-01

    This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

  5. Quantum numbers and band topology of nanotubes

    Energy Technology Data Exchange (ETDEWEB)

    Damnjanovic, M [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Milosevic, I [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Vukovic, T [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Maultzsch, J [Institut fuer Festkoerper Physik, Technische Universitaet Berlin, Hardenbergstr. 36, 10623 Berlin (Germany)

    2003-05-30

    Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.

  6. Quantum numbers and band topology of nanotubes

    International Nuclear Information System (INIS)

    Damnjanovic, M; Milosevic, I; Vukovic, T; Maultzsch, J

    2003-01-01

    Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities

  7. Quantum numbers and band topology of nanotubes

    CERN Document Server

    Damnjanovic, M; Vukovic, T; Maultzsch, J

    2003-01-01

    Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.

  8. Topological quantum numbers in nonrelativistic physics

    CERN Document Server

    Thouless, David James

    1998-01-01

    Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect,

  9. Numbers at work a cultural perspective

    CERN Document Server

    Taschner , Rudolf

    2007-01-01

    Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as ""Pythagoras: Numbers and Symbol""; ""Bach: Numbers and Music""; ""Descartes: Numb

  10. Generation of pseudo-random numbers

    Science.gov (United States)

    Howell, L. W.; Rheinfurth, M. H.

    1982-01-01

    Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

  11. Microcomputer-Assisted Discoveries: Random Numbers.

    Science.gov (United States)

    Kimberling, Clark

    1983-01-01

    A programing contest was designed to promote interest in mathematical randomness. Student-developed programs making clever uses of random numbers are presented. Modifications users might make are suggested. (MNS)

  12. Using Random Numbers in Science Research Activities.

    Science.gov (United States)

    Schlenker, Richard M.; And Others

    1996-01-01

    Discusses the importance of science process skills and describes ways to select sets of random numbers for selection of subjects for a research study in an unbiased manner. Presents an activity appropriate for grades 5-12. (JRH)

  13. Generalized catalan numbers, sequences and polynomials

    OpenAIRE

    KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül

    2010-01-01

    In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.

  14. Muon number nonconservation in gauge theories

    International Nuclear Information System (INIS)

    Cheng, T.P.; Li, L.F.

    1977-01-01

    The question of separate conservation of muon and electron number is considered in the context of unified gauge theories of weak and electromagnetic interactions. Theories with heavy neutral leptons, Higgs scalars, and doubly charged heavy leptons are discussed. 28 references

  15. Biometric National Identification Number Generation for Secure ...

    African Journals Online (AJOL)

    Biometric National Identification Number Generation for Secure Network Authentication Based Fingerprint. ... Username, Password, Remember me, or Register ... In this paper an authentication based finger print biometric system is proposed ...

  16. Distribution function of faint galaxy numbers

    International Nuclear Information System (INIS)

    Fesenko, L.M.

    1981-01-01

    The Lick observatory counts of galaxies are considered. The distribution of number of galaxies in elementary regions (ER) of 1 degx1 deg is investigated. Each field of 6 degx6 deg was treated separately At b>40 deg the probab+lity to observe of n galaxies in ER is an exponential decreasing function of n, if unequality n> were fulfilled. The mean apparent multiplicity of a galaxy (2.8+-0.9) was derived. The galaxy number distribution was simple model for the number of various systems of galaxies. The supperclustering of galaxies was not introduced. Based on that model the approximate expression for galaxy number distribution was considered and was compared with observed distributions. The agreement between these distributions become better with reducing of the interstellar absorption of light

  17. New technique for number-plate recognition

    Science.gov (United States)

    Guo, Jie; Shi, Peng-Fei

    2001-09-01

    This paper presents an alternative algorithm for number plate recognition. The algorithm consists of three modules. Respectively, they are number plate location module, character segmentation module and character recognition module. Number plate location module extracts the number plate from the detected car image by analyzing the color and the texture properties. Different from most license plate location methods, the algorithm has fewer limits to the car size, the car position in the image and the image background. Character segmentation module applies connected region algorithm both to eliminate noise points and to segment characters. Touching characters and broken characters can be processed correctly. Character recognition module recognizes characters with HHIC (Hierarchical Hybrid Integrated Classifier). The system has been tested with 100 images obtained from crossroad and parking lot, etc, where the cars have different size, position, background and illumination. Successful recognition rate is about 92%. The average processing time is 1.2 second.

  18. Introduction to the geometry of complex numbers

    CERN Document Server

    Deaux, Roland

    2008-01-01

    Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

  19. Opening the Door on Triangular Numbers

    Science.gov (United States)

    McMartin, Kimberley; McMaster, Heather

    2016-01-01

    As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

  20. Random Number Generation for High Performance Computing

    Science.gov (United States)

    2015-01-01

    number streams, a quality metric for the parallel random number streams. * * * * * Atty. Dkt . No.: 5660-14400 Customer No. 35690 Eric B. Meyertons...responsibility to ensure timely payment of maintenance fees when due. Pagel of3 PTOL-85 (Rev. 02/11) Atty. Dkt . No.: 5660-14400 Page 1 Meyertons...with each subtask executed by a separate thread or process (henceforth, process). Each process has Atty. Dkt . No.: 5660-14400 Page 2 Meyertons

  1. Hodge numbers for all CICY quotients

    International Nuclear Information System (INIS)

    Constantin, Andrei; Gray, James; Lukas, Andre

    2017-01-01

    We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

  2. All-optical fast random number generator.

    Science.gov (United States)

    Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong

    2010-09-13

    We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.

  3. CAT-ASVAB Technical Bulletin Number 1

    Science.gov (United States)

    2006-03-01

    CAT -ASVAB Technical Bulletin #1 Personnel Testing Division Defense Manpower Data Center March 2006 Report...2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE CAT -ASVAB Technical Bulletin #1 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c...Hetter, R. D. "Psychometric Procedures for Administering CAT -ASVAB" (pp. 131-140) Chapter 4 Hetter, R. D., & Sympson J. B. "Item Exposure

  4. Large number discrimination in newborn fish.

    Directory of Open Access Journals (Sweden)

    Laura Piffer

    Full Text Available Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14 in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density, three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.

  5. On the Fibonacci k-numbers

    International Nuclear Information System (INIS)

    Falcon, Sergio; Plaza, Angel

    2007-01-01

    We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {F k,n } n=0 ∼ were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra

  6. Fibonacci and Lucas numbers with applications

    CERN Document Server

    Koshy, Thomas

    2011-01-01

    [Koshy's] book is without doubt the most comprehensive and scholarly work on Fibonacci numbers to date and I am sure that it will quickly signal its presence and impose itself as an authoritative reference manual on Fibonacci numbers. -Napoleon Gauthier, Royal Military College of Canada, Kingston, ON What a gem this is! [...] My only regrest about the book is that it wasn't around years ago. It fills such a void. -Monte Zerger, Adams State College, Alamosa, CO

  7. Hodge numbers for all CICY quotients

    Energy Technology Data Exchange (ETDEWEB)

    Constantin, Andrei [Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala (Sweden); Gray, James [Physics Department, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)

    2017-01-02

    We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

  8. Number skills are maintained in healthy ageing.

    Science.gov (United States)

    Cappelletti, Marinella; Didino, Daniele; Stoianov, Ivilin; Zorzi, Marco

    2014-03-01

    Numerical skills have been extensively studied in terms of their development and pathological decline, but whether they change in healthy ageing is not well known. Longer exposure to numbers and quantity-related problems may progressively refine numerical skills, similar to what happens to other cognitive abilities like verbal memory. Alternatively, number skills may be sensitive to ageing, reflecting either a decline of number processing itself or of more auxiliary cognitive abilities that are involved in number tasks. To distinguish between these possibilities we tested 30 older and 30 younger participants on an established numerosity discrimination task requiring to judge which of two sets of items is more numerous, and on arithmetical tasks. Older participants were remarkably accurate in performing arithmetical tasks although their numerosity discrimination (also known as 'number acuity') was impaired. Further analyses indicate that this impairment was limited to numerosity trials requiring inhibiting information incongruent to numerosity (e.g., fewer but larger items), and that this also correlated with poor inhibitory processes measured by standard tests. Therefore, rather than a numerical impairment, poor numerosity discrimination is likely to reflect elderly's impoverished inhibitory processes. This conclusion is supported by simulations with a recent neuro-computational model of numerosity perception, where only the specific degradation of inhibitory processes produced a pattern that closely resembled older participants' performance. Numeracy seems therefore resilient to ageing but it is influenced by the decline of inhibitory processes supporting number performance, consistent with the 'Inhibitory Deficit' Theory. Copyright © 2013 Elsevier Inc. All rights reserved.

  9. Persistent consequences of atypical early number concepts

    Directory of Open Access Journals (Sweden)

    Michèle M. M. Mazzocco

    2013-09-01

    Full Text Available How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders’ number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes.

  10. Complex architecture of primes and natural numbers.

    Science.gov (United States)

    García-Pérez, Guillermo; Serrano, M Ángeles; Boguñá, Marián

    2014-08-01

    Natural numbers can be divided in two nonoverlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.

  11. A new pseudorandom number generator based on a complex number chaotic equation

    International Nuclear Information System (INIS)

    Liu Yang; Tong Xiao-Jun

    2012-01-01

    In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties

  12. Number density structures in the inner heliosphere

    Science.gov (United States)

    Stansby, D.; Horbury, T. S.

    2018-06-01

    Aims: The origins and generation mechanisms of the slow solar wind are still unclear. Part of the slow solar wind is populated by number density structures, discrete patches of increased number density that are frozen in to and move with the bulk solar wind. In this paper we aimed to provide the first in-situ statistical study of number density structures in the inner heliosphere. Methods: We reprocessed in-situ ion distribution functions measured by Helios in the inner heliosphere to provide a new reliable set of proton plasma moments for the entire mission. From this new data set we looked for number density structures measured within 0.5 AU of the Sun and studied their properties. Results: We identified 140 discrete areas of enhanced number density. The structures occurred exclusively in the slow solar wind and spanned a wide range of length scales from 50 Mm to 2000 Mm, which includes smaller scales than have been previously observed. They were also consistently denser and hotter that the surrounding plasma, but had lower magnetic field strengths, and therefore remained in pressure balance. Conclusions: Our observations show that these structures are present in the slow solar wind at a wide range of scales, some of which are too small to be detected by remote sensing instruments. These structures are rare, accounting for only 1% of the slow solar wind measured by Helios, and are not a significant contribution to the mass flux of the solar wind.

  13. Number theory in the spirit of Ramanujan

    CERN Document Server

    Berndt, Bruce C

    2006-01-01

    Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of q-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematic...

  14. Unpredictability and the transmission of numbers

    Science.gov (United States)

    Myers, John M.; Madjid, F. Hadi

    2016-03-01

    Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.

  15. On Generalizations of the Stirling Number Triangles

    Science.gov (United States)

    Lang, Wolfdieter

    2000-09-01

    Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k;n,m) and S1(k;n,m) with k in Z. The original Stirling number triangles of the second and first kind arise when k = 1. S2(2;n,m) is identical with the unsigned S1(2;n,m) triangle, called S1p(2;n,m), which also represents the triangle of signless Lah numbers. Certain associated number triangles, denoted by s2(k;n,m) and s1(k;n,m), are also defined. Both s2(2;n,m) and s1(2;n + 1, m + 1) form Pascal's triangle, and s2(-1,n,m) turns out to be Catalan's triangle. Generating functions are given for the columns of these triangles. Each S2(k) and S1(k) matrix is an example of a Jabotinsky matrix. Therefore the generating functions for the rows of these triangular arrays constitute exponential convolution polynomials. The sequences of the row sums of these triangles are also considered. These triangles are related to the problem of obtaining finite transformations from infinitesimal ones generated by x^k d/dx, for k in Z.

  16. Approximate particle number projection in hot nuclei

    International Nuclear Information System (INIS)

    Kosov, D.S.; Vdovin, A.I.

    1995-01-01

    Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab

  17. True random numbers from amplified quantum vacuum.

    Science.gov (United States)

    Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V

    2011-10-10

    Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.

  18. The distribution of prime numbers and associated problems in number theory

    International Nuclear Information System (INIS)

    Nair, M.

    1991-01-01

    Some problems in number theory, namely the gaps between consecutive primes, the distribution of primes in arithmetic progressions, Brun-Titchmarsh theorem, Fermat's last theorem, The Thue equation, the gaps between square-free numbers are discussed

  19. Microsoft Support Phone Number +1-877-353-1149(toll-free) Microsoft Helpline Phone Number

    OpenAIRE

    Allina willson

    2018-01-01

    Microsoft Helpline Phone Number Call Now: +1-877-353-1149 for Microsoft support and services. This is Trusted Microsoft Support number provide instant support.if you get any problem while using Microsoft office just relaxed because Microsoft support phone number +1-877-353-1149 is here to provide instant help of microsoft issues. Just dial our Microsoft support phone number +1-877-353-1149 and get instant online support.

  20. Large numbers hypothesis. II - Electromagnetic radiation

    Science.gov (United States)

    Adams, P. J.

    1983-01-01

    This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.

  1. Room Airflows with Low Reynolds Number Effects

    DEFF Research Database (Denmark)

    Topp, Claus; Nielsen, Peter V.; Davidson, Lars

    The behaviour of room airflows under fully turbulent conditions is well known both in terms of experiments and, numerical calculations by computational fluid dynamics (CFD). For room airflows where turbulence is not fully developed though, i.e. flows at low Reynolds numbers, the existing knowledge...... is limited. It has been the objective to investigate the behaviour of a plane isothermal wall jet in a full-scale ventilated room at low Reynolds numbers, i.e. when the flow is not fully turbulent. The results are significantly different from known theory for fully turbulent flows. It was found that the jet...... constants are a strong function of the Reynolds number up to a level of Reh≈500....

  2. Seniority Number in Valence Bond Theory.

    Science.gov (United States)

    Chen, Zhenhua; Zhou, Chen; Wu, Wei

    2015-09-08

    In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.

  3. Baryon number nonconservation in extreme conditions

    International Nuclear Information System (INIS)

    Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Shaposhnikov, M.E.

    1988-01-01

    In gauge theories with the left-right asymmetric fermionic content (e.g. in standard electroweak theory) fermion number F is not conserved due to the anomaly. It is shown that anomalous processes, while being exponentially suppressed, under normal conditions, are in fact rapid. The mechanism of fermionic number nonconservation connected with a level crossing phenomenon in external gauge fields is described. The theory and experimental consequences of monopole catalysis of a proton decay is reviewed. It is shown that cold dense fermionic matter is stable only up to some limiting density. It is demonstrated that there is no exponential suppression of the rate F nonconservation at high temperatures. The cosmological implications of this fact are discussed. The strong anomalous fermionic number violation in decays of superheavy fermions technibaryons is considered

  4. Lepton number violating processes and Majorana neutrinos

    International Nuclear Information System (INIS)

    Dib, C.; Schmidt, I.; Gribanov, V.; Kovalenko, S.

    2001-01-01

    Some generic properties of lepton number violating processes and their relation to different entries of the Majorana neutrino mass matrix are discussed. Present and near future experiments searching for these processes, except the neutrinoless double beta decay, are unable to probe light (eV mass region) and heavy (hundred GeV mass region) neutrinos. On the other hand, due to the effect of a resonant enhancement, some of lepton number violating decays can be very sensitive to the intermediate-mass neutrinos with typical masses in the hundred MeV region. These neutrinos may appear as admixtures of the three active and an arbitrary number of sterile neutrino species. The experimental constraints on these massive neutrino states are analyzed and their possible cosmological and astrophysical implications are discussed

  5. Motzkin numbers out of Random Domino Automaton

    Energy Technology Data Exchange (ETDEWEB)

    Białecki, Mariusz, E-mail: bialecki@igf.edu.pl [Institute of Geophysics, Polish Academy of Sciences, ul. Ks. Janusza 64, 01-452 Warszawa (Poland)

    2012-10-01

    Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton. -- Highlights: ► Motzkin numbers are derived from stochastic cellular automaton with avalanches. ► Explicit solution of toy model of earthquakes is presented. ► Case with inverse-power distribution of avalanches is found.

  6. Number in Plato’s Philebus

    Directory of Open Access Journals (Sweden)

    Shetnikov, Andrey

    2009-06-01

    Full Text Available The paper concerns the concept of number (arithmos, important for dialectical method of later Plato. It becomes clear that the arithmos in Plato’s dialectics should be understood as a concrete operation, a sort of tekhne, such as counting, enumeration, compilation of a comprehensive and systematic list, etc., rather then the theoretical number of abstract arithmetic. The author analyses a series of grammatical, musical and rhetorical examples, supplied by Plato in the Philebus and other dialogues, and traces the usage of arithmos and similar words in the earlier tradition, particularly, in Homer, Hesiod, the classical tragedy, and Herodotus.

  7. Dynamical real numbers and living systems

    International Nuclear Information System (INIS)

    Datta, Dhurjati Prasad

    2004-01-01

    Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical representation of the ordinary real number system. Every real number can be visualized as a living cell-like structure, endowed with a definite evolutionary arrow. We discuss the relevance of this extended calculus in the study of living systems. We also present an intelligent version of the Newton's first law of motion

  8. Type number and rigidity of fibred surfaces

    International Nuclear Information System (INIS)

    Markov, P E

    2001-01-01

    Infinitesimal l-th order bendings, 1≤l≤∞, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for l=∞ an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the (r,l)-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an (r,l)-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number ≥3 and the class of (r,l)-rigid fibred surfaces is distinguished

  9. The number density of a charged relic

    International Nuclear Information System (INIS)

    Berger, C.F.; Kraml, S.; Palorini, F.

    2008-07-01

    We investigate scenarios in which a charged, long-lived scalar particle decouples from the primordial plasma in the Early Universe. We compute the number density at time of freeze-out considering both the cases of abelian and non-abelian interactions and including the effect of Sommerfeld enhancement at low initial velocity. We also discuss as extreme case the maximal cross section that fulfils the unitarity bound. We then compare these number densities to the exotic nuclei searches for stable relics and to the BBN bounds on unstable relics and draw conclusions for the cases of a stau or stop NLSP in supersymmetric models with a gravitino or axino LSP. (orig.)

  10. Searches for violation of muon number conservation

    International Nuclear Information System (INIS)

    Redwine, R.P.

    1981-01-01

    The question of violation of muon number conservation is one which has occupied considerable attention and resources in recent years. The first generation of experiments at the medium energy accelerators has now been completed and the next generation of experiments is ready to begin. The history of muon number conservation is reviewed, including the reasons for the present belief that the conservation law may not be exact. The experiments that have been completed in the last few years are discussed. The new experiments that are being mounted and planned at several laboratories are discussed, and the relationship of these types of experiments to other studies, such as searches for neutrino oscillations, are considered

  11. Energy information data base: report number codes

    Energy Technology Data Exchange (ETDEWEB)

    None

    1979-09-01

    Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used. (RWR)

  12. The number density of a charged relic

    Energy Technology Data Exchange (ETDEWEB)

    Berger, C.F. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics]|[California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Covi, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kraml, S. [CNRS/IN2P3, Grenoble (France). Lab. de Physique Subatomique et de Cosmologie; Palorini, F. [Lyon Univ., UCBL, CNRS/IN2P3, Villeurbanne (France). IPN de Lyon

    2008-07-15

    We investigate scenarios in which a charged, long-lived scalar particle decouples from the primordial plasma in the Early Universe. We compute the number density at time of freeze-out considering both the cases of abelian and non-abelian interactions and including the effect of Sommerfeld enhancement at low initial velocity. We also discuss as extreme case the maximal cross section that fulfils the unitarity bound. We then compare these number densities to the exotic nuclei searches for stable relics and to the BBN bounds on unstable relics and draw conclusions for the cases of a stau or stop NLSP in supersymmetric models with a gravitino or axino LSP. (orig.)

  13. Formulation of baryon number violating collisions

    International Nuclear Information System (INIS)

    Funakubo, Koichi; Otsuki, Shoichiro; Takenaga, Kazunori; Toyoda, Fumihiko.

    1992-01-01

    A new formalism based on path-integral expression of time-evolution operator during tunneling is presented. Instead of instanton calculus in the LSZ formalism, a classical bounce solution leading to sphaleron (instanton action) at high (low) energies is adopted as the tunneling configuration. The formalism is applied to O(3) nonlinear sigma model in two dimensions. For the coupling constant g 2 ≅ 0.1, which may be physical in the sense that the number of produced particles ≅ 100, comparable with that of electroweak theory, the baryon number violating cross section is smaller by orders of magnitude than the so-called unitarity bound. (author)

  14. Number sense how the mind creates mathematics

    CERN Document Server

    Dehaene, Stanislas

    2011-01-01

    Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudime

  15. Nielsen number of a covering map

    Directory of Open Access Journals (Sweden)

    Jerzy Jezierski

    2006-02-01

    Full Text Available We consider a finite regular covering pH:X˜H→X over a compact polyhedron and a map f:X→X admitting a lift f˜:X˜H→X˜H. We show some formulae expressing the Nielsen number N(f as a linear combination of the Nielsen numbers of its lifts.

  16. A finite particle number approach to physics

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1984-01-01

    Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules the author constructs: the scale constants of physics (3, 10, 137, 1.7x10 38 ); 3+1 Minkowski space with a discrete metric and the algebraic bound ΔepsilonΔtau >= 1; the Einstein-deBroglie relation; algebraic 'double slit' interference; a single time momentum space scattering theory connected to laboratory experience; an approximation to 'wave functions'; 'local' phase severence and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; msub(p)/msub(e); a cosmology not in disagreement with current observations. (Auth.)

  17. Parametric number covariance in quantum chaotic spectra.

    Science.gov (United States)

    Vinayak; Kumar, Sandeep; Pandey, Akhilesh

    2016-03-01

    We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

  18. Number theory and the periodicity of matter

    CERN Document Server

    Boeyens, Jan C A

    2008-01-01

    Presents a fully scientific account of the use of the golden ratio and explores the observation that stable nucleides obey a number theory based general lawThe interest in number theory is worldwide and covers the entire spectrum of human knowledge. Those aspects covered here will not be immediately accessible to the general lay readership, but, scientists of all pursuations immediately appreciate the importance of the applications described hereThe well-known interest of engineers, medical practitioners and information technologists in popular scientific matters, should make this an attractive buy for such individuals. Undergraduate students in these disciplines should be equally interested.

  19. History of the theory of numbers

    CERN Document Server

    Dickson, Leonard Eugene

    2005-01-01

    The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include

  20. Energy information data base: report number codes

    International Nuclear Information System (INIS)

    1979-09-01

    Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used

  1. The effect of the cranial bone CT numbers on the brain CT numbers

    Energy Technology Data Exchange (ETDEWEB)

    Fukuda, Hitoshi; Kobayashi, Shotai; Koide, Hiromi; Yamaguchi, Shuhei; Okada, Kazunori; Shimote, Koichi; Tsunematsu, Tokugoro (Shimane Medical Univ., Izumo (Japan))

    1989-06-01

    The effects of the cranial size and the computed tomography (CT) numbers of the cranial bone on that of the brain were studied in 70 subjects, aged from 30 to 94 years. The subjects had no histories of cerebrovascular accidents and showed no abnormalities in the central nervous system upon physical examinations and a CT scan. We measured the average attenuation values (CT numbers) of each elliptical region (165 pixels, 0.39 cm{sup 2}) at the bilateral thalamus and at twelve areas of the deep white matter. Multiple regression analysis was used to assess the effects of age, cranial size, and cranial bone CT numbers on the brain CT numbers. The effect of the cranial bone CT numbers on the brain CT numbers was statistically significant. The brain CT numbers increased with the increase in the cranial bone CT numbers. There was, however, no significant correlation between brain CT numbers and cranial size. In measuring the brain CT numbers, it is desirable that consideration be given to the cranial bone CT numbers. (author).

  2. The Learning Potentials of Number Blocks

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten

    2012-01-01

    This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher...

  3. The 17 GHz active region number

    Energy Technology Data Exchange (ETDEWEB)

    Selhorst, C. L.; Pacini, A. A. [IP and D-Universidade do Vale do Paraíba-UNIVAP, São José dos Campos (Brazil); Costa, J. E. R. [CEA, Instituto Nacional de Pesquisas Espaciais, São José dos Campos (Brazil); Giménez de Castro, C. G.; Valio, A. [CRAAM, Universidade Presbiteriana Mackenzie, São Paulo (Brazil); Shibasaki, K., E-mail: caius@univap.br [Nobeyama Solar Radio Observatory/NAOJ, Minamisaku, Nagano 384-1305 (Japan)

    2014-08-01

    We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, which also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long-term variation mimics the solar cycle; however, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease in the number of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last few years.

  4. Defense Horizons. Number 78, March 2015

    Science.gov (United States)

    2015-03-01

    and antelope Valley College (aVC) results in increases in number of scientists, engi- neers, and technicians from which to draw employees for the...should address best prac- tices for project valuation , what types of formalized arrangements are acceptable, and legal precedents that allow such

  5. Identification of copy number variants in horses

    KAUST Repository

    Doan, R.; Cohen, N.; Harrington, J.; Veazy, K.; Juras, R.; Cothran, G.; McCue, M. E.; Skow, L.; Dindot, S. V.

    2012-01-01

    identical CNVs from each animal yielded 775 CNV regions (CNVRs), involving 1707 protein- and RNA-coding genes. The number of CNVs per animal ranged from 55 to 347, with median and mean sizes of CNVs of 5.3 kb and 99.4 kb, respectively. Approximately 6

  6. Irrational Numbers Can "In-Spiral" You

    Science.gov (United States)

    Lewis, Leslie D.

    2007-01-01

    This article describes the instructional process of helping students visualize irrational numbers. Students learn to create a spiral, called "the wheel of Theodorus," which demonstrates irrational and rational lengths. Examples of student work help the reader appreciate the delightful possibilities of this project. (Contains 4 figures.)

  7. Identifying jet quantum numbers event by event

    International Nuclear Information System (INIS)

    Teper, M.J.

    1979-12-01

    A method is proposed to identify the parton that gives rise to any particular jet. The method improves with the number of particles in the jet, and should indicate which of the jets in a three jet event at PETRA is the gluon jet. (author)

  8. Natural occupation numbers: When do they vanish?

    NARCIS (Netherlands)

    Giesbertz, K.J.H.; Van Leeuwen, R.

    The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the

  9. Chinese Number Words, Culture, and Mathematics Learning

    Science.gov (United States)

    Ng, Sharon Sui Ngan; Rao, Nirmala

    2010-01-01

    This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…

  10. Distribution of squares modulo a composite number

    OpenAIRE

    Aryan, Farzad

    2015-01-01

    In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.

  11. Learning Random Numbers: A Matlab Anomaly

    Czech Academy of Sciences Publication Activity Database

    Savický, Petr; Robnik-Šikonja, M.

    2008-01-01

    Roč. 22, č. 3 (2008), s. 254-265 ISSN 0883-9514 R&D Projects: GA AV ČR 1ET100300517 Institutional research plan: CEZ:AV0Z10300504 Keywords : random number s * machine learning * classification * attribute evaluation * regression Subject RIV: BA - General Mathematics Impact factor: 0.795, year: 2008

  12. Boundary induced nonlinearities at small Reynolds numbers

    NARCIS (Netherlands)

    Sbragaglia, M.; Sugiyama, K.

    2007-01-01

    We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag

  13. On gauged Baryon and Lepton numbers

    International Nuclear Information System (INIS)

    Rajpoot, S.

    1990-01-01

    The observation that Baryon number and Lepton number are conserved in nature provides strong motivation for associating gauge symmetries to these conserved numbers. This endeavor requires that the gauge group of electroweak interactions be extended from SU(2) L X U(1) Y to SU(2) L X U(1) R X U(1) Lepton where U(1) R couples only to the right-handed quarks and leptons. If it furthur postulated that right-handed currents exist on par with the left-handed ones, then the full electroweak symmetry is SU(2) L X SU(2) R X U(1) Baryon X U(1) Lepton . The SU(2) L X SU(2) R X U(1) Baryon X U(1) Lepton model is described in some detail. The triangle anomalies of the three families of quarks and leptons in the model are cancelled invoking leptoquark matter which is new fermionic matter that carries baryon as well as lepton numbers. In addition to the standard neutral boson (Z degree), the theory predicts two neutral gauge bosons with mass lower bounds of 120 GeV and 210 GeV which makes these particles prospective candidates for production at LEP, the TEVATRON and the SSC

  14. Metric propositional neighborhood logics on natural numbers

    DEFF Research Database (Denmark)

    Bresolin, Davide; Della Monica, Dario; Goranko, Valentin

    2013-01-01

    Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is “met by” the current one and to an interval that “meets” the current one, plus an infinite set of length constraints, regarded as atomic propositions...

  15. Production of Numbers about the Future

    DEFF Research Database (Denmark)

    Huikku, Jari; Mouritsen, Jan; Silvola, Hanna

    of prominent Finnish business managers, auditors, analysts, investors, financial supervisory authority, academics and media, the paper extends prior research which has used large data. The paper analyses impairment testing as a process where network of human and non-human actors produce numbers about...

  16. Some Functional Equations Originating from Number Theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  17. Preferential solvation: dividing surface vs excess numbers.

    Science.gov (United States)

    Shimizu, Seishi; Matubayasi, Nobuyuki

    2014-04-10

    How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.

  18. Contributions to Analytic Number Theory | Lucht | Quaestiones ...

    African Journals Online (AJOL)

    This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on analytic number theory. They concern weighted inversion theorems of the. Wiener type, mean-value theorems for multiplicative functions, and, Ramanujan

  19. A Geometrical Application of Number Theory

    Science.gov (United States)

    Srinivasan, V. K.

    2013-01-01

    Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…

  20. p-adic numbers in physics

    International Nuclear Information System (INIS)

    Brekke, L.; Freund, P.G.O.

    1993-01-01

    The boundary of the ordinary open string world sheet is the real line. Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers). The world sheet itself is then no longer a continuous manifold but becomes a discrete homogeneous Bethe lattice, or Bruhat-Tits tree of incidence number p + 1. The p-adic strings thus correspond to specific discretizations of the world sheet. Studying all these discretizations (one for each prime p) together, as suggested by number theory, sheds new light on the ordinary string, via adelic product formulae. One is also led this way to a new type of string, the adelic string. These issues and their generalization to closed strings are discussed after a self-contained mathematical introduction. Other physical systems with natural p-adic counterparts are considered and in their context the connection between p-adic theories and quantum groups is explored. (orig.)

  1. IEEE Standard for Floating Point Numbers

    Indian Academy of Sciences (India)

    IAS Admin

    Floating point numbers are an important data type in compu- tation which is used ... quite large! Integers are ... exp, the value of the exponent will be taken as (exp –127). The ..... bit which is truncated is 1, add 1 to the least significant bit, else.

  2. Synesthesia and Number Cognition in Children

    Science.gov (United States)

    Green, Jennifer A. K.; Goswami, Usha

    2008-01-01

    Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…

  3. Reproduction numbers of infectious disease models

    Directory of Open Access Journals (Sweden)

    Pauline van den Driessche

    2017-08-01

    Full Text Available This primer article focuses on the basic reproduction number, ℛ0, for infectious diseases, and other reproduction numbers related to ℛ0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of ℛ0 determining whether or not the disease dies out. The next generation matrix method of calculating ℛ0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease, cholera in humans (a disease with two transmission pathways, anthrax in animals (a disease that can be spread by dead carcasses and spores, and Zika in humans (spread by mosquitoes and sexual contacts. Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate ℛ0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity. Keywords: Basic reproduction number, Disease control, West Nile virus, Cholera, Anthrax, Zika virus

  4. 9 CFR 355.8 - Official number.

    Science.gov (United States)

    2010-01-01

    ... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION, AND... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY...

  5. Baryon number violation and particle collider experiments

    International Nuclear Information System (INIS)

    Klinkhamer, F.R.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1992-09-01

    Baryon number non-conservation, due to non-perturbative effects (sphalerons) in the standard model, may have been important in the early Universe. In this paper the possibility is discussed that similar effects could show up at future particle collider experiments. (author). 16 refs.; 3 figs

  6. Maple Explorations, Perfect Numbers, and Mersenne Primes

    Science.gov (United States)

    Ghusayni, B.

    2005-01-01

    Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

  7. New feature for an old large number

    International Nuclear Information System (INIS)

    Novello, M.; Oliveira, L.R.A.

    1986-01-01

    A new context for the appearance of the Eddington number (10 39 ), which is due to the examination of elastic scattering of scalar particles (ΠK → ΠK) non-minimally coupled to gravity, is presented. (author) [pt

  8. About the lepton number non conservation

    International Nuclear Information System (INIS)

    Bernabeu, J

    1989-01-01

    The possibility of lepton number non conservation through the mixing of lepton flavours, as well as the IΔLI=2 lepton antilepton conversion, is discussed. The paper follows the scheme: i) Experimental Situation; ii) Relation with the Neutrino Mass problem; iii) Majorana Neutrinos?; iv) Extensions of the Standard Model; v) Lepton Flavour Violating Decays of μ and τ; vi) Z∞ Boson Decays. (Author)

  9. Gauge transformations with fractional winding numbers

    International Nuclear Information System (INIS)

    Abouelsaood, A.

    1996-01-01

    The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a θFF term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of open-quote open-quote large close-quote close-quote gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the θ parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. copyright 1996 The American Physical Society

  10. Hidden supersymmetry and Fermion number fractionalization

    International Nuclear Information System (INIS)

    Akhoury, R.

    1985-01-01

    This paper discusses how a hidden supersymmetry of the underlying field theories can be used to interpret and to calculate fermion number fractionalization in different dimensions. This is made possible by relating it to a corresponding Witten index of the hidden supersymmetry. The closely related anomalies in odd dimensions are also discussed

  11. Visualizing the Arithmetic of Complex Numbers

    Science.gov (United States)

    Soto-Johnson, Hortensia

    2014-01-01

    The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

  12. The number of expats is rather stable

    DEFF Research Database (Denmark)

    Andersen, Torben

    2008-01-01

    aggregate data from the Danish economist’s and the engineer’s trade unions show that during the last decade there has been stagnation in the number of expatriates. Taking into consideration that the three trade unions cover the very large majority of Danish knowledge workers occupying foreign jobs...

  13. Radical Software. Number Two. The Electromagnetic Spectrum.

    Science.gov (United States)

    Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.

    1970-01-01

    In an effort to foster the innovative uses of television technology, this tabloid format periodical details social, educational, and artistic experiments with television and lists a large number of experimental videotapes available from various television-centered groups and individuals. The principal areas explored in this issue include cable…

  14. Forecasting distribution of numbers of large fires

    Science.gov (United States)

    Haiganoush K. Preisler; Jeff Eidenshink; Stephen Howard; Robert E. Burgan

    2015-01-01

    Systems to estimate forest fire potential commonly utilize one or more indexes that relate to expected fire behavior; however they indicate neither the chance that a large fire will occur, nor the expected number of large fires. That is, they do not quantify the probabilistic nature of fire danger. In this work we use large fire occurrence information from the...

  15. Topics in the theory of numbers

    CERN Document Server

    Erdős, Paul

    2003-01-01

    This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös. Janos Suranyis vast teaching experience successfully complements Paul Erdös'ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing...

  16. Where Are All the Typical Numbers - 1

    Indian Academy of Sciences (India)

    inequality, independence. B V Rao was a Professor at the Indian Statistical. Institute, Kolkata. He is currently with the. Chennai Mathematical. Institute. The entire discussion below, except the first few paragraphs, takes place on the interval (0;1], so you can relax. In this two-part article, we show that decimal digits of numbers ...

  17. Poison control center - Emergency number (image)

    Science.gov (United States)

    For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...

  18. String fields, higher spins and number theory

    CERN Document Server

    Polyakov, Dimitri

    2018-01-01

    The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.

  19. A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers

    Science.gov (United States)

    Tavelli, Maurizio; Dumbser, Michael

    2017-07-01

    addition, all the volume and surface integrals needed by the scheme depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessing stage. This leads to significant savings in terms of computational effort for the time evolution part. In this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step. The viscous terms and the heat flux are also discretized making use of the staggered grid by defining the viscous stress tensor and the heat flux vector on the dual grid, which corresponds to the use of a lifting operator, but on the dual grid. The time step of our new numerical method is limited by a CFL condition based only on the fluid velocity and not on the sound speed. This makes the method particularly interesting for low Mach number flows. Finally, a very simple combination of artificial viscosity and the a posteriori MOOD technique allows to deal with shock waves and thus permits also to simulate high Mach number flows. We show computational results for a large set of two and three-dimensional benchmark problems, including both low and high Mach number flows and using polynomial approximation degrees up to p = 4.

  20. Optokinetic stimulation modulates neglect for the number space: Evidence from mental number interval bisection

    Directory of Open Access Journals (Sweden)

    Konstantinos ePriftis

    2012-02-01

    Full Text Available Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL, an analogical, visuo-spatial representation of number magnitude. The MNL is left-to-right oriented, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in processing the left side of the MNL and show a rightward deviation in the mental bisection of numerical intervals. In the present study we investigated the effects of optokinetic stimulation (OKS -a technique inducing spatial attention shifts by means of activation of the optokinetic nystagmus- on mental number interval bisection. One patient with left neglect following right hemisphere stroke (BG and four control patients with right hemisphere damage, but without neglect, performed the mental number interval bisection task in three experimental conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, but again to the right of the midpoint following rightward OKS. In contrast, the performance of controls was not significantly affected by the direction of OKS. We argue that shifts of visuospatial attention, induced by OKS, may affect the mental number interval bisection, suggesting the presence of an interaction between the processing of number magnitude and the processing of the perceptual space, in patients with neglect for the mental number space.