WorldWideScience

Sample records for elliptic function expansion

  1. Jacobian elliptic function expansion solutions of nonlinear stochastic equations

    International Nuclear Information System (INIS)

    Wei Caimin; Xia Zunquan; Tian Naishuo

    2005-01-01

    Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

  2. An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong; Zhang Hongqing

    2005-01-01

    With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

  3. Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

    International Nuclear Information System (INIS)

    Song Lina; Zhang Hongqing

    2007-01-01

    In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

  4. Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinates

    Science.gov (United States)

    Salman, Yehonatan

    2017-09-01

    The aim of this paper is to introduce a new inversion procedure for recovering functions, defined on R2 , from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by Norton (J Acoust Soc Am 67:1266-1273, 1980) for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [24] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the eigenfunction expansion of the Bessel function in elliptical coordinates.

  5. Fast computation of complete elliptic integrals and Jacobian elliptic functions

    Science.gov (United States)

    Fukushima, Toshio

    2009-12-01

    As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K( m) and E( m), for the standard domain of the elliptic parameter, 0 procedure to compute simultaneously three Jacobian elliptic functions, sn( u| m), cn( u| m), and dn( u| m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic argument, u, after its domain is reduced to the standard range, 0 ≤ u procedure is 25-70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K( m) is not taken into account.

  6. The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

    Science.gov (United States)

    Ahmedov, Anvarjon

    2018-03-01

    In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral

  7. Newton flows for elliptic functions

    NARCIS (Netherlands)

    Helminck, G.F.; Twilt, F.

    2015-01-01

    Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational (complex) and the elliptic (i.e., doubly

  8. Electromagnetic fields and Green functions in elliptical vacuum chambers

    CERN Document Server

    AUTHOR|(CDS)2084216; Biancacci, Nicolo; Migliorati, Mauro; Palumbo, Luigi; Vaccaro, Vittorio; CERN. Geneva. ATS Department

    2017-01-01

    In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be diffe...

  9. Elliptic hypergeometric functions associated with root systems

    OpenAIRE

    Rosengren, Hjalmar; Warnaar, S. Ole

    2017-01-01

    We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson).

  10. Asymptotic expansions for high-contrast elliptic equations

    KAUST Repository

    Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan

    2014-01-01

    In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.

  11. Asymptotic expansions for high-contrast elliptic equations

    KAUST Repository

    Calo, Victor M.

    2014-03-01

    In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.

  12. Elliptic hypergeometric functions and the representation theory

    International Nuclear Information System (INIS)

    Spiridonov, V.P.

    2011-01-01

    Full text: (author)Elliptic hypergeometric functions were discovered around ten years ago. They represent the top level known generalization of the Euler beta integral and Euler-Gauss 2 F 1 hypergeometric function. In general form they are defined by contour integrals involving elliptic gamma functions. We outline the structure of the simplest examples of such functions and discuss their relations to the representation theory of the classical Lie groups and their various deformations. In one of the constructions elliptic hypergeometric integrals describe purely group-theoretical objects having the physical meaning of superconformal indices of four-dimensional supersymmetric gauge field theories

  13. Local identities involving Jacobi elliptic functions

    Indian Academy of Sciences (India)

    systematize the local identities by deriving four local 'master identities' analogous to the ... involving Jacobi elliptic functions can be explicitly evaluated and a number of .... most of these integrals do not seem to be known in the literature. In §6 ...

  14. Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

    International Nuclear Information System (INIS)

    Chen Yong; Wang Qi; Li Biao

    2005-01-01

    Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

  15. Newton flows for elliptic functions: A pilot study

    NARCIS (Netherlands)

    Twilt, F.; Helminck, G.F.; Snuverink, M.; van den Brug, L.

    2008-01-01

    Elliptic Newton flows are generated by a continuous, desingularized Newton method for doubly periodic meromorphic functions on the complex plane. In the special case, where the functions underlying these elliptic Newton flows are of second-order, we introduce various, closely related, concepts of

  16. Expansions for Coulomb wave functions

    NARCIS (Netherlands)

    Boersma, J.

    1969-01-01

    In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are

  17. Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals

    Science.gov (United States)

    Schwalm, William A.

    2015-12-01

    This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

  18. Type-2 fuzzy elliptic membership functions for modeling uncertainty

    DEFF Research Database (Denmark)

    Kayacan, Erdal; Sarabakha, Andriy; Coupland, Simon

    2018-01-01

    Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs...... in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance...... advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem...

  19. Orbits in general relativity: the Jacobian elliptic function

    Energy Technology Data Exchange (ETDEWEB)

    Miro Rodriguez, C

    1987-03-11

    The Jacobian elliptic functions are applied to the motion of nonzero-rest-mass particles in the Schwarzschild geometry. The bound and unbound trajectories are analysed together with their classical and special-relativity limits.

  20. Scattering by an infinite homogenous anisotropic elliptic cylinder in terms of Mathieu functions and Fourier series.

    Science.gov (United States)

    Mao, Shi-Chun; Wu, Zhen-Sen

    2008-12-01

    An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.

  1. Refined functional relations for the elliptic SOS model

    Energy Technology Data Exchange (ETDEWEB)

    Galleas, W., E-mail: w.galleas@uu.nl [ARC Centre of Excellence for the Mathematics and Statistics of Complex Systems, University of Melbourne, VIC 3010 (Australia)

    2013-02-21

    In this work we refine the method presented in Galleas (2012) [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation arises from the dynamical Yang-Baxter relation and its solution is given in terms of multiple contour integrals.

  2. Refined functional relations for the elliptic SOS model

    International Nuclear Information System (INIS)

    Galleas, W.

    2013-01-01

    In this work we refine the method presented in Galleas (2012) [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation arises from the dynamical Yang–Baxter relation and its solution is given in terms of multiple contour integrals.

  3. The SOS model partition function and the elliptic weight functions

    International Nuclear Information System (INIS)

    Pakuliak, S; Silantyev, A; Rubtsov, V

    2008-01-01

    We generalized a recent observation (Khoroshkin and Pakuliak 2005 Theor. Math. Phys. 145 1373) that the partition function of the six-vertex model with domain wall boundary conditions can be obtained from a calculation of projections of the product of total currents in the quantum affine algebra U q (sl 2 -hat) in its current realization. A generalization is done for the elliptic current algebra (Enriquez and Felder 1998 Commun. Math. Phys. 195 651, Enriquez and Rubtsov 1997 Ann. Sci. Ecole Norm. Sup. 30 821). The projections of the product of total currents in this case are calculated explicitly and are presented as integral transforms of a product of the total currents. It is proved that the integral kernel of this transform is proportional to the partition function of the SOS model with domain wall boundary conditions

  4. A Primer on Elliptic Functions with Applications in Classical Mechanics

    Science.gov (United States)

    Brizard, Alain J.

    2009-01-01

    The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

  5. Arithmetical Fourier and Limit values of elliptic modular functions

    Indian Academy of Sciences (India)

    2

    In order to remove singularities, Riemann used a well-known device of taking the odd part (3.2) or an alternate sum (3.3) to be stated in §3. In §2 of this note we shall reveal that the limit values of elliptic modular functions in Riemann's fragment II evaluated by the differences of polyloga- rithm function l1(x) of order 1 (cf.

  6. An Inverse of the Elliptic Coverage Function

    National Research Council Canada - National Science Library

    Didonato, Armido

    2005-01-01

    .... Given a circular target T centered at (h, k); r, the radius of T, is determined for a specified probability P of a shot falling in T under a two-dimensional normal distribution function with mean zero and standard deviations u, v...

  7. A new extended elliptic equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

    International Nuclear Information System (INIS)

    Wang Baodong; Song Lina; Zhang Hongqing

    2007-01-01

    In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions

  8. Expansion of passive safety function

    International Nuclear Information System (INIS)

    Inai, Nobuhiko; Nei, Hiromichi; Kumada, Toshiaki.

    1995-01-01

    Expansion of the use of passive safety functions is proposed. Two notions are presented. One is that, in the design of passive safety nuclear reactors where aversion of active components is stressed, some active components are purposely introduced, by which a system is built in such a way that it behaves in an apparently passive manner. The second notion is that, instead of using a passive safety function alone, a passive safety function is combined with some active components, relating the passivity in the safety function with enhanced controllability in normal operation. The nondormant system which the authors propose is one example of the first notion. This is a system in which a standby safety system is a portion of the normal operation system. An interpretation of the nondormant system via synergetics is made. As an example of the second notion, a PIUS density lock aided with active components is proposed and is discussed

  9. Generation of an elliptic hollow beam using Mathieu and Bessel functions.

    Science.gov (United States)

    Chakraborty, Rijuparna; Ghosh, Ajay

    2006-09-01

    A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

  10. Mathieu functions and its useful approximation for elliptical waveguides

    Science.gov (United States)

    Pillay, Shamini; Kumar, Deepak

    2017-11-01

    The standard form of the Mathieu differential equation is where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.

  11. Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations

    International Nuclear Information System (INIS)

    Yu Jianping; Sun Yongli

    2008-01-01

    This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations

  12. Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong

    2007-01-01

    With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time

  13. Elliptic curves, modular forms, and their L-functions

    CERN Document Server

    Lozano-Robledo, Alvaro

    2011-01-01

    Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and L-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some moti...

  14. Discrete expansions of continuum functions. General concepts

    International Nuclear Information System (INIS)

    Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

    1979-01-01

    Different discrete expansions of the continuum wave functions are considered: pole expansion (according to the Mittag-Lefler theorem), Weinberg states. The general property of these groups of states is their completeness in the finite region of space. They satisfy the Schroedinger type equations and are matched with free solutions of the Schroedinger equation at the boundary. Convergence of expansions for the S matrix, the Green functions and the continuous-spectrum wave functions is studied. A new group of states possessing the best convergence is introduced

  15. Oblique photon expansion of QED structure functions

    International Nuclear Information System (INIS)

    Chahine, C.

    1986-01-01

    In the oblique photon expansion, the collinear part of photon emission is summed up to all orders in perturbation theory. The number of oblique or non-collinear photons is the expansion order. Unlike in perturbation theory, every term of the expansion is both infrared finite and gauge invariant. The zero oblique photon contribution to the electromagnetic structure tensor in QED is computed in detail. The behaviors of the structure functions F1 and F2 are discussed in the soft and ultra-soft limits

  16. Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions

    Czech Academy of Sciences Publication Activity Database

    Siegl, Petr; Štampach, F.

    2017-01-01

    Roč. 11, č. 4 (2017), s. 901-928 ISSN 1846-3886 Grant - others:GA ČR(CZ) GA13-11058S Institutional support: RVO:61389005 Keywords : Non-self-adjoint Jacobi operator * Weyl m-function * Jacobian elliptic functions Subject RIV: BE - Theoretical Physics OBOR OECD: Pure mathematics Impact factor: 0.440, year: 2016

  17. Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions

    International Nuclear Information System (INIS)

    Smirnov, A.O.

    1989-01-01

    A reduction theorem is formulated and proved. Smooth real solutions of the Abelian Toda chain of genus 4 and 5 are obtained in elliptic functions. Solutions of genus 2g and 2g + 1 of the discrete Peierls-Froehlich model in the absence of intramolecular deformation are constructed in terms of g-dimensional theta functions

  18. Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

    International Nuclear Information System (INIS)

    Zhang Liang; Zhang Lifeng; Li Chongyin

    2008-01-01

    By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions

  19. FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation

    International Nuclear Information System (INIS)

    Cody, W.J.; Garbow, Burton S.

    1975-01-01

    1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations

  20. Discrete expansions of continuum wave functions

    International Nuclear Information System (INIS)

    Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

    1980-01-01

    Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)

  1. Comment on star–star relations in statistical mechanics and elliptic gamma-function identities

    International Nuclear Information System (INIS)

    Bazhanov, Vladimir V; Kels, Andrew P; Sergeev, Sergey M

    2013-01-01

    We prove a recently conjectured star–star relation, which plays the role of an integrability condition for a class of 2D Ising-type models with multicomponent continuous spin variables. Namely, we reduce this relation to an identity for elliptic gamma functions, previously obtained by Rains. (fast track communication)

  2. Expansion of continuum functions on resonance wave functions and amplitudes

    International Nuclear Information System (INIS)

    Bang, J.; Gareev, F.A.; Gizzatkulov, M.H.; Goncharov, S.A.

    1978-01-01

    To overcome difficulties encountered with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions with positive energies are considered. It is shown that resonance functions (the Gamov functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials and for the Coulomb repulsion potential are obtained and discussed. It is shown that the application of the method to nuclear structure calculations leads to simple algebraic equations

  3. Temporal quadratic expansion nodal Green's function method

    International Nuclear Information System (INIS)

    Liu Cong; Jing Xingqing; Xu Xiaolin

    2000-01-01

    A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

  4. Edgeworth expansion for functionals of continuous diffusion processes

    DEFF Research Database (Denmark)

    Podolskij, Mark; Yoshida, Nakahiro

    This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes....... Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations.......This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes...

  5. Estimates of azimuthal numbers associated with elementary elliptic cylinder wave functions

    Science.gov (United States)

    Kovalev, V. A.; Radaev, Yu. N.

    2014-05-01

    The paper deals with issues related to the construction of solutions, 2 π-periodic in the angular variable, of the Mathieu differential equation for the circular elliptic cylinder harmonics, the associated characteristic values, and the azimuthal numbers needed to form the elementary elliptic cylinder wave functions. A superposition of the latter is one possible form for representing the analytic solution of the thermoelastic wave propagation problem in long waveguides with elliptic cross-section contour. The classical Sturm-Liouville problem for the Mathieu equation is reduced to a spectral problem for a linear self-adjoint operator in the Hilbert space of infinite square summable two-sided sequences. An approach is proposed that permits one to derive rather simple algorithms for computing the characteristic values of the angular Mathieu equation with real parameters and the corresponding eigenfunctions. Priority is given to the application of the most symmetric forms and equations that have not yet been used in the theory of the Mathieu equation. These algorithms amount to constructing a matrix diagonalizing an infinite symmetric pentadiagonal matrix. The problem of generalizing the notion of azimuthal number of a wave propagating in a cylindrical waveguide to the case of elliptic geometry is considered. Two-sided mutually refining estimates are constructed for the spectral values of the Mathieu differential operator with periodic and half-periodic (antiperiodic) boundary conditions.

  6. Swarm formation control utilizing elliptical surfaces and limiting functions.

    Science.gov (United States)

    Barnes, Laura E; Fields, Mary Anne; Valavanis, Kimon P

    2009-12-01

    In this paper, we present a strategy for organizing swarms of unmanned vehicles into a formation by utilizing artificial potential fields that were generated from normal and sigmoid functions. These functions construct the surface on which swarm members travel, controlling the overall swarm geometry and the individual member spacing. Nonlinear limiting functions are defined to provide tighter swarm control by modifying and adjusting a set of control variables that force the swarm to behave according to set constraints, formation, and member spacing. The artificial potential functions and limiting functions are combined to control swarm formation, orientation, and swarm movement as a whole. Parameters are chosen based on desired formation and user-defined constraints. This approach is computationally efficient and scales well to different swarm sizes, to heterogeneous systems, and to both centralized and decentralized swarm models. Simulation results are presented for a swarm of 10 and 40 robots that follow circle, ellipse, and wedge formations. Experimental results are included to demonstrate the applicability of the approach on a swarm of four custom-built unmanned ground vehicles (UGVs).

  7. Origin of a bottom-heavy stellar initial mass function in elliptical galaxies

    International Nuclear Information System (INIS)

    Bekki, Kenji

    2013-01-01

    We investigate the origin of a bottom-heavy stellar initial mass function (IMF) recently observed in elliptical galaxies by using chemical evolution models with a non-universal IMF. We adopt the variable Kroupa IMF with the three slopes (α 1 , α 2 , and α 3 ) dependent on metallicities ([Fe/H]) and densities (ρ g ) of star-forming gas clouds and thereby search for the best IMF model that can reproduce (1) the observed steep IMF slope (α 2 ∼ 3, i.e., bottom-heavy) for low stellar masses (m ≤ 1 M ☉ ) and (2) the correlation of α 2 with chemical properties of elliptical galaxies in a self-consistent manner. We find that if the IMF slope α 2 depends on both [Fe/H] and ρ g , then elliptical galaxies with higher [Mg/Fe] can have steeper α 2 (∼3) in our models. We also find that the observed positive correlation of stellar mass-to-light ratios (M/L) with [Mg/Fe] in elliptical galaxies can be quantitatively reproduced in our models with α 2 ∝β[Fe/H] + γlog ρ g , where β ∼ 0.5 and γ ∼ 2. We discuss whether the IMF slopes for low-mass (α 2 ) and high-mass stars (α 3 ) need to vary independently from each other to explain a number of IMF-related observational results self-consistently. We also briefly discuss why α 2 depends differently on [Fe/H] in dwarf and giant elliptical galaxies.

  8. Parabolic cyclinder functions : examples of error bounds for asymptotic expansions

    NARCIS (Netherlands)

    R. Vidunas; N.M. Temme (Nico)

    2002-01-01

    textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.

  9. A summation procedure for expansions in orthogonal polynomials

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Grinstein, F.F.

    1977-01-01

    Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges

  10. Density-functional expansion methods: Grand challenges.

    Science.gov (United States)

    Giese, Timothy J; York, Darrin M

    2012-03-01

    We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

  11. A random matrix model for elliptic curve L-functions of finite conductor

    International Nuclear Information System (INIS)

    Dueñez, E; Huynh, D K; Keating, J P; Snaith, N C; Miller, S J

    2012-01-01

    We propose a random-matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of the critical zeros of these L-functions away from the centre of the critical strip was observed numerically by Miller (2006 Exp. Math. 15 257–79); such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros (for large conductors this distribution is expected to approach the one-level density of eigenvalues of orthogonal matrices after appropriate rescaling). Our purpose here is to provide a random-matrix model for Miller’s surprising discovery. We consider the family of even quadratic twists of a given elliptic curve. The main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra. We call this sub-ensemble of SO(2N) the excised orthogonal ensemble. The sieving-off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of L-functions implied by the formulae of Waldspurger and Kohnen–Zagier. The cut-off scale appropriate to modelling elliptic curve L-functions is exponentially small relative to the matrix size N. The one-level density of the excised ensemble can be expressed in terms of that of the well-known Jacobi ensemble, enabling the former to be explicitly calculated. It exhibits an exponentially small (on the scale of the mean spacing) hard gap determined by the cut-off value, followed by soft repulsion on a much larger scale. Neither of these features is present in the one-level density of SO(2N). When N → ∞ we recover the limiting orthogonal behaviour. Our results agree qualitatively with Miller’s discrepancy. Choosing the cut-off appropriately gives a model in good quantitative agreement with the number-theoretical data. (paper)

  12. The effects of the initial mass function on the chemical evolution of elliptical galaxies

    Science.gov (United States)

    De Masi, Carlo; Matteucci, F.; Vincenzo, F.

    2018-03-01

    We describe the use of our chemical evolution model to reproduce the abundance patterns observed in a catalogue of elliptical galaxies from the Sloan Digital Sky Survey Data Release 4. The model assumes ellipticals form by fast gas accretion, and suffer a strong burst of star formation followed by a galactic wind, which quenches star formation. Models with fixed initial mass function (IMF) failed in simultaneously reproducing the observed trends with the galactic mass. So, we tested a varying IMF; contrary to the diffused claim that the IMF should become bottom heavier in more massive galaxies, we find a better agreement with data by assuming an inverse trend, where the IMF goes from being bottom heavy in less massive galaxies to top heavy in more massive ones. This naturally produces a downsizing in star formation, favouring massive stars in largest galaxies. Finally, we tested the use of the integrated Galactic IMF, obtained by averaging the canonical IMF over the mass distribution function of the clusters where star formation is assumed to take place. We combined two prescriptions, valid for different SFR regimes, to obtain the Integrated Initial Mass Function values along the whole evolution of the galaxies in our models. Predicted abundance trends reproduce the observed slopes, but they have an offset relative to the data. We conclude that bottom-heavier IMFs do not reproduce the properties of the most massive ellipticals, at variance with previous suggestions. On the other hand, an IMF varying with galactic mass from bottom heavier to top heavier should be preferred.

  13. Resolving the faint end of the satellite luminosity function for the nearest elliptical Centaurus A

    Science.gov (United States)

    Crnojevic, Denija

    2014-10-01

    We request HST/ACS imaging to follow up 15 new faint candidate dwarfs around the nearest elliptical Centaurus A (3.8 Mpc). The dwarfs were found via a systematic ground-based (Magellan/Megacam) survey out to ~150 kpc, designed to directly confront the "missing satellites" problem in a wholly new environment. Current Cold Dark Matter models for structure formation fail to reproduce the shallow slope of the satellite luminosity function in spiral-dominated groups for which dwarfs fainter than M_V<-14 have been surveyed (the Local Group and the nearby, interacting M81 group). Clusters of galaxies show a better agreement with cosmological predictions, suggesting an environmental dependence of the (poorly-understood) physical processes acting on the evolution of low mass galaxies (e.g., reionization). However, the luminosity function completeness for these rich environments quickly drops due to the faintness of the satellites and to the difficult cluster membership determination. We target a yet unexplored "intermediate" environment, a nearby group dominated by an elliptical galaxy, ideal due to its proximity: accurate (10%) distance determinations for its members can be derived from resolved stellar populations. The proposed observations of the candidate dwarfs will confirm their nature, group membership, and constrain their luminosities, metallicities, and star formation histories. We will obtain the first complete census of dwarf satellites of an elliptical down to an unprecedented M_V<-9. Our results will crucially constrain cosmological predictions for the faint end of the satellite luminosity function to achieve a more complete picture of the galaxy formation process.

  14. Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

    KAUST Repository

    Kuchment, Peter

    2012-06-21

    Precise asymptotics known for the Green\\'s function of the Laplace operator have found their analogs for periodic elliptic operators of the second order at and below the bottom of the spectrum. Due to the band-gap structure of the spectra of such operators, the question arises whether similar results can be obtained near or at the edges of spectral gaps. As the result of this work shows, this is possible at a spectral edge when the dimension d ≥ 3. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  15. Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

    KAUST Repository

    Kuchment, Peter; Raich, Andrew

    2012-01-01

    Precise asymptotics known for the Green's function of the Laplace operator have found their analogs for periodic elliptic operators of the second order at and below the bottom of the spectrum. Due to the band-gap structure of the spectra of such operators, the question arises whether similar results can be obtained near or at the edges of spectral gaps. As the result of this work shows, this is possible at a spectral edge when the dimension d ≥ 3. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  16. Stellar populations as a function of radius in giant elliptical galaxies

    NARCIS (Netherlands)

    Peletier, Reynier F.; Valentijn, Edwin A.

    Accurate surface photometry has been obtained in J and K for 12 giant elliptical galaxies. Ellipses have been fitted, to obtain luminosity, ellipticity, and major axis position angle profiles. The results have been combined with visual profiles from CCD observations. It is found that elliptical

  17. Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies

    Energy Technology Data Exchange (ETDEWEB)

    Bonora, L., E-mail: bonora@sissa.it [International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A., E-mail: abyts@uel.br [Departamento de Fisica, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina (Brazil)

    2011-11-11

    There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS{sub 3}, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.

  18. Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type

    Directory of Open Access Journals (Sweden)

    Tomasz S. Zabawa

    2005-01-01

    Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.

  19. Robust Improvement in Estimation of a Covariance Matrix in an Elliptically Contoured Distribution Respect to Quadratic Loss Function

    Directory of Open Access Journals (Sweden)

    Z. Khodadadi

    2008-03-01

    Full Text Available Let S be matrix of residual sum of square in linear model Y = Aβ + e where matrix e is distributed as elliptically contoured with unknown scale matrix Σ. In present work, we consider the problem of estimating Σ with respect to squared loss function, L(Σˆ , Σ = tr(ΣΣˆ −1 −I 2 . It is shown that improvement of the estimators were obtained by James, Stein [7], Dey and Srivasan [1] under the normality assumption remains robust under an elliptically contoured distribution respect to squared loss function

  20. Graph approach to the gradient expansion of density functionals

    International Nuclear Information System (INIS)

    Kozlowski, P.M.; Nalewajski, R.F.

    1986-01-01

    A graph representation of terms in the gradient expansion of the kinetic energy density functional is presented. They briefly discuss the implications of the virial theorem for the graph structure and relations between possible graphs at a given order of expansion

  1. Off-diagonal series expansion for quantum partition functions

    Science.gov (United States)

    Hen, Itay

    2018-05-01

    We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.

  2. The auxiliary elliptic-like equation and the exp-function method

    Indian Academy of Sciences (India)

    exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. ... (NEE) have been paid attention by many researchers, especially the investigations of exact solutions for ... elliptic-like equation with the aid of the travelling wave reduction are introduced. The exact solutions of ...

  3. Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method

    International Nuclear Information System (INIS)

    Song Lina; Wang Weiguo

    2010-01-01

    In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.

  4. Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications.

    Science.gov (United States)

    Chen, Jun; Hu, Lei; Deng, Jinxia; Xing, Xianran

    2015-06-07

    Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so on. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a "perfect" NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

  5. Multipole expansion of vertex functions with two final particles

    International Nuclear Information System (INIS)

    Daumens, Michel

    1977-01-01

    The expansions of the usual vertex functions are generalized to the vertex functions with two final particles. For four vector functions, expressions are similar to those of Chew, Goldberger, Low and Nambu, and of Adler and the consequences of the isobaric model are studied [fr

  6. Planar elliptic growth

    Energy Technology Data Exchange (ETDEWEB)

    Mineev, Mark [Los Alamos National Laboratory

    2008-01-01

    The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for areapreserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.

  7. Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions

    International Nuclear Information System (INIS)

    Celledoni, E; Saefstroem, N

    2006-01-01

    If the three moments of inertia are distinct, the solution to the Euler equations for the free rigid body is given in terms of Jacobi elliptic functions. Using the arithmetic-geometric mean algorithm (Abramowitz and Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)), these functions can be calculated efficiently and accurately. Compared to standard numerical ODE and Lie-Poisson solvers, the overall approach yields a faster and more accurate numerical solution to the Euler equations. This approach is designed for mass asymmetric rigid bodies. In the case of symmetric bodies, the exact solution is available in terms of trigonometric functions, see Dullweber et al (1997 J. Chem. Phys. 107 5840-51), Reich (1996 Fields Inst. Commun. 10 181-91) and Benettin et al (2001 SIAM J. Sci. Comp. 23 1189-203) for details. In this paper, we consider the case of asymmetric rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in Reich (1996 Fields Inst. Commun. 10 181-91) and Dullweber et al (1997 J. Chem. Phys. 107 5840-51). The method proposed here is time-symmetric. We decompose the vector field of our problem into a free rigid body (FRB) problem and another completely integrable vector field. The FRB problem consists of the Euler equations and a differential equation for the 3 x 3 orientation matrix. The Euler equations are integrated exactly while the matrix equation is approximated using a truncated Magnus series. In our experiments, we observe that the overall numerical solution benefits greatly from the very accurate solution of the Euler equations. We apply the method to the heavy top and the simulation of artificial satellite attitude dynamics

  8. Superposition of elliptic functions as solutions for a large number of nonlinear equations

    International Nuclear Information System (INIS)

    Khare, Avinash; Saxena, Avadh

    2014-01-01

    For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

  9. Improved wave functions for large-N expansions

    International Nuclear Information System (INIS)

    Imbo, T.; Sukhatme, U.

    1985-01-01

    Existing large-N expansions of radial wave functions phi/sub n/,l(r) are only accurate near the minimum of the effective potential. Within the framework of the shifted 1/N expansion, we use known analytic results to motivate a simple modification so that the improved wave functions are accurate over a wide range of r and any choice of quantum numbers n and l. It is shown that these wave functions yield simple and accurate analytic expressions for certain quantities of interest in quarkonium physics

  10. Conformal four point functions and the operator product expansion

    International Nuclear Information System (INIS)

    Dolan, F.A.; Osborn, H.

    2001-01-01

    Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion

  11. Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties

    NARCIS (Netherlands)

    Derkach, Vladimir; Hassi, Seppo; de Snoo, Hendrik

    2007-01-01

    Asymptotic expansions of generalized Nevanlinna functions Q are investigated by means of a factorization model involving a part of the generalized zeros and poles of nonpositive type of the function Q. The main results in this paper arise from the explicit construction of maximal Jordan chains in

  12. New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

    International Nuclear Information System (INIS)

    Pandir, Yusuf; Duzgun, Hasan Huseyin

    2017-01-01

    In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

  13. Fourier expansions and multivariable Bessel functions concerning radiation programmes

    International Nuclear Information System (INIS)

    Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

    1996-01-01

    The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

  14. Evolution of elliptic and triangular flow as a function of beam energy in a hybrid model

    International Nuclear Information System (INIS)

    Auvinen, J; Petersen, H

    2014-01-01

    Elliptic flow has been one of the key observables for establishing the finding of the quark-gluon plasma (QGP) at the highest energies of Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). As a sign of collectively behaving matter, one would expect the elliptic flow to decrease at lower beam energies, where the QGP is not produced. However, in the recent RHIC beam energy scan, it has been found that the inclusive charged hadron elliptic flow changes relatively little in magnitude in the energies between 7.7 and 39 GeV per nucleon-nucleon collision. We study the collision energy dependence of the elliptic and triangular flow utilizing a Boltzmann + hydrodynamics hybrid model. Such a hybrid model provides a natural framework for the transition from high collision energies, where the hydrodynamical description is essential, to smaller energies, where the hadron transport dominates. This approach is thus suitable to investigate the relative importance of these two mechanisms for the production of the collective flow at different values of beam energy. Extending the examined range down to 5 GeV per nucleon-nucleon collision allows also making predictions for the CBM experiment at FAIR.

  15. Asymptotic expansions of Mathieu functions in wave mechanics

    International Nuclear Information System (INIS)

    Hunter, G.; Kuriyan, M.

    1976-01-01

    Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states

  16. Multipole expansion of vertex functions in an arbitrary frame

    International Nuclear Information System (INIS)

    Daumens, Michel

    1977-01-01

    Vertex functions are expanded on the bases of tensor spherical harmonics and tensor multipoles. The coefficients of the expansions are rotational invariant form factors. The relations with those defined in particular frames by Durand, De Celles and Marr, and by De Rafael are exhibited. Finally multipolar form factors are built which are irreducible under pure Lorentz transformations [fr

  17. The linear potential propagator via wave function expansion

    International Nuclear Information System (INIS)

    Nassar, Antonio B.; Cattani, Mauro S.D.

    2002-01-01

    We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)

  18. Recurrence formulas for evaluating expansion series of depletion functions

    International Nuclear Information System (INIS)

    Vukadin, Z.

    1991-01-01

    A high-accuracy analytical method for solving the depletion equations for chains of radioactive nuclides is based on the formulation of depletion functions. When all the arguments of the depletion function are too close to each other, series expansions of the depletion function have to be used. However, the high-accuracy series expressions for the depletion functions of high index become too complicated. Recursion relations are derived which enable an efficient high-accuracy evaluation of the depletion functions with high indices. (orig.) [de

  19. General post-Minkowskian expansion of time transfer functions

    International Nuclear Information System (INIS)

    Teyssandier, Pierre; Poncin-Lafitte, Christophe Le

    2008-01-01

    Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation

  20. General post-Minkowskian expansion of time transfer functions

    Energy Technology Data Exchange (ETDEWEB)

    Teyssandier, Pierre; Poncin-Lafitte, Christophe Le [Departement Systemes de Reference Temps et Espace, CNRS/UMR 8630, Observatoire de Paris, 61 avenue de l' Observatoire, F-75014 Paris (France)

    2008-07-21

    Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

  1. Bounds for the integral points on elliptic curves over function fields

    OpenAIRE

    Sedunova, Alisa

    2017-01-01

    In this paper we give an upper bound for the number of integral points on an elliptic curve E over F_q[T] in terms of its conductor N and q. We proceed by applying the lower bounds for the canonical height that are analogous to those given by Silverman and extend the technique developed by Helfgott-Venkatesh to express the number of integral points on E in terms of its algebraic rank. We also use the sphere packing results to optimize the size of an implied constant. In the end we use partial...

  2. Nucleon structure functions from lattice operator product expansion

    Energy Technology Data Exchange (ETDEWEB)

    Chambers, A.J.; Somfleth, K.; Young, R.D.; Zanotti, J.M. [Adelaide Univ., SA (Australia). CSSM, Dept. of Physics; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2017-03-15

    Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

  3. Nucleon structure functions from lattice operator product expansion

    International Nuclear Information System (INIS)

    Chambers, A.J.; Somfleth, K.; Young, R.D.; Zanotti, J.M.; Perlt, H.; Schiller, A.

    2017-03-01

    Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

  4. Nucleon Structure Functions from Operator Product Expansion on the Lattice.

    Science.gov (United States)

    Chambers, A J; Horsley, R; Nakamura, Y; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A; Somfleth, K; Young, R D; Zanotti, J M

    2017-06-16

    Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

  5. Elliptical concentrators.

    Science.gov (United States)

    Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio

    2006-10-10

    Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

  6. Elliptic Determinantal Processes and Elliptic Dyson Models

    Science.gov (United States)

    Katori, Makoto

    2017-10-01

    We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families {A}_{N-1}, {B}_N, {C}_N and {D}_N, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.

  7. Derivation of the density functional theory from the cluster expansion.

    Science.gov (United States)

    Hsu, J Y

    2003-09-26

    The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

  8. Neural substrate expansion for the restoration of brain function

    Directory of Open Access Journals (Sweden)

    Han-Chiao Isaac Chen

    2016-01-01

    Full Text Available Restoring neurological and cognitive function in individuals who have suffered brain damage is one of the principal objectives of modern translational neuroscience. Electrical stimulation approaches, such as deep-brain stimulation, have achieved the most clinical success, but they ultimately may be limited by the computational capacity of the residual cerebral circuitry. An alternative strategy is brain substrate expansion, in which the computational capacity of the brain is augmented through the addition of new processing units and the reconstitution of network connectivity. This latter approach has been explored to some degree using both biological and electronic means but thus far has not demonstrated the ability to reestablish the function of large-scale neuronal networks. In this review, we contend that fulfilling the potential of brain substrate expansion will require a significant shift from current methods that emphasize direct manipulations of the brain (e.g., injections of cellular suspensions and the implantation of multi-electrode arrays to the generation of more sophisticated neural tissues and neural-electric hybrids in vitro that are subsequently transplanted into the brain. Drawing from neural tissue engineering, stem cell biology, and neural interface technologies, this strategy makes greater use of the manifold techniques available in the laboratory to create biocompatible constructs that recapitulate brain architecture and thus are more easily recognized and utilized by brain networks.

  9. CONFIRMATION OF ENHANCED DWARF-SENSITIVE ABSORPTION FEATURES IN THE SPECTRA OF MASSIVE ELLIPTICAL GALAXIES: FURTHER EVIDENCE FOR A NON-UNIVERSAL INITIAL MASS FUNCTION

    International Nuclear Information System (INIS)

    Van Dokkum, Pieter G.; Conroy, Charlie

    2011-01-01

    We recently found that massive cluster elliptical galaxies have strong Na I λ8183, 8195 and FeH λ9916 Wing-Ford band absorption, indicating the presence of a very large population of stars with masses ∼ sun . Here we test this result by comparing the elliptical galaxy spectra to those of luminous globular clusters associated with M31. These globular clusters have similar metallicities, abundance ratios, and ages as massive elliptical galaxies but their low dynamical mass-to-light ratios rule out steep stellar initial mass functions (IMFs). From high-quality Keck spectra we find that the dwarf-sensitive absorption lines in globular clusters are significantly weaker than in elliptical galaxies and consistent with normal IMFs. The differences in the Na I and Wing-Ford indices are 0.027 ± 0.007 mag and 0.017 ± 0.006 mag, respectively. We directly compare the two classes of objects by subtracting the averaged globular cluster spectrum from the averaged elliptical galaxy spectrum. The difference spectrum is well fit by the difference between a stellar population synthesis model with a bottom-heavy IMF and one with a bottom-light IMF. We speculate that the slope of the IMF may vary with velocity dispersion, although it is not yet clear what physical mechanism would be responsible for such a relation.

  10. A nonlinear analytic function expansion nodal method for transient calculations

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1998-12-31

    The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

  11. A nonlinear analytic function expansion nodal method for transient calculations

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1999-12-31

    The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

  12. Analytic function expansion nodal method for nuclear reactor core design

    International Nuclear Information System (INIS)

    Noh, Hae Man

    1995-02-01

    In most advanced nodal methods the transverse integration is commonly used to reduce the multi-dimensional diffusion equation into equivalent one- dimensional diffusion equations when derving the nodal coupling equations. But the use of the transverse integration results in some limitations. The first limitation is that the transverse leakage term which appears in the transverse integration procedure must be appropriately approximated. The second limitation is that the one-dimensional flux shapes in each spatial direction resulted from the nodal calculation are not accurate enough to be directly used in reconstructing the pinwise flux distributions. Finally the transverse leakage defined for a non-rectangular node such as a hexagonal node or a triangular node is too complicated to be easily handled and may contain non-physical singular terms of step-function and delta-function types. In this thesis, the Analytic Function Expansion Nodal (AFEN) method and its two variations : the Polynomial Expansion Nodal (PEN) method and the hybrid of the AFEN and PEN methods, have been developed to overcome the limitations of the transverse integration procedure. All of the methods solve the multidimensional diffusion equation without the transverse integration. The AFEN method which we believe is the major contribution of this study to the reactor core analysis expands the homogeneous flux distributions within a node in non-separable analytic basis functions satisfying the neutron diffusion equations at any point of the node and expresses the coefficients of the flux expansion in terms of the nodal unknowns which comprise a node-average flux, node-interface fluxes, and corner-point fluxes. Then, the nodal coupling equations composed of the neutron balance equations, the interface current continuity equations, and the corner-point leakage balance equations are solved iteratively to determine all the nodal unknowns. Since the AFEN method does not use the transverse integration in

  13. An approach to one-dimensional elliptic quasi-exactly solvable models

    Indian Academy of Sciences (India)

    potentials in different areas of physics (see above) motivated us to study these potentials and find some new elliptic potentials using generalized master function ... It is straightforward to show that the operator L is a self-adjoint linear operator ... should satisfy with (k − 2) coefficients of Taylor expansion of B as the only un-.

  14. Hydrodynamic simulation of elliptic flow

    CERN Document Server

    Kolb, P F; Ruuskanen, P V; Heinz, Ulrich W

    1999-01-01

    We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of radial and elliptic flow. We show that at high energies elliptic flow is generated only during the initial stages of the expansion while radial flow continues to grow until freeze-out. Quantitative comparisons with SPS data from semiperipheral Pb+Pb collisions suggest the applicability of hydrodynamical concepts already $\\approx$ 1 fm/c after impact.

  15. Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2010-01-01

    textabstractExpansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic

  16. Expansion of a function about a displaced centre

    International Nuclear Information System (INIS)

    Rashid, M.A.

    1981-07-01

    We review the progress recently made in obtaining closed form expressions for the expansion of general orbitals about a displaced centre and establish the equivalence between different expansions. We also examine how these expressions do have the desired limit as the displacement approaches zero. (author)

  17. [Application of the elliptic fourier functions to the description of avian egg shape].

    Science.gov (United States)

    Ávila, Dennis Denis

    2014-12-01

    Egg shape is difficult to quantify due to the lack of an exact formula to describe its geometry. Here I described a simple algorithm to characterize and compare egg shapes using Fourier functions. These functions can delineate any closed contour and had been previously applied to describe several biological objects. I described, step by step, the process of data acquisition, processing and the use of the SHAPE software to extract function coefficients in a study case. I compared egg shapes in three birds' species representing different reproductive strategies: Cuban Parakeet (Aratinga euops), Royal Tern (Thalasseus maximus) and Cuban Blackbird (Dives atroviolaceus). Using 73 digital pictures of eggs kept in Cuban scientific collections, I calculated Fourier descriptors with 4, 6, 8, 16 and 20 harmonics. Descriptors were reduced by a Principal Component Analysis and the scores of the eigen-values that account for 90% of variance were used in a Lineal Discriminant Function to analyze the possibility to differentiate eggs according to its shapes. Using four harmonics, the first five component accounted for 97% of shape variances; more harmonics diluted the variance increasing to eight the number of components needed to explain most of the variation. Convex polygons in the discriminant space showed a clear separation between species, allowing trustful discrimination (classification errors between 7-15%). Misclassifications were related to specific egg shape variability between species. In the study case, A. euops eggs were perfectly classified, but for the other species, errors ranged from 5 to 29% of misclassifications, in relation to the numbers or harmonics and components used. The proposed algorithm, despite its apparent mathematical complexity, showed many advantages to describe eggs shape allowing a deeper understanding of factors related to this variable.

  18. Acoustic scattering by multiple elliptical cylinders using collocation multipole method

    International Nuclear Information System (INIS)

    Lee, Wei-Ming

    2012-01-01

    This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

  19. Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation

    Science.gov (United States)

    Butuzov, V. F.

    2017-06-01

    We construct and justify asymptotic expansions of solutions of a singularly perturbed elliptic problem with Dirichlet boundary conditions in the case when the corresponding degenerate equation has a triple root. In contrast to the case of a simple root, the expansion is with respect to fractional (non-integral) powers of the small parameter, the boundary-layer variables have another scaling, and the boundary layer has three zones. This gives rise to essential modifications in the algorithm for constructing the boundary functions. Solutions of the elliptic problem are stationary solutions of the corresponding parabolic problem. We prove that such a stationary solution is asymptotically stable and find its global domain of attraction.

  20. Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Lin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division

    2013-10-28

    We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic system in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.

  1. THE GRAVITATIONAL SHEAR-INTRINSIC ELLIPTICITY CORRELATION FUNCTIONS OF LUMINOUS RED GALAXIES IN OBSERVATION AND IN THE ΛCDM MODEL

    International Nuclear Information System (INIS)

    Okumura, Teppei; Jing, Y. P.

    2009-01-01

    We examine whether the gravitational shear-intrinsic ellipticity (GI) correlation function of the luminous red galaxies (LRGs) can be modeled with the distribution function of a misalignment angle advocated recently by Okumura et al. For this purpose, we have accurately measured the GI correlation for the LRGs in the Data Release 6 (DR6) of the Sloan Digital Sky Survey (SDSS), which confirms the results of Hirata et al. who used the DR4 data. By comparing the GI correlation functions in the simulation and in the observation, we find that the GI correlation can be modeled in the current ΛCDM model if the misalignment follows a Gaussian distribution with a zero mean and a typical misalignment angle σ θ = 34.9 +1.9 -2.1 degrees. We also find a correlation between the axis ratios and intrinsic alignments of LRGs. This effect should be taken into account in theoretical modeling of the GI and intrinsic ellipticity-ellipticity correlations for weak lensing surveys.

  2. Anisotropic elliptic optical fibers

    Science.gov (United States)

    Kang, Soon Ahm

    1991-05-01

    The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

  3. Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions

    International Nuclear Information System (INIS)

    Altac, Zekeriya

    2007-01-01

    Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values

  4. Derivations of the solid angle subtended at a point by first- and second-order surfaces and volumes as a function of elliptic integrals

    International Nuclear Information System (INIS)

    Cramer, S.N.

    1999-01-01

    An analytical study of the solid angle subtended at a point by objects of first and second algebraic order has been made. It is shown that the derived solid angle for all such objects is in the form of a general elliptic integral, which can be written as a linear combination of elliptic integrals of the first and third kind and elementary functions. Many common surfaces and volumes have been investigated, including the conic sections and their volumes of revolution. The principal feature of the study is the manipulation of solid-angle equations into integral forms that can be matched with those found in handbook tables. These integrals are amenable to computer special function library routine analysis requiring no direct interaction with elliptic integrals by the user. The general case requires the solution of a fourth-order equation before specific solid-angle formulations can be made, but for many common geometric objects this equation can be solved by elementary means. Methods for the testing and application of solid-angle equations with Monte Carlo rejection and estimation techniques are presented. Approximate and degenerate forms of the equations are shown, and methods for the evaluation of the solid angle of a torus are outlined

  5. Ellipticities of Elliptical Galaxies in Different Environments

    Science.gov (United States)

    Chen, Cheng-Yu; Hwang, Chorng-Yuan; Ko, Chung-Ming

    2016-10-01

    We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between -21 and -22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.

  6. On the divergence of gradient expansions for kinetic energy functionals in the potential functional theory

    International Nuclear Information System (INIS)

    Sergeev, Alexey; Jovanovic, Raka; Kais, Sabre; Alharbi, Fahhad H

    2016-01-01

    We consider the density of a fermionic system as a functional of the potential, in one-dimensional case, where it is approximated by the Thomas–Fermi term plus semiclassical corrections through the gradient expansion. We compare this asymptotic series with the exact answer for the case of the harmonic oscillator and the Morse potential. It is found that the leading (Thomas–Fermi) term is in agreement with the exact density, but the subdominant term does not agree in terms of the asymptotic behavior because of the presence of oscillations in the exact density, but their absence in the gradient expansion. However, after regularization of the density by convolution with a Gaussian, the agreement can be established even in the subdominant term. Moreover, it is found that the expansion is always divergent, and its terms grow proportionally to the factorial function of the order, similar to the well-known divergence of perturbation series in field theory and the quantum anharmonic oscillator. Padé–Hermite approximants allow summation of the series, and one of the branches of the approximants agrees with the density. (paper)

  7. Functional perturbative RG and CFT data in the ϵ -expansion

    DEFF Research Database (Denmark)

    Codello, A.; Safari, M.; Vacca, G. P.

    2018-01-01

    We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straight......We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified...... several results for the whole family of renormalizable multi-critical models ϕ2 n. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks....

  8. Scattering by a conducting elliptic cylinder with a multilayer dielectric coating

    Science.gov (United States)

    Caorsi, Salvatore; Pastorino, Matteo; Raffetto, Mirco

    1997-11-01

    A solution to the electromagnetic scattering of a transverse magnetic plane wave due to a perfectly conducting elliptic cylinder coated by a lossless, nonmagnetic, and elliptic multilayer dielectric is proposed. Despite the lack of orthogonality of the eigenfunctions of the field inside different layers, an efficient recursive procedure for the computation of the solution is devised. It is based on series expansions of the fields in terms of Mathieu functions and on a Galerkin approach. An outline of the procedure is given, and some numerical results, concerning both the field quantities and the radar cross section per unit length, are provided.

  9. A Novel Algorithm for the Sound Field of Elliptically Shaped Transducers

    Science.gov (United States)

    Ding, De-Sheng; Lü, Hua; Shen, Chang-Sheng

    2014-06-01

    An alternative extension to the Gaussian-beam expansion technique is presented for efficient computation of the Fresnel field integral for elliptically symmetric sources. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel—Fourier transform. Two expansions are together inserted into this integral, it is then expressible in terms of the simple algebraic functions. The numerical examples for the elliptical and uniform piston transducers are presented, in good agreement with the results given by other methods. The approach is applicable to treat the field radiation problem for a large and important group of piston sources in acoustics.

  10. Quantum field theory in the presence of a medium: Green's function expansions

    Energy Technology Data Exchange (ETDEWEB)

    Kheirandish, Fardin [Department of Physics, Islamic Azad University, Shahreza-Branch, Shahreza (Iran, Islamic Republic of); Salimi, Shahriar [Department of Physics, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2011-12-15

    Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.

  11. Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities

    Science.gov (United States)

    Bakker, Mark

    2004-05-01

    Two new analytic element solutions are presented for steady flow problems with elliptical boundaries. The first solution concerns groundwater flow to shallow elliptical lakes with leaky lake beds in a single-aquifer. The second solution concerns groundwater flow through elliptical cylinder inhomogeneities in a multi-aquifer system. Both the transmissivity of each aquifer and the resistance of each leaky layer may differ between the inside and the outside of an inhomogeneity. The elliptical inhomogeneity may be bounded on top by a shallow elliptical lake with a leaky lake bed. Analytic element solutions are obtained for both problems through separation of variables of the Laplace and modified-Helmholtz differential equations in elliptical coordinates. The resulting equations for the discharge potential consist of infinite sums of products of exponentials, trigonometric functions, and modified-Mathieu functions. The series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately, but up to machine accuracy provided enough terms are used. The head and flow may be computed analytically at any point in the aquifer. Examples are given of uniform flow through an elliptical lake, a well pumping near two elliptical lakes, and uniform flow through three elliptical inhomogeneities in a multi-aquifer system. Mathieu functions may be applied in a similar fashion to solve other groundwater flow problems in semi-confined aquifers and leaky aquifer systems with elliptical internal or external boundaries.

  12. Effects of an Off-Axis Pivoting Elliptical Training Program on Gait Function in Persons With Spastic Cerebral Palsy: A Preliminary Study.

    Science.gov (United States)

    Tsai, Liang-Ching; Ren, Yupeng; Gaebler-Spira, Deborah J; Revivo, Gadi A; Zhang, Li-Qun

    2017-07-01

    This preliminary study examined the effects of off-axis elliptical training on reducing transverse-plane gait deviations and improving gait function in 8 individuals with cerebral palsy (CP) (15.5 ± 4.1 years) who completed an training program using a custom-made elliptical trainer that allows transverse-plane pivoting of the footplates during exercise. Lower-extremity off-axis control during elliptical exercise was evaluated by quantifying the root-mean-square and maximal angular displacement of the footplate pivoting angle. Lower-extremity pivoting strength was assessed. Gait function and balance were evaluated using 10-m walk test, 6-minute-walk test, and Pediatric Balance Scale. Toe-in angles during gait were quantified. Participants with CP demonstrated a significant decrease in the pivoting angle (root mean square and maximal angular displacement; effect size, 1.00-2.00) and increase in the lower-extremity pivoting strength (effect size = 0.91-1.09) after training. Reduced 10-m walk test time (11.9 ± 3.7 seconds vs. 10.8 ± 3.0 seconds; P = 0.004; effect size = 1.46), increased Pediatric Balance Scale score (43.6 ± 12.9 vs. 45.6 ± 10.8; P = 0.042; effect size = 0.79), and decreased toe-in angle (3.7 ± 10.5 degrees vs. 0.7 ± 11.7 degrees; P = 0.011; effect size = 1.22) were observed after training. We present an intervention to challenge lower-extremity off-axis control during a weight-bearing and functional activity for individuals with CP. Our preliminary findings suggest that this intervention was effective in enhancing off-axis control, gait function, and balance and reducing in-toeing gait in persons with CP.

  13. A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d-Finite Functions

    Directory of Open Access Journals (Sweden)

    Agata Bezubik

    2006-03-01

    Full Text Available This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.

  14. Expansion of infinite series containing modified Bessel functions of the second kind

    International Nuclear Information System (INIS)

    Fucci, Guglielmo; Kirsten, Klaus

    2015-01-01

    The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)

  15. Task-Specific and Functional Effects of Speed-Focused Elliptical or Motor-Assisted Cycle Training in Children With Bilateral Cerebral Palsy: Randomized Clinical Trial.

    Science.gov (United States)

    Damiano, Diane L; Stanley, Christopher J; Ohlrich, Laurie; Alter, Katharine E

    2017-08-01

    Locomotor training using treadmills or robotic devices is commonly utilized to improve gait in cerebral palsy (CP); however, effects are inconsistent and fail to exceed those of equally intense alternatives. Possible limitations of existing devices include fixed nonvariable rhythm and too much limb or body weight assistance. To quantify and compare effectiveness of a motor-assisted cycle and a novel alternative, an elliptical, in CP to improve interlimb reciprocal coordination through intensive speed-focused leg training. A total of 27 children with bilateral CP, 5 to 17 years old, were randomized to 12 weeks of 20 minutes, 5 days per week home-based training (elliptical = 14; cycle = 13) at a minimum of 40 revolutions per minute, with resistance added when speed target was achieved. Primary outcomes were self-selected and fastest voluntary cadence on the devices and gait speed. Secondary outcomes included knee muscle strength, and selective control and functional mobility measures. Cadence on trained but not nontrained devices increased, demonstrating task specificity of training and increased exercise capability. Mean gait speed did not increase in either group, nor did parent-reported functional mobility. Knee extensor strength increased in both. An interaction between group and time was seen in selective control with scores slightly increasing for the elliptical and decreasing for the cycle, possibly related to tighter limb coupling with cycling. Task-specific effects were similarly positive across groups, but no transfer was seen to gait or function. Training dose was low (≤20 hours) compared with intensive upper-limb training recommendations and may be insufficient to produce appreciable clinical change.

  16. Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

    Directory of Open Access Journals (Sweden)

    Zeyu Liu

    2018-01-01

    Full Text Available A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC. Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

  17. The elliptic genus and Hidden symmetry

    International Nuclear Information System (INIS)

    Jaffe, A.

    2001-01-01

    We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also partially break the supersymmetry. In spite of the regularization, one can establish a homotopy of the elliptic genus in a coupling parameter. Our construction relies on a priori estimates and other methods from constructive quantum field theory; this mathematical underpinning allows us to justify evaluating the elliptic genus at one endpoint of the homotopy. We obtain a version of Witten's proposed formula for the elliptic genus in terms of classical theta functions. As a consequence, the elliptic genus has a hidden SL(2,Z) symmetry characteristic of conformal theory, even though the underlying theory is not conformal. (orig.)

  18. Fast evaluation of nonlinear functionals of tensor product wavelet expansions

    NARCIS (Netherlands)

    Schwab, C.; Stevenson, R.

    2011-01-01

    Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree

  19. The P(phi)2 Green's functions; asymptotic perturbation expansion

    International Nuclear Information System (INIS)

    Dimock, J.

    1976-01-01

    The real time Green's functions in the P(phi) 2 quantum field theory are infinitely differentiable functions of the coupling constant lambda up to and including lamba=0. It follows that the perturbation series are asymptotic as lambda→0 + . (Auth.)

  20. Centrality dependence of directed and elliptic flow at the SPS

    International Nuclear Information System (INIS)

    Poskanzer, A.M.; Voloshin, S.A.; Baechler, J.; Barna, D.; Barnby, L.S.; Bartke, J.; Barton, R.A.; Betev, L.; Bialkowska, H.; Billmeier, A.; Blume, C.; Blyth, C.O.; Boimska, B.; Bracinik, J.; Brady, F.P.; Brockmann, R.; Brun, R.; Buncic, P.; Carr, L.; Cebra, D.; Cooper, G.E.; Cramer, J.G.; Csato, P.; Eckardt, V.; Eckhardt, F.; Ferenc, D.; Fischer, H.G.; Fodor, Z.; Foka, P.; Freund, P.; Friese, V.; Ftacnik, J.; Gal, J.; Ganz, R.; Gazdzicki, M.; Gladysz, E.; Grebieszkow, J.; Harris, J.W.; Hegyi, S.; Hlinka, V.; Hoehne, C.; Igo, G.; Ivanov, M.; Jacobs, P.; Janik, R.; Jones, P.G.; Kadija, K.; Kolesnikov, V.I.; Kowalski, M.; Lasiuk, B.; Levai, P.; Malakhov, A.I.; Margetis, S.; Markert, C.; Mayes, B.W.; Melkumov, G.L.; Molnar, J.; Nelson, J.M.; Odyniec, G.; Oldenburg, M.D.; Palla, G.; Panagiotou, A.D.; Petridis, A.; Pikna, M.; Pinsky, L.; Poskanzer, A.M.; Prindle, D.J.; Puehlhofer, F.; Reid, J.G.; Renfordt, R.; Retyk, W.; Ritter, H.G.; Roehrich, D.; Roland, C.; Roland, G.; Rybicki, A.; Sammer, T.; Sandoval, A.; Sann, H.; Semenov, A.Yu.; Schaefer, E.; Schmitz, N.; Seyboth, P.; Sikler, F.; Sitar, B.; Skrzypczak, E.; Snellings, R.; Squier, G.T.A.; Stock, R.; Strmen, P.; Stroebele, H.; Susa, T.; Szarka, I.; Szentpetery, I.; Sziklai, J.; Toy, M.; Trainor, T.A.; Trentalange, S.; Ullrich, T.; Varga, D.; Vassiliou, M.; Veres, G.I.; Vesztergombi, G.; Voloshin, S.; Vranic, D.; Wang, F.; Weerasundara, D.D.; Wenig, S.; Whitten, C.; Xu, N.; Yates, T.A.; Yoo, I.K.; Zimanyi, J.

    1999-01-01

    New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models

  1. Regge expansion of a casual spectral function in electroproduction

    International Nuclear Information System (INIS)

    Ahmed, M.A.; Taha, M.O.

    1975-01-01

    The conjecture that a term in the Regge espansion of the Deser-Gilbert-Sudarshan spectral function in electroproduction may identically vanish is investigated. It is shown that this conjecture does not appear to be in agreement with experiment

  2. Expansion of Sobolev functions in series in Laguerre polynomials

    International Nuclear Information System (INIS)

    Selyakov, K.I.

    1985-01-01

    The solution of the integral equation for the Sobolev functions is represented in the form of series in Laguerre polynomials. The coefficients of these series are simultaneously the coefficients of the power series for the Ambartsumyan-Chandrasekhar H functions. Infinite systems of linear algebraic equations with Toeplitz matrices are given for the coefficients of the series. Numerical results and approximate expressions are given for the case of isotropic scattering

  3. Note on twisted elliptic genus of K3 surface

    Energy Technology Data Exchange (ETDEWEB)

    Eguchi, Tohru, E-mail: eguchi@yukawa.kyoto-u.ac.j [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Hikami, Kazuhiro, E-mail: KHikami@gmail.co [Department of Mathematics, Naruto University of Education, Tokushima 772-8502 (Japan)

    2011-01-03

    We discuss the possibility of Mathieu group M{sub 24} acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M{sub 24} so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M{sub 24}. In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

  4. Note on twisted elliptic genus of K3 surface

    International Nuclear Information System (INIS)

    Eguchi, Tohru; Hikami, Kazuhiro

    2011-01-01

    We discuss the possibility of Mathieu group M 24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M 24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M 24 . In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

  5. Design and Realization of a Three Degrees of Freedom Displacement Measurement System Composed of Hall Sensors Based on Magnetic Field Fitting by an Elliptic Function

    Directory of Open Access Journals (Sweden)

    Bo Zhao

    2015-09-01

    Full Text Available This paper presents the design and realization of a three degrees of freedom (DOFs displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system.

  6. Elliptical excisions: variations and the eccentric parallelogram.

    Science.gov (United States)

    Goldberg, Leonard H; Alam, Murad

    2004-02-01

    The elliptical (fusiform) excision is a basic tool of cutaneous surgery. To assess the design, functionality, ease of construction, and aesthetic outcomes of the ellipse. A systematic review of elliptical designs and their site-specific benefits and limitations. In particular, we consider the (1). context of prevailing relaxed skin tension lines and tissue laxity; and (2). removal of the smallest possible amount of tissue around the lesion and in the "dog-ears." Attention is focused on intuitive methods that can be reproducibly planned and executed. Elliptical variations are easily designed and can be adapted to many situations. The eccentric parallelogram excision is offered as a new technique that minimizes notching and focal tension in the center of an elliptical closure. Conclusion The elliptical (fusiform) excision is an efficient, elegant, and versatile technique that will remain a mainstay of the cutaneous surgical armamentarium.

  7. Efficient molecular density functional theory using generalized spherical harmonics expansions.

    Science.gov (United States)

    Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

    2017-09-07

    We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

  8. The Expansion of Criminal Control: A Critical to Feather Functions

    Directory of Open Access Journals (Sweden)

    Mariel Muraro

    2015-12-01

    Full Text Available This article aims to relate the theories of punishment, retributive and preventive, with the criminological discourse, and make brief notes about the negative theories and criticism of the sentence. The article begins by making a few notes on the mass incarceration of the phenomenon, then going to discuss and present the form of action of the police state. Then they present the theories of punishment under the critical perspective, and then work the two main critical theories of punishment, thus treating the position Prof. Eugenio Raúl Zaffaroni and Prof. Juarez Cirino dos Santos. These presentations and discussions have left the critical discourse, not taking our work as end revisit the theoretical construction of the functions of the pen, just to demonstrate how the discourse of shame built by criminal law legitimizes selective and violent actions of the penal system.

  9. Trinucleon wave functions from separable expansions of the N-N interaction

    International Nuclear Information System (INIS)

    Birrell, N.D.

    1976-09-01

    This work is intended to determine whether a separable expansion for the N-N interaction can be used to obtain trinucleon wave functions of high quality. The expansions used in the study are the Unitary Pole expansion of Harms, Afnan and Read, and the expansion of Adhikari and Sloan. We first compare the calculation of the RSC potential Triton binding energy with the two methods, and find that the results agree quite closely. However, while it is found necessary to use t-matrix perturbation theory to obtain the UPE result, such is not the case with the ASE, thus offering a considerable improvement on the previously used method. We then proceed to calculate the L-S coupling probabilities for the wave function, and in so doing, discover a source of inaccuracy in the work of other authors. We also find that the UPE and ASE give probabilities in good agreement with one another. The calculation of the He 3 charge form factor turns out to be the most critical judge of the accuracy of the wave function. Although both expansions give quite satisfactory results for the charge form factor, those obtained with the ASE are exceptionally pleasing. We finally apply both methods to the OBEP of Holinde and Machleidt, and find that the UPE is quite unsuitable for such application. The ASE, however, once again gives very good results, indicating the high quality of the trinucleon wave function obtained with it. (author)

  10. Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites

    Science.gov (United States)

    Hasheminejad, Seyyed M.; Sanaei, Roozbeh

    2007-11-01

    Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.

  11. Excursion Processes Associated with Elliptic Combinatorics

    Science.gov (United States)

    Baba, Hiroya; Katori, Makoto

    2018-06-01

    Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying q-analogues. Recently Schlosser proposed a lattice path model in the square lattice with a family of totally elliptic weight-functions including several complex parameters and discussed an elliptic extension of the binomial theorem. In the present paper, we introduce a family of discrete-time excursion processes on Z starting from the origin and returning to the origin in a given time duration 2 T associated with Schlosser's elliptic combinatorics. The processes are inhomogeneous both in space and time and hence expected to provide new models in non-equilibrium statistical mechanics. By numerical calculation we show that the maximum likelihood trajectories on the spatio-temporal plane of the elliptic excursion processes and of their reduced trigonometric versions are not straight lines in general but are nontrivially curved depending on parameters. We analyze asymptotic probability laws in the long-term limit T → ∞ for a simplified trigonometric version of excursion process. Emergence of nontrivial curves of trajectories in a large scale of space and time from the elementary elliptic weight-functions exhibits a new aspect of elliptic combinatorics.

  12. Estimates of radiation over clouds and dust aerosols: Optimized number of terms in phase function expansion

    International Nuclear Information System (INIS)

    Ding Shouguo; Xie Yu; Yang Ping; Weng Fuzhong; Liu Quanhua; Baum, Bryan; Hu Yongxiang

    2009-01-01

    The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase function. Use of more terms in the expansion gives more accurate re-construction of the phase function, but the issue remains as to how many terms are necessary for different applications. To explore this issue further, the bidirectional reflectances associated with dust aerosols, water clouds, and ice clouds are simulated with various numbers of Legendre expansion terms. To have relative numerical errors smaller than 5%, the present analyses indicate that, in the visible spectrum, 16 Legendre polynomials should be used for dust aerosols, while 32 Legendre expansion terms should be used for both water and ice clouds. In the infrared spectrum, the brightness temperatures at the top of the atmosphere are computed by using the scattering properties of dust aerosols, water clouds and ice clouds. Although small differences of brightness temperatures compared with the counterparts computed with 4, 8, 128 expansion terms are observed at large viewing angles for each layer, it is shown that 4 terms of Legendre polynomials are sufficient in the radiative transfer computation at infrared wavelengths for practical applications.

  13. Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

    KAUST Repository

    Nobile, F.

    2015-10-30

    In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.

  14. Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

    KAUST Repository

    Nobile, F.; Tamellini, L.; Tempone, Raul

    2015-01-01

    In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.

  15. The propagator for the step potential and delta function potential using the path decomposition expansion

    Energy Technology Data Exchange (ETDEWEB)

    Yearsley, James M [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)

    2008-07-18

    We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.

  16. Functional expansion for evolution operators in a system of many fermions with many conditions

    International Nuclear Information System (INIS)

    Barrios, S.C.

    1985-01-01

    We present a mean field expansion for many body system, using integral functionals. The problem is formulated as a initial conditions one and it is studied the effective dynamics of the body density with given initial conditions. (M.W.O.) [pt

  17. On mod 2 and higher elliptic genera

    International Nuclear Information System (INIS)

    Liu Kefeng

    1992-01-01

    In the first part of this paper, we construct mod 2 elliptic genera on manifolds of dimensions 8k+1, 8k+2 by mod 2 index formulas of Dirac operators. They are given by mod 2 modular forms or mod 2 automorphic functions. We also obtain an integral formula for the mod 2 index of the Dirac operator. As a by-product we find topological obstructions to group actions. In the second part, we construct higher elliptic genera and prove some of their rigidity properties under group actions. In the third part we write down characteristic series for all Witten genera by Jacobi theta-functions. The modular property and transformation formulas of elliptic genera then follow easily. We shall also prove that Krichever's genera, which come from integrable systems, can be written as indices of twisted Dirac operators for SU-manifolds. Some general discussions about elliptic genera are given. (orig.)

  18. Functional differential equation approach to the large N expansion and mean field perturbation theory

    International Nuclear Information System (INIS)

    Bender, C.M.; Cooper, F.

    1985-01-01

    An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

  19. Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method

    OpenAIRE

    Banerjee, Subhabrata; Jacobi, Anthony M.

    2012-01-01

    The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...

  20. Covariant spectator theory of $np$ scattering:\\\\ Effective range expansions and relativistic deuteron wave functions

    Energy Technology Data Exchange (ETDEWEB)

    Franz Gross, Alfred Stadler

    2010-09-01

    We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.

  1. Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

    Science.gov (United States)

    Zylka, Christian; Vojta, Guenter

    1993-01-01

    The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

  2. Analytic structure and power series expansion of the Jost function for the two-dimensional problem

    International Nuclear Information System (INIS)

    Rakityansky, S A; Elander, N

    2012-01-01

    For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)

  3. Finite-temperature correlation function for the one-dimensional quantum Ising model:The virial expansion

    Science.gov (United States)

    Reyes, S. A.; Tsvelik, A. M.

    2006-06-01

    We rewrite the exact expression for the finite-temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial expansion (expansion in powers of the soliton density).

  4. Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling

    Energy Technology Data Exchange (ETDEWEB)

    Alimi, J.M.; Reverdy, V. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Golubtsova, A.A. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

    2014-10-15

    We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions. (orig.)

  5. Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.

    Energy Technology Data Exchange (ETDEWEB)

    Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry

    2009-12-01

    In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.

  6. Elliptic genus derivation of 4d holomorphic blocks

    Science.gov (United States)

    Poggi, Matteo

    2018-03-01

    We study elliptic vortices on ℂ × T 2 by considering the 2d quiver gauge theory describing their moduli spaces. The elliptic genus of these moduli spaces is the elliptic version of vortex partition function of the 4d theory. We focus on two examples: the first is a N = 1, U( N ) gauge theory with fundamental and anti-fundamental matter; the second is a N = 2, U( N ) gauge theory with matter in the fundamental representation. The results are instances of 4d "holomorphic blocks" into which partition functions on more complicated surfaces factorize. They can also be interpreted as free-field representations of elliptic Virasoro algebrae.

  7. Application of wavelet scaling function expansion continuous-energy resonance calculation method to MOX fuel problem

    International Nuclear Information System (INIS)

    Yang, W.; Wu, H.; Cao, L.

    2012-01-01

    More and more MOX fuels are used in all over the world in the past several decades. Compared with UO 2 fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for 240 Pu and 242 Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)

  8. Triaxiality in elliptical galaxies

    Energy Technology Data Exchange (ETDEWEB)

    Benacchio, L; Galletta, G [Padua Univ. (Italy). Ist. di Astronomia

    1980-12-01

    The existence of a triaxial shape for elliptical galaxies has been considered in recent years to explain the new kinematical and geometrical findings, i.e. (a) the low rotation/velocity dispersion ratio found also in some flat systems, (b) the presence of twisting in the isophotes, (c) the recently found correlation between maximum twisting and maximum flattening, (d) the presence of rotation along the minor axis. A simple geometrical model of elliptical galaxies having shells with different axial ratios c/a, b/a has been produced to interpret three fundamental key-features of elliptical galaxies: (i) the distribution of the maximum flattening observed; (ii) the percentage of ellipticals showing twisting; and (iii) the correlation between maximum twisting and maximum flattening. The model has been compared with observational data for 348 elliptical systems as given by Strom and Strom. It is found that a triaxial ellipsoid with coaxial shells having axial ratios c/a and b/a mutually dependent in a linear way can satisfy the observations.

  9. Hadronic wave functions at short distances and the operator product expansion

    International Nuclear Information System (INIS)

    Brodsky, S.J.; Lepage, G.P.

    1980-01-01

    The operator product expansion, of appropriate products of quark fields, is used to find the anamalous dimensions which control the short distance behavior of hadronic wave functions. This vehavior in turn controls the high-Q 2 limit of hadronic form factors. In particular, we relate each anamalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal αsub(s)(Q 2 )/Q 2 fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements. (orig.)

  10. Momentum autocorrelation function of a classic diatomic chain

    Energy Technology Data Exchange (ETDEWEB)

    Yu, Ming B., E-mail: mingbyu@gmail.com

    2016-10-23

    A classical harmonic diatomic chain is studied using the recurrence relations method. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical contributions are derived as even-order Bessel function expansions with coefficients given in terms of integrals of elliptic functions in real axis and a contour parallel to the imaginary axis, respectively. - Highlights: • Momentum autocorrelation function of a classic diatomic chain is studied. • It is derived as even-order Bessel function expansion using the convolution theorem. • The expansion coefficients are integrals of elliptic functions. • Addition theorem is used to reduce complex elliptic function to complex sum of real ones.

  11. Functional perturbative RG and CFT data in the ε-expansion

    Energy Technology Data Exchange (ETDEWEB)

    Codello, A. [Southern Denmark Univ., Odense (Denmark). CP3-Origins; INFN-Sezione di Bologna, Bologna (Italy); Safari, M. [INFN-Sezione di Bologna, Bologna (Italy); Bologna Univ. (Italy). Dipt di Fisica e Astronomia; Vacca, G.P. [INFN-Sezione di Bologna, Bologna (Italy); Zanusso, O. [INFN-Sezione di Bologna, Bologna (Italy); Jena Univ. (Germany). Theoretisch-Physikalisches Inst.

    2018-01-15

    We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the ε-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models φ{sup 2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks. (orig.)

  12. Wrapping interactions and the genus expansion of the 2-point function of composite operators

    International Nuclear Information System (INIS)

    Sieg, Christoph; Torrielli, Alessandro

    2005-01-01

    We perform a systematic analysis of wrapping interactions for a general class of theories with color degrees of freedom, including N=4 SYM. Wrapping interactions arise in the genus expansion of the 2-point function of composite operators as finite size effects that start to appear at a certain order in the coupling constant at which the range of the interaction is equal to the length of the operators. We analyze in detail the relevant genus expansions, and introduce a strategy to single out the wrapping contributions, based on adding spectator fields. We use a toy model to demonstrate our procedure, performing all computations explicitly. Although completely general, our treatment should be particularly useful for applications to the recent problem of wrapping contributions in some checks of the AdS/CFT correspondence

  13. Analysis of water hammer in pipelines by partial fraction expansion of transfer function in frequency domain

    International Nuclear Information System (INIS)

    Lee, Jun Shin; Lee, Wook Ryun; Oh, Ki Yong; Kim, Bong Ki

    2010-01-01

    Understanding water hammer is very important to the prevention of excessive pressure build-up in pipelines. Many researchers have studied this phenomenon, drawing effective solutions through the time- and frequency-domain approaches. For the purposes of enhancing the advantages of the frequency-domain approach and, thereby, rendering investigations of the dynamic characteristics of pipelines more effective, we propose partial fraction expansion of the transfer function between the unsteady flow source and a given section. We simulate the proposed approach using a vibration element inserted into a simple pipeline, deducing much useful physical information pertaining to pipeline design. We conclude that locating the resonance of the vibration element between the first and second resonances of the pipeline can mitigate the excessive pressure build-up attendant on the occurrence of water hammer. Our method of partial fraction expansion is expected to be useful and effective in analyses of unsteady flows in pipelines

  14. Thermal expansion of an amorphous alloy. Reciprocal-space versus real-space distribution functions

    International Nuclear Information System (INIS)

    Louzguine-Luzgin, Dmitri V.; Inoue, Akihisa

    2007-01-01

    This paper describes the relation between the change in the position of the first X-ray diffraction maximum in reciprocal space and the first maximum of the distribution function in real space for the Ge 50 Al 40 Cr 10 amorphous alloy. It is also shown that the first diffraction maximum of the interference function carries the most significant information about the interatomic distances in real space while the subsequent peaks of the interference function are responsible for the shoulders of the main peak of the real-space distribution function. The results are used to support validity of the method previously used to monitor thermal expansion of the glassy alloys using an X-ray diffraction profile

  15. Operator expansions in the minimal subtraction scheme. II. Explicit formulas for coefficient functions

    International Nuclear Information System (INIS)

    Chetyrkin, K.G.

    1989-01-01

    It is shown in an arbitrary model that the coefficient functions of the operator expansion (renormalized in the minimal subtraction scheme) are finite. Explicit formulas convenient for calculating them in practice are obtained. The gluing method and the formalism of the R* operation are used to transform the formulas in such a way that the coefficient functions can be expressed in terms of ordinary diagrams containing neither nonstandard propagators nor an additional loop integration. An important feature of the representation for the coefficient functions is that the R* operation, which subtracts simultaneously the ultraviolet and infrared divergences, guarantees the existence of the coefficient functions in the limit when the dimensional regularization is lifted without any restrictions

  16. More on zeta-function regularization of high-temperature expansions

    International Nuclear Information System (INIS)

    Actor, A.

    1987-01-01

    A recent paper using the Riemann ζ-function to regularize the (divergent) coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet-type series Σ m a m (x i )/m s into power series in the dimensionless parameters x i . The coefficients occurring in the power series are (proportional to) ζ-functions evaluated away from their poles - this is where the regularization occurs. High-temperature expansions are just one example of this highly-nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in which a m (x i ) is a product of trigonometric, algebraic and Bessel function factors. The ζ-function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of temperature gauge theories. (author)

  17. A new approach to stochastic transport via the functional Volterra expansion

    International Nuclear Information System (INIS)

    Ziya Akcasu, A.; Corngold, N.

    2005-01-01

    In this paper we present a new algorithm (FDA) for the calculation of the mean and the variance of the flux in stochastic transport when the transport equation contains a spatially random parameter θ(r), such as the density of the medium. The approach is based on the renormalized functional Volterra expansion of the flux around its mean. The attractive feature of the approach is that it explicitly displays the functional dependence of the flux on the products of θ(r i ), and hence enables one to take ensemble averages directly to calculate the moments of the flux in terms of the correlation functions of the underlying random process. The renormalized deterministic transport equation for the mean flux has been obtained to the second order in θ(r), and a functional relationship between the variance and the mean flux has been derived to calculate the variance to this order. The feasibility and accuracy of FDA has been demonstrated in the case of stochastic diffusion, using the diffusion equation with a spatially random diffusion coefficient. The connection of FDA with the well-established approximation schemes in the field of stochastic linear differential equations, such as the Bourret approximation, developed by Van Kampen using cumulant expansion, and by Terwiel using projection operator formalism, which has recently been extended to stochastic transport by Corngold. We hope that FDA's potential will be explored numerically in more realistic applications of the stochastic transport. (authors)

  18. POLYGALACTURONASE INVOLVED IN EXPANSION1 functions in cell elongation and flower development in Arabidopsis.

    Science.gov (United States)

    Xiao, Chaowen; Somerville, Chris; Anderson, Charles T

    2014-03-01

    Pectins are acidic carbohydrates that comprise a significant fraction of the primary walls of eudicotyledonous plant cells. They influence wall porosity and extensibility, thus controlling cell and organ growth during plant development. The regulated degradation of pectins is required for many cell separation events in plants, but the role of pectin degradation in cell expansion is poorly defined. Using an activation tag screen designed to isolate genes involved in wall expansion, we identified a gene encoding a putative polygalacturonase that, when overexpressed, resulted in enhanced hypocotyl elongation in etiolated Arabidopsis thaliana seedlings. We named this gene POLYGALACTURONASE INVOLVED IN EXPANSION1 (PGX1). Plants lacking PGX1 display reduced hypocotyl elongation that is complemented by transgenic PGX1 expression. PGX1 is expressed in expanding tissues throughout development, including seedlings, roots, leaves, and flowers. PGX1-GFP (green fluorescent protein) localizes to the apoplast, and heterologously expressed PGX1 displays in vitro polygalacturonase activity, supporting a function for this protein in apoplastic pectin degradation. Plants either overexpressing or lacking PGX1 display alterations in total polygalacturonase activity, pectin molecular mass, and wall composition and also display higher proportions of flowers with extra petals, suggesting PGX1's involvement in floral organ patterning. These results reveal new roles for polygalacturonases in plant development.

  19. Ellipticity dependence of the near-threshold harmonics of H2 in an elliptical strong laser field.

    Science.gov (United States)

    Yang, Hua; Liu, Peng; Li, Ruxin; Xu, Zhizhan

    2013-11-18

    We study the ellipticity dependence of the near-threshold (NT) harmonics of pre-aligned H2 molecules using the time-dependent density functional theory. The anomalous maximum appearing at a non-zero ellipticity for the generated NT harmonics can be attributed to multiphoton effects of the orthogonally polarized component of the elliptical driving laser field. Our calculation also shows that the structure of the bound-state, such as molecular alignment and bond length, can be sensitively reflected on the ellipticity dependence of the near-threshold harmonics.

  20. Superconducting elliptical cavities

    CERN Document Server

    Sekutowicz, J K

    2011-01-01

    We give a brief overview of the history, state of the art, and future for elliptical superconducting cavities. Principles of the cell shape optimization, criteria for multi-cell structures design, HOM damping schemes and other features are discussed along with examples of superconducting structures for various applications.

  1. Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

    Science.gov (United States)

    Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

    2018-06-01

    We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure mathematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals, and we develop a formalism that enables us to compute these Feynman integrals in terms of our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

  2. Spherical cavity-expansion forcing function in PRONTO 3D for application to penetration problems

    Energy Technology Data Exchange (ETDEWEB)

    Warren, T.L.; Tabbara, M.R.

    1997-05-01

    In certain penetration events the primary mode of deformation of the target can be approximated by known analytical expressions. In the context of an analysis code, this approximation eliminates the need for modeling the target as well as the need for a contact algorithm. This technique substantially reduces execution time. In this spirit, a forcing function which is derived from a spherical-cavity expansion analysis has been implemented in PRONTO 3D. This implementation is capable of computing the structural and component responses of a projectile due to three dimensional penetration events. Sample problems demonstrate good agreement with experimental and analytical results.

  3. Asymptotic expansion of a partition function related to the sinh-model

    CERN Document Server

    Borot, Gaëtan; Kozlowski, Karol K

    2016-01-01

    This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...

  4. Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions

    International Nuclear Information System (INIS)

    Rudaz, S.

    1990-01-01

    Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences

  5. The Zernike expansion--an example of a merit function for 2D/3D registration based on orthogonal functions.

    Science.gov (United States)

    Dong, Shuo; Kettenbach, Joachim; Hinterleitner, Isabella; Bergmann, Helmar; Birkfellner, Wolfgang

    2008-01-01

    Current merit functions for 2D/3D registration usually rely on comparing pixels or small regions of images using some sort of statistical measure. Problems connected to this paradigm the sometimes problematic behaviour of the method if noise or artefacts (for instance a guide wire) are present on the projective image. We present a merit function for 2D/3D registration which utilizes the decomposition of the X-ray and the DRR under comparison into orthogonal Zernike moments; the quality of the match is assessed by an iterative comparison of expansion coefficients. Results in a imaging study on a physical phantom show that--compared to standard cross--correlation the Zernike moment based merit function shows better robustness if histogram content in images under comparison is different, and that time expenses are comparable if the merit function is constructed out of a few significant moments only.

  6. Nonlinear elliptic partial differential equations an introduction

    CERN Document Server

    Le Dret, Hervé

    2018-01-01

    This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

  7. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    International Nuclear Information System (INIS)

    Gao, Z.; Xu, Y.; Downar, T.

    2013-01-01

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  8. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Gao, Z. [Rice University, MS 318, 6100 Main Street, Houston, TX 77005 (United States); Xu, Y. [Argonne National Laboratory, 9700 South Case Ave., Argonne, IL 60439 (United States); Downar, T. [Department of Nuclear Engineering, University of Michigan, 2355 Bonisteel blvd., Ann Arbor, MI 48109 (United States)

    2013-07-01

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  9. A direct method to transform between expansions in the configuration state function and Slater determinant bases

    International Nuclear Information System (INIS)

    Olsen, Jeppe

    2014-01-01

    A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10 6 coefficients in the CSF basis is obtained from the 150 × 10 6 coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require

  10. Low-temperature expansions and correlation functions of the Z3-chiral Potts model

    International Nuclear Information System (INIS)

    Han, N.S.; Honecker, A.

    1993-04-01

    Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z 3 -chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z n -spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z 3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length. (orig.)

  11. Two-dimensional steady unsaturated flow through embedded elliptical layers

    Science.gov (United States)

    Bakker, Mark; Nieber, John L.

    2004-12-01

    New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.

  12. Patterns of coordinated cortical remodeling during adolescence and their associations with functional specialization and evolutionary expansion.

    Science.gov (United States)

    Sotiras, Aristeidis; Toledo, Jon B; Gur, Raquel E; Gur, Ruben C; Satterthwaite, Theodore D; Davatzikos, Christos

    2017-03-28

    During adolescence, the human cortex undergoes substantial remodeling to support a rapid expansion of behavioral repertoire. Accurately quantifying these changes is a prerequisite for understanding normal brain development, as well as the neuropsychiatric disorders that emerge in this vulnerable period. Past accounts have demonstrated substantial regional heterogeneity in patterns of brain development, but frequently have been limited by small samples and analytics that do not evaluate complex multivariate imaging patterns. Capitalizing on recent advances in multivariate analysis methods, we used nonnegative matrix factorization (NMF) to uncover coordinated patterns of cortical development in a sample of 934 youths ages 8-20, who completed structural neuroimaging as part of the Philadelphia Neurodevelopmental Cohort. Patterns of structural covariance (PSCs) derived by NMF were highly reproducible over a range of resolutions, and differed markedly from common gyral-based structural atlases. Moreover, PSCs were largely symmetric and showed correspondence to specific large-scale functional networks. The level of correspondence was ordered according to their functional role and position in the evolutionary hierarchy, being high in lower-order visual and somatomotor networks and diminishing in higher-order association cortex. Furthermore, PSCs showed divergent developmental associations, with PSCs in higher-order association cortex networks showing greater changes with age than primary somatomotor and visual networks. Critically, such developmental changes within PSCs were significantly associated with the degree of evolutionary cortical expansion. Together, our findings delineate a set of structural brain networks that undergo coordinated cortical thinning during adolescence, which is in part governed by evolutionary novelty and functional specialization.

  13. Quasilinear infiltration from an elliptical cavity

    Science.gov (United States)

    Kuhlman, Kristopher L.; Warrick, Arthur W.

    2008-08-01

    We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270-8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range.

  14. Satellite orbits perturbed by direct solar radiation pressure: general expansion of the disturbing function

    International Nuclear Information System (INIS)

    Hughes, S.

    1977-01-01

    An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method (Astr. J.; 67:300 (1962)). The Kaula inclination functions are replaced by an equivalent set of modified Allan (Proc. R. Soc. A.; 288:60 (1965)) inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, Cel. Mech.; 13:89 (1976)), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonance with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure. (author)

  15. Partition function expansion on region graphs and message-passing equations

    International Nuclear Information System (INIS)

    Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong

    2011-01-01

    Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

  16. Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions

    Science.gov (United States)

    Kerimov, M. K.

    2018-01-01

    This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.

  17. High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem

    Directory of Open Access Journals (Sweden)

    Takashi Ito

    2016-01-01

    Full Text Available Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α between perturbed and perturbing bodies in the inner case (α1. The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems.

  18. The properties of radio ellipticals

    International Nuclear Information System (INIS)

    Sparks, W.B.; Disney, M.J.; Rodgers, A.W.

    1984-01-01

    Optical and additional radio data are presented for the bright galaxies of the Disney and Wall survey (1977 Mon. Not. R. Astron. Soc. 179, 235). These data form the basis of a statistical comparison of the properties of radio elliptical galaxies to radio-quiet ellipticals. The correlations may be explained by the depth of the gravitational potential well in which the galaxy resides governing the circumstances under which an elliptical galaxy rids itself of internally produced gas. (author)

  19. Uniformization of elliptic curves

    OpenAIRE

    Ülkem, Özge; Ulkem, Ozge

    2015-01-01

    Every elliptic curve E defined over C is analytically isomorphic to C*=qZ for some q ∊ C*. Similarly, Tate has shown that if E is defined over a p-adic field K, then E is analytically isomorphic to K*=qZ for some q ∊ K . Further the isomorphism E(K) ≅ K*/qZ respects the action of the Galois group GK/K, where K is the algebraic closure of K. I will explain the construction of this isomorphism.

  20. Elliptic partial differential equations

    CERN Document Server

    Han, Qing

    2011-01-01

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

  1. Applying the expansion method in hierarchical functions to the solution of Navier-Stokes equations for incompressible fluids

    International Nuclear Information System (INIS)

    Sabundjian, Gaiane

    1999-01-01

    This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)

  2. RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

    KAUST Repository

    Farrell, Patricio; Wendland, Holger

    2013-01-01

    In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly

  3. Multilevel quadrature of elliptic PDEs with log-normal diffusion

    KAUST Repository

    Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus

    2015-01-01

    Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number

  4. Exchange splitting of the interaction energy and the multipole expansion of the wave function

    Energy Technology Data Exchange (ETDEWEB)

    Gniewek, Piotr, E-mail: pgniewek@tiger.chem.uw.edu.pl; Jeziorski, Bogumił, E-mail: jeziorsk@chem.uw.edu.pl [Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw (Poland)

    2015-10-21

    The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.

  5. Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters

    Energy Technology Data Exchange (ETDEWEB)

    Kalmykov, M.Yu.; Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2008-07-15

    We prove the following theorems: 1) The Laurent expansions in {epsilon} of the Gauss hypergeometric functions {sub 2}F{sub 1}(I{sub 1}+a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z), {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+a{epsilon},I{sub 2}+(p/q)+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z) and {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+ a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z), where I{sub 1},I{sub 2},I{sub 3},p,q are arbitrary integers, a,b,c are arbitrary numbers and {epsilon} is an infinitesimal parameter, are expressible in terms of multiple polylogarithms of q-roots of unity with coefficients that are ratios of polynomials; 2) The Laurent expansion of the Gauss hypergeometric function {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+c{epsilon};z) is expressible in terms of multiple polylogarithms of q-roots of unity times powers of logarithm with coefficients that are ratios of polynomials; 3) The multiple inverse rational sums {sigma}{sup {infinity}}{sub j=1}({gamma}(j))/({gamma}(1+j-(p)/(q))) (z{sup j})/(j{sup c}) S{sub a{sub 1}}(j-1).. S{sub a{sub p}}(j-1) and the multiple rational sums {sigma}{sup {infinity}}{sub j=1} ({gamma}(j+(p)/(q)))/({gamma}(1+j)) (z{sup j})/(j{sup c}) S{sub a{sub 1}}(j-1).. S{sub a{sub p}}(j-1), where S{sub a}(j)={sigma}{sup j}{sub k=1}(1)/(k{sup a}) is a harmonic series and c is an arbitrary integer, are expressible in terms of multiple polylogarithms; 4) The generalized hypergeometric functions {sub p}F{sub p.1}((vector)A+(vector)a{epsilon};(vector)B+(vector)b{epsilon},(p)/(q)+B{sub p-1};z) and {sub p}F{sub p-1}((vector)A+(vector)a{epsilon},(p)/(q)+A{sub p};(vector)B+(vector)b{epsilon};z) are expressible in terms of multiple polylogarithms with coefficients that are ratios of polynomials. (orig.)

  6. A new diffusion nodal method based on analytic basis function expansion

    International Nuclear Information System (INIS)

    Noh, J.M.; Cho, N.Z.

    1993-01-01

    The transverse integration procedure commonly used in most advanced nodal methods results in some limitations. The first is that the transverse leakage term that appears in the transverse integration procedure must be appropriately approximated. In most advanced nodal methods, this term is expanded in a quadratic polynomial. The second arises when reconstructing the pinwise flux distribution within a node. The available one-dimensional flux shapes from nodal calculation in each spatial direction cannot be used directly in the flux reconstruction. Finally, the transverse leakage defined for a hexagonal node becomes so complicated as not to be easily handled and contains nonphysical singular terms. In this paper, a new nodal method called the analytic function expansion nodal (AFEN) method is described for both the rectangular geometry and the hexagonal geometry in order to overcome these limitations. This method does not solve the transverse-integrated one-dimensional diffusion equations but instead solves directly the original multidimensional diffusion equation within a node. This is a accomplished by expanding the solution (or the intranodal homogeneous flux distribution) in terms of nonseparable analytic basis functions satisfying the diffusion equation at any point in the node

  7. Tailored functional materials with controlled thermal expansion and excellent thermal conductivity

    International Nuclear Information System (INIS)

    Korb, G.; Sebo, P.

    1997-01-01

    Engineering materials are mainly used for structures. Therefore high-strength, stiffness and sufficient toughness are of prime importance. For a long time engineers thought first in terms of metals. Material scientists developed alloys tailored to the needs of industry. Ceramics are known to be brittle and therefore not suitable in the first place for structural application under stress. Polymers with their low modulus became attractive when reinforced with high-strength fibres. Composites processed by polymer, metal or ceramic matrices and high-strength reinforcements have been introduced into many sectors of industry. Engineering materials for structural applications fulfil a function: they withstand high stresses, temperatures, fatigue, creep etc. But usually we do not call them functional materials. Functional materials serve applications apart from classical engineering fields. Electricity conducting materials, semi conductors, memory alloys and many others are called functional materials. Because of the fact that the basic physical properties cannot be changed in single-phase materials, the combination of two and more materials with different properties lead to components with new and tailored properties. A few techniques for preparation are described as powder metallurgy, infiltration of prepegs and compaction of precoated fibres/particles. The lecture is focusing on carbon fibre/particle reinforced Metal Matrix Materials. The achievable properties, in particular the thermal conductivity originating from the base materials is depending on the orientation of the fibres and interfacial contacts in the composite. The carefully controlled expansion behaviour is the most important property to use the material as a heat sink in electronic assemblies. (author)

  8. Expanded functional diversity of shaker K(+ channels in cnidarians is driven by gene expansion.

    Directory of Open Access Journals (Sweden)

    Timothy Jegla

    Full Text Available The genome of the cnidarian Nematostella vectensis (starlet sea anemone provides a molecular genetic view into the first nervous systems, which appeared in a late common ancestor of cnidarians and bilaterians. Nematostella has a surprisingly large and diverse set of neuronal signaling genes including paralogs of most neuronal signaling molecules found in higher metazoans. Several ion channel gene families are highly expanded in the sea anemone, including three subfamilies of the Shaker K(+ channel gene family: Shaker (Kv1, Shaw (Kv3 and Shal (Kv4. In order to better understand the physiological significance of these voltage-gated K(+ channel expansions, we analyzed the function of 18 members of the 20 gene Shaker subfamily in Nematostella. Six of the Nematostella Shaker genes express functional homotetrameric K(+ channels in vitro. These include functional orthologs of bilaterian Shakers and channels with an unusually high threshold for voltage activation. We identified 11 Nematostella Shaker genes with a distinct "silent" or "regulatory" phenotype; these encode subunits that function only in heteromeric channels and serve to further diversify Nematostella Shaker channel gating properties. Subunits with the regulatory phenotype have not previously been found in the Shaker subfamily, but have evolved independently in the Shab (Kv2 family in vertebrates and the Shal family in a cnidarian. Phylogenetic analysis indicates that regulatory subunits were present in ancestral cnidarians, but have continued to diversity at a high rate after the split between anthozoans and hydrozoans. Comparison of Shaker family gene complements from diverse metazoan species reveals frequent, large scale duplication has produced highly unique sets of Shaker channels in the major metazoan lineages.

  9. Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves.

    Science.gov (United States)

    Mitri, F G

    2016-03-01

    This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. Copyright © 2015 Elsevier B.V. All rights reserved.

  10. Reciprocal expansion of modified Bessel function in simple fractions and obtaining general summation relationships containing its zeros

    Science.gov (United States)

    Sherstyukov, V. B.; Sumin, E. V.

    2017-12-01

    Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.

  11. Elliptic curves for applications (Tutorial)

    NARCIS (Netherlands)

    Lange, T.; Bernstein, D.J.; Chatterjee, S.

    2011-01-01

    More than 25 years ago, elliptic curves over finite fields were suggested as a group in which the Discrete Logarithm Problem (DLP) can be hard. Since then many researchers have scrutinized the security of the DLP on elliptic curves with the result that for suitably chosen curves only exponential

  12. The resonance expansion for the Green's function of the Schroedinger and wave equations

    International Nuclear Information System (INIS)

    Albeverio, S.; Aix-Marseille-2 Univ., 13 - Marseille; Hoeegh-Krohn, R.; Oslo Univ.

    1984-01-01

    We give a survey of some recent mathematical work on resonances, in particular on perturbation series, low energy expansions and on resonances for point interactions. Expansions of the kernels of esup(-it)√sup(H+) and esup(-itH) in terms of resonances are also given (where Hsub(+) is the positive part of the Hamiltonian). (orig.)

  13. The exponential function expansion of the intra-nodal cross sections for the spectral history gradient correction

    International Nuclear Information System (INIS)

    Cho, J. Y.; Noh, J. M.; Cheong, H. K.; Choo, H. K.

    1998-01-01

    In order to simplify the previous spectral history effect correction based on the polynomial expansion nodal method, a new spectral history effect correction is proposed. The new spectral history correction eliminates four microscopic depletion points out of total 13 depletion points in the previous correction by approximating the group cross sections with exponential function. The neutron flux to homogenize the group cross sections for the correction of the spectral history effect is calculated by the analytic function expansion nodal method in stead of the conventional polynomial expansion nodal method. This spectral history correction model is verified against the three MOX benchmark cores: a checkerboard type, a small core with 25 fuel assemblies, and a large core with 177 fuel assemblies. The benchmark results prove that this new spectral history correction model is superior to the previous one even with the reduced number of the local microscopic depletion points

  14. Investigation on computation of elliptical microwave plasma cavity

    Science.gov (United States)

    Liao, Xiaoli; Liu, Hua; Zhang, Kai

    2008-12-01

    In recent years, the advance of the elliptical resonant cavity and focus cavity is known by many people. There are homogeneous and multipatternal virtues in the focus dimensional microwave field of the elliptical resonant cavity. It is very suitable for applying the low power microwave biological effect equipment. However, when designing the elliptical resonant cavity may meet the problems of complex and huge computation need to be solved. This paper proposed the simple way of approximate processing the Mathieu function. It can greatly simplify the difficulty and decrease the scale of computation. This method can satisfy the requirements of research and development within project permitted precision.

  15. Multilevel quadrature of elliptic PDEs with log-normal diffusion

    KAUST Repository

    Harbrecht, Helmut

    2015-01-07

    We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.

  16. Output Tracking Control of Switched Hybrid Systems: A Fliess Functional Expansion Approach

    Directory of Open Access Journals (Sweden)

    Fenghua He

    2013-01-01

    Full Text Available The output tracking problem is investigated for a nonlinear affine system with multiple modes of continuous control inputs. We convert the family of nonlinear affine systems under consideration into a switched hybrid system by introducing a multiple-valued logic variable. The Fliess functional expansion is adopted to express the input and output relationship of the switched hybrid system. The optimal switching control is determined for a multiple-step output tracking performance index. The proposed approach is applied to a multitarget tracking problem for a flight vehicle aiming for one real target with several decoys flying around it in the terminal guidance course. These decoys appear as apparent targets and have to be distinguished with the approaching of the flight vehicle. The guidance problem of one flight vehicle versus multiple apparent targets should be considered if no large miss distance might be caused due to the limitation of the flight vehicle maneuverability. The target orientation at each time interval is determined. Simulation results show the effectiveness of the proposed method.

  17. Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2002-01-01

    textabstractThe use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders ($K_{ia}(x)$) near the transition point $x=a$, is discussed. In [2], an algorithm for the evaluation of $K_{ia}(x)$ was presented, which made use

  18. Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

    Czech Academy of Sciences Publication Activity Database

    Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan

    2013-01-01

    Roč. 87, č. 1 (2013), "014008-1"-"014008-14" ISSN 1550-7998 R&D Projects: GA MŠk(CZ) LG13031 Institutional support: RVO:68378271 Keywords : perturbative expansion * Borel transformation * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013

  19. Elliptic flow from Coulomb interaction and low density elastic scattering

    Science.gov (United States)

    Sun, Yuliang; Li, Qingfeng; Wang, Fuqiang

    2018-04-01

    In high energy heavy ion collisions and interacting cold atom systems, large elliptic flow anisotropies have been observed. For the large opacity (ρ σ L ˜103 ) of the latter hydrodynamics is a natural consequence, but for the small opacity (ρ σ L ˜1 ) of the former the hydrodynamic description is questionable. To shed light onto the situation, we simulate the expansion of a low density argon ion (or atom) system, initially trapped in an elliptical region, under the Coulomb interaction (or elastic scattering). Significant elliptic anisotropy is found in both cases, and the anisotropy depends on the initial spatial eccentricity and the density of the system. The results may provide insights into the physics of anisotropic flow in high energy heavy ion collisions and its role in the study of quantum chromodynamics.

  20. C1,1 regularity for degenerate elliptic obstacle problems

    Science.gov (United States)

    Daskalopoulos, Panagiota; Feehan, Paul M. N.

    2016-03-01

    The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

  1. A Jacobian elliptic single-field inflation

    Energy Technology Data Exchange (ETDEWEB)

    Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile); Centro de Astrofisica de Valparaiso, Valparaiso (Chile); Gallo, Emanuel [FaMAF, Universidad Nacional de Cordoba, Cordoba (Argentina); Instituto de Fisica Enrique Gaviola (IFEG), CONICET, Cordoba (Argentina)

    2015-06-15

    In the scenario of single-field inflation, this field is described in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analyzed using the Hamilton-Jacobi approach and then the main results are contrasted with the recent measurements obtained from the Planck 2015 data. (orig.)

  2. ON ELLIPTICALLY POLARIZED ANTENNAS IN THE PRESENCE OF GROUND

    Science.gov (United States)

    The effect of ground reflections upon the far field of an elliptically polarized antenna of ar itrary orientation with r spect to ground is...investigated. The equation of the polarization ellipse produced by an elliptically polarized antenna in the presence of ground is derived, AND SEVERAL...EXAMPLES ILLUSTRATE THE VARIATION IN THE AXIS RATIO OF THE POLARIZATION ELLIPSE AS A FUNCTION OF THE GEOMETRY OF THE MEASURING SETUP. A method is presented

  3. Elliptic flow based on a relativistic hydrodynamic model

    Energy Technology Data Exchange (ETDEWEB)

    Hirano, Tetsufumi [Department of Physics, Waseda Univ., Tokyo (Japan)

    1999-08-01

    Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution of hot and dense nuclear matter produced in non-central relativistic heavy-ion collisions is discussed. The elliptic flow parameter v{sub 2} is obtained by Fourier analysis of the azimuthal distribution of pions and protons which are emitted from the freeze-out hypersurface. As a function of rapidity, the pion and proton elliptic flow parameters both have a peak at midrapidity. (author)

  4. Central $L$-values of elliptic curves and local polynomials

    OpenAIRE

    Ehlen, Stephan; Guerzhoy, Pavel; Kane, Ben; Rolen, Larry

    2018-01-01

    Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves in terms of finite sums over canonical binary quadratic forms. This yields vastly simpler formulas related to work of Birch and Swinnerton-Dyer for such $L$-values, and extends beyond their framework to special non-CM elliptic curves.

  5. New calibration methodology for calorimetric determination of isobaric thermal expansivity of liquids as a function of temperature and pressure

    Energy Technology Data Exchange (ETDEWEB)

    Navia, Paloma; Troncoso, Jacobo [Departamento de Fisica Aplicada, Facultad de Ciencias de Ourense, Campus As Lagoas, 32004 Ourense (Spain); Romani, Luis [Departamento de Fisica Aplicada, Facultad de Ciencias de Ourense, Campus As Lagoas, 32004 Ourense (Spain)], E-mail: romani@uvigo.es

    2008-11-15

    A new method for determining isobaric thermal expansivity of liquids as a function of temperature and pressure through calorimetric measurements against pressure is described. It is based on a previously reported measurement technique, but due to the different kind of calorimeter and experimental set up, a new calibration procedure was developed. Two isobaric thermal expansivity standards are needed; in this work, with a view on the quality of the available literature data, hexane and water are chosen. The measurements were carried out in the temperature and pressure intervals (278.15 to 348.15) K and (0.5 to 55) MPa for a set of liquids, and experimental values are compared with the available literature data in order to evaluate the precision of the experimental procedure. The analysis of the results reveals that the proposed methodology is highly accurate for isobaric thermal expansivity determination, and it allows obtaining a precise characterisation of the temperature and pressure dependence of this thermodynamic coefficient.

  6. New calibration methodology for calorimetric determination of isobaric thermal expansivity of liquids as a function of temperature and pressure

    International Nuclear Information System (INIS)

    Navia, Paloma; Troncoso, Jacobo; Romani, Luis

    2008-01-01

    A new method for determining isobaric thermal expansivity of liquids as a function of temperature and pressure through calorimetric measurements against pressure is described. It is based on a previously reported measurement technique, but due to the different kind of calorimeter and experimental set up, a new calibration procedure was developed. Two isobaric thermal expansivity standards are needed; in this work, with a view on the quality of the available literature data, hexane and water are chosen. The measurements were carried out in the temperature and pressure intervals (278.15 to 348.15) K and (0.5 to 55) MPa for a set of liquids, and experimental values are compared with the available literature data in order to evaluate the precision of the experimental procedure. The analysis of the results reveals that the proposed methodology is highly accurate for isobaric thermal expansivity determination, and it allows obtaining a precise characterisation of the temperature and pressure dependence of this thermodynamic coefficient

  7. Elliptic differential equations theory and numerical treatment

    CERN Document Server

    Hackbusch, Wolfgang

    2017-01-01

    This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

  8. Type A Jacobi Elliptic One-Monopole

    International Nuclear Information System (INIS)

    Teh, Rosy; Wong, Khai-Ming

    2010-01-01

    We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with Θ-winding number m = 1 and φ-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing. This solution is a regular non-BPS finite energy solution.

  9. Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

    Science.gov (United States)

    Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

    2018-05-01

    Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure

  10. Electron energy spectrum in core-shell elliptic quantum wire

    Directory of Open Access Journals (Sweden)

    V.Holovatsky

    2007-01-01

    Full Text Available The electron energy spectrum in core-shell elliptic quantum wire and elliptic semiconductor nanotubes are investigated within the effective mass approximation. The solution of Schrodinger equation based on the Mathieu functions is obtained in elliptic coordinates. The dependencies of the electron size quantization spectrum on the size and shape of the core-shell nanowire and nanotube are calculated. It is shown that the ellipticity of a quantum wire leads to break of degeneration of quasiparticle energy spectrum. The dependences of the energy of odd and even electron states on the ratio between semiaxes are of a nonmonotonous character. The anticrosing effects are observed at the dependencies of electron energy spectrum on the transversal size of the core-shell nanowire.

  11. Comparative and functional triatomine genomics reveals reductions and expansions in insecticide resistance-related gene families.

    Science.gov (United States)

    Traverso, Lucila; Lavore, Andrés; Sierra, Ivana; Palacio, Victorio; Martinez-Barnetche, Jesús; Latorre-Estivalis, José Manuel; Mougabure-Cueto, Gaston; Francini, Flavio; Lorenzo, Marcelo G; Rodríguez, Mario Henry; Ons, Sheila; Rivera-Pomar, Rolando V

    2017-02-01

    Triatomine insects are vectors of Trypanosoma cruzi, a protozoan parasite that is the causative agent of Chagas' disease. This is a neglected disease affecting approximately 8 million people in Latin America. The existence of diverse pyrethroid resistant populations of at least two species demonstrates the potential of triatomines to develop high levels of insecticide resistance. Therefore, the incorporation of strategies for resistance management is a main concern for vector control programs. Three enzymatic superfamilies are thought to mediate xenobiotic detoxification and resistance: Glutathione Transferases (GSTs), Cytochromes P450 (CYPs) and Carboxyl/Cholinesterases (CCEs). Improving our knowledge of key triatomine detoxification enzymes will strengthen our understanding of insecticide resistance processes in vectors of Chagas' disease. The discovery and description of detoxification gene superfamilies in normalized transcriptomes of three triatomine species: Triatoma dimidiata, Triatoma infestans and Triatoma pallidipennis is presented. Furthermore, a comparative analysis of these superfamilies among the triatomine transcriptomes and the genome of Rhodnius prolixus, also a triatomine vector of Chagas' disease, and other well-studied insect genomes was performed. The expression pattern of detoxification genes in R. prolixus transcriptomes from key organs was analyzed. The comparisons reveal gene expansions in Sigma class GSTs, CYP3 in CYP superfamily and clade E in CCE superfamily. Moreover, several CYP families identified in these triatomines have not yet been described in other insects. Conversely, several groups of insecticide resistance related enzymes within each enzyme superfamily are reduced or lacking in triatomines. Furthermore, our qRT-PCR results showed an increase in the expression of a CYP4 gene in a T. infestans population resistant to pyrethroids. These results could point to an involvement of metabolic detoxification mechanisms on the high

  12. Comparative and functional triatomine genomics reveals reductions and expansions in insecticide resistance-related gene families.

    Directory of Open Access Journals (Sweden)

    Lucila Traverso

    2017-02-01

    Full Text Available Triatomine insects are vectors of Trypanosoma cruzi, a protozoan parasite that is the causative agent of Chagas' disease. This is a neglected disease affecting approximately 8 million people in Latin America. The existence of diverse pyrethroid resistant populations of at least two species demonstrates the potential of triatomines to develop high levels of insecticide resistance. Therefore, the incorporation of strategies for resistance management is a main concern for vector control programs. Three enzymatic superfamilies are thought to mediate xenobiotic detoxification and resistance: Glutathione Transferases (GSTs, Cytochromes P450 (CYPs and Carboxyl/Cholinesterases (CCEs. Improving our knowledge of key triatomine detoxification enzymes will strengthen our understanding of insecticide resistance processes in vectors of Chagas' disease.The discovery and description of detoxification gene superfamilies in normalized transcriptomes of three triatomine species: Triatoma dimidiata, Triatoma infestans and Triatoma pallidipennis is presented. Furthermore, a comparative analysis of these superfamilies among the triatomine transcriptomes and the genome of Rhodnius prolixus, also a triatomine vector of Chagas' disease, and other well-studied insect genomes was performed. The expression pattern of detoxification genes in R. prolixus transcriptomes from key organs was analyzed. The comparisons reveal gene expansions in Sigma class GSTs, CYP3 in CYP superfamily and clade E in CCE superfamily. Moreover, several CYP families identified in these triatomines have not yet been described in other insects. Conversely, several groups of insecticide resistance related enzymes within each enzyme superfamily are reduced or lacking in triatomines. Furthermore, our qRT-PCR results showed an increase in the expression of a CYP4 gene in a T. infestans population resistant to pyrethroids. These results could point to an involvement of metabolic detoxification mechanisms

  13. Tyrosine kinase receptor RON functions downstream of the erythropoietin receptor to induce expansion of erythroid progenitors

    NARCIS (Netherlands)

    van den Akker, Emile; van Dijk, Thamar; Parren-van Amelsvoort, Martine; Grossmann, Katja S.; Schaeper, Ute; Toney-Earley, Kenya; Waltz, Susan E.; Löwenberg, Bob; von Lindern, Marieke

    2004-01-01

    Erythropoietin (EPO) is required for cell survival during differentiation and for progenitor expansion during stress erythropoiesis. Although signaling pathways may couple directly to docking sites on the EPO receptor (EpoR), additional docking molecules expand the signaling platform of the

  14. ELLIPT2D: A Flexible Finite Element Code Written Python

    International Nuclear Information System (INIS)

    Pletzer, A.; Mollis, J.C.

    2001-01-01

    The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research

  15. Calculation of complete or incomplete elliptic integrals of the first and second kind

    International Nuclear Information System (INIS)

    Guillermin, J.M.; Guerin, M.

    1968-01-01

    The structure of the article is as following: inversion of the Jacobi function Sn (U, K), definition of the functions F (PHI, K) and E (PHI, K), Landen transformation, calculation of elliptic integrals F (PHI, K) and E (PHI, K), particular case of complete elliptic integrals, realised programs [fr

  16. Elliptic Genera of Symmetric Products and Second Quantized Strings

    CERN Document Server

    Dijkgraaf, R; Verlinde, Erik; Verlinde, Herman L

    1997-01-01

    In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \\times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.

  17. Rational points on elliptic curves

    CERN Document Server

    Silverman, Joseph H

    2015-01-01

    The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and ...

  18. Energy and the Elliptical Orbit

    Science.gov (United States)

    Nettles, Bill

    2009-03-01

    In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.

  19. Interstellar matter within elliptical galaxies

    Science.gov (United States)

    Jura, Michael

    1988-01-01

    Multiwavelength observations of elliptical galaxies are reviewed, with an emphasis on their implications for theoretical models proposed to explain the origin and evolution of the interstellar matter. Particular attention is given to interstellar matter at T less than 100 K (atomic and molecular gas and dust), gas at T = about 10,000 K, and gas at T = 10 to the 6th K or greater. The data are shown to confirm the occurrence of mass loss from evolved stars, significant accretion from companion galaxies, and cooling inflows; no evidence is found for large mass outflow from elliptical galaxies.

  20. The nonlocal operator expansion for structure functions of e+e- annihilation

    International Nuclear Information System (INIS)

    Balitsky, I.I.; Braun, V.M.

    1989-01-01

    The Wilson operator expansion is generalized to inclusive particle production in e + e - annihilation. This turns out to be possible at the price of doubling the number of quantum quark and gluon fields in a similar fashion that gives rise to the Keldysh technique for nonequilibrium processes. Well-known results on the leading logarithmic contributions to inclusive production are reproduced as the one-loop evolution of the string operator of the leading twist. The general structure of the power corrections 1/Q 2 is outlined. (orig.)

  1. Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

    Science.gov (United States)

    Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

    2017-07-10

    This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

  2. Isotropic oscillator in the space of constant positive curvature. Interbasis expansions

    International Nuclear Information System (INIS)

    Akopyan, E.M.; Pogosyan, G.S.; Sisakyan, A.N.; Vinitskij, S.I.

    1997-01-01

    The Schroedinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the spherical and cylindrical bases of the oscillator are calculated. It is shown that the relevant coefficients are expressed through the generalised hypergeometric functions 4 F 3 of the unit argument or 6j Racah symbols extended over their indices to the region of real values. Limiting transitions to a free motion and flat space are considered in detail. Elliptic bases of the oscillator are constructed in the form of expansion over the spherical and cylindrical bases. The corresponding expansion coefficients are shown to obey the three-term recurrence relations expansion coefficients are shown to obey the three-term recurrence relations

  3. Guided modes of elliptical metamaterial waveguides

    International Nuclear Information System (INIS)

    Halterman, Klaus; Feng, Simin; Overfelt, P. L.

    2007-01-01

    The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity ε and permeability μ are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide

  4. Functional and Structural Characterization of a Receptor-Like Kinase Involved in Germination and Cell Expansion in Arabidopsis

    Science.gov (United States)

    Wu, Zhen; Liang, Shan; Song, Wen; Lin, Guangzhong; Wang, Weiguang; Zhang, Heqiao; Han, Zhifu; Chai, Jijie

    2017-01-01

    Leucine-rich repeat receptor-like kinases (LRR-RLKs) are widespread in different plant species and play important roles in growth and development. Germination inhibition is vital for the completion of seed maturation and cell expansion is a fundamental cellular process driving plant growth. Here, we report genetic and structural characterizations of a functionally uncharacterized LRR-RLK, named GRACE (Germination Repression and Cell Expansion receptor-like kinase). Overexpression of GRACE in Arabidopsis exhibited delayed germination, enlarged cotyledons, rosette leaves and stubbier petioles. Conversely, these phenotypes were reversed in the T-DNA insertion knock-down mutant grace-1 plants. A crystal structure of the extracellular domain of GRACE (GRACE-LRR) determined at the resolution of 3.0 Å revealed that GRACE-LRR assumed a right-handed super-helical structure with an island domain (ID). Structural comparison showed that structure of the ID in GRACE-LRR is strikingly different from those observed in other LRR-RLKs. This structural observation implies that GRACE might perceive a new ligand for signaling. Collectively, our data support roles of GRACE in repressing seed germination and promoting cell expansion of Arabidopsis, presumably by perception of unknown ligand(s). PMID:29213277

  5. Elliptic net and its cryptographic application

    Science.gov (United States)

    Muslim, Norliana; Said, Mohamad Rushdan Md

    2017-11-01

    Elliptic net is a generalization of elliptic divisibility sequence and in cryptography field, most cryptographic pairings that are based on elliptic curve such as Tate pairing can be improved by applying elliptic nets algorithm. The elliptic net is constructed by using n dimensional array of values in rational number satisfying nonlinear recurrence relations that arise from elliptic divisibility sequences. The two main properties hold in the recurrence relations are for all positive integers m>n, hm +nhm -n=hm +1hm -1hn2-hn +1hn -1hm2 and hn divides hm whenever n divides m. In this research, we discuss elliptic divisibility sequence associated with elliptic nets based on cryptographic perspective and its possible research direction.

  6. Coercive properties of elliptic-parabolic operator

    International Nuclear Information System (INIS)

    Duong Min Duc.

    1987-06-01

    Using a generalized Poincare inequality, we study the coercive properties of a class of elliptic-parabolic partial differential equations, which contains many degenerate elliptic equations considered by the other authors. (author). 16 refs

  7. Hörmander spaces, interpolation, and elliptic problems

    CERN Document Server

    Mikhailets, Vladimir A; Malyshev, Peter V

    2014-01-01

    The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

  8. Hydroforming of elliptical cavities

    Science.gov (United States)

    Singer, W.; Singer, X.; Jelezov, I.; Kneisel, P.

    2015-02-01

    Activities of the past several years in developing the technique of forming seamless (weldless) cavity cells by hydroforming are summarized. An overview of the technique developed at DESY for the fabrication of single cells and multicells of the TESLA cavity shape is given and the major rf results are presented. The forming is performed by expanding a seamless tube with internal water pressure while simultaneously swaging it axially. Prior to the expansion the tube is necked at the iris area and at the ends. Tube radii and axial displacements are computer controlled during the forming process in accordance with results of finite element method simulations for necking and expansion using the experimentally obtained strain-stress relationship of tube material. In cooperation with industry different methods of niobium seamless tube production have been explored. The most appropriate and successful method is a combination of spinning or deep drawing with flow forming. Several single-cell niobium cavities of the 1.3 GHz TESLA shape were produced by hydroforming. They reached accelerating gradients Eacc up to 35 MV /m after buffered chemical polishing (BCP) and up to 42 MV /m after electropolishing (EP). More recent work concentrated on fabrication and testing of multicell and nine-cell cavities. Several seamless two- and three-cell units were explored. Accelerating gradients Eacc of 30 - 35 MV /m were measured after BCP and Eacc up to 40 MV /m were reached after EP. Nine-cell niobium cavities combining three three-cell units were completed at the company E. Zanon. These cavities reached accelerating gradients of Eacc=30 - 35 MV /m . One cavity is successfully integrated in an XFEL cryomodule and is used in the operation of the FLASH linear accelerator at DESY. Additionally the fabrication of bimetallic single-cell and multicell NbCu cavities by hydroforming was successfully developed. Several NbCu clad single-cell and double-cell cavities of the TESLA shape have been

  9. Hydroforming of elliptical cavities

    Directory of Open Access Journals (Sweden)

    W. Singer

    2015-02-01

    Full Text Available Activities of the past several years in developing the technique of forming seamless (weldless cavity cells by hydroforming are summarized. An overview of the technique developed at DESY for the fabrication of single cells and multicells of the TESLA cavity shape is given and the major rf results are presented. The forming is performed by expanding a seamless tube with internal water pressure while simultaneously swaging it axially. Prior to the expansion the tube is necked at the iris area and at the ends. Tube radii and axial displacements are computer controlled during the forming process in accordance with results of finite element method simulations for necking and expansion using the experimentally obtained strain-stress relationship of tube material. In cooperation with industry different methods of niobium seamless tube production have been explored. The most appropriate and successful method is a combination of spinning or deep drawing with flow forming. Several single-cell niobium cavities of the 1.3 GHz TESLA shape were produced by hydroforming. They reached accelerating gradients E_{acc} up to 35  MV/m after buffered chemical polishing (BCP and up to 42  MV/m after electropolishing (EP. More recent work concentrated on fabrication and testing of multicell and nine-cell cavities. Several seamless two- and three-cell units were explored. Accelerating gradients E_{acc} of 30–35  MV/m were measured after BCP and E_{acc} up to 40  MV/m were reached after EP. Nine-cell niobium cavities combining three three-cell units were completed at the company E. Zanon. These cavities reached accelerating gradients of E_{acc}=30–35  MV/m. One cavity is successfully integrated in an XFEL cryomodule and is used in the operation of the FLASH linear accelerator at DESY. Additionally the fabrication of bimetallic single-cell and multicell NbCu cavities by hydroforming was successfully developed. Several NbCu clad single-cell and

  10. Ex Vivo Expansion of Functional Human UCB-HSCs/HPCs by Coculture with AFT024-hkirre Cells

    Directory of Open Access Journals (Sweden)

    Muti ur Rehman Khan

    2014-01-01

    Full Text Available Kiaa1867 (human Kirre, hKirre has a critical role in brain development and/or maintenance of the glomerular slit diaphragm in kidneys. Murine homolog of this gene, mKirre expressed in OP9 and AFT024 cells could support hematopoietic stem cells/hematopoietic progenitor cells (HSC/HPC expansion in vitro. HKirre is also expressed in human FBMOB-hTERT cell line and fetal liver fibroblast-like cells but its function has remained unclear. In this paper, we cloned a hKirre gene from human fetal liver fibroblast-like cells and established a stably overexpressing hKirre-AFT024 cell line. Resultant cells could promote self-renewal and ex vivo expansion of HSCs/HPCs significantly higher than AFT024-control cells transformed with mock plasmid. The Expanded human umbilical cord blood (hUCB CD34+ cells retained the capacity of multipotent differentiation as long as 8 weeks and successfully repopulated the bone marrow of sublethally irradiated NOD/SCID mice, which demonstrated the expansion of long-term primitive transplantable HSCs/HPCs. Importantly, hkirre could upregulate the expressions of Wnt-5A, BMP4, and SDF-1 and downregulate TGF-β with other hematopoietic growth factors. By SDS-PAGE and Western Blot analysis, a ~89 kDa protein in total lysate of AFT024-hKirre was identified. Supernatants from AFT024-hkirre could also support CD34+CD38− cells expansion. These results demonstrated that the AFT024-hKirre cells have the ability to efficiently expand HSCs/HPCs.

  11. Expansion and Functional Divergence of AP2 Group Genes in Spermatophytes Determined by Molecular Evolution and Arabidopsis Mutant Analysis

    Directory of Open Access Journals (Sweden)

    Pengkai Wang

    2016-09-01

    Full Text Available The APETALA2 (AP2 genes represent the AP2 group within a large group of DNA-binding proteins called AP2/EREBP. The AP2 gene is functional and necessary for flower development, stem cell maintenance, and seed development, whereas the other members of AP2 group redundantly affect flowering time. Here we study the phylogeny of AP2 group genes in spermatophytes. Spermatophyte AP2 group genes can be classified into AP2 and TOE types, six clades, and we found that the AP2 group homologs in gymnosperms belong to the AP2 type, whereas TOE types are absent, which indicates the AP2 type gene are more ancient and TOE type was split out of AP2 type and losing the major function. In Brassicaceae, the expansion of AP2 and TOE type lead to the gene number of AP2 group were up to six. Purifying selection appears to have been the primary driving force of spermatophyte AP2 group evolution, although positive selection occurred in the AP2 clade. The transition from exon to intron of AtAP2 in Arabidopsis mutant leads to the loss of gene function and the same situation was found in AtTOE2. Combining this evolutionary analysis and published research, the results suggest that typical AP2 group genes may first appear in gymnosperms and diverged in angiosperms, following expansion of group members and functional differentiation. In angiosperms, AP2 genes (AP2 clade inherited key functions from ancestors and other genes of AP2 group lost most function but just remained flowering time controlling in gene formation. In this study, the phylogenies of AP2 group genes in spermatophytes was analyzed, which supported the evidence for the research of gene functional evolution of AP2 group.

  12. Diffeomorphisms of elliptic 3-manifolds

    CERN Document Server

    Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam

    2012-01-01

    This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

  13. Elliptic curves and primality proving

    Science.gov (United States)

    Atkin, A. O. L.; Morain, F.

    1993-07-01

    The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret.

  14. Color gradients in elliptical galaxies

    International Nuclear Information System (INIS)

    Franx, M.; Illingworth, G.

    1990-01-01

    The relationship of the color gradients within ellipticals and the color differences between them are studied. It is found that the local color appears to be strongly related to the escape velocity. This suggests that the local escape velocity is the primary factor that determines the metallicity of the stellar population. Models with and without dark halos give comparable results. 27 refs

  15. Second order degenerate elliptic equations

    International Nuclear Information System (INIS)

    Duong Minh Duc.

    1988-08-01

    Using an improved Sobolev inequality we study a class of elliptic operators which is degenerate inside the domain and strongly degenerate near the boundary of the domain. Our results are applicable to the L 2 -boundary value problem and the mixed boundary problem. (author). 18 refs

  16. Long-Term Reserve Expansion of Power Systems With High Wind Power Penetration Using Universal Generating Function Methods

    DEFF Research Database (Denmark)

    DING, YI; Wang, Peng; Goel, Lalit

    2010-01-01

    from long term planning point of view utilizing universal generating function (UGF) methods. The reliability models of wind farms and conventional generators are represented as the correspondin UGFs and the special operators for these UGFs are defined to evaluate the customer and the system...... reliabilities. The effect of transmission network on customer reliabilities is also considered in the system UGF. The power output models of wind turbine generators in a wind farm considering wind speed correlation and un-correlation are developed, respectively. A reliability-based reserve expansion method...

  17. Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem

    Energy Technology Data Exchange (ETDEWEB)

    Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)

    1996-12-31

    The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.

  18. Elliptical shape of the coma cluster

    International Nuclear Information System (INIS)

    Schipper, L.; King, I.R.

    1978-01-01

    The elliptical shape of the Coma cluster is examined quantitatively. The degree of ellipticity is high and depends to some extent on the radial distance of the sample from the Coma center as well as on the brightness of the sample. The elliptical shape does not appear to be caused by rotation; other possible causes are briefly discussed

  19. A class of strongly degenerate elliptic operators

    International Nuclear Information System (INIS)

    Duong Minh Duc.

    1988-04-01

    Using a weighted Poincare inequality, we study (ω 1 ,...,ω n )-elliptic operators. This method is applicable to solve singular elliptic equations with conditions in W 1,2 on the boundary. We also get a result about the regularity of solutions of singular elliptic equations. An application to (ω 1 ,...ω n )-parabolic equations is given. (author). 33 refs

  20. Mass spectra and wave functions of meson systems and the covariant oscillator quark model as an expansion basis

    International Nuclear Information System (INIS)

    Oda, Ryuichi; Ishida, Shin; Wada, Hiroaki; Yamada, Kenji; Sekiguchi, Motoo

    1999-01-01

    We examine mass spectra and wave functions of the nn-bar, cc-bar and bb-bar meson systems within the framework of the covariant oscillator quark model with the boosted LS-coupling scheme. We solve nonperturbatively an eigenvalue problem for the squared-mass operator, which incorporates the four-dimensional color-Coulomb-type interaction, by taking a set of covariant oscillator wave functions as an expansion basis. We obtain mass spectra of these meson systems, which reproduce quite well their experimental behavior. The resultant manifestly covariant wave functions, which are applicable to analyses of various reaction phenomena, are given. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model. (author)

  1. Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model

    Science.gov (United States)

    Lu, Yi; Haverkort, Maurits W.

    2017-12-01

    We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

  2. The analytical solution of wake-fields in an elliptical pillbox cavity

    International Nuclear Information System (INIS)

    Yang, J.S.; Chen, K.W.

    1991-01-01

    The wake potential of a bunch of relativistic charged particles traversing an elliptical pillbox cavity is derived analytically in the limit of vanishing aperture. It is found that the resonant modes of an elliptical cavity can be expressed in terms of Mathieu functions. Calculation results are presented and compared with numerical ones. (author) 10 refs., 10 figs., 2 tabs

  3. First non-zero terms for the Taylor expansion at 1 of the Conway potential function

    NARCIS (Netherlands)

    Buryak, A.Y.

    2011-01-01

    The Conway potential function ∇ L (t 1,...,t l ) of an ordered oriented link L = L 1 ∪ L 2 ∪ ... ∪ L l ⊂ S 3 is considered. In general, this function is not determined by the linking numbers and the Conway potential functions of the components. However, the first two nonzero terms of the Taylor

  4. Advanced topics in the arithmetic of elliptic curves

    CERN Document Server

    Silverman, Joseph H

    1994-01-01

    In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...

  5. The two-loop sunrise integral and elliptic polylogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Adams, Luise; Weinzierl, Stefan [Institut fuer Physik, Johannes Gutenberg-Universitaet Mainz (Germany); Bogner, Christian [Institut fuer Physik, Humboldt-Universitaet zu Berlin (Germany)

    2016-07-01

    In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.

  6. A comparison of two nodal codes : Advanced nodal code (ANC) and analytic function expansion nodal (AFEN) code

    International Nuclear Information System (INIS)

    Chung, S.K.; Hah, C.J.; Lee, H.C.; Kim, Y.H.; Cho, N.Z.

    1996-01-01

    Modern nodal methods usually employs the transverse integration technique in order to reduce a multi-dimensional diffusion equation to one-dimensional diffusion equations. The use of the transverse integration technique requires two major approximations such as a transverse leakage approximation and a one-dimensional flux approximation. Both the transverse leakage and the one-dimensional flux are approximated by polynomials. ANC (Advanced Nodal Code) developed by Westinghouse employs a modern nodal expansion method for the flux calculation, the equivalence theory for the homogenization error reduction and a group theory for pin power recovery. Unlike the conventional modern nodal methods, AFEN (Analytic Function Expansion Nodal) method expands homogeneous flux distributions within a node into non-separable analytic basis functions, which eliminate two major approximations of the modern nodal methods. A comparison study of AFEN with ANC has been performed to see the applicability of AFEN to commercial PWR and different types of reactors such as MOX fueled reactor. The qualification comparison results demonstrate that AFEN methodology is accurate enough to apply for commercial PWR analysis. The results show that AFEN provides very accurate results (core multiplication factor and assembly power distribution) for cores that exhibit strong flux gradients as in a MOX loaded core. (author)

  7. Elliptic Diophantine equations a concrete approach via the elliptic logarithm

    CERN Document Server

    Tzanakis, Nikos

    2013-01-01

    This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages, like Magma. This book is suitable for students in mathematics, as well as professional mathematicians.

  8. A summary of numerical computation for special functions

    International Nuclear Information System (INIS)

    Zhang Shanjie

    1992-01-01

    In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed

  9. Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation

    International Nuclear Information System (INIS)

    Wang Dengshan; Zhang Hongqing

    2005-01-01

    In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions

  10. System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow

    Science.gov (United States)

    Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Hołyński, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.

    2007-06-01

    This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.

  11. Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas

    Science.gov (United States)

    Stefanucci, G.; Pavlyukh, Y.; Uimonen, A.-M.; van Leeuwen, R.

    2014-09-01

    We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-step procedure: We first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions, whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte Carlo momentum integrations to evaluate the diagrams.

  12. Correlation between isothermal expansion and functional properties change of the Fe81B13Si4C2 amorphous alloy

    Directory of Open Access Journals (Sweden)

    Kalezić-Glišović A.

    2009-01-01

    Full Text Available The structural changes effect on functional properties of ribbon shaped samples of the Fe81B13Si4C2 amorphous alloy during annealing process was investigated in this paper. Differential scanning calorimetry method has shown that this alloy crystallizes in one stage, in temperature range from room temperature up to 700°C. Structural relaxation process was investigated by sensitive dilatation method in nonisothermal and isothermal conditions. It has been shown that structural relaxation process occurs in two stages by measuring thermal expansion at constant temperatures of t1=420°C, t2 = 440°C and t3 = 460°C. The first stage is characterized by linear logarithmic dependence of thermal expansion upon time at constant temperature. The second stage of structural relaxation process is characterized by linear dependence of isothermal expansion upon the square root of process time. These results imply that the first stage of structural relaxation process is a rapid kinetic process, while the second stage of structural relaxation process is a slow diffusion process. The rate constants k11 = 2,27⋅10- 3 s-1, k12 = 2,79⋅10-3 s-1, k13 = 3,6⋅10-3 s-1, k21 = 0,67⋅10-4 s-1, k22 = 3,72⋅10-4 s-1, k23 = 21,53⋅10-4 s-1 and activation energies E1 = 48,64 kJ/mol and E2 = 366, 23 kJ/mol were determined for both stages of structural relaxation process. The distinct correlation between structural relaxation process and magnetic susceptibility relative change was determined by thermomagnetic measurements. It has been shown that magnetic susceptibility can be increased by up to 80%, by convenient annealings after structural relaxation process, at magnetic field intensity of 8 kA/m.

  13. Expansion of X-ray form factor for close shell using uncorrelated wave function

    Energy Technology Data Exchange (ETDEWEB)

    AL-Robayi, Enas M. [Babylon University , College of Science for Women, laser Physics Department, Hilla (Iraq)

    2013-12-16

    The atomic scattering factor has been studied for Be+ve, and B+2ve ions using the uncorrelated wave function (Hartree-Fock (HF)) for inter particle electronic shells. The physical importance of this factor appears in its relation to several important atomic properties as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the geometrical structure factor. Also there is one atomic properties the one particle radial density distribution function D(r)has been studied using the partitioning technique.

  14. Integral formula for elliptic SOS models with domain walls and a reflecting end

    Energy Technology Data Exchange (ETDEWEB)

    Lamers, Jules, E-mail: j.lamers@uu.nl

    2015-12-15

    In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic SOS model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.

  15. Modeling and analysis of waves in a heat conducting thermo-elastic plate of elliptical shape

    Directory of Open Access Journals (Sweden)

    R. Selvamani

    Full Text Available Wave propagation in heat conducting thermo elastic plate of elliptical cross-section is studied using the Fourier expansion collocation method based on Suhubi's generalized theory. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of elliptical cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by using the boundary conditions along outer and inner surface of elliptical cross-sectional plate using Fourier expansion collocation method. The computed non-dimensional frequency, velocity and quality factor are plotted in dispersion curves for longitudinal and flexural (symmetric and antisymmetric modes of vibrations.

  16. Global weighted estimates for second-order nondivergence elliptic ...

    Indian Academy of Sciences (India)

    Fengping Yao

    2018-03-21

    Mar 21, 2018 ... One of the key a priori estimates in the theory of second-order elliptic .... It is well known that the maximal functions satisfy strong p–p .... Here we prove the following auxiliary result, which will be a crucial ingredient in the proof.

  17. Existence of positive solutions to semilinear elliptic problems with ...

    Indian Academy of Sciences (India)

    57

    In mathematical modeling, elliptic partial differential equations are used together with boundary conditions specifying the .... Note that the trace map X ↩→ Lq(∂Ω) is compact for q ∈ [1, 2∗) (see, e.g., [4, ..... [2] Ambrosetti A and Rabinowitz P H, Dual variational methods in critical point theory and applications, J. Functional ...

  18. hp Spectral element methods for three dimensional elliptic problems

    Indian Academy of Sciences (India)

    elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.

  19. An elliptic analogue of the Franklin-Schneider theorem

    NARCIS (Netherlands)

    Bijlsma, A.

    1980-01-01

    Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. Let a and b be complex numbers such that a and b are not among the poles of p. A lower bound is given for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers, expressed in their heights and degrees. By

  20. Transfer coefficients in elliptical tubes and plate fin heat exchangers

    International Nuclear Information System (INIS)

    Saboya, S.M.

    1979-09-01

    Mean transfer coefficients in elliptical tubes and plate fin heat exchangers were determined by application of heat and mass transfer analogy in conjunction with the naphthalene sublimation technique. The transfer coefficients are presented in a dimensionless form as functions of the Reynolds number. By using the least squares method analytical expressions for the transfer coefficients were determined with low scattering. (E.G.) [pt

  1. On the spherical harmonic expansion of the neutron angular distribution function

    Energy Technology Data Exchange (ETDEWEB)

    Depken, Sven

    1959-03-15

    The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.

  2. On the spherical harmonic expansion of the neutron angular distribution function

    International Nuclear Information System (INIS)

    Depken, Sven

    1959-03-01

    The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases

  3. Elliptical and lenticular galaxies evolution

    International Nuclear Information System (INIS)

    Vigroux, L.

    1981-01-01

    Different evolutionnary models for elliptical and lenticular galaxies are discussed. In the first part, we show that, at least some peculiar early types galaxies exhibit some activity. Then we describe the observationnal constraints: the color-magnitude diagram, the color gradient and the high metallicity of intraclusters gas. Among the different models, only the dissipation collapse followed by a hot wind driven by supernovae explosion explain in a natural way these constraints. Finally, the origin of SO is briefly discussed [fr

  4. Holomorphic bundles over elliptic manifolds

    International Nuclear Information System (INIS)

    Morgan, J.W.

    2000-01-01

    In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves

  5. Can mergers make slowly rotating elliptical galaxies

    International Nuclear Information System (INIS)

    White, S.D.M.

    1979-01-01

    The results of numerical experiments are used to guide an analytic discussion of hyperbolic mergers among an uncorrelated galaxy population. The expected merger rate is derived as a function of progenitor mass and relative angular momentum, and is used to predict the distribution of the parameter V/sub c//sigma 0 for merger products where V/sub c/ is the maximum observed rotation velocity in a galaxy and sigma 0 is its central velocity dispersion. The median value of this parameter for mergers between comparable galaxies is estimated to be 0.65 and is higher than the observed value in any of the 14 galaxies for which data are available. It seems unlikely that most elliptical galaxies are the result of single or multiple mergers between initially unbound stellar systems; further observational and theoretical work is suggested which should lead to a conclusive test of this picture. The present arguments cannot, however, exclude formation from low angular momentum elliptical orbits

  6. Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions.

    Science.gov (United States)

    Wang, Kun; Schoonover, Robert W; Su, Richard; Oraevsky, Alexander; Anastasio, Mark A

    2014-05-01

    Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

  7. Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity

    Directory of Open Access Journals (Sweden)

    F. Hamzezadeh

    2014-01-01

    Full Text Available In many systems such as computer network, fuel distribution, and transportation system, it is necessary to change the capacity of some arcs in order to increase maximum flow value from source s to sink t, while the capacity change incurs minimum cost. In real-time networks, some factors cause loss of arc’s flow. For example, in some flow distribution systems, evaporation, erosion or sediment in pipes waste the flow. Here we define a real capacity, or the so-called functional capacity, which is the operational capacity of an arc. In other words, the functional capacity of an arc equals the possible maximum flow that may pass through the arc. Increasing the functional arcs capacities incurs some cost. There is a certain resource available to cover the costs. First, we construct a mathematical model to minimize the total cost of expanding the functional capacities to the required levels. Then, we consider the loss of flow on each arc as a stochastic variable and compute the system reliability.

  8. Coiled-Coil Proteins Facilitated the Functional Expansion of the Centrosome

    Science.gov (United States)

    Kuhn, Michael; Hyman, Anthony A.; Beyer, Andreas

    2014-01-01

    Repurposing existing proteins for new cellular functions is recognized as a main mechanism of evolutionary innovation, but its role in organelle evolution is unclear. Here, we explore the mechanisms that led to the evolution of the centrosome, an ancestral eukaryotic organelle that expanded its functional repertoire through the course of evolution. We developed a refined sequence alignment technique that is more sensitive to coiled coil proteins, which are abundant in the centrosome. For proteins with high coiled-coil content, our algorithm identified 17% more reciprocal best hits than BLAST. Analyzing 108 eukaryotic genomes, we traced the evolutionary history of centrosome proteins. In order to assess how these proteins formed the centrosome and adopted new functions, we computationally emulated evolution by iteratively removing the most recently evolved proteins from the centrosomal protein interaction network. Coiled-coil proteins that first appeared in the animal–fungi ancestor act as scaffolds and recruit ancestral eukaryotic proteins such as kinases and phosphatases to the centrosome. This process created a signaling hub that is crucial for multicellular development. Our results demonstrate how ancient proteins can be co-opted to different cellular localizations, thereby becoming involved in novel functions. PMID:24901223

  9. Improved Green’s function measurement for hybridization expansion quantum Monte Carlo

    Czech Academy of Sciences Publication Activity Database

    Augustinský, Pavel; Kuneš, Jan

    2013-01-01

    Roč. 184, č. 9 (2013), s. 2119-2126 ISSN 0010-4655 Institutional support: RVO:68378271 Keywords : continuous time quantum Monte Carlo method * Green function estimator Subject RIV: BE - Theoretical Physics Impact factor: 2.407, year: 2013

  10. Expansion of the Kano model to identify relevant customer segments and functional requirements

    DEFF Research Database (Denmark)

    Atlason, Reynir Smari; Stefansson, Arnaldur Smari; Wietz, Miriam

    2017-01-01

    The Kano model of customer satisfaction has been widely used to analyse perceived needs of customers. The model provides product developers valuable information about if, and then how much a given functional requirement (FR) will impact customer satisfaction if implemented within a product, system...... or a service. A current limitation of the Kano model is that it does not allow developers to visualise which combined sets of FRs would provide the highest satisfaction between different customer segments. In this paper, a stepwise method to address this particular shortcoming is presented. First......, a traditional Kano analysis is conducted for the different segments of interest. Second, for each FR, relationship functions are integrated between x=0 and x=1. Third, integrals are inserted into a combination matrix crossing segments and FRs, where FRs with the highest sum across the chosen segments...

  11. Molecular evolution and the role of oxidative stress in the expansion and functional diversification of cytosolic glutathione transferases

    Directory of Open Access Journals (Sweden)

    Vasconcelos Vítor

    2010-09-01

    Full Text Available Abstract Background Cytosolic glutathione transferases (cGST are a large group of ubiquitous enzymes involved in detoxification and are well known for their undesired side effects during chemotherapy. In this work we have performed thorough phylogenetic analyses to understand the various aspects of the evolution and functional diversification of cGSTs. Furthermore, we assessed plausible correlations between gene duplication and substrate specificity of gene paralogs in humans and selected species, notably in mammalian enzymes and their natural substrates. Results We present a molecular phylogeny of cytosolic GSTs that shows that several classes of cGSTs are more ubiquitous and thus have an older ancestry than previously thought. Furthermore, we found that positive selection is implicated in the diversification of cGSTs. The number of duplicate genes per class is generally higher for groups of enzymes that metabolize products of oxidative damage. Conclusions 1 Protection against oxidative stress seems to be the major driver of positive selection in mammalian cGSTs, explaining the overall expansion pattern of this subfamily; 2 Given the functional redundancy of GSTs that metabolize xenobiotic chemicals, we would expect the loss of gene duplicates, but by contrast we observed a gene expansion of this family, which likely has been favored by: i the diversification of endogenous substrates; ii differential tissue expression; and iii increased specificity for a particular molecule; 3 The increased availability of sequence data from diversified taxa is likely to continue to improve our understanding of the early origin of the different cGST classes.

  12. Intrinsic shapes of discy and boxy ellipticals

    International Nuclear Information System (INIS)

    Fasano, Giovanni

    1991-01-01

    Statistical tests for intrinsic shapes of elliptical galaxies have given so far inconclusive and sometimes contradictory results. These failures have been often charged to the fact that classical tests consider only the two axisymmetric shapes (oblate versus prolate), while ellipticals are truly triaxial bodies. On the other hand, recent analyses indicate that the class of elliptical galaxies could be a mixture of (at least) two families having different morphology and dynamical behaviour: (i) a family of fast-rotating, disc-like ellipticals (discy); (ii) a family of slow-rotating, box-shaped ellipticals (boxy). In this paper we review the tests for instrinsic shapes of elliptical galaxies using data of better quality (CCD) with respect to previous applications. (author)

  13. Angular ellipticity correlations in a composite alignment model for elliptical and spiral galaxies and inference from weak lensing

    Science.gov (United States)

    Tugendhat, Tim M.; Schäfer, Björn Malte

    2018-05-01

    We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak-lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between ℓ ≃ 40 and ℓ ≃ 400 before that of spiral galaxies dominates on higher multipoles. The predominant term on intermediate scales is the negative cross-correlation between intrinsic alignments and weak gravitational lensing (GI-alignment). We simulate parameter inference from weak gravitational lensing with intrinsic alignments unaccounted; the bias induced by ignoring intrinsic alignments in a survey like Euclid is shown to be several times larger than the statistical error and can lead to faulty conclusions when comparing to other observations. The biases generally point into different directions in parameter space, such that in some cases one can observe a partial cancellation effect. Furthermore, it is shown that the biases increase with the number of tomographic bins used for the parameter estimation process. We quantify this parameter estimation bias in units of the statistical error and compute the loss of Bayesian evidence for a model due to the presence of systematic errors as well as the Kullback-Leibler divergence to quantify the distance between the true model and the wrongly inferred one.

  14. Research on AutoCAD secondary development and function expansion based on VBA technology

    Science.gov (United States)

    Zhang, Runmei; Gu, Yehuan

    2017-06-01

    AutoCAD is the most widely used drawing tool among the similar design drawing products. In the process of drawing different types of design drawings of the same product, there are a lot of repetitive and single work contents. The traditional manual method uses a drawing software AutoCAD drawing graphics with low efficiency, high error rate and high input cost shortcomings and many more. In order to solve these problems, the design of the parametric drawing system of the hot-rolled I-beam (steel beam) cross-section is completed by using the VBA secondary development tool and the Access database software with large-capacity storage data, and the analysis of the functional extension of the plane drawing and the parametric drawing design in this paper. For the secondary development of AutoCAD functions, the system drawing work will be simplified and work efficiency also has been greatly improved. This introduction of parametric design of AutoCAD drawing system to promote the industrial mass production and related industries economic growth rate similar to the standard I-beam hot-rolled products.

  15. Interleukin 21 and its receptor are involved in NK cell expansion and regulation of lymphocyte function.

    Science.gov (United States)

    Parrish-Novak, J; Dillon, S R; Nelson, A; Hammond, A; Sprecher, C; Gross, J A; Johnston, J; Madden, K; Xu, W; West, J; Schrader, S; Burkhead, S; Heipel, M; Brandt, C; Kuijper, J L; Kramer, J; Conklin, D; Presnell, S R; Berry, J; Shiota, F; Bort, S; Hambly, K; Mudri, S; Clegg, C; Moore, M; Grant, F J; Lofton-Day, C; Gilbert, T; Rayond, F; Ching, A; Yao, L; Smith, D; Webster, P; Whitmore, T; Maurer, M; Kaushansky, K; Holly, R D; Foster, D

    2000-11-02

    Cytokines are important in the regulation of haematopoiesis and immune responses, and can influence lymphocyte development. Here we have identified a class I cytokine receptor that is selectively expressed in lymphoid tissues and is capable of signal transduction. The full-length receptor was expressed in BaF3 cells, which created a functional assay for ligand detection and cloning. Conditioned media from activated human CD3+ T cells supported proliferation of the assay cell line. We constructed a complementary DNA expression library from activated human CD3+ T cells, and identified a cytokine with a four-helix-bundle structure using functional cloning. This cytokine is most closely related to IL2 and IL15, and has been designated IL21 with the receptor designated IL21 R. In vitro assays suggest that IL21 has a role in the proliferation and maturation of natural killer (NK) cell populations from bone marrow, in the proliferation of mature B-cell populations co-stimulated with anti-CD40, and in the proliferation of T cells co-stimulated with anti-CD3.

  16. Overdetermined elliptic problems in topological disks

    Science.gov (United States)

    Mira, Pablo

    2018-06-01

    We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

  17. Flattening and radio emission among elliptical galaxies

    International Nuclear Information System (INIS)

    Disney, M.J.; Sparks, W.B.; Wall, J.V.

    1984-01-01

    In a sample of 132 bright elliptical galaxies it is shown that there is a strong correlation between radio activity and flattening in the sense that radio ellipticals are both apparently and inherently rounder than the average elliptical. Both extended and compact sources are subject to the same correlation. No galaxies with axial ratios below 0.65 are found to be radio emitters. (author)

  18. On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

    Science.gov (United States)

    Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

    2017-09-01

    The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

  19. Explanatory Factors of the Expansion of Recreation Function on the Bank of Danube River in Budapest

    Directory of Open Access Journals (Sweden)

    Pál Szabó

    2015-10-01

    Full Text Available In a city's development a river and riverbank played important role, however in recent decades the functions of them have changed, transformed, especially in major cities in the more developed countries, so the city administration was faced with a new phenomenon and geographical space: the changing riverbanks, and the utilization, development, revitalization of them has become a key issue. The various real processes showed the direction that these areas should be provided to the people, and the recreation service will be important for the local residents and tourists. Overall, the urban waterfront development is an increasingly important researched topic and policy. The question is: can we realize it in Budapest also nowadays? In recent years, those processes took place in Budapest, which resulted in an increasing utilization of the Danube and its banks for recreational functions. On the one hand, local social and economic processes have led to the waterfront sites released, on the other hand the needs of the residential population and tourists using the river and the riverside for recreational purposes have increased, and thirdly, the new city administration decided to renew the banks of the Danube, mainly to create new recreational areas. In this paper, we analyze these three factors, focusing on a past short period, because there is an exceptional cohesion between the processes, the needs and the new development goals. Two case studies are in the paper also: the Margaret Island as the oldest traditional recreational area in Budapest, and the Kopaszi-dam, as the newest and successful recreational area of Budapest. The analysis of the processes is based on data and literature, the analysis of the needs is based on a survey, and the analysis of the goals is based on the different development documents.

  20. Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2012-01-01

    Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

  1. Arbitrarily elliptical-cylindrical invisible cloaking

    International Nuclear Information System (INIS)

    Jiang Weixiang; Cui Tiejun; Yu Guanxia; Lin Xianqi; Cheng Qiang; Chin, J Y

    2008-01-01

    Based on the idea of coordinate transformation (Pendry, Schurig and Smith 2006 Science 312 1780), arbitrarily elliptical-cylindrical cloaks are proposed and designed. The elliptical cloak, which is composed of inhomogeneous anisotropic metamaterials in an elliptical-shell region, will deflect incoming electromagnetic (EM) waves and guide them to propagate around the inner elliptical region. Such EM waves will return to their original propagation directions without distorting the waves outside the elliptical cloak. General formulations of the inhomogeneous and anisotropic permittivity and permeability tensors are derived for arbitrarily elliptical axis ratio k, which can also be used for the circular cloak when k = 1. Hence the elliptical cloaks can make a large range of objects invisible, from round objects (when k approaches 1) to long and thin objects (when k is either very large or very small). We also show that the material parameters in elliptical cloaking are singular at only two points, instead of on the whole inner circle for circular cloaking, which are much easier to be realized in actual applications. Full-wave simulations are given to validate the arbitrarily elliptical cloaking

  2. Elliptic-symmetry vector optical fields.

    Science.gov (United States)

    Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian

    2014-08-11

    We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

  3. Doppler Velocity Signatures of Idealized Elliptical Vortices

    Directory of Open Access Journals (Sweden)

    Wen-Chau Lee

    2006-01-01

    Full Text Available Doppler radar observations have revealed a class of atmospheric vortices (tropical cyclones, tornadoes, dust devils that possess elliptical radar reflectivity signatures. One famous example is Typhoon Herb (1996 that maintained its elliptical reflectivity structure over a 40-hour period. Theoretical work and dual-Doppler analyses of observed tropical cyclones have suggested two physical mechanisms that can explain the formation of two types of elliptical vortices observed in nature, namely, the combination of a circular vortex with either a wavenumber two vortex Rossby wave or a deformation field. The characteristics of these two types of elliptical vortices and their corresponding Doppler velocity signatures have not been previously examined.

  4. Dark matter in elliptical galaxies

    Science.gov (United States)

    Carollo, C. M.; Zeeuw, P. T. DE; Marel, R. P. Van Der; Danziger, I. J.; Qian, E. E.

    1995-01-01

    We present measurements of the shape of the stellar line-of-sight velocity distribution out to two effective radii along the major axes of the four elliptical galaxies NGC 2434, 2663, 3706, and 5018. The velocity dispersion profiles are flat or decline gently with radius. We compare the data to the predictions of f = f(E, L(sub z)) axisymmetric models with and without dark matter. Strong tangential anisotropy is ruled out at large radii. We conclude from our measurements that massive dark halos must be present in three of the four galaxies, while for the fourth galaxy (NGC 2663) the case is inconclusive.

  5. Stellar Populations in Elliptical Galaxies

    Science.gov (United States)

    Angeletti, Lucio; Giannone, Pietro

    The R1/n law for the radial surface brightness of elliptical galaxies and the "Best Accretion Model" together with the "Concentration Model" have been combined in order to determine the mass and dynamical structure of largely-populated star systems. Families of models depending on four parameters have been used to fit the observed surface radial profiles of some spectro-photometric indices of a sample of eleven galaxies. We present the best agreements of the spectral index Mg2 with observations for three selected galaxies representative of the full sample. For them we have also computed the spatial distributions of the metal abundances, which are essential to achieve a population synthesis.

  6. MicroRNA-155 Modulates Acute Graft-versus-Host Disease by Impacting T Cell Expansion, Migration, and Effector Function.

    Science.gov (United States)

    Zitzer, Nina C; Snyder, Katiri; Meng, Xiamoei; Taylor, Patricia A; Efebera, Yvonne A; Devine, Steven M; Blazar, Bruce R; Garzon, Ramiro; Ranganathan, Parvathi

    2018-06-15

    MicroRNA-155 (miR-155) is a small noncoding RNA critical for the regulation of inflammation as well as innate and adaptive immune responses. MiR-155 has been shown to be dysregulated in both donor and recipient immune cells during acute graft-versus-host disease (aGVHD). We previously reported that miR-155 is upregulated in donor T cells of mice and humans with aGVHD and that mice receiving miR-155-deficient (miR155 -/- ) splenocytes had markedly reduced aGVHD. However, molecular mechanisms by which miR-155 modulates T cell function in aGVHD have not been fully investigated. We identify that miR-155 expression in both donor CD8 + T cells and conventional CD4 + CD25 - T cells is pivotal for aGVHD pathogenesis. Using murine aGVHD transplant experiments, we show that miR-155 strongly impacts alloreactive T cell expansion through multiple distinct mechanisms, modulating proliferation in CD8 + donor T cells and promoting exhaustion in donor CD4 + T cells in both the spleen and colon. Additionally, miR-155 drives a proinflammatory Th1 phenotype in donor T cells in these two sites, and miR-155 -/- donor T cells are polarized toward an IL-4-producing Th2 phenotype. We further demonstrate that miR-155 expression in donor T cells regulates CCR5 and CXCR4 chemokine-dependent migration. Notably, we show that miR-155 expression is crucial for donor T cell infiltration into multiple target organs. These findings provide further understanding of the role of miR-155 in modulating aGVHD through T cell expansion, effector cytokine production, and migration. Copyright © 2018 by The American Association of Immunologists, Inc.

  7. RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

    International Nuclear Information System (INIS)

    Hackbusch, W.

    1983-01-01

    1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

  8. Revisiting the Fourier expansion of Mie scattering matrices in generalized spherical functions

    International Nuclear Information System (INIS)

    Sanghavi, Suniti

    2014-01-01

    Mie computations of the scattering properties of large particles are a time consuming step in the radiative transfer modeling of aerosol and clouds. Currently, there exist two methods based on the use of spherical functions for computing the Fourier moments of the phase matrix of a given spherical particle or particulate polydispersion: The first, developed over the years before being presented in a convenient form by Siewert [31], required an intermediate computation of the phase matrix over which numerical integration was performed to deliver the required Fourier components. The second, suggested by Domke [9], promised a direct computation of the Fourier moments using Wigner 3-j symbols. While the former was relatively easy to implement and is thus the most commonly used to date, its numerical implementation using an arbitrary user choice of angular quadrature (NAI-1) can produce inaccurate results. Numerical integration using quadrature points as recommended by de Rooij and van der Stap [5] (NAI-2) delivers accurate results with high computational efficiency. Domke's method enables a direct computation of the exact number of required Fourier components. However, the original manuscript contained several misprints, many of which were subsequently corrected by de Rooij and van der Stap [5]. Unfortunately, the main recurrence relationship used in Domke [9] remained uncorrected. In this paper, the corrected relationship is presented along with other minor corrections. de Rooij and van der Stap [5] had found the straightforward application of Domke's method viable only for size parameters smaller than ∼120 due to issues involving computer storage. A means of implementing the corrected Domke formalism using precomputed tabulations of Wigner 3-j symbols (PCW) is presented here, making it more computationally economical and applicable over much broader particle size ranges. The accuracy of PCW is only limited by machine precision. For a single particle, NAI-2 is found

  9. Spanish juniper gain expansion opportunities by counting on a functionally diverse dispersal assemblage community.

    Science.gov (United States)

    Escribano-Ávila, Gema; Pías, Beatriz; Sanz-Pérez, Virginia; Virgós, Emilio; Escudero, Adrián; Valladares, Fernando

    2013-10-01

    Seed dispersal is typically performed by a diverse array of species assemblages with different behavioral and morphological traits which determine dispersal quality (DQ, defined as the probability of recruitment of a dispersed seed). Fate of ecosystems to ongoing environmental changes is critically dependent on dispersal and mainly on DQ in novel scenarios. We assess here the DQ, thus the multiplicative effect of germination and survival probability to the first 3 years of life, for seeds dispersed by several bird species (Turdus spp.) and carnivores (Vulpes vulpes, Martes foina) in mature woodland remnants of Spanish juniper (Juniperus thurifera) and old fields which are being colonized by this species. Results showed that DQ was similar in mature woodlands and old fields. Germination rate for seeds dispersed by carnivores (11.5%) and thrushes (9.12%) was similar, however, interacted with microhabitat suitability. Seeds dispersed by carnivores reach the maximum germination rate on shrubs (16%), whereas seeds dispersed by thrushes did on female juniper canopies (15.5) indicating that each group of dispersers performed a directed dispersal. This directional effect was diluted when survival probability was considered: thrushes selected smaller seeds which had higher mortality in the seedling stage (70%) in relation to seedlings dispersed by carnivores (40%). Overall, thrushes resulted low-quality dispersers which provided a probability or recruitment of 2.5%, while a seed dispersed by carnivores had a probability of recruitment of 6.5%. Our findings show that generalist dispersers (i.e., carnivores) can provide a higher probability of recruitment than specialized dispersers (i.e., Turdus spp.). However, generalist species are usually opportunistic dispersers as their role as seed dispersers is dependent on the availability of trophic resources and species feeding preferences. As a result, J. thurifera dispersal community is composed by two functional groups of

  10. Detection of Buried Inhomogeneous Elliptic Cylinders by a Memetic Algorithm

    OpenAIRE

    Caorsi, Salvatore; Massa, Andrea; Pastorino, Matteo; Raffetto, Mirco; Randazzo, Andrea

    2003-01-01

    The application of a global optimization procedure to the detection of buried inhomogeneities is studied in the present paper. The object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. An efficient recursive analytical procedure is used for the forward scattering computation. A functional is constructed in which the field is expressed in series solution of Mathieu functions. Starting by the input scattered data, the iterative minimiza...

  11. Structure and stellar content of dwarf elliptical galaxies

    International Nuclear Information System (INIS)

    Caldwell, N.

    1983-01-01

    A small number of low-luminosity elliptical galaxies in the Virgo cluster and around other prominent galaxies have been studied using photoelectric and photographic techniques. The color-magnitude relation for ellipticals now extends from M/sub v/ = -23 to -15, and is linear over that range with a slope of 0.10 in U-V per visual magnitude. Galaxies which are known to contain a large number of young stars (''extreme cases'') are from 0.10 to 0.20 mag bluer in U-V than the lower envelope of the dwarf elliptical color-magnitude relation. This difference can be accounted for if the dwarf elliptical galaxies are young, but do not contain the massive blue stars that probably exist in the young populations of the extreme cases. Surface brightness profiles of the dwarfs have revealed some interesting distinctions between themselves and the brighter E's. In general, their intensity profiles are shallower than those of the bright E's, meaning they are of lower mean density. These mean densities are also a function of the total luminosity. Unlike the bright E's, the surface brightnesses near the centers are also a strong function of the total luminosity. The presence of a nucleation, which can be as much as 2 mag brighter than what the outer envelope would predict, does not appear to depend on any other measurable property of the galaxies. The variation in surface brightness profiles at the same total luminosity is suggestive that the low-luminosity dwarfs formed in more than one way. The flattening distribution of the dwarfs is like that of the bright ellipticals, and is also similar to the flattening distribution of field irregular galaxies

  12. Elliptic nozzle aspect ratio effect on controlled jet propagation

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, S M Aravindh; Rathakrishnan, Ethirajan, E-mail: aravinds@iitk.ac.in, E-mail: erath@iitk.ac.in [Department of Aerospace Engineering, Indian Institute of Technology, Kanpur (India)

    2017-04-15

    The present study deals with the control of a Mach 2 elliptic jet from a convergent–divergent elliptic nozzle of aspect ratio 4 using tabs at the nozzle exit. The experiments were carried out for rectangular and triangular tabs of the same blockage, placed along the major and minor axes of the nozzle exit, at different levels of nozzle expansion. The triangular tabs along the minor axis promoted superior mixing compared to the other controlled jets and caused substantial core length reduction at all the nozzle pressure ratios studied. The rectangular tabs along the minor axis caused core length reduction at all pressure ratios, but the values were minimal compared to that of triangular tabs along the minor axis. For all the test conditions, the mixing promotion caused by tabs along the major axis was inferior to that of tabs along the minor axis. The waves present in the core of controlled jets were visualized using a shadowgraph. Comparison of the present results with the results of a controlled Mach 2 elliptic jet of aspect ratio 2 (Aravindh Kumar and Sathakrishnan 2016 J. Propulsion Power 32 121–33, Aravindh Kumar and Rathakrishnan 2016 J. Aerospace Eng. at press (doi:10.1177/0954410016652921)) show that for all levels of expansion, the mixing effectiveness of triangular tabs along the minor axis of an aspect ratio 4 nozzle is better than rectangular or triangular tabs along the minor axis of an aspect ratio 2 nozzle. (paper)

  13. Elliptic nozzle aspect ratio effect on controlled jet propagation

    International Nuclear Information System (INIS)

    Kumar, S M Aravindh; Rathakrishnan, Ethirajan

    2017-01-01

    The present study deals with the control of a Mach 2 elliptic jet from a convergent–divergent elliptic nozzle of aspect ratio 4 using tabs at the nozzle exit. The experiments were carried out for rectangular and triangular tabs of the same blockage, placed along the major and minor axes of the nozzle exit, at different levels of nozzle expansion. The triangular tabs along the minor axis promoted superior mixing compared to the other controlled jets and caused substantial core length reduction at all the nozzle pressure ratios studied. The rectangular tabs along the minor axis caused core length reduction at all pressure ratios, but the values were minimal compared to that of triangular tabs along the minor axis. For all the test conditions, the mixing promotion caused by tabs along the major axis was inferior to that of tabs along the minor axis. The waves present in the core of controlled jets were visualized using a shadowgraph. Comparison of the present results with the results of a controlled Mach 2 elliptic jet of aspect ratio 2 (Aravindh Kumar and Sathakrishnan 2016 J. Propulsion Power 32 121–33, Aravindh Kumar and Rathakrishnan 2016 J. Aerospace Eng. at press (doi:10.1177/0954410016652921)) show that for all levels of expansion, the mixing effectiveness of triangular tabs along the minor axis of an aspect ratio 4 nozzle is better than rectangular or triangular tabs along the minor axis of an aspect ratio 2 nozzle. (paper)

  14. Phylogenetic Analysis, Lineage-Specific Expansion and Functional Divergence of seed dormancy 4-Like Genes in Plants.

    Directory of Open Access Journals (Sweden)

    Saminathan Subburaj

    Full Text Available The rice gene seed dormancy 4 (OsSdr4 functions in seed dormancy and is a major factor associated with pre-harvest sprouting (PHS. Although previous studies of this protein family were reported for rice and other species, knowledge of the evolution of genes homologous to OsSdr4 in plants remains inadequate. Fifty four Sdr4-like (hereafter designated Sdr4L genes were identified in nine plant lineages including 36 species. Phylogenetic analysis placed these genes in eight subfamilies (I-VIII. Genes from the same lineage clustered together, supported by analysis of conserved motifs and exon-intron patterns. Segmental duplications were present in both dicot and monocot clusters, while tandemly duplicated genes occurred only in monocot clusters indicating that both tandem and segmental duplications contributed to expansion of the grass I and II subfamilies. Estimation of the approximate ages of the duplication events indicated that ancestral Sdr4 genes evolved from a common angiosperm ancestor, about 160 million years ago (MYA. Moreover, diversification of Sdr4L genes in mono and dicot plants was mainly associated with genome-wide duplication and speciation events. Functional divergence was observed in all subfamily pairs, except IV/VIIIa. Further analysis indicated that functional constraints between subfamily pairs I/II, I/VIIIb, II/VI, II/VIIIb, II/IV, and VI/VIIIb were statistically significant. Site and branch-site model analyses of positive selection suggested that these genes were under strong adaptive selection pressure. Critical amino acids detected for both functional divergence and positive selection were mostly located in the loops, pointing to functional importance of these regions in this protein family. In addition, differential expression studies by transcriptome atlas of 11 Sdr4L genes showed that the duplicated genes may have undergone divergence in expression between plant species. Our findings showed that Sdr4L genes are

  15. The Ising model: from elliptic curves to modular forms and Calabi-Yau equations

    International Nuclear Information System (INIS)

    Bostan, A; Boukraa, S; Hassani, S; Zenine, N; Van Hoeij, M; Maillard, J-M; Weil, J-A

    2011-01-01

    We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions of the susceptibility of the Ising model for n ≤ 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z 2 , F 2 , F 3 , L-tilde 3 can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-4 globally nilpotent linear differential operator is not reducible to this elliptic curve, modular form scheme. This operator is shown to actually correspond to a natural generalization of this elliptic curve, modular form scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected 4 F 3 hypergeometric function. This hypergeometric function can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back (square root extension), the corresponding Calabi-Yau fourth order differential operator having a symplectic differential Galois group SP(4,C). The mirror maps and higher order Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms, in particular an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2,Z) symmetry group.

  16. M-strings, Elliptic Genera and N=4 String Amplitudes

    CERN Document Server

    Hohenegger, Stefan

    2014-01-01

    We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of R^4 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T^2, which we calculate explicitly.

  17. Convex bodies with many elliptic sections

    OpenAIRE

    Arelio, Isaac; Montejano, Luis

    2014-01-01

    {We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

  18. Kinematically Decoupled Cores in Dwarf (Elliptical) Galaxies

    NARCIS (Netherlands)

    Toloba, E.; Peletier, R. F.; Guhathakurta, P.; van de Ven, G.; Boissier, S.; Boselli, A.; Brok, M. d.; Falcón-Barroso, J.; Hensler, G.; Janz, J.; Laurikainen, E.; Lisker, T.; Paudel, S.; Ryś, A.; Salo, H.

    An overview is given of what we know about the frequency of kinematically decoupled cores in dwarf elliptical galaxies. New observations show that kinematically decoupled cores happen just as often in dwarf elliptical as in ordinary early-type galaxies. This has important consequences for the

  19. Drinfeld currents of dynamical elliptic algebra

    International Nuclear Information System (INIS)

    Hou Boyu; Fan Heng; Yang Wenli; Cao Junpeng

    2000-01-01

    From the generalized Yang-Baxter relations RLL=LLR*, where R and R* are the dynamical R-matrix of A n-1 (1) type face model with the elliptic module shifted by the center of the algebra, using the Ding-Frenkel correspondence, the authors obtain the Drinfeld currents of dynamical elliptic algebra

  20. Effect of Strong Acid Functional Groups on Electrode Rise Potential in Capacitive Mixing by Double Layer Expansion

    KAUST Repository

    Hatzell, Marta C.; Raju, Muralikrishna; Watson, Valerie J.; Stack, Andrew G.; van Duin, Adri C. T.; Logan, Bruce E.

    2014-01-01

    © 2014 American Chemical Society. The amount of salinity-gradient energy that can be obtained through capacitive mixing based on double layer expansion depends on the extent the electric double layer (EDL) is altered in a low salt concentration (LC) electrolyte (e.g., river water). We show that the electrode-rise potential, which is a measure of the EDL perturbation process, was significantly (P = 10-5) correlated to the concentration of strong acid surface functional groups using five types of activated carbon. Electrodes with the lowest concentration of strong acids (0.05 mmol g-1) had a positive rise potential of 59 ± 4 mV in the LC solution, whereas the carbon with the highest concentration (0.36 mmol g-1) had a negative rise potential (-31 ± 5 mV). Chemical oxidation of a carbon (YP50) using nitric acid decreased the electrode rise potential from 46 ± 2 mV (unaltered) to -6 ± 0.5 mV (oxidized), producing a whole cell potential (53 ± 1.7 mV) that was 4.4 times larger than that obtained with identical electrode materials (from 12 ± 1 mV). Changes in the EDL were linked to the behavior of specific ions in a LC solution using molecular dynamics and metadynamics simulations. The EDL expanded in the LC solution when a carbon surface (pristine graphene) lacked strong acid functional groups, producing a positive-rise potential at the electrode. In contrast, the EDL was compressed for an oxidized surface (graphene oxide), producing a negative-rise electrode potential. These results established the linkage between rise potentials and specific surface functional groups (strong acids) and demonstrated on a molecular scale changes in the EDL using oxidized or pristine carbons.

  1. Effect of Strong Acid Functional Groups on Electrode Rise Potential in Capacitive Mixing by Double Layer Expansion

    KAUST Repository

    Hatzell, Marta C.

    2014-12-02

    © 2014 American Chemical Society. The amount of salinity-gradient energy that can be obtained through capacitive mixing based on double layer expansion depends on the extent the electric double layer (EDL) is altered in a low salt concentration (LC) electrolyte (e.g., river water). We show that the electrode-rise potential, which is a measure of the EDL perturbation process, was significantly (P = 10-5) correlated to the concentration of strong acid surface functional groups using five types of activated carbon. Electrodes with the lowest concentration of strong acids (0.05 mmol g-1) had a positive rise potential of 59 ± 4 mV in the LC solution, whereas the carbon with the highest concentration (0.36 mmol g-1) had a negative rise potential (-31 ± 5 mV). Chemical oxidation of a carbon (YP50) using nitric acid decreased the electrode rise potential from 46 ± 2 mV (unaltered) to -6 ± 0.5 mV (oxidized), producing a whole cell potential (53 ± 1.7 mV) that was 4.4 times larger than that obtained with identical electrode materials (from 12 ± 1 mV). Changes in the EDL were linked to the behavior of specific ions in a LC solution using molecular dynamics and metadynamics simulations. The EDL expanded in the LC solution when a carbon surface (pristine graphene) lacked strong acid functional groups, producing a positive-rise potential at the electrode. In contrast, the EDL was compressed for an oxidized surface (graphene oxide), producing a negative-rise electrode potential. These results established the linkage between rise potentials and specific surface functional groups (strong acids) and demonstrated on a molecular scale changes in the EDL using oxidized or pristine carbons.

  2. Multicolor surface photometry of 17 ellipticals

    International Nuclear Information System (INIS)

    Franx, M.; Illingworth, G.; Heckman, T.

    1989-01-01

    Multicolor two-dimensional surface photometry was used to obtain radial profiles for surface brightness, color, ellipticity, position angle, and the residuals from the fitted ellipses described by the cos(n phi) and sin(n phi) terms (where n = 3 and 4) for 17 elliptical galaxies. It is found that at radii as large as five times the seeing FWHM, seeing can affect the ellipticity at the 10 percent level and introduce uncertainty in the position angles of several degrees, particularly for very round ellipticals. The present profiles are found to agree well with previous data, with rms differences of 0.02 in ellipticity and 2 deg in position angle. The observed color gradients are consistent with a decrease in the metallicity by a factor of about 2 per decade in radius. 61 refs

  3. Beam energy dependence of elliptic flow in heavy-ion collision

    International Nuclear Information System (INIS)

    Otuka, Naohiko; Isse, Masatsugu; Ohnishi, Akira; Pradip Kumar Sahu; Nara, Yasushi

    2002-01-01

    We study radial flow and elliptic flow in relativistic heavy-ion collisions at energies from GSI-SIS to BNL-RHIC energies using hadronic cascade model JAM. The excitation function of radial flow shows the softening of hadronic matter from BNL-AGS to CERN-SPS energies. JAM model reproduces transverse mass spectra at BNL-AGS, CERN-SPS at BNL-RHIC energies as well as elliptic flow upto CERN-SPS. For elliptic flow at BNL-RHIC energy (√s=130 GeV), while JAM gives the enough flow at fragment region, it fails at mid rapidity. (author)

  4. Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Kolb, Peter F.; Heinz, Ulrich; Huovinen, Pasi; Eskola, Kari J.; Tuominen, Kimmo

    2001-03-21

    The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p{sub T}-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p{sub T}-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initialization.

  5. Clonal expansion of genome-intact HIV-1 in functionally polarized Th1 CD4+ T cells.

    Science.gov (United States)

    Lee, Guinevere Q; Orlova-Fink, Nina; Einkauf, Kevin; Chowdhury, Fatema Z; Sun, Xiaoming; Harrington, Sean; Kuo, Hsiao-Hsuan; Hua, Stephane; Chen, Hsiao-Rong; Ouyang, Zhengyu; Reddy, Kavidha; Dong, Krista; Ndung'u, Thumbi; Walker, Bruce D; Rosenberg, Eric S; Yu, Xu G; Lichterfeld, Mathias

    2017-06-30

    HIV-1 causes a chronic, incurable disease due to its persistence in CD4+ T cells that contain replication-competent provirus, but exhibit little or no active viral gene expression and effectively resist combination antiretroviral therapy (cART). These latently infected T cells represent an extremely small proportion of all circulating CD4+ T cells but possess a remarkable long-term stability and typically persist throughout life, for reasons that are not fully understood. Here we performed massive single-genome, near-full-length next-generation sequencing of HIV-1 DNA derived from unfractionated peripheral blood mononuclear cells, ex vivo-isolated CD4+ T cells, and subsets of functionally polarized memory CD4+ T cells. This approach identified multiple sets of independent, near-full-length proviral sequences from cART-treated individuals that were completely identical, consistent with clonal expansion of CD4+ T cells harboring intact HIV-1. Intact, near-full-genome HIV-1 DNA sequences that were derived from such clonally expanded CD4+ T cells constituted 62% of all analyzed genome-intact sequences in memory CD4 T cells, were preferentially observed in Th1-polarized cells, were longitudinally detected over a duration of up to 5 years, and were fully replication- and infection-competent. Together, these data suggest that clonal proliferation of Th1-polarized CD4+ T cells encoding for intact HIV-1 represents a driving force for stabilizing the pool of latently infected CD4+ T cells.

  6. Seiberg-Witten curves and double-elliptic integrable systems

    International Nuclear Information System (INIS)

    Aminov, G.; Braden, H.W.; Mironov, A.; Morozov, A.; Zotov, A.

    2015-01-01

    An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.

  7. Fuel Thermal Expansion (FTHEXP)

    International Nuclear Information System (INIS)

    Reymann, G.A.

    1978-07-01

    A model is presented which deals with dimensional changes in LWR fuel pellets caused by changes in temperature. It is capable of dealing with any combination of UO 2 and PuO 2 in solid, liquid or mixed phase states, and includes expansion due to the solid-liquid phase change. The function FTHEXP models fuel thermal expansion as a function of temperature, fraction of PuO 2 , and the fraction of fuel which is molten

  8. Thermal expansion

    International Nuclear Information System (INIS)

    Yun, Y.

    2015-01-01

    Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)

  9. Domain decomposition method for solving elliptic problems in unbounded domains

    International Nuclear Information System (INIS)

    Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1991-01-01

    Computational aspects of the box domain decomposition (DD) method for solving boundary value problems in an unbounded domain are discussed. A new variant of the DD-method for elliptic problems in unbounded domains is suggested. It is based on the partitioning of an unbounded domain adapted to the given asymptotic decay of an unknown function at infinity. The comparison of computational expenditures is given for boundary integral method and the suggested DD-algorithm. 29 refs.; 2 figs.; 2 tabs

  10. The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group

    International Nuclear Information System (INIS)

    Keitel, Jan; Bartosch, Lorenz

    2012-01-01

    We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)

  11. Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of the S U (Nc) conformal anomaly and studies of the conformal symmetry limit

    Science.gov (United States)

    Cvetič, Gorazd; Kataev, A. L.

    2016-07-01

    We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.

  12. Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

    International Nuclear Information System (INIS)

    Mitri, F. G.

    2015-01-01

    The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries

  13. Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

    Science.gov (United States)

    Mitri, F. G.

    2015-12-01

    The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

  14. Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

    Energy Technology Data Exchange (ETDEWEB)

    Mitri, F. G., E-mail: F.G.Mitri@ieee.org [Chevron, Area 52 Technology–ETC, Santa Fe, New Mexico 87508 (United States)

    2015-12-07

    The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

  15. Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

    Science.gov (United States)

    Cho, Yumi

    2018-05-01

    We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

  16. International Workshop on Elliptic and Parabolic Equations

    CERN Document Server

    Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

    2015-01-01

    This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

  17. Structure and Formation of Elliptical and Spheroidal Galaxies

    Science.gov (United States)

    Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf

    2009-05-01

    New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sérsic log I vprop r 1/n functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes MVT 4 uncorrelated with MVT . They also are α-element enhanced, implying short star-formation timescales. And their stellar populations have a variety of ages but mostly are very old. Extra light ellipticals generally rotate rapidly, are more isotropic than core Es, and have disky isophotes. We show that they have n sime 3 ± 1 almost uncorrelated with MVT and younger and less α-enhanced stellar populations. These are new clues to galaxy formation. We suggest that extra light ellipticals got their low Sérsic indices by forming in relatively few binary mergers, whereas giant ellipticals have n > 4 because they formed in larger numbers of mergers of more galaxies at once plus later heating during hierarchical clustering. We confirm that core Es contain X-ray-emitting gas whereas extra light Es generally do not. This leads us to suggest why the E-E dichotomy arose. If energy feedback from active galactic nuclei (AGNs) requires a "working surface" of hot gas, then this is present in core galaxies but absent in extra light galaxies. We suggest that AGN energy feedback is a strong function of galaxy mass: it is weak enough in small Es not to prevent merger starbursts but strong enough in giant Es and their progenitors to make dry mergers dry and to protect old stellar populations from late star formation. Finally, we verify that there is a strong

  18. Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    Lee, Joo Hee

    2006-02-01

    There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

  19. Cys-X scanning for expansion of active-site residues and modulation of catalytic functions in a glutathione transferase.

    Science.gov (United States)

    Norrgård, Malena A; Hellman, Ulf; Mannervik, Bengt

    2011-05-13

    We propose Cys-X scanning as a semisynthetic approach to engineer the functional properties of recombinant proteins. As in the case of Ala scanning, key residues in the primary structure are identified, and one of them is replaced by Cys via site-directed mutagenesis. The thiol of the residue introduced is subsequently modified by alternative chemical reagents to yield diverse Cys-X mutants of the protein. This chemical approach is orthogonal to Ala or Cys scanning and allows the expansion of the repertoire of amino acid side chains far beyond those present in natural proteins. In its present application, we have introduced Cys-X residues in human glutathione transferase (GST) M2-2, replacing Met-212 in the substrate-binding site. To achieve selectivity of the modifications, the Cys residues in the wild-type enzyme were replaced by Ala. A suite of simple substitutions resulted in a set of homologous Met derivatives ranging from normethionine to S-heptyl-cysteine. The chemical modifications were validated by HPLC and mass spectrometry. The derivatized mutant enzymes were assayed with alternative GST substrates representing diverse chemical reactions: aromatic substitution, epoxide opening, transnitrosylation, and addition to an ortho-quinone. The Cys substitutions had different effects on the alternative substrates and differentially enhanced or suppressed catalytic activities depending on both the Cys-X substitution and the substrate assayed. As a consequence, the enzyme specificity profile could be changed among the alternative substrates. The procedure lends itself to large-scale production of Cys-X modified protein variants.

  20. The Expansion and Functional Diversification of the Mammalian Ribonuclease A Superfamily Epitomizes the Efficiency of Multigene Families at Generating Biological Novelty

    Science.gov (United States)

    Goo, Stephen M.; Cho, Soochin

    2013-01-01

    The ribonuclease (RNase) A superfamily is a vertebrate-specific gene family. Because of a massive expansion that occurred during the early mammalian evolution, extant mammals in general have much more RNase genes than nonmammalian vertebrates. Mammalian RNases have been associated with diverse physiological functions including digestion, cytotoxicity, angiogenesis, male reproduction, and host defense. However, it is still uncertain when their expansion occurred and how a wide array of functions arose during their evolution. To answer these questions, we generate a compendium of all RNase genes identified in 20 complete mammalian genomes including the platypus, Ornithorhynchus anatinus. Using this, we delineate 13 ancient RNase gene lineages that arose before the divergence between the monotreme and the other mammals (∼220 Ma). These 13 ancient gene lineages are differentially retained in the 20 mammals, and the rate of protein sequence evolution is highly variable among them, which suggest that they have undergone extensive functional diversification. In addition, we identify 22 episodes of recent expansion of RNase genes, many of which have signatures of adaptive functional differentiation. Exemplifying this, bursts of gene duplication occurred for the RNase1, RNase4, and RNase5 genes of the little brown bat (Myotis lucifugus), which might have contributed to the species’ effective defense against heavier pathogen loads caused by its communal roosting behavior. Our study illustrates how host-defense systems can generate new functions efficiently by employing a multigene family, which is crucial for a host organism to adapt to its ever-changing pathogen environment. PMID:24162010

  1. Fully plastic solutions of semi-elliptical surface cracks

    International Nuclear Information System (INIS)

    Yagawa, Genki; Yoshimura, Shinobu; Kitajima, Yasumi; Ueda, Hiroyoshi.

    1990-01-01

    Nonlinear finite element analyses of semi-elliptical surface cracks are performed under the fully plastic condition. The power-law hardening materials and the deformation theory of plasticity are assumed. Either the penalty function method or the Uzawa's algorithm is utilized to treat the incompressibility of plastic strains. The local and global J-integral values are obtained using a virtual crack extension technique for plates and cylinders with semi-elliptical surface cracks subjected to uniform tensions. The fully plastic solutions for surface cracked plates are given in the form of polynominals with geometric parameters a/t, a/c and the strain hardening exponent (n). In addition, the effects of curvature on fully plastic solutions are discussed through the comparison between the results of plates and cylinders. (author)

  2. Pressure algorithm for elliptic flow calculations with the PDF method

    Science.gov (United States)

    Anand, M. S.; Pope, S. B.; Mongia, H. C.

    1991-01-01

    An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.

  3. Partial differential operators of elliptic type

    CERN Document Server

    Shimakura, Norio

    1992-01-01

    This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

  4. Exact solution and thermodynamics of a spin chain with long-range elliptic interactions

    International Nuclear Information System (INIS)

    Finkel, Federico; González-López, Artemio

    2014-01-01

    We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane–Shastry chain. (paper)

  5. Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

    International Nuclear Information System (INIS)

    Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

    2014-01-01

    We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

  6. Constructing elliptic curves from Galois representations

    OpenAIRE

    Snowden, Andrew; Tsimerman, Jacob

    2017-01-01

    Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse $\\ell$-adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforward properties: cyclotomic determinant, finite ramification, rational traces of Frobenius, and somewhere not potentially good reduction. We prove that any lisse sheaf of rank two possessing these properties comes from an elliptic curve.

  7. Elliptic and parabolic equations for measures

    Energy Technology Data Exchange (ETDEWEB)

    Bogachev, Vladimir I [M. V. Lomonosov Moscow State University, Moscow (Russian Federation); Krylov, Nikolai V [University of Minnesota, Minneapolis, MN (United States); Roeckner, Michael [Universitat Bielefeld, Bielefeld (Germany)

    2009-12-31

    This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L{sup p}-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.

  8. A transmission line model for propagation in elliptical core optical fibers

    Science.gov (United States)

    Georgantzos, E.; Papageorgiou, C.; Boucouvalas, A. C.

    2015-12-01

    The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell's equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.

  9. A transmission line model for propagation in elliptical core optical fibers

    International Nuclear Information System (INIS)

    Georgantzos, E.; Boucouvalas, A. C.; Papageorgiou, C.

    2015-01-01

    The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method

  10. Classical and quantum dynamics of driven elliptical billiards

    Energy Technology Data Exchange (ETDEWEB)

    Lenz, Florian

    2009-12-09

    Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

  11. Classical and quantum dynamics of driven elliptical billiards

    International Nuclear Information System (INIS)

    Lenz, Florian

    2009-01-01

    Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

  12. On the Equisummability of Hermite and Fourier Expansions

    Indian Academy of Sciences (India)

    We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.

  13. Fabrication of elliptical SRF cavities

    Science.gov (United States)

    Singer, W.

    2017-03-01

    The technological and metallurgical requirements of material for high-gradient superconducting cavities are described. High-purity niobium, as the preferred metal for the fabrication of superconducting accelerating cavities, should meet exact specifications. The content of interstitial impurities such as oxygen, nitrogen, and carbon must be below 10 μg g-1. The hydrogen content should be kept below 2 μg g-1 to prevent degradation of the quality factor (Q-value) under certain cool-down conditions. The material should be free of flaws (foreign material inclusions or cracks and laminations) that can initiate a thermal breakdown. Traditional and alternative cavity mechanical fabrication methods are reviewed. Conventionally, niobium cavities are fabricated from sheet niobium by the formation of half-cells by deep drawing, followed by trim machining and electron beam welding. The welding of half-cells is a delicate procedure, requiring intermediate cleaning steps and a careful choice of weld parameters to achieve full penetration of the joints. A challenge for a welded construction is the tight mechanical and electrical tolerances. These can be maintained by a combination of mechanical and radio-frequency measurements on half-cells and by careful tracking of weld shrinkage. The main aspects of quality assurance and quality management are mentioned. The experiences of 800 cavities produced for the European XFEL are presented. Another cavity fabrication approach is slicing discs from the ingot and producing cavities by deep drawing and electron beam welding. Accelerating gradients at the level of 35-45 MV m-1 can be achieved by applying electrochemical polishing treatment. The single-crystal option (grain boundary free) is discussed. It seems that in this case, high performance can be achieved by a simplified treatment procedure. Fabrication of the elliptical resonators from a seamless pipe as an alternative is briefly described. This technology has yielded good

  14. Effect of an anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions

    Science.gov (United States)

    Jaiswal, Amaresh; Bhaduri, Partha Pratim

    2018-04-01

    We study the effect of an anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions. We use the Glauber model to generate initial conditions and ignore hydrodynamic expansion in the transverse direction. We employ the Beer-Lambert law to allow for the transmittance of produced hadrons in the medium and calculate the anisotropy generated due to the suppression of particles traversing through the medium. To separate non-flow contribution due to surface bias effects, we ignore hydrodynamic expansion in the transverse direction and consider purely longitudinal boost-invariant expansion. We calculate the transverse momentum dependence of elliptic flow, generated from an anisotropic escape mechanism due to surface bias effects, for various centralities in √{sN N}=200 GeV Au +Au collisions at the Relativistic Heavy Ion Collider and √{sN N}=2.76 TeV Pb +Pb collisions at the Large Hadron Collider. We find that the surface bias effects make a sizable contribution to the total elliptic flow observed in heavy-ion collisions, indicating that the viscosity of the QCD matter extracted from hydrodynamic simulations may be underestimated.

  15. Lace expansion for dummies

    NARCIS (Netherlands)

    Bolthausen, Erwin; Van Der Hofstad, Remco; Kozma, Gady

    2018-01-01

    We show Green's function asymptotic upper bound for the two-point function of weakly self-Avoiding walk in d >4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier

  16. Sensitivity of Rayleigh wave ellipticity and implications for surface wave inversion

    Science.gov (United States)

    Cercato, Michele

    2018-04-01

    The use of Rayleigh wave ellipticity has gained increasing popularity in recent years for investigating earth structures, especially for near-surface soil characterization. In spite of its widespread application, the sensitivity of the ellipticity function to the soil structure has been rarely explored in a comprehensive and systematic manner. To this end, a new analytical method is presented for computing the sensitivity of Rayleigh wave ellipticity with respect to the structural parameters of a layered elastic half-space. This method takes advantage of the minor decomposition of the surface wave eigenproblem and is numerically stable at high frequency. This numerical procedure allowed to retrieve the sensitivity for typical near surface and crustal geological scenarios, pointing out the key parameters for ellipticity interpretation under different circumstances. On this basis, a thorough analysis is performed to assess how ellipticity data can efficiently complement surface wave dispersion information in a joint inversion algorithm. The results of synthetic and real-world examples are illustrated to analyse quantitatively the diagnostic potential of the ellipticity data with respect to the soil structure, focusing on the possible sources of misinterpretation in data inversion.

  17. Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

    KAUST Repository

    Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.

    2015-01-01

    We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some

  18. Surfaces immersed in Lie algebras associated with elliptic integrals

    International Nuclear Information System (INIS)

    Grundland, A M; Post, S

    2012-01-01

    The objective of this work is to adapt the Fokas–Gel’fand immersion formula to ordinary differential equations written in the Lax representation. The formalism of generalized vector fields and their prolongation structure is employed to establish necessary and sufficient conditions for the existence and integration of immersion functions for surfaces in Lie algebras. As an example, a class of second-order, integrable, ordinary differential equations is considered and the most general solutions for the wavefunctions of the linear spectral problem are found. Several explicit examples of surfaces associated with Jacobian and P-Weierstrass elliptic functions are presented. (paper)

  19. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Radu, C.S.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Van Hoeij, M.; Imamoglu, E. [Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics; Raab, C.G. [Linz Univ. (Austria). Inst. for Algebra

    2017-05-15

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as {sub 2}F{sub 1} Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ{sub i} functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η{sup κ}(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  20. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    International Nuclear Information System (INIS)

    Ablinger, J.; Radu, C.S.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Van Hoeij, M.; Imamoglu, E.; Raab, C.G.

    2017-05-01

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as _2F_1 Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ_i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η"κ(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  1. Expansion and functional properties of extruded snacks enriched with nutrition sources from food processing by-products.

    Science.gov (United States)

    Korkerd, Sopida; Wanlapa, Sorada; Puttanlek, Chureerat; Uttapap, Dudsadee; Rungsardthong, Vilai

    2016-01-01

    Rich sources of protein and dietary fiber from food processing by-products, defatted soybean meal, germinated brown rice meal, and mango peel fiber, were added to corn grit at 20 % (w/w) to produce fortified extruded snacks. Increase of total dietary fiber from 4.82 % (wb) to 5.92-17.80 % (wb) and protein from 5.03 % (wb) to 5.46-13.34 % were observed. The product indicated high expansion and good acceptance tested by sensory panels. There were 22.33-33.53 and 5.30-11.53 fold increase in the phenolics and antioxidant activity in the enriched snack products. The effects of feed moisture content, screw speed, and barrel temperature on expansion and nutritional properties of the extruded products were investigated by using response surface methodology. Regression equations describing the effect of each variable on the product responses were obtained. The snacks extruded with feed moisture 13-15 % (wb) and extrusion temperature at 160-180 °C indicated the products with high preference in terms of expansion ratio between insoluble dietary fiber and soluble dietary fiber balance. The results showed that the by-products could be successfully used for nutritional supplemented expanded snacks.

  2. Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Padé approximant

    Science.gov (United States)

    Sergeev, A.; Alharbi, F. H.; Jovanovic, R.; Kais, S.

    2016-04-01

    The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke’s law model for two-electron atoms.

  3. Expansion dynamics

    International Nuclear Information System (INIS)

    Knoll, J.

    1985-10-01

    A quantum dynamical model is suggested which describes the expansion and disassembly phase of highly excited compounds formed in energetic heavy-ion collisions. First applications in two space and one time dimensional model world are discussed and qualitatively compared to standard freeze-out concepts. (orig.)

  4. expansion method

    Indian Academy of Sciences (India)

    of a system under investigation is to model the system in terms of some ... The organization of the paper is as follows: In §2, a brief account of the (G /G)- expansion ...... It is interesting to note that from the general results, one can easily recover.

  5. Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?

    Science.gov (United States)

    Genzel, R.; Tacconi, L. J.; Rigopoulou, D.; Lutz, D.; Tecza, M.

    2001-12-01

    We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~0.5" resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are ``ellipticals in formation.'' Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrotsini/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history. Based on observations at the European Southern Observatory, Chile (ESO 65.N-0266, 65.N-0289), and on observations at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, The University of California, and the National Aeronautics and Space Administration. The Keck Observatory was made possible by the general financial support by the W. M. Keck Foundation.

  6. Hot interstellar matter in elliptical galaxies

    CERN Document Server

    Kim, Dong-Woo

    2012-01-01

    Based on a number of new discoveries resulting from 10 years of Chandra and XMM-Newton observations and corresponding theoretical works, this is the first book to address significant progress in the research of the Hot Interstellar Matter in Elliptical Galaxies. A fundamental understanding of the physical properties of the hot ISM in elliptical galaxies is critical, because they are directly related to the formation and evolution of elliptical galaxies via star formation episodes, environmental effects such as stripping, infall, and mergers, and the growth of super-massive black holes. Thanks to the outstanding spatial resolution of Chandra and the large collecting area of XMM-Newton, various fine structures of the hot gas have been imaged in detail and key physical quantities have been accurately measured, allowing theoretical interpretations/predictions to be compared and tested against observational results. This book will bring all readers up-to-date on this essential field of research.

  7. Nonlinear elliptic equations of the second order

    CERN Document Server

    Han, Qing

    2016-01-01

    Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

  8. Elliptical cross section fuel rod study II

    International Nuclear Information System (INIS)

    Taboada, H.; Marajofsky, A.

    1996-01-01

    In this paper it is continued the behavior analysis and comparison between cylindrical fuel rods of circular and elliptical cross sections. Taking into account the accepted models in the literature, the fission gas swelling and release were studied. An analytical comparison between both kinds of rod reveals a sensible gas release reduction in the elliptical case, a 50% swelling reduction due to intragranular bubble coalescence mechanism and an important swelling increase due to migration bubble mechanism. From the safety operation point of view, for the same linear power, an elliptical cross section rod is favored by lower central temperatures, lower gas release rates, greater gas store in ceramic matrix and lower stored energy rates. (author). 6 refs., 8 figs., 1 tab

  9. Expansion and functional properties of extruded snacks enriched with nutrition sources from food processing by-products

    OpenAIRE

    Korkerd, Sopida; Wanlapa, Sorada; Puttanlek, Chureerat; Uttapap, Dudsadee; Rungsardthong, Vilai

    2015-01-01

    Rich sources of protein and dietary fiber from food processing by-products, defatted soybean meal, germinated brown rice meal, and mango peel fiber, were added to corn grit at 20 % (w/w) to produce fortified extruded snacks. Increase of total dietary fiber from 4.82 % (wb) to 5.92–17.80 % (wb) and protein from 5.03 % (wb) to 5.46–13.34 % were observed. The product indicated high expansion and good acceptance tested by sensory panels. There were 22.33–33.53 and 5.30–11.53 fold increase in the ...

  10. Electromagnetic Invisibility of Elliptic Cylinder Cloaks

    International Nuclear Information System (INIS)

    Kan, Yao; Chao, Li; Fang, Li

    2008-01-01

    Structures with unique electromagnetic properties are designed based on the approach of spatial coordinate transformations of Maxwell's equations. This approach is applied to scheme out invisible elliptic cylinder cloaks, which provide more feasibility for cloaking arbitrarily shaped objects. The transformation expressions for the anisotropic material parameters and the field distribution are derived. The cloaking performances of ideal and lossy elliptic cylinder cloaks are investigated by finite element simulations. It is found that the cloaking performance will degrade in the forward direction with increasing loss. (fundamental areas of phenomenology (including applications))

  11. Quantum W-algebras and elliptic algebras

    International Nuclear Information System (INIS)

    Feigin, B.; Kyoto Univ.; Frenkel, E.

    1996-01-01

    We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

  12. Elliptic Tales Curves, Counting, and Number Theory

    CERN Document Server

    Ash, Avner

    2012-01-01

    Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from

  13. Abundance ratios in dwarf elliptical galaxies

    Science.gov (United States)

    Şen, Ş.; Peletier, R. F.; Boselli, A.; den Brok, M.; Falcón-Barroso, J.; Hensler, G.; Janz, J.; Laurikainen, E.; Lisker, T.; Mentz, J. J.; Paudel, S.; Salo, H.; Sybilska, A.; Toloba, E.; van de Ven, G.; Vazdekis, A.; Yesilyaprak, C.

    2018-04-01

    We determine abundance ratios of 37 dwarf ellipticals (dEs) in the nearby Virgo cluster. This sample is representative of the early-type population of galaxies in the absolute magnitude range -19.0 originate from late-type dwarfs or small spirals. Na-yields appear to be very metal-dependent, in agreement with studies of giant ellipticals, probably due to the large dependence on the neutron-excess in stars. We conclude that dEs have undergone a considerable amount of chemical evolution, they are therefore not uniformly old, but have extended SFH, similar to many of the Local Group galaxies.

  14. The history of the Universe is an elliptic curve

    Science.gov (United States)

    Coquereaux, Robert

    2015-06-01

    Friedmann-Lemaître equations with contributions coming from matter, curvature, cosmological constant, and radiation, when written in terms of conformal time u rather than in terms of cosmic time t, can be solved explicitly in terms of standard Weierstrass elliptic functions. The spatial scale factor, the temperature, the densities, the Hubble function, and almost all quantities of cosmological interest (with the exception of t itself) are elliptic functions of u, in particular they are bi-periodic with respect to a lattice of the complex plane, when one takes u complex. After recalling the basics of the theory, we use these explicit expressions, as well as the experimental constraints on the present values of density parameters (we choose for the curvature density a small value in agreement with experimental bounds) to display the evolution of the main cosmological quantities for one real period 2{{ω }r} of conformal time (the cosmic time t ‘never ends’ but it goes to infinity for a finite value {{u}f}\\lt 2{{ω }r} of u). A given history of the Universe, specified by the measured values of present-day densities, is associated with a lattice in the complex plane, or with an elliptic curve, and therefore with two Weierstrass invariants {{g}2},{{g}3}. Using the same experimental data we calculate the values of these invariants, as well as the associated modular parameter and the corresponding Klein j-invariant. If one takes the flat case k = 0, the lattice is only defined up to homotheties, and if one, moreover, neglects the radiation contribution, the j-invariant vanishes and the corresponding modular parameter τ can be chosen in one corner of the standard fundamental domain of the modular group (equihanharmonic case: τ =exp (2iπ /3)). Several exact—i.e., non-numerical—results of independent interest are obtained in that case.

  15. Resonant state expansions

    International Nuclear Information System (INIS)

    Lind, P.

    1993-02-01

    The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.)

  16. Transverse magnetic scattering by parallel conducting elliptic cylinders

    Science.gov (United States)

    Sebak, A.

    1991-10-01

    A boundary value solution to the problem of transverse magnetic multiple scattering by M parallel perfectly conducting elliptic cylinders is presented. The solution is an exact one and based on the separation-of-variables technique and the addition theorem for Mathieu functions. It is expressed in terms of a system of simultaneous linear equations of infinite order, which is then truncated for numerical computations. Representative numerical results for the scattered field by two cylinders are then generated, for some selected sizes and orientations parameters, and presented.

  17. Index profile measurement of asymmetrical elliptical preforms or fibers

    NARCIS (Netherlands)

    Blitterswijk, van W.; Smit, M.K.

    1987-01-01

    An extension of the beam-deflection method to the case of elliptical preforms with eccentric core (asymmetrical elliptical preforms) is presented, which can be easily implemented on automatic measurement equipment

  18. Mantle cloaks for elliptical cylinders excited by an electric line source

    DEFF Research Database (Denmark)

    Kaminski, Piotr Marek; Yakovlev, Alexander B.; Arslanagic, Samel

    2016-01-01

    We investigate the ability of surface impedance mantle cloaks for cloaking of elliptical cylinders excited by an electric line source. The exact analytical solution of the problem utilizing Mathieu functions is obtained and is used to derive optimal surface impedances to cloak a number of configu......We investigate the ability of surface impedance mantle cloaks for cloaking of elliptical cylinders excited by an electric line source. The exact analytical solution of the problem utilizing Mathieu functions is obtained and is used to derive optimal surface impedances to cloak a number...

  19. Elliptic genus of singular algebraic varieties and quotients

    Science.gov (United States)

    Libgober, Anatoly

    2018-02-01

    This paper discusses the basic properties of various versions of the two-variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the theories regarding the elliptic genera of phases on N  =  2 introduced in Witten (1993 Nucl. Phys. B 403 159-222).

  20. Development of a neutronics code based on analytic function expansion nodal method for pebble-type High Temperature Gas-cooled Reactor design

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo [Korea Advanced Institute of Science and Tehcnology, Daejeon (Korea, Republic of)

    2006-03-15

    There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis.

  1. Development of a neutronics code based on analytic function expansion nodal method for pebble-type High Temperature Gas-cooled Reactor design

    International Nuclear Information System (INIS)

    Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo

    2006-03-01

    There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis

  2. Impedances in lossy elliptical vacuum chambers

    International Nuclear Information System (INIS)

    Piwinski, A.

    1994-04-01

    The wake fields of a bunched beam caused by the resistivity of the chamber walls are investigated for a vacuum chamber with elliptical cross section. The longitudinal and transverse impedances are calculated for arbitrary energies and for an arbitrary position of the beam in the chamber. (orig.)

  3. Carleman estimates for some elliptic systems

    International Nuclear Information System (INIS)

    Eller, M

    2008-01-01

    A Carleman estimate for a certain first order elliptic system is proved. The proof is elementary and does not rely on pseudo-differential calculus. This estimate is used to prove Carleman estimates for the isotropic Lame system as well as for the isotropic Maxwell system with C 1 coefficients

  4. Spatial scan statistics using elliptic windows

    DEFF Research Database (Denmark)

    Christiansen, Lasse Engbo; Andersen, Jens Strodl; Wegener, Henrik Caspar

    2006-01-01

    The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in SatScan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic...

  5. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  6. Vortex precession in thin elliptical ferromagnetic nanodisks

    Energy Technology Data Exchange (ETDEWEB)

    Zaspel, C.E., E-mail: craig.zaspel@umwestern.edu

    2017-07-01

    Highlights: • A general form for the magnetostatic energy is calculated for the vortex state in a ferromagnetic ellipse. • The ellipse magnetostatic energy is minimized by conformal mapping the circular disk onto the ellipse. • The gyrotropic precession frequency is obtained in general for a range of ellipticities. - Abstract: The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk. It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.

  7. Abundance Ratios in Dwarf Elliptical Galaxies

    NARCIS (Netherlands)

    Sen, Seyda; Peletier, Reynier F.; Toloba, Elisa; Mentz, Jaco J.

    The aim of this study is to determine abundance ratios and star formation histories (SFH) of dwarf ellipticals in the nearby Virgo cluster. We perform a stellar population analysis of 39 dEs and study them using index-index and scaling relations. We find an unusual behaviour where [Na/Fe] is

  8. Elastic plastic buckling of elliptical vessel heads

    International Nuclear Information System (INIS)

    Alix, M.; Roche, R.L.

    1981-08-01

    The risks of buckling of dished vessel head increase when the vessel is thin walled. This paper gives the last results on experimental tests of 3 elliptical heads and compares all the results with some empirical formula dealing with elastic and plastic buckling

  9. Equivalent operator preconditioning for elliptic problems

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Karátson, J.

    2009-01-01

    Roč. 50, č. 3 (2009), s. 297-380 ISSN 1017-1398 Institutional research plan: CEZ:AV0Z30860518 Keywords : Elliptic problem * Conjugate gradient method * preconditioning * equivalent operators * compact operators Subject RIV: BA - General Mathematics Impact factor: 0.716, year: 2009 http://en.scientificcommons.org/42514649

  10. Hyper-and-elliptic-curve cryptography

    NARCIS (Netherlands)

    Bernstein, D.J.; Lange, T.

    2014-01-01

    This paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast

  11. Elliptic genera from multi-centers

    Energy Technology Data Exchange (ETDEWEB)

    Gaddam, Nava [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, 3508 TD Utrecht (Netherlands)

    2016-05-13

    I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera — explicitly verifying this in the cases of the quintic in ℙ{sup 4}, the sextic in Wℙ{sub (2,1,1,1,1)}, the octic in Wℙ{sub (4,1,1,1,1)} and the dectic in Wℙ{sub (5,2,1,1,1)}. With an input of the corresponding ‘single-center’ indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in N=2 supergravity.

  12. Elliptic Flow, Initial Eccentricity and Elliptic Flow Fluctuations in Heavy Ion Collisions at RHIC

    Science.gov (United States)

    Nouicer, Rachid; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holzman, B.; Iordanova, A.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wysłouch, B.

    2008-12-01

    We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.

  13. Systematics of elliptic flow in heavy-ion collisions

    Indian Academy of Sciences (India)

    We analyze elliptic flow from SIS to RHIC energies systematically in a realistic dynamical cascade model. We compare our results with the recent data from STAR and PHOBOS collaborations on elliptic flow of charged particles at midrapidity in Au + Au collisions at RHIC. In the analysis of elliptic flow at RHIC energy, we find ...

  14. Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at $\\sqrt{s_{NN}}$ = 2.76 TeV

    CERN Document Server

    Chatrchyan, Serguei; Sirunyan, Albert M; Tumasyan, Armen; Adam, Wolfgang; Bergauer, Thomas; Dragicevic, Marko; Erö, Janos; Fabjan, Christian; Friedl, Markus; Fruehwirth, Rudolf; Ghete, Vasile Mihai; Hammer, Josef; Hörmann, Natascha; Hrubec, Josef; Jeitler, Manfred; Kiesenhofer, Wolfgang; Krammer, Manfred; Liko, Dietrich; Mikulec, Ivan; Pernicka, Manfred; Rahbaran, Babak; Rohringer, Christine; Rohringer, Herbert; Schöfbeck, Robert; Strauss, Josef; Taurok, Anton; Teischinger, Florian; Wagner, Philipp; Waltenberger, Wolfgang; Walzel, Gerhard; Widl, Edmund; Wulz, Claudia-Elisabeth; Mossolov, Vladimir; Shumeiko, Nikolai; Suarez Gonzalez, Juan; Bansal, Sunil; Cerny, Karel; Cornelis, Tom; De Wolf, Eddi A; Janssen, Xavier; Luyckx, Sten; Maes, Thomas; Mucibello, Luca; Ochesanu, Silvia; Roland, Benoit; Rougny, Romain; Selvaggi, Michele; Van Haevermaet, Hans; Van Mechelen, Pierre; Van Remortel, Nick; Van Spilbeeck, Alex; Blekman, Freya; Blyweert, Stijn; D'Hondt, Jorgen; Gonzalez Suarez, Rebeca; Kalogeropoulos, Alexis; Maes, Michael; Olbrechts, Annik; Van Doninck, Walter; Van Mulders, Petra; Van Onsem, Gerrit Patrick; Villella, Ilaria; Charaf, Otman; Clerbaux, Barbara; De Lentdecker, Gilles; Dero, Vincent; Gay, Arnaud; Hreus, Tomas; Léonard, Alexandre; Marage, Pierre Edouard; Reis, Thomas; Thomas, Laurent; Vander Velde, Catherine; Vanlaer, Pascal; Adler, Volker; Beernaert, Kelly; Cimmino, Anna; Costantini, Silvia; Garcia, Guillaume; Grunewald, Martin; Klein, Benjamin; Lellouch, Jérémie; Marinov, Andrey; Mccartin, Joseph; Ocampo Rios, Alberto Andres; Ryckbosch, Dirk; Strobbe, Nadja; Thyssen, Filip; Tytgat, Michael; Vanelderen, Lukas; Verwilligen, Piet; Walsh, Sinead; Yazgan, Efe; Zaganidis, Nicolas; Basegmez, Suzan; Bruno, Giacomo; Ceard, Ludivine; Delaere, Christophe; Du Pree, Tristan; Favart, Denis; Forthomme, Laurent; Giammanco, Andrea; Hollar, Jonathan; Lemaitre, Vincent; Liao, Junhui; Militaru, Otilia; Nuttens, Claude; Pagano, Davide; Pin, Arnaud; Piotrzkowski, Krzysztof; Schul, Nicolas; Beliy, Nikita; Caebergs, Thierry; Daubie, Evelyne; Hammad, Gregory Habib; Alves, Gilvan; Correa Martins Junior, Marcos; De Jesus Damiao, Dilson; Martins, Thiago; Pol, Maria Elena; Henrique Gomes E Souza, Moacyr; Aldá Júnior, Walter Luiz; Carvalho, Wagner; Custódio, Analu; Melo Da Costa, Eliza; De Oliveira Martins, Carley; Fonseca De Souza, Sandro; Matos Figueiredo, Diego; Mundim, Luiz; Nogima, Helio; Oguri, Vitor; Prado Da Silva, Wanda Lucia; Santoro, Alberto; Silva Do Amaral, Sheila Mara; Soares Jorge, Luana; Sznajder, Andre; Souza Dos Anjos, Tiago; Bernardes, Cesar Augusto; De Almeida Dias, Flavia; Tomei, Thiago; De Moraes Gregores, Eduardo; Lagana, Caio; Da Cunha Marinho, Franciole; Mercadante, Pedro G; Novaes, Sergio F; Padula, Sandra; Genchev, Vladimir; Iaydjiev, Plamen; Piperov, Stefan; Rodozov, Mircho; Stoykova, Stefka; Sultanov, Georgi; Tcholakov, Vanio; Trayanov, Rumen; Vutova, Mariana; Dimitrov, Anton; Hadjiiska, Roumyana; Kozhuharov, Venelin; Litov, Leander; Pavlov, Borislav; Petkov, Peicho; Bian, Jian-Guo; Chen, Guo-Ming; Chen, He-Sheng; Jiang, Chun-Hua; Liang, Dong; Liang, Song; Meng, Xiangwei; Tao, Junquan; Wang, Jian; Wang, Jian; Wang, Xianyou; Wang, Zheng; Xiao, Hong; Xu, Ming; Zang, Jingjing; Zhang, Zhen; Asawatangtrakuldee, Chayanit; Ban, Yong; Guo, Shuang; Guo, Yifei; Li, Wenbo; Liu, Shuai; Mao, Yajun; Qian, Si-Jin; Teng, Haiyun; Wang, Siguang; Zhu, Bo; Zou, Wei; Avila, Carlos; Gomez Moreno, Bernardo; Osorio Oliveros, Andres Felipe; Sanabria, Juan Carlos; Godinovic, Nikola; Lelas, Damir; Plestina, Roko; Polic, Dunja; Puljak, Ivica; Antunovic, Zeljko; Dzelalija, Mile; Kovac, Marko; Brigljevic, Vuko; Duric, Senka; Kadija, Kreso; Luetic, Jelena; Morovic, Srecko; Attikis, Alexandros; Galanti, Mario; Mavromanolakis, Georgios; Mousa, Jehad; Nicolaou, Charalambos; Ptochos, Fotios; Razis, Panos A; Finger, Miroslav; Finger Jr, Michael; Assran, Yasser; Elgammal, Sherif; Ellithi Kamel, Ali; Khalil, Shaaban; Mahmoud, Mohammed; Radi, Amr; Kadastik, Mario; Müntel, Mait; Raidal, Martti; Rebane, Liis; Tiko, Andres; Azzolini, Virginia; Eerola, Paula; Fedi, Giacomo; Voutilainen, Mikko; Härkönen, Jaakko; Heikkinen, Mika Aatos; Karimäki, Veikko; Kinnunen, Ritva; Kortelainen, Matti J; Lampén, Tapio; Lassila-Perini, Kati; Lehti, Sami; Lindén, Tomas; Luukka, Panja-Riina; Mäenpää, Teppo; Peltola, Timo; Tuominen, Eija; Tuominiemi, Jorma; Tuovinen, Esa; Ungaro, Donatella; Wendland, Lauri; Banzuzi, Kukka; Korpela, Arja; Tuuva, Tuure; Besancon, Marc; Choudhury, Somnath; Dejardin, Marc; Denegri, Daniel; Fabbro, Bernard; Faure, Jean-Louis; Ferri, Federico; Ganjour, Serguei; Givernaud, Alain; Gras, Philippe; Hamel de Monchenault, Gautier; Jarry, Patrick; Locci, Elizabeth; Malcles, Julie; Millischer, Laurent; Nayak, Aruna; Rander, John; Rosowsky, André; Shreyber, Irina; Titov, Maksym; Baffioni, Stephanie; Beaudette, Florian; Benhabib, Lamia; Bianchini, Lorenzo; Bluj, Michal; Broutin, Clementine; Busson, Philippe; Charlot, Claude; Daci, Nadir; Dahms, Torsten; Dobrzynski, Ludwik; Granier de Cassagnac, Raphael; Haguenauer, Maurice; Miné, Philippe; Mironov, Camelia; Ochando, Christophe; Paganini, Pascal; Sabes, David; Salerno, Roberto; Sirois, Yves; Veelken, Christian; Zabi, Alexandre; Agram, Jean-Laurent; Andrea, Jeremy; Bloch, Daniel; Bodin, David; Brom, Jean-Marie; Cardaci, Marco; Chabert, Eric Christian; Collard, Caroline; Conte, Eric; Drouhin, Frédéric; Ferro, Cristina; Fontaine, Jean-Charles; Gelé, Denis; Goerlach, Ulrich; Juillot, Pierre; Karim, Mehdi; Le Bihan, Anne-Catherine; Van Hove, Pierre; Fassi, Farida; Mercier, Damien; Beauceron, Stephanie; Beaupere, Nicolas; Bondu, Olivier; Boudoul, Gaelle; Brun, Hugues; Chasserat, Julien; Chierici, Roberto; Contardo, Didier; Depasse, Pierre; El Mamouni, Houmani; Fay, Jean; Gascon, Susan; Gouzevitch, Maxime; Ille, Bernard; Kurca, Tibor; Lethuillier, Morgan; Mirabito, Laurent; Perries, Stephane; Sordini, Viola; Tosi, Silvano; Tschudi, Yohann; Verdier, Patrice; Viret, Sébastien; Tsamalaidze, Zviad; Anagnostou, Georgios; Beranek, Sarah; Edelhoff, Matthias; Feld, Lutz; Heracleous, Natalie; Hindrichs, Otto; Jussen, Ruediger; Klein, Katja; Merz, Jennifer; Ostapchuk, Andrey; Perieanu, Adrian; Raupach, Frank; Sammet, Jan; Schael, Stefan; Sprenger, Daniel; Weber, Hendrik; Wittmer, Bruno; Zhukov, Valery; Ata, Metin; Caudron, Julien; Dietz-Laursonn, Erik; Duchardt, Deborah; Erdmann, Martin; Güth, Andreas; Hebbeker, Thomas; Heidemann, Carsten; Hoepfner, Kerstin; Klimkovich, Tatsiana; Klingebiel, Dennis; Kreuzer, Peter; Lanske, Dankfried; Lingemann, Joschka; Magass, Carsten; Merschmeyer, Markus; Meyer, Arnd; Olschewski, Mark; Papacz, Paul; Pieta, Holger; Reithler, Hans; Schmitz, Stefan Antonius; Sonnenschein, Lars; Steggemann, Jan; Teyssier, Daniel; Weber, Martin; Bontenackels, Michael; Cherepanov, Vladimir; Davids, Martina; Flügge, Günter; Geenen, Heiko; Geisler, Matthias; Haj Ahmad, Wael; Hoehle, Felix; Kargoll, Bastian; Kress, Thomas; Kuessel, Yvonne; Linn, Alexander; Nowack, Andreas; Perchalla, Lars; Pooth, Oliver; Rennefeld, Jörg; Sauerland, Philip; Stahl, Achim; Aldaya Martin, Maria; Behr, Joerg; Behrenhoff, Wolf; Behrens, Ulf; Bergholz, Matthias; Bethani, Agni; Borras, Kerstin; Burgmeier, Armin; Cakir, Altan; Calligaris, Luigi; Campbell, Alan; Castro, Elena; Costanza, Francesco; Dammann, Dirk; Eckerlin, Guenter; Eckstein, Doris; Fischer, David; Flucke, Gero; Geiser, Achim; Glushkov, Ivan; Habib, Shiraz; Hauk, Johannes; Jung, Hannes; Kasemann, Matthias; Katsas, Panagiotis; Kleinwort, Claus; Kluge, Hannelies; Knutsson, Albert; Krämer, Mira; Krücker, Dirk; Kuznetsova, Ekaterina; Lange, Wolfgang; Lohmann, Wolfgang; Lutz, Benjamin; Mankel, Rainer; Marfin, Ihar; Marienfeld, Markus; Melzer-Pellmann, Isabell-Alissandra; Meyer, Andreas Bernhard; Mnich, Joachim; Mussgiller, Andreas; Naumann-Emme, Sebastian; Olzem, Jan; Perrey, Hanno; Petrukhin, Alexey; Pitzl, Daniel; Raspereza, Alexei; Ribeiro Cipriano, Pedro M; Riedl, Caroline; Rosin, Michele; Salfeld-Nebgen, Jakob; Schmidt, Ringo; Schoerner-Sadenius, Thomas; Sen, Niladri; Spiridonov, Alexander; Stein, Matthias; Walsh, Roberval; Wissing, Christoph; Autermann, Christian; Blobel, Volker; Bobrovskyi, Sergei; Draeger, Jula; Enderle, Holger; Erfle, Joachim; Gebbert, Ulla; Görner, Martin; Hermanns, Thomas; Höing, Rebekka Sophie; Kaschube, Kolja; Kaussen, Gordon; Kirschenmann, Henning; Klanner, Robert; Lange, Jörn; Mura, Benedikt; Nowak, Friederike; Pietsch, Niklas; Rathjens, Denis; Sander, Christian; Schettler, Hannes; Schleper, Peter; Schlieckau, Eike; Schmidt, Alexander; Schröder, Matthias; Schum, Torben; Seidel, Markus; Stadie, Hartmut; Steinbrück, Georg; Thomsen, Jan; Barth, Christian; Berger, Joram; Chwalek, Thorsten; De Boer, Wim; Dierlamm, Alexander; Feindt, Michael; Guthoff, Moritz; Hackstein, Christoph; Hartmann, Frank; Heinrich, Michael; Held, Hauke; Hoffmann, Karl-Heinz; Honc, Simon; Husemann, Ulrich; Katkov, Igor; Komaragiri, Jyothsna Rani; Martschei, Daniel; Mueller, Steffen; Müller, Thomas; Niegel, Martin; Nürnberg, Andreas; Oberst, Oliver; Oehler, Andreas; Ott, Jochen; Peiffer, Thomas; Quast, Gunter; Rabbertz, Klaus; Ratnikov, Fedor; Ratnikova, Natalia; Röcker, Steffen; Saout, Christophe; Scheurer, Armin; Schilling, Frank-Peter; Schmanau, Mike; Schott, Gregory; Simonis, Hans-Jürgen; Stober, Fred-Markus Helmut; Troendle, Daniel; Ulrich, Ralf; Wagner-Kuhr, Jeannine; Weiler, Thomas; Zeise, Manuel; Ziebarth, Eva Barbara; Daskalakis, Georgios; Geralis, Theodoros; Kesisoglou, Stilianos; Kyriakis, Aristotelis; Loukas, Demetrios; Manolakos, Ioannis; Markou, Athanasios; Markou, Christos; Mavrommatis, Charalampos; Ntomari, Eleni; Gouskos, Loukas; Mertzimekis, Theodoros; Panagiotou, Apostolos; Saoulidou, Niki; Evangelou, Ioannis; Foudas, Costas; Kokkas, Panagiotis; Manthos, Nikolaos; Papadopoulos, Ioannis; Patras, Vaios; Bencze, Gyorgy; Hajdu, Csaba; Hidas, Pàl; Horvath, Dezso; Krajczar, Krisztian; Radics, Balint; Sikler, Ferenc; Veszpremi, Viktor; Vesztergombi, Gyorgy; Beni, Noemi; Czellar, Sandor; Molnar, Jozsef; Palinkas, Jozsef; Szillasi, Zoltan; Karancsi, János; Raics, Peter; Trocsanyi, Zoltan Laszlo; Ujvari, Balazs; Beri, Suman Bala; Bhatnagar, Vipin; Dhingra, Nitish; Gupta, Ruchi; Jindal, Monika; Kaur, Manjit; Kohli, Jatinder Mohan; Mehta, Manuk Zubin; Nishu, Nishu; Saini, Lovedeep Kaur; Sharma, Archana; Singh, Jasbir; Singh, Supreet Pal; Ahuja, Sudha; Choudhary, Brajesh C; Kumar, Ashok; Kumar, Arun; Malhotra, Shivali; Naimuddin, Md; Ranjan, Kirti; Sharma, Varun; Shivpuri, Ram Krishen; Banerjee, Sunanda; Bhattacharya, Satyaki; Dutta, Suchandra; Gomber, Bhawna; Jain, Sandhya; Jain, Shilpi; Khurana, Raman; Sarkar, Subir; Abdulsalam, Abdulla; Choudhury, Rajani Kant; Dutta, Dipanwita; Kailas, Swaminathan; Kumar, Vineet; Mohanty, Ajit Kumar; Pant, Lalit Mohan; Shukla, Prashant; Aziz, Tariq; Ganguly, Sanmay; Guchait, Monoranjan; Gurtu, Atul; Maity, Manas; Majumder, Gobinda; Mazumdar, Kajari; Mohanty, Gagan Bihari; Parida, Bibhuti; Sudhakar, Katta; Wickramage, Nadeesha; Banerjee, Sudeshna; Dugad, Shashikant; Arfaei, Hessamaddin; Bakhshiansohi, Hamed; Etesami, Seyed Mohsen; Fahim, Ali; Hashemi, Majid; Hesari, Hoda; Jafari, Abideh; Khakzad, Mohsen; Mohammadi, Abdollah; Mohammadi Najafabadi, Mojtaba; Paktinat Mehdiabadi, Saeid; Safarzadeh, Batool; Zeinali, Maryam; Abbrescia, Marcello; Barbone, Lucia; Calabria, Cesare; Chhibra, Simranjit Singh; Colaleo, Anna; Creanza, Donato; De Filippis, Nicola; De Palma, Mauro; Fiore, Luigi; Iaselli, Giuseppe; Lusito, Letizia; Maggi, Giorgio; Maggi, Marcello; Marangelli, Bartolomeo; My, Salvatore; Nuzzo, Salvatore; Pacifico, Nicola; Pompili, Alexis; Pugliese, Gabriella; Selvaggi, Giovanna; Silvestris, Lucia; Singh, Gurpreet; Zito, Giuseppe; Abbiendi, Giovanni; Benvenuti, Alberto; Bonacorsi, Daniele; Braibant-Giacomelli, Sylvie; Brigliadori, Luca; Capiluppi, Paolo; Castro, Andrea; Cavallo, Francesca Romana; Cuffiani, Marco; Dallavalle, Gaetano-Marco; Fabbri, Fabrizio; Fanfani, Alessandra; Fasanella, Daniele; Giacomelli, Paolo; Grandi, Claudio; Guiducci, Luigi; Marcellini, Stefano; Masetti, Gianni; Meneghelli, Marco; Montanari, Alessandro; Navarria, Francesco; Odorici, Fabrizio; Perrotta, Andrea; Primavera, Federica; Rossi, Antonio; Rovelli, Tiziano; Siroli, Gianni; Travaglini, Riccardo; Albergo, Sebastiano; Cappello, Gigi; Chiorboli, Massimiliano; Costa, Salvatore; Potenza, Renato; Tricomi, Alessia; Tuve, Cristina; Barbagli, Giuseppe; Ciulli, Vitaliano; Civinini, Carlo; D'Alessandro, Raffaello; Focardi, Ettore; Frosali, Simone; Gallo, Elisabetta; Gonzi, Sandro; Meschini, Marco; Paoletti, Simone; Sguazzoni, Giacomo; Tropiano, Antonio; Benussi, Luigi; Bianco, Stefano; Colafranceschi, Stefano; Fabbri, Franco; Piccolo, Davide; Fabbricatore, Pasquale; Musenich, Riccardo; Benaglia, Andrea; De Guio, Federico; Di Matteo, Leonardo; Fiorendi, Sara; Gennai, Simone; Ghezzi, Alessio; Malvezzi, Sandra; Manzoni, Riccardo Andrea; Martelli, Arabella; Massironi, Andrea; Menasce, Dario; Moroni, Luigi; Paganoni, Marco; Pedrini, Daniele; Ragazzi, Stefano; Redaelli, Nicola; Sala, Silvano; Tabarelli de Fatis, Tommaso; Buontempo, Salvatore; Carrillo Montoya, Camilo Andres; Cavallo, Nicola; De Cosa, Annapaola; Dogangun, Oktay; Fabozzi, Francesco; Iorio, Alberto Orso Maria; Lista, Luca; Meola, Sabino; Merola, Mario; Paolucci, Pierluigi; Azzi, Patrizia; Bacchetta, Nicola; Bellan, Paolo; Biasotto, Massimo; Bisello, Dario; Branca, Antonio; Checchia, Paolo; Dorigo, Tommaso; Dosselli, Umberto; Gasparini, Fabrizio; Gozzelino, Andrea; Gulmini, Michele; Kanishchev, Konstantin; Lacaprara, Stefano; Lazzizzera, Ignazio; Margoni, Martino; Maron, Gaetano; Meneguzzo, Anna Teresa; Perrozzi, Luca; Pozzobon, Nicola; Ronchese, Paolo; Simonetto, Franco; Torassa, Ezio; Tosi, Mia; Vanini, Sara; Gabusi, Michele; Ratti, Sergio P; Riccardi, Cristina; Torre, Paola; Vitulo, Paolo; Bilei, Gian Mario; Fanò, Livio; Lariccia, Paolo; Lucaroni, Andrea; Mantovani, Giancarlo; Menichelli, Mauro; Nappi, Aniello; Romeo, Francesco; Saha, Anirban; Santocchia, Attilio; Taroni, Silvia; Azzurri, Paolo; Bagliesi, Giuseppe; Boccali, Tommaso; Broccolo, Giuseppe; Castaldi, Rino; D'Agnolo, Raffaele Tito; Dell'Orso, Roberto; Fiori, Francesco; Foà, Lorenzo; Giassi, Alessandro; Kraan, Aafke; Ligabue, Franco; Lomtadze, Teimuraz; Martini, Luca; Messineo, Alberto; Palla, Fabrizio; Palmonari, Francesco; Rizzi, Andrea; Serban, Alin Titus; Spagnolo, Paolo; Squillacioti, Paola; Tenchini, Roberto; Tonelli, Guido; Venturi, Andrea; Verdini, Piero Giorgio; Barone, Luciano; Cavallari, Francesca; Del Re, Daniele; Diemoz, Marcella; Fanelli, Cristiano; Grassi, Marco; Longo, Egidio; Meridiani, Paolo; Micheli, Francesco; Nourbakhsh, Shervin; Organtini, Giovanni; Pandolfi, Francesco; Paramatti, Riccardo; Rahatlou, Shahram; Sigamani, Michael; Soffi, Livia; Amapane, Nicola; Arcidiacono, Roberta; Argiro, Stefano; Arneodo, Michele; Biino, Cristina; Botta, Cristina; Cartiglia, Nicolo; Castello, Roberto; Costa, Marco; Demaria, Natale; Graziano, Alberto; Mariotti, Chiara; Maselli, Silvia; Migliore, Ernesto; Monaco, Vincenzo; Musich, Marco; Obertino, Maria Margherita; Pastrone, Nadia; Pelliccioni, Mario; Potenza, Alberto; Romero, Alessandra; Ruspa, Marta; Sacchi, Roberto; Sola, Valentina; Solano, Ada; Staiano, Amedeo; Vilela Pereira, Antonio; Belforte, Stefano; Cossutti, Fabio; Della Ricca, Giuseppe; Gobbo, Benigno; Marone, Matteo; Montanino, Damiana; Penzo, Aldo; Schizzi, Andrea; Heo, Seong Gu; Kim, Tae Yeon; Nam, Soon-Kwon; Chang, Sunghyun; Chung, Jin Hyuk; Kim, Dong Hee; Kim, Gui Nyun; Kong, Dae Jung; Park, Hyangkyu; Ro, Sang-Ryul; Son, Dong-Chul; Son, Taejin; Kim, Jae Yool; Kim, Zero Jaeho; Song, Sanghyeon; Jo, Hyun Yong; Choi, Suyong; Gyun, Dooyeon; Hong, Byung-Sik; Jo, Mihee; Kim, Hyunchul; Kim, Tae Jeong; Lee, Kyong Sei; Moon, Dong Ho; Park, Sung Keun; Seo, Eunsung; Choi, Minkyoo; Kang, Seokon; Kim, Hyunyong; Kim, Ji Hyun; Park, Chawon; Park, Inkyu; Park, Sangnam; Ryu, Geonmo; Cho, Yongjin; Choi, Young-Il; Choi, Young Kyu; Goh, Junghwan; Kim, Min Suk; Kwon, Eunhyang; Lee, Byounghoon; Lee, Jongseok; Lee, Sungeun; Seo, Hyunkwan; Yu, Intae; Bilinskas, Mykolas Jurgis; Grigelionis, Ignas; Janulis, Mindaugas; Juodagalvis, Andrius; Castilla-Valdez, Heriberto; De La Cruz-Burelo, Eduard; Heredia-de La Cruz, Ivan; Lopez-Fernandez, Ricardo; Magaña Villalba, Ricardo; Martínez-Ortega, Jorge; Sánchez-Hernández, Alberto; Villasenor-Cendejas, Luis Manuel; Carrillo Moreno, Salvador; Vazquez Valencia, Fabiola; Salazar Ibarguen, Humberto Antonio; Casimiro Linares, Edgar; Morelos Pineda, Antonio; Reyes-Santos, Marco A; Krofcheck, David; Bell, Alan James; Butler, Philip H; Doesburg, Robert; Reucroft, Steve; Silverwood, Hamish; Ahmad, Muhammad; Asghar, Muhammad Irfan; Hoorani, Hafeez R; Khalid, Shoaib; Khan, Wajid Ali; Khurshid, Taimoor; Qazi, Shamona; Shah, Mehar Ali; Shoaib, Muhammad; Brona, Grzegorz; Bunkowski, Karol; Cwiok, Mikolaj; Dominik, Wojciech; Doroba, Krzysztof; Kalinowski, Artur; Konecki, Marcin; Krolikowski, Jan; Bialkowska, Helena; Boimska, Bozena; Frueboes, Tomasz; Gokieli, Ryszard; Górski, Maciej; Kazana, Malgorzata; Nawrocki, Krzysztof; Romanowska-Rybinska, Katarzyna; Szleper, Michal; Wrochna, Grzegorz; Zalewski, Piotr; Almeida, Nuno; Bargassa, Pedrame; David Tinoco Mendes, Andre; Faccioli, Pietro; Ferreira Parracho, Pedro Guilherme; Gallinaro, Michele; Musella, Pasquale; Seixas, Joao; Varela, Joao; Vischia, Pietro; Afanasiev, Serguei; Belotelov, Ivan; Bunin, Pavel; Gavrilenko, Mikhail; Golutvin, Igor; Kamenev, Alexey; Karjavin, Vladimir; Kozlov, Guennady; Lanev, Alexander; Malakhov, Alexander; Moisenz, Petr; Palichik, Vladimir; Perelygin, Victor; Shmatov, Sergey; Smirnov, Vitaly; Volodko, Anton; Zarubin, Anatoli; Evstyukhin, Sergey; Golovtsov, Victor; Ivanov, Yury; Kim, Victor; Levchenko, Petr; Murzin, Victor; Oreshkin, Vadim; Smirnov, Igor; Sulimov, Valentin; Uvarov, Lev; Vavilov, Sergey; Vorobyev, Alexey; Vorobyev, Andrey; Andreev, Yuri; Dermenev, Alexander; Gninenko, Sergei; Golubev, Nikolai; Kirsanov, Mikhail; Krasnikov, Nikolai; Matveev, Viktor; Pashenkov, Anatoli; Tlisov, Danila; Toropin, Alexander; Epshteyn, Vladimir; Erofeeva, Maria; Gavrilov, Vladimir; Kossov, Mikhail; Lychkovskaya, Natalia; Popov, Vladimir; Safronov, Grigory; Semenov, Sergey; Stolin, Viatcheslav; Vlasov, Evgueni; Zhokin, Alexander; Belyaev, Andrey; Boos, Edouard; Ershov, Alexander; Gribushin, Andrey; Klyukhin, Vyacheslav; Kodolova, Olga; Korotkikh, Vladimir; Lokhtin, Igor; Markina, Anastasia; Obraztsov, Stepan; Perfilov, Maxim; Petrushanko, Sergey; Sarycheva, Ludmila; Savrin, Viktor; Snigirev, Alexander; Vardanyan, Irina; Andreev, Vladimir; Azarkin, Maksim; Dremin, Igor; Kirakosyan, Martin; Leonidov, Andrey; Mesyats, Gennady; Rusakov, Sergey V; Vinogradov, Alexey; Azhgirey, Igor; Bayshev, Igor; Bitioukov, Sergei; Grishin, Viatcheslav; Kachanov, Vassili; Konstantinov, Dmitri; Korablev, Andrey; Krychkine, Victor; Petrov, Vladimir; Ryutin, Roman; Sobol, Andrei; Tourtchanovitch, Leonid; Troshin, Sergey; Tyurin, Nikolay; Uzunian, Andrey; Volkov, Alexey; Adzic, Petar; Djordjevic, Milos; Ekmedzic, Marko; Krpic, Dragomir; Milosevic, Jovan; Aguilar-Benitez, Manuel; Alcaraz Maestre, Juan; Arce, Pedro; Battilana, Carlo; Calvo, Enrique; Cerrada, Marcos; Chamizo Llatas, Maria; Colino, Nicanor; De La Cruz, Begona; Delgado Peris, Antonio; Diez Pardos, Carmen; Domínguez Vázquez, Daniel; Fernandez Bedoya, Cristina; Fernández Ramos, Juan Pablo; Ferrando, Antonio; Flix, Jose; Fouz, Maria Cruz; Garcia-Abia, Pablo; Gonzalez Lopez, Oscar; Goy Lopez, Silvia; Hernandez, Jose M; Josa, Maria Isabel; Merino, Gonzalo; Puerta Pelayo, Jesus; Redondo, Ignacio; Romero, Luciano; Santaolalla, Javier; Senghi Soares, Mara; Willmott, Carlos; Albajar, Carmen; Codispoti, Giuseppe; de Trocóniz, Jorge F; Cuevas, Javier; Fernandez Menendez, Javier; Folgueras, Santiago; Gonzalez Caballero, Isidro; Lloret Iglesias, Lara; Piedra Gomez, Jonatan; Vizan Garcia, Jesus Manuel; Brochero Cifuentes, Javier Andres; Cabrillo, Iban Jose; Calderon, Alicia; Chuang, Shan-Huei; Duarte Campderros, Jordi; Felcini, Marta; Fernandez, Marcos; Gomez, Gervasio; 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Kayis Topaksu, Aysel; Onengut, Gulsen; Ozdemir, Kadri; Ozturk, Sertac; Polatoz, Ayse; Sogut, Kenan; Sunar Cerci, Deniz; Tali, Bayram; Topakli, Huseyin; Vergili, Latife Nukhet; Vergili, Mehmet; Akin, Ilina Vasileva; Aliev, Takhmasib; Bilin, Bugra; Bilmis, Selcuk; Deniz, Muhammed; Gamsizkan, Halil; Guler, Ali Murat; Ocalan, Kadir; Ozpineci, Altug; Serin, Meltem; Sever, Ramazan; Surat, Ugur Emrah; Yalvac, Metin; Yildirim, Eda; Zeyrek, Mehmet; Deliomeroglu, Mehmet; Gülmez, Erhan; Isildak, Bora; Kaya, Mithat; Kaya, Ozlem; Ozkorucuklu, Suat; Sonmez, Nasuf; Cankocak, Kerem; Levchuk, Leonid; Bostock, Francis; Brooke, James John; Clement, Emyr; Cussans, David; Flacher, Henning; Frazier, Robert; Goldstein, Joel; Grimes, Mark; Heath, Greg P; Heath, Helen F; Kreczko, Lukasz; Metson, Simon; Newbold, Dave M; Nirunpong, Kachanon; Poll, Anthony; Senkin, Sergey; Smith, Vincent J; Williams, Thomas; Basso, Lorenzo; Belyaev, Alexander; Brew, Christopher; Brown, Robert M; Cockerill, David JA; Coughlan, John A; Harder, Kristian; Harper, Sam; Jackson, James; Kennedy, Bruce W; Olaiya, Emmanuel; Petyt, David; Radburn-Smith, Benjamin Charles; Shepherd-Themistocleous, Claire; Tomalin, Ian R; Womersley, William John; Bainbridge, Robert; Ball, Gordon; Beuselinck, Raymond; Buchmuller, Oliver; Colling, David; Cripps, Nicholas; Cutajar, Michael; Dauncey, Paul; Davies, Gavin; Della Negra, Michel; Ferguson, William; Fulcher, Jonathan; Futyan, David; Gilbert, Andrew; Guneratne Bryer, Arlo; Hall, Geoffrey; Hatherell, Zoe; Hays, Jonathan; Iles, Gregory; Jarvis, Martyn; Karapostoli, Georgia; Lyons, Louis; Magnan, Anne-Marie; Marrouche, Jad; Mathias, Bryn; Nandi, Robin; Nash, Jordan; Nikitenko, Alexander; Papageorgiou, Anastasios; Pela, Joao; Pesaresi, Mark; Petridis, Konstantinos; Pioppi, Michele; Raymond, David Mark; Rogerson, Samuel; Rompotis, Nikolaos; Rose, Andrew; Ryan, Matthew John; Seez, Christopher; Sharp, Peter; Sparrow, Alex; Tapper, Alexander; Vazquez Acosta, Monica; Virdee, Tejinder; Wakefield, Stuart; Wardle, Nicholas; Whyntie, Tom; Barrett, Matthew; Chadwick, Matthew; Cole, Joanne; Hobson, Peter R; Khan, Akram; Kyberd, Paul; Leggat, Duncan; Leslie, Dawn; Martin, William; Reid, Ivan; Symonds, Philip; Teodorescu, Liliana; Turner, Mark; Hatakeyama, Kenichi; Liu, Hongxuan; Scarborough, Tara; Henderson, Conor; Rumerio, Paolo; Avetisyan, Aram; Bose, Tulika; Fantasia, Cory; Heister, Arno; St John, Jason; Lawson, Philip; Lazic, Dragoslav; Rohlf, James; Sperka, David; Sulak, Lawrence; Alimena, Juliette; Bhattacharya, Saptaparna; Cutts, David; Ferapontov, Alexey; Heintz, Ulrich; Jabeen, Shabnam; Kukartsev, Gennadiy; Landsberg, Greg; Luk, Michael; Narain, Meenakshi; Nguyen, Duong; Segala, Michael; Sinthuprasith, Tutanon; Speer, Thomas; Tsang, Ka Vang; Breedon, Richard; Breto, Guillermo; Calderon De La Barca Sanchez, Manuel; Chauhan, Sushil; Chertok, Maxwell; Conway, John; Conway, Rylan; Cox, Peter Timothy; Dolen, James; Erbacher, Robin; Gardner, Michael; Houtz, Rachel; Ko, Winston; Kopecky, Alexandra; Lander, Richard; Mall, Orpheus; Miceli, Tia; Nelson, Randy; Pellett, Dave; Rutherford, Britney; Searle, Matthew; Smith, John; Squires, Michael; Tripathi, Mani; Vasquez Sierra, Ricardo; Andreev, Valeri; Cline, David; Cousins, Robert; Duris, Joseph; Erhan, Samim; Everaerts, Pieter; Farrell, Chris; Hauser, Jay; Ignatenko, Mikhail; Plager, Charles; Rakness, Gregory; Schlein, Peter; Tucker, Jordan; Valuev, Vyacheslav; Weber, Matthias; Babb, John; Clare, Robert; Dinardo, Mauro Emanuele; Ellison, John Anthony; Gary, J William; Giordano, Ferdinando; Hanson, Gail; Jeng, Geng-Yuan; Liu, Hongliang; Long, Owen Rosser; Luthra, Arun; Nguyen, Harold; Paramesvaran, Sudarshan; Sturdy, Jared; Sumowidagdo, Suharyo; Wilken, Rachel; Wimpenny, Stephen; Andrews, Warren; Branson, James G; Cerati, Giuseppe Benedetto; Cittolin, Sergio; Evans, David; Golf, Frank; Holzner, André; Kelley, Ryan; Lebourgeois, Matthew; Letts, James; Macneill, Ian; Mangano, Boris; Muelmenstaedt, Johannes; Padhi, Sanjay; Palmer, Christopher; Petrucciani, Giovanni; Pieri, Marco; Ranieri, Riccardo; Sani, Matteo; Sharma, Vivek; Simon, Sean; Sudano, Elizabeth; Tadel, Matevz; Tu, Yanjun; Vartak, Adish; Wasserbaech, Steven; Würthwein, Frank; Yagil, Avraham; Yoo, Jaehyeok; Barge, Derek; Bellan, Riccardo; Campagnari, Claudio; D'Alfonso, Mariarosaria; Danielson, Thomas; Flowers, Kristen; Geffert, Paul; Incandela, Joe; Justus, Christopher; Kalavase, Puneeth; Koay, Sue Ann; Kovalskyi, Dmytro; Krutelyov, Vyacheslav; Lowette, Steven; Mccoll, Nickolas; Pavlunin, Viktor; Rebassoo, Finn; Ribnik, Jacob; Richman, Jeffrey; Rossin, Roberto; Stuart, David; To, Wing; West, Christopher; Apresyan, Artur; Bornheim, Adolf; Chen, Yi; Di Marco, Emanuele; Duarte, Javier; Gataullin, Marat; Ma, Yousi; Mott, Alexander; Newman, Harvey B; Rogan, Christopher; Timciuc, Vladlen; Traczyk, Piotr; Veverka, Jan; Wilkinson, Richard; Yang, Yong; Zhu, Ren-Yuan; Akgun, Bora; Carroll, Ryan; Ferguson, Thomas; Iiyama, Yutaro; Jang, Dong Wook; Liu, Yueh-Feng; Paulini, Manfred; Vogel, Helmut; Vorobiev, Igor; Cumalat, John Perry; Drell, Brian Robert; Edelmaier, Christopher; Ford, William T; Gaz, Alessandro; Heyburn, Bernadette; Luiggi Lopez, Eduardo; Smith, James; Stenson, Kevin; Ulmer, Keith; Wagner, Stephen Robert; Agostino, Lorenzo; Alexander, James; Chatterjee, Avishek; Eggert, Nicholas; Gibbons, Lawrence Kent; Heltsley, Brian; Hopkins, Walter; Khukhunaishvili, Aleko; Kreis, Benjamin; Mirman, Nathan; Nicolas Kaufman, Gala; Patterson, Juliet Ritchie; Ryd, Anders; Salvati, Emmanuele; Sun, Werner; Teo, Wee Don; Thom, Julia; Thompson, Joshua; Vaughan, Jennifer; Weng, Yao; Winstrom, Lucas; Wittich, Peter; Winn, Dave; Abdullin, Salavat; Albrow, Michael; Anderson, Jacob; Bauerdick, Lothar AT; Beretvas, Andrew; Berryhill, Jeffrey; Bhat, Pushpalatha C; Bloch, Ingo; Burkett, Kevin; Butler, Joel Nathan; Chetluru, Vasundhara; Cheung, Harry; Chlebana, Frank; Elvira, Victor Daniel; Fisk, Ian; Freeman, Jim; Gao, Yanyan; Green, Dan; Gutsche, Oliver; Hahn, Alan; Hanlon, Jim; Harris, Robert M; Hirschauer, James; Hooberman, Benjamin; Jindariani, Sergo; Johnson, Marvin; Joshi, Umesh; Kilminster, Benjamin; Klima, Boaz; Kunori, Shuichi; Kwan, Simon; Lincoln, Don; Lipton, Ron; Lueking, Lee; Lykken, Joseph; Maeshima, Kaori; Marraffino, John Michael; Maruyama, Sho; Mason, David; McBride, Patricia; Mishra, Kalanand; Mrenna, Stephen; Musienko, Yuri; Newman-Holmes, Catherine; O'Dell, Vivian; Prokofyev, Oleg; Sexton-Kennedy, Elizabeth; Sharma, Seema; Spalding, William J; Spiegel, Leonard; Tan, Ping; Taylor, Lucas; Tkaczyk, Slawek; Tran, Nhan Viet; Uplegger, Lorenzo; Vaandering, Eric Wayne; Vidal, Richard; Whitmore, Juliana; Wu, Weimin; Yang, Fan; Yumiceva, Francisco; Yun, Jae Chul; Acosta, Darin; Avery, Paul; Bourilkov, Dimitri; Chen, Mingshui; Das, Souvik; De Gruttola, Michele; Di Giovanni, Gian Piero; Dobur, Didar; Drozdetskiy, Alexey; Field, Richard D; Fisher, Matthew; Fu, Yu; Furic, Ivan-Kresimir; Gartner, Joseph; Hugon, Justin; Kim, Bockjoo; Konigsberg, Jacobo; Korytov, Andrey; Kropivnitskaya, Anna; Kypreos, Theodore; Low, Jia Fu; Matchev, Konstantin; Milenovic, Predrag; Mitselmakher, Guenakh; Muniz, Lana; Remington, Ronald; Rinkevicius, Aurelijus; Sellers, Paul; Skhirtladze, Nikoloz; Snowball, Matthew; Yelton, John; Zakaria, Mohammed; Gaultney, Vanessa; Lebolo, Luis Miguel; Linn, Stephan; Markowitz, Pete; Martinez, German; Rodriguez, Jorge Luis; Adams, Todd; Askew, Andrew; Bochenek, Joseph; Chen, Jie; Diamond, Brendan; Gleyzer, Sergei V; Haas, Jeff; Hagopian, Sharon; Hagopian, Vasken; Jenkins, Merrill; Johnson, Kurtis F; Prosper, Harrison; Veeraraghavan, Venkatesh; Weinberg, Marc; Baarmand, Marc M; Dorney, Brian; Hohlmann, Marcus; Kalakhety, Himali; Vodopiyanov, Igor; Adams, Mark Raymond; Anghel, Ioana Maria; Apanasevich, Leonard; Bai, Yuting; Bazterra, Victor Eduardo; Betts, Russell Richard; Callner, Jeremy; Cavanaugh, Richard; Dragoiu, Cosmin; Evdokimov, Olga; Garcia-Solis, Edmundo Javier; Gauthier, Lucie; Gerber, Cecilia Elena; Hofman, David Jonathan; Khalatyan, Samvel; Lacroix, Florent; Malek, Magdalena; O'Brien, Christine; Silkworth, Christopher; Strom, Derek; Varelas, Nikos; Akgun, Ugur; Albayrak, Elif Asli; Bilki, Burak; Chung, Kwangzoo; Clarida, Warren; Duru, Firdevs; Griffiths, Scott; Lae, Chung Khim; Merlo, Jean-Pierre; Mermerkaya, Hamit; Mestvirishvili, Alexi; Moeller, Anthony; Nachtman, Jane; Newsom, Charles Ray; Norbeck, Edwin; Olson, Jonathan; Onel, Yasar; Ozok, Ferhat; Sen, Sercan; Tiras, Emrah; Wetzel, James; Yetkin, Taylan; Yi, Kai; Barnett, Bruce Arnold; Blumenfeld, Barry; Bolognesi, Sara; Fehling, David; Giurgiu, Gavril; Gritsan, Andrei; Guo, Zijin; Hu, Guofan; Maksimovic, Petar; Rappoccio, Salvatore; Swartz, Morris; Whitbeck, Andrew; Baringer, Philip; Bean, Alice; Benelli, Gabriele; Grachov, Oleg; Kenny Iii, Raymond Patrick; Murray, Michael; Noonan, Daniel; Radicci, Valeria; Sanders, Stephen; Stringer, Robert; Tinti, Gemma; Wood, Jeffrey Scott; Zhukova, Victoria; Barfuss, Anne-Fleur; Bolton, Tim; Chakaberia, Irakli; Ivanov, Andrew; Khalil, Sadia; Makouski, Mikhail; Maravin, Yurii; Shrestha, Shruti; Svintradze, Irakli; Gronberg, Jeffrey; Lange, David; Wright, Douglas; Baden, Drew; Boutemeur, Madjid; Calvert, Brian; Eno, Sarah Catherine; Gomez, Jaime; Hadley, Nicholas John; Kellogg, Richard G; Kirn, Malina; Kolberg, Ted; Lu, Ying; Marionneau, Matthieu; Mignerey, Alice; Peterman, Alison; Rossato, Kenneth; Skuja, Andris; Temple, Jeffrey; Tonjes, Marguerite; Tonwar, Suresh C; Twedt, Elizabeth; Bauer, Gerry; Bendavid, Joshua; Busza, Wit; Butz, Erik; Cali, Ivan Amos; Chan, Matthew; Dutta, Valentina; Gomez Ceballos, Guillelmo; Goncharov, Maxim; Hahn, Kristan Allan; Kim, Yongsun; Klute, Markus; Lee, Yen-Jie; Li, Wei; Luckey, Paul David; Ma, Teng; Nahn, Steve; Paus, Christoph; Ralph, Duncan; Roland, Christof; Roland, Gunther; Rudolph, Matthew; Stephans, George; Stöckli, Fabian; Sumorok, Konstanty; Sung, Kevin; Velicanu, Dragos; Wenger, Edward Allen; Wolf, Roger; Wyslouch, Bolek; Xie, Si; Yang, Mingming; Yilmaz, Yetkin; Yoon, Sungho; Zanetti, Marco; Cooper, Seth; Cushman, Priscilla; Dahmes, Bryan; De Benedetti, Abraham; Franzoni, Giovanni; Gude, Alexander; Haupt, Jason; Kao, Shih-Chuan; Klapoetke, Kevin; Kubota, Yuichi; Mans, Jeremy; Pastika, Nathaniel; Rusack, Roger; Sasseville, Michael; Singovsky, Alexander; Tambe, Norbert; Turkewitz, Jared; Cremaldi, Lucien Marcus; Kroeger, Rob; Perera, Lalith; Rahmat, Rahmat; Sanders, David A; Avdeeva, Ekaterina; Bloom, Kenneth; Bose, Suvadeep; Butt, Jamila; Claes, Daniel R; Dominguez, Aaron; Eads, Michael; Jindal, Pratima; Keller, Jason; Kravchenko, Ilya; Lazo-Flores, Jose; Malbouisson, Helena; Malik, Sudhir; Snow, Gregory R; Baur, Ulrich; Godshalk, Andrew; Iashvili, Ia; Jain, Supriya; Kharchilava, Avto; Kumar, Ashish; Shipkowski, Simon Peter; Smith, Kenneth; Alverson, George; Barberis, Emanuela; Baumgartel, Darin; Chasco, Matthew; Haley, Joseph; Trocino, Daniele; Wood, Darien; Zhang, Jinzhong; Anastassov, Anton; Kubik, Andrew; Mucia, Nicholas; Odell, Nathaniel; Ofierzynski, Radoslaw Adrian; Pollack, Brian; Pozdnyakov, Andrey; Schmitt, Michael Henry; Stoynev, Stoyan; Velasco, Mayda; Won, Steven; Antonelli, Louis; Berry, Douglas; Brinkerhoff, Andrew; Hildreth, Michael; Jessop, Colin; Karmgard, Daniel John; Kolb, Jeff; Lannon, Kevin; Luo, Wuming; Lynch, Sean; Marinelli, Nancy; Morse, David Michael; Pearson, Tessa; Ruchti, Randy; Slaunwhite, Jason; Valls, Nil; Warchol, Jadwiga; Wayne, Mitchell; Wolf, Matthias; Ziegler, Jill; Bylsma, Ben; Durkin, Lloyd Stanley; Hill, Christopher; Hughes, Richard; Killewald, Phillip; Kotov, Khristian; Ling, Ta-Yung; Puigh, Darren; Rodenburg, Marissa; Vuosalo, Carl; Williams, Grayson; Winer, Brian L; Adam, Nadia; Berry, Edmund; Elmer, Peter; Gerbaudo, Davide; Halyo, Valerie; Hebda, Philip; Hegeman, Jeroen; Hunt, Adam; Laird, Edward; Lopes Pegna, David; Lujan, Paul; Marlow, Daniel; Medvedeva, Tatiana; Mooney, Michael; Olsen, James; Piroué, Pierre; Quan, Xiaohang; Raval, Amita; Saka, Halil; Stickland, David; Tully, Christopher; Werner, Jeremy Scott; Zuranski, Andrzej; Acosta, Jhon Gabriel; Huang, Xing Tao; Lopez, Angel; Mendez, Hector; Oliveros, Sandra; Ramirez Vargas, Juan Eduardo; Zatserklyaniy, Andriy; Alagoz, Enver; Barnes, Virgil E; Benedetti, Daniele; Bolla, Gino; Bortoletto, Daniela; De Mattia, Marco; Everett, Adam; Hu, Zhen; Jones, Matthew; Koybasi, Ozhan; Kress, Matthew; Laasanen, Alvin T; Leonardo, Nuno; Maroussov, Vassili; Merkel, Petra; Miller, David Harry; Neumeister, Norbert; Shipsey, Ian; Silvers, David; Svyatkovskiy, Alexey; Vidal Marono, Miguel; Yoo, Hwi Dong; Zablocki, Jakub; Zheng, Yu; Guragain, Samir; Parashar, Neeti; Adair, Antony; Boulahouache, Chaouki; Cuplov, Vesna; Ecklund, Karl Matthew; Geurts, Frank JM; Padley, Brian Paul; Redjimi, Radia; Roberts, Jay; Zabel, James; Betchart, Burton; Bodek, Arie; Chung, Yeon Sei; Covarelli, Roberto; de Barbaro, Pawel; Demina, Regina; Eshaq, Yossof; Garcia-Bellido, Aran; Goldenzweig, Pablo; Gotra, Yury; Han, Jiyeon; Harel, Amnon; Korjenevski, Sergey; Miner, Daniel Carl; Vishnevskiy, Dmitry; Zielinski, Marek; Bhatti, Anwar; Ciesielski, Robert; Demortier, Luc; Goulianos, Konstantin; Lungu, Gheorghe; Malik, Sarah; Mesropian, Christina; Arora, Sanjay; Barker, Anthony; Chou, John Paul; Contreras-Campana, Christian; Contreras-Campana, Emmanuel; Duggan, Daniel; Ferencek, Dinko; Gershtein, Yuri; Gray, Richard; Halkiadakis, Eva; Hidas, Dean; Hits, Dmitry; Lath, Amitabh; Panwalkar, Shruti; Park, Michael; Patel, Rishi; Rekovic, Vladimir; Richards, Alan; Robles, Jorge; Rose, Keith; Salur, Sevil; Schnetzer, Steve; Seitz, Claudia; Somalwar, Sunil; Stone, Robert; Thomas, Scott; Cerizza, Giordano; Hollingsworth, Matthew; Spanier, Stefan; Yang, Zong-Chang; York, Andrew; Eusebi, Ricardo; Flanagan, Will; Gilmore, Jason; Kamon, Teruki; Khotilovich, Vadim; Montalvo, Roy; Osipenkov, Ilya; Pakhotin, Yuriy; Perloff, Alexx; Roe, Jeffrey; Safonov, Alexei; Sakuma, Tai; Sengupta, Sinjini; Suarez, Indara; Tatarinov, Aysen; Toback, David; Akchurin, Nural; Damgov, Jordan; Dudero, Phillip Russell; Jeong, Chiyoung; Kovitanggoon, Kittikul; Lee, Sung Won; Libeiro, Terence; Roh, Youn; Volobouev, Igor; Appelt, Eric; Engh, Daniel; Florez, Carlos; Greene, Senta; Gurrola, Alfredo; Johns, Willard; Kurt, Pelin; Maguire, Charles; Melo, Andrew; Sheldon, Paul; Snook, Benjamin; Tuo, Shengquan; Velkovska, Julia; Arenton, Michael Wayne; Balazs, Michael; Boutle, Sarah; Cox, Bradley; Francis, Brian; Goodell, Joseph; Hirosky, Robert; Ledovskoy, Alexander; Lin, Chuanzhe; Neu, Christopher; Wood, John; Yohay, Rachel; Gollapinni, Sowjanya; Harr, Robert; Karchin, Paul Edmund; Kottachchi Kankanamge Don, Chamath; Lamichhane, Pramod; Sakharov, Alexandre; Anderson, Michael; Bachtis, Michail; Belknap, Donald; Borrello, Laura; Carlsmith, Duncan; Cepeda, Maria; Dasu, Sridhara; Gray, Lindsey; Grogg, Kira Suzanne; Grothe, Monika; Hall-Wilton, Richard; Herndon, Matthew; Hervé, Alain; Klabbers, Pamela; Klukas, Jeffrey; Lanaro, Armando; Lazaridis, Christos; Leonard, Jessica; Loveless, Richard; Mohapatra, Ajit; Ojalvo, Isabel; Pierro, Giuseppe Antonio; Ross, Ian; Savin, Alexander; Smith, Wesley H; Swanson, Joshua

    2013-01-07

    The anisotropy of the azimuthal distributions of charged particles produced in PbPb collisions with a nucleon-nucleon center-of-mass energy of 2.76 TeV is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee--Yang zeros. The anisotropy is presented as a function of transverse momentum (pt), pseudorapidity (eta) over a broad kinematic range: 0.3 < pt < 20 GeV, abs(eta) < 2.4, and in 12 classes of collision centrality from 0 to 80%. The results are compared to those obtained at lower center-of-mass energies, and various scaling behaviors are examined. When scaled by the geometric eccentricity of the collision zone, the elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies.

  15. Virial Expansion Bounds

    Science.gov (United States)

    Tate, Stephen James

    2013-10-01

    In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.

  16. Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets

    International Nuclear Information System (INIS)

    Aquilanti, Vincenzo; Tonzani, Stefano

    2004-01-01

    Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known 'symmetric' and 'asymmetric' parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems

  17. Modeling Asymmetric Flow of Viscoelastic Fluid in Symmetric Planar Sudden Expansion Geometry Based on User-Defined Function in FLUENT CFD Package

    Directory of Open Access Journals (Sweden)

    Zhi-Ying Zheng

    2013-01-01

    Full Text Available Through embedding an in-house subroutine into FLUENT code by utilizing the functionalization of user-defined function provided by the software, a new numerical simulation methodology on viscoelastic fluid flows has been established. In order to benchmark this methodology, numerical simulations under different viscoelastic fluid solution concentrations (with solvent viscosity ratio varied from 0.2 to 0.9, extensibility parameters (100≤L2≤500, Reynolds numbers (0.1 ≤ Re ≤ 100, and Weissenberg numbers (0 ≤ Wi ≤ 20 are conducted on unsteady laminar flows through a symmetric planar sudden expansion with expansion ratio of 1: 3 for viscoelastic fluid flows. The constitutive model used to describe the viscoelastic effect of viscoelastic fluid flow is FENE-P (finitely extensive nonlinear elastic-Peterlin model. The numerical simulation results show that the influences of elasticity, inertia, and concentration on the flow bifurcation characteristics are more significant than those of extensibility. The present simulation results including the critical Reynolds number for which the flow becomes asymmetric, vortex size, bifurcation diagram, velocity distribution, streamline, and pressure loss show good agreements with some published results. That means the newly established method based on FLUENT software platform for simulating peculiar flow behaviors of viscoelastic fluid is credible and suitable for the study of viscoelastic fluid flows.

  18. Magnetic properties of spinels GeNi2-xCoxO4 systems: Green's function and high-temperature series expansions

    Science.gov (United States)

    El Grini, A.; Salmi, S.; Masrour, R.; Hamedoun, M.; Bouslykhane, K.; Marzouk, A.; Hourmatallah, A.; Benzakour, N.

    2018-06-01

    The Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2-xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 - xCoxO4 systems. The critical exponents ? and ? and associated with the magnetic susceptibility ? and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.

  19. Heterodyne detector for measuring the characteristic of elliptically polarized microwaves

    DEFF Research Database (Denmark)

    Leipold, Frank; Nielsen, Stefan Kragh; Michelsen, Susanne

    2008-01-01

    In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light (ellipticity, angle of ellipticity, and direction of rotation) for microwave radiation at a frequency of 110 GHz. The device consists of two perpendicu......In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light (ellipticity, angle of ellipticity, and direction of rotation) for microwave radiation at a frequency of 110 GHz. The device consists of two...... be calculated. Results from measured and calculated wave characteristics of an elliptically polarized 110 GHz microwave beam for plasma heating launched into the TEXTOR-tokamak experiment are presented. Measurement and calculation are in good agreement. ©2008 American Institute of Physics...

  20. Developing a composite based elliptic spring for automotive applications

    International Nuclear Information System (INIS)

    Talib, Abdul Rahim Abu; Ali, Aidy; Goudah, G.; Lah, Nur Azida Che; Golestaneh, A.F.

    2010-01-01

    An automotive suspension system is designed to provide both safety and comfort for the vehicle occupants. In this study, finite element models were developed to optimize the material and geometry of the composite elliptical spring based on the spring rate, log life and shear stress parameters. The influence of the ellipticity ratio on the performance of woven roving-wrapped composite elliptical springs was investigated both experimentally and numerically. The study demonstrated that composite elliptical springs can be used for light and heavy trucks with substantial weight reduction. The results showed that the ellipticity ratio significantly influenced the design parameters. Composite elliptic springs with ellipticity ratios of a/b = 2 had the optimum spring parameters.

  1. Boundary-value problems with free boundaries for elliptic systems of equations

    CERN Document Server

    Monakhov, V N

    1983-01-01

    This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

  2. Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

    Directory of Open Access Journals (Sweden)

    Espen R. Jakobsen

    2002-05-01

    Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.

  3. Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

    Science.gov (United States)

    Nigsch, Martin

    2007-07-01

    A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

  4. RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

    KAUST Repository

    Farrell, Patricio

    2013-01-01

    In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.

  5. Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

    Czech Academy of Sciences Publication Activity Database

    Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan

    2013-01-01

    Roč. 88, č. 3 (2013), "034026-1"-"034026-16" ISSN 1550-7998 Institutional support: RVO:68378271 Keywords : Borel transformation * asymptotic series * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013

  6. Performance of an elliptically tapered neutron guide

    International Nuclear Information System (INIS)

    Muehlbauer, Sebastian; Stadlbauer, Martin; Boeni, Peter; Schanzer, Christan; Stahn, Jochen; Filges, Uwe

    2006-01-01

    Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics

  7. A holomorphic anomaly in the elliptic genus

    International Nuclear Information System (INIS)

    Murthy, Sameer

    2014-01-01

    We consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2,2) superconformal field theories in the infra-red, a prototype of which is the SL(2,ℝ)/U(1) (cigar) coset. We compute the elliptic genus of the GLSMs as a path-integral on the torus using supersymmetric localization. We find that the result is a Jacobi-like form that is non-holomorphic in the modular parameter τ of the torus, with mock modular behavior. This agrees with a previously-computed expression in the cigar coset. We show that the lack of holomorphicity of the elliptic genus arises from the contributions of a compact boson carrying momentum and winding excitations. This boson has an axionic shift symmetry and plays the role of a compensator field that is needed to cancel the chiral anomaly in the rest of the theory.

  8. Nonlinear elliptic equations and nonassociative algebras

    CERN Document Server

    Nadirashvili, Nikolai; Vlăduţ, Serge

    2014-01-01

    This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

  9. On rotational solutions for elliptically excited pendulum

    International Nuclear Information System (INIS)

    Belyakov, Anton O.

    2011-01-01

    The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear dampings. Comparison between approximate and numerical solutions is made for different values of the damping parameter. -- Highlights: → We study rotations of the mathematical pendulum when its pivot moves along an ellipse. → There are stable exact solutions for a circular pivot trajectory and zero gravity. → Asymptotic solutions are found for an elliptical pivot trajectory

  10. A FUNDAMENTAL LINE FOR ELLIPTICAL GALAXIES

    International Nuclear Information System (INIS)

    Nair, Preethi; Van den Bergh, Sidney; Abraham, Roberto G.

    2011-01-01

    Recent studies have shown that massive galaxies in the distant universe are surprisingly compact, with typical sizes about a factor of three smaller than equally massive galaxies in the nearby universe. It has been suggested that these massive galaxies grow into systems resembling nearby galaxies through a series of minor mergers. In this model the size growth of galaxies is an inherently stochastic process, and the resulting size-luminosity relationship is expected to have considerable environmentally dependent scatter. To test whether minor mergers can explain the size growth in massive galaxies, we have closely examined the scatter in the size-luminosity relation of nearby elliptical galaxies using a large new database of accurate visual galaxy classifications. We demonstrate that this scatter is much smaller than has been previously assumed, and may even be so small as to challenge the plausibility of the merger-driven hierarchical models for the formation of massive ellipticals.

  11. Modelling the Inflation of Polyisobutylene Into an Elliptic and a Circular Cylinder

    DEFF Research Database (Denmark)

    Rasmussen, Henrik Koblitz; Gøttsche, Søren; Kjær, Erik Michael

    2000-01-01

    The isothermal inflation of a sheet of a Polyisobutylene melt into a circular and an elliptic cylinder is modelled using the 3D Lagrangian Integral Method. The non-linear properties of the Polyisobutylene are modelled with the Factorized K-BKZ constitutive equation, using a potential function bas...

  12. A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

    OpenAIRE

    Wang, Xu-Jia

    2006-01-01

    In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

  13. Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces

    KAUST Repository

    Efendiev, Yalchin; Galvis, Juan; Lazarov, Raytcho; Weiß er, Steffen

    2014-01-01

    We present a Boundary Element Method (BEM)-based FEM for mixed formulations of second order elliptic problems in two dimensions. The challenge, we would like to address, is a proper construction of H(div)-conforming vector valued trial functions

  14. Dynamics of self-focusing and self-phase modulation of elliptic ...

    Indian Academy of Sciences (India)

    Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of non-linearity and diffraction on wave propagation of optical beam in a homogeneous bulk Kerr-medium is presented. Particular emphasis is put on the variation of beam width and longitudinal phase delay with the ...

  15. Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

    Energy Technology Data Exchange (ETDEWEB)

    Zielinski, Lech [Universite du Littoral, LMPA, Centre Mi-Voix (France)], E-mail: Lech.Zielinski@lmpa.univ-littoral.fr

    2006-02-15

    We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order.

  16. Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

    International Nuclear Information System (INIS)

    Zielinski, Lech

    2006-01-01

    We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order

  17. Integrable mappings via rational elliptic surfaces

    International Nuclear Information System (INIS)

    Tsuda, Teruhisa

    2004-01-01

    We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented

  18. On a fourth order superlinear elliptic problem

    Directory of Open Access Journals (Sweden)

    M. Ramos

    2001-01-01

    Full Text Available We prove the existence of a nonzero solution for the fourth order elliptic equation $$Delta^2u= mu u +a(xg(u$$ with boundary conditions $u=Delta u=0$. Here, $mu$ is a real parameter, $g$ is superlinear both at zero and infinity and $a(x$ changes sign in $Omega$. The proof uses a variational argument based on the argument by Bahri-Lions cite{BL}.

  19. Expansion in the presence of FGF-2 enhances the functional development of cartilaginous tissues engineered using infrapatellar fat pad derived MSCs.

    Science.gov (United States)

    Buckley, C T; Kelly, D J

    2012-07-01

    MSCs from non-cartilaginous knee joint tissues such as the infrapatellar fat pad (IFP) and synovium possess significant chondrogenic potential and provide a readily available and clinically feasible source of chondroprogenitor cells. Fibroblast growth factor-2 (FGF-2) has been shown to be a potent mitotic stimulator during ex vivo expansion of MSCs, as well as regulating their subsequent differentiation potential. The objective of this study was to investigate the longer term effects of FGF-2 expansion on the functional development of cartilaginous tissues engineered using MSCs derived from the IFP. IFP MSCs were isolated and expanded to passage 2 in a standard media formulation with or without FGF-2 (5 ng/ml) supplementation. Expanded cells were encapsulated in agarose hydrogels, maintained in chondrogenic media for 42 days and analysed to determine their mechanical properties and biochemical composition. Culture media, collected at each feed, was also analysed for biochemical constituents. MSCs expanded in the presence of FGF-2 proliferated more rapidly, with higher cell yields and lower population doubling times. FGF-2 expanded MSCs generated the most mechanically functional tissue. Matrix accumulation was dramatically higher after 21 days for FGF-2 expanded MSCs, but decreased between day 21 and 42. By day 42, FGF-2 expanded MSCs had still accumulated ∼1.4 fold higher sGAG and ∼1.7 fold higher collagen compared to control groups. The total amount of sGAG synthesised (retained in hydrogels and released into the media) was ∼2.4 fold higher for FGF-2 expanded MSCs, with only ∼25% of the total amount generated being retained within the constructs. Further studies are required to investigate whether IFP derived MSCs have a diminished capacity to synthesise other matrix components important in the aggregation, assembly and retention of proteoglycans. In conclusion, expanding MSCs in the presence of FGF-2 rapidly accelerates chondrogenesis in 3D agarose

  20. The elliptic model for communication fluxes

    International Nuclear Information System (INIS)

    Herrera-Yagüe, C; Schneider, C M; González, M C; Smoreda, Z; Couronné, T; Zufiria, P J

    2014-01-01

    In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry of transportation models, the new model considers that the number of relationships between two locations is inversely proportional to the population in the ellipse whose foci are in these two locations. The elliptic model is evaluated by considering the anonymous communications patterns of 25 million users from three different countries, where a location has been assigned to each user based on their most used phone tower or billing zip code. With this information, spatial social networks are built at three levels of resolution: tower, city and region for each of the three countries. The elliptic model achieves a similar performance when predicting communication fluxes as transportation models do when predicting trips. This shows that human relationships are influenced at least as much by geography as is human mobility. (paper)

  1. Can elliptical galaxies be equilibrium systems

    Energy Technology Data Exchange (ETDEWEB)

    Caimmi, R [Padua Univ. (Italy). Ist. di Astronomia

    1980-08-01

    This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational + centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes with n = 0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Young et al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical galaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

  2. Determining mass-to-light ratios in elliptical galaxies

    International Nuclear Information System (INIS)

    Mathews, W.G.

    1988-01-01

    If the endstate of cooling hot gas in elliptical galaxies is a population of optically dark, low-mass stars near the galactic cores, the mass-to-light ratio could be expected to vary significantly with projected radius. No strong variation in M/L is observed. To investigate the sensitivity and reliability of observational mass-to-light determinations for a variety of galactic parameters, model galaxies having de Vaucouleurs profiles (but with central cores and outer cutoffs), variable velocity ellipsoid structure, and extended dark halos are constructed. Spurious radial variations in M/L can occur when none are present if the properties of the galactic models are processed similar to observational data. Conversely, when a population of diffuse dark stellar matter is added near the galactic cores, large gradients in M/L can escape detection. However, the magnitude of the central velocity dispersion and its variation with projected radius within the effective radius both suggest that a component of dark stars is unlikely to be more massive than about 30 times the core mass of luminous stars. This restriction is important in establishing the initial mass function of stars in elliptical galaxies and the history of winds and cooling inflows in the interstellar medium. 35 references

  3. Lessons on black holes from the elliptic genus

    Energy Technology Data Exchange (ETDEWEB)

    Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem, 91904 (Israel); Itzhaki, Nissan [Physics Department, Tel-Aviv University,Ramat-Aviv, 69978 (Israel); Troost, Jan [Laboratoire de Physique Théorique, Unité Mixte du CNRS et de l’École Normale Supérieure associée à l’Université Pierre et Marie Curie 6, École Normale Supérieure, Rue Lhomond Paris (France)

    2014-04-28

    We further study the elliptic genus of the cigar SL(2,ℝ){sub k}/U(1) coset superconformal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar’s throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have important consequences for the physics near horizons, even for parametrically large black holes.

  4. A heterogeneous stochastic FEM framework for elliptic PDEs

    International Nuclear Information System (INIS)

    Hou, Thomas Y.; Liu, Pengfei

    2015-01-01

    We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage

  5. Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

    Science.gov (United States)

    Nishimoto, Yoshio

    2015-09-07

    We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

  6. Assessing Impairment of Executive Function and Psychomotor Speed in Premanifest and Manifest Huntington's Disease Gene-expansion Carriers

    DEFF Research Database (Denmark)

    Unmack Larsen, Ida; Vinther-Jensen, Tua; Gade, Anders

    2015-01-01

    Executive functions (EF) and psychomotor speed (PMS) has been widely studied in Huntington's disease (HD). Most studies have focused on finding markers of disease progression by comparing group means at different disease stages. Our aim was to investigate performances on nine measures of EF and PMS...

  7. The anisotropic Ising correlations as elliptic integrals: duality and differential equations

    International Nuclear Information System (INIS)

    McCoy, B M; Maillard, J-M

    2016-01-01

    We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers–Wannier duality to anisotropic correlation functions, and the linear differential equations for these anisotropic correlations. More precisely, we show that the anisotropic correlation functions are homogeneous polynomials of the complete elliptic integrals of the first, second and third kind. We give the exact dual transformation matching the correlation functions and the dual correlation functions. We show that the linear differential operators annihilating the general two-point correlation functions are factorized in a very simple way, in operators of decreasing orders. (paper)

  8. ZONAL TOROIDAL HARMONIC EXPANSIONS OF EXTERNAL GRAVITATIONAL FIELDS FOR RING-LIKE OBJECTS

    Energy Technology Data Exchange (ETDEWEB)

    Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp [National Astronomical Observatory, Ohsawa, Mitaka, Tokyo 181-8588 (Japan)

    2016-08-01

    We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.

  9. Elliptic CY3folds and non-perturbative modular transformation

    International Nuclear Information System (INIS)

    Iqbal, Amer; Shabbir, Khurram

    2016-01-01

    We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

  10. Elliptic CY3folds and non-perturbative modular transformation

    Energy Technology Data Exchange (ETDEWEB)

    Iqbal, Amer [Government College University, Abdus Salam School of Mathematical Sciences, Lahore (Pakistan); Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)

    2016-03-15

    We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

  11. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

    Science.gov (United States)

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-01-01

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

  12. Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

    Science.gov (United States)

    Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

    2014-01-01

    In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

  13. The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion

    International Nuclear Information System (INIS)

    Dominicis, C. de

    1961-01-01

    The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z (α,β) takes a form where, besides trivial dependences, α and β only appear through a statistical factor F k - = [1 + e -α+βε k 0 -βW k ] -1 . W k is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z (α,β) under variations of F k - . The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [fr

  14. Elliptical Galaxies: Rotationally Distorted, After All

    Directory of Open Access Journals (Sweden)

    Caimmi, R.

    2009-12-01

    Full Text Available On the basis of earlier investigations onhomeoidally striated Mac Laurin spheroids and Jacobi ellipsoids (Caimmi and Marmo2005, Caimmi 2006a, 2007, different sequences of configurations are defined and represented in the ellipticity-rotation plane, $({sf O}hat{e}chi_v^2$. The rotation parameter, $chi_v^2$, is defined as the ratio, $E_mathrm{rot}/E_mathrm{res}$, of kinetic energy related to the mean tangential equatorial velocity component, $M(overline{v_phi}^2/2$, to kineticenergy related to tangential equatorial component velocity dispersion, $Msigma_{phiphi}^2/2$, andresidual motions, $M(sigma_{ww}^2+sigma_{33}^2/2$.Without loss of generality (above a thresholdin ellipticity values, the analysis is restricted to systems with isotropic stress tensor, whichmay be considered as adjoint configurationsto any assigned homeoidally striated density profile with anisotropic stress tensor, different angular momentum, and equal remaining parameters.The description of configurations in the$({sf O}hat{e}chi_v^2$ plane is extendedin two respects, namely (a from equilibriumto nonequilibrium figures, where the virialequations hold with additional kinetic energy,and (b from real to imaginary rotation, wherethe effect is elongating instead of flattening,with respect to the rotation axis.An application is made toa subsample $(N=16$ of elliptical galaxies extracted from richer samples $(N=25,~N=48$of early type galaxies investigated within theSAURON project (Cappellari et al. 2006, 2007.Sample objects are idealized as homeoidallystriated MacLaurinspheroids and Jacobi ellipsoids, and theirposition in the $({sf O}hat{e}chi_v^2$plane is inferred from observations followinga procedure outlined in an earlier paper(Caimmi 2009b. The position of related adjoint configurations with isotropic stresstensor is also determined. With a singleexception (NGC 3379, slow rotators arecharacterized by low ellipticities $(0lehat{e}<0.2$, low anisotropy parameters$(0ledelta<0

  15. Characterization of the mycobacterial acyl-CoA carboxylase holo complexes reveals their functional expansion into amino acid catabolism.

    Directory of Open Access Journals (Sweden)

    Matthias T Ehebauer

    2015-02-01

    Full Text Available Biotin-mediated carboxylation of short-chain fatty acid coenzyme A esters is a key step in lipid biosynthesis that is carried out by multienzyme complexes to extend fatty acids by one methylene group. Pathogenic mycobacteria have an unusually high redundancy of carboxyltransferase genes and biotin carboxylase genes, creating multiple combinations of protein/protein complexes of unknown overall composition and functional readout. By combining pull-down assays with mass spectrometry, we identified nine binary protein/protein interactions and four validated holo acyl-coenzyme A carboxylase complexes. We investigated one of these--the AccD1-AccA1 complex from Mycobacterium tuberculosis with hitherto unknown physiological function. Using genetics, metabolomics and biochemistry we found that this complex is involved in branched amino-acid catabolism with methylcrotonyl coenzyme A as the substrate. We then determined its overall architecture by electron microscopy and found it to be a four-layered dodecameric arrangement that matches the overall dimensions of a distantly related methylcrotonyl coenzyme A holo complex. Our data argue in favor of distinct structural requirements for biotin-mediated γ-carboxylation of α-β unsaturated acid esters and will advance the categorization of acyl-coenzyme A carboxylase complexes. Knowledge about the underlying structural/functional relationships will be crucial to make the target category amenable for future biomedical applications.

  16. Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

    Science.gov (United States)

    Jia, Weile; Lin, Lin

    2017-10-01

    Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

  17. Goodness-of-Fit Tests For Elliptical and Independent Copulas through Projection Pursuit

    Directory of Open Access Journals (Sweden)

    Jacques Touboul

    2011-04-01

    Full Text Available Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology that we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets.

  18. Performances study of UWB monopole antennas using half-elliptic radiator conformed on elliptical surface

    Energy Technology Data Exchange (ETDEWEB)

    Djidel, S.; Bouamar, M.; Khedrouche, D., E-mail: dkhedrouche@yahoo.com [LASS (Laboratoired’Analyse des Signaux et Systèmes), Department of Electronics, University of M’sila BP.166, Route Ichebilia, M’sila, 28000 Algeria (Algeria)

    2016-04-21

    This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.

  19. A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions.

    Science.gov (United States)

    van Meer, R; Gritsenko, O V; Baerends, E J

    2018-03-14

    Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH 4 , NH 3 , H 2 O, FH, and N 2 ) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron.

  20. A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions

    Science.gov (United States)

    van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

    2018-03-01

    Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH4, NH3, H2O, FH, and N2) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron.

  1. Statistics about elliptic curves over finite prime fields

    OpenAIRE

    Gekeler, Ernst-Ulrich

    2006-01-01

    We derive formulas for the probabilities of various properties (cyclicity, squarefreeness, generation by random points) of the point groups of randomly chosen elliptic curves over random prime fields.

  2. COLORS OF ELLIPTICALS FROM GALEX TO SPITZER

    Energy Technology Data Exchange (ETDEWEB)

    Schombert, James M., E-mail: jschombe@uoregon.edu [Department of Physics, University of Oregon, Eugene, OR 97403 (United States)

    2016-12-01

    Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

  3. Constraints on stellar populations in elliptical galaxies

    International Nuclear Information System (INIS)

    Rose, J.A.

    1985-01-01

    Photographic image-tube spectra in the wavelength interval 3400--4500 A have been obtained for 12 elliptical galaxy nuclei and for a number of Galactic globular and open clusters in integrated light. The spectra have a wavelength resolution of 2.5 A and a high signal-to-noise ratio. A new quantitative three-dimensional spectral-classification system that has been calibrated on a sample of approx.200 individual stars (Rose 1984) is used to analyze the integrated spectra of the ellipical galaxy nuclei and to compare them with those of the globular clusters. This system is based on spectral indices that are formed by comparing neighborhood spectral features and is unaffected by reddening. The following results have been found: (1) Hot stars (i.e., spectral types A and B) contribute only 2% to the integrated spectra of elliptical galaxies at approx.4000 A, except in the nucleus of NGC 205, where the hot component dominates. This finding is based on a spectral index formed from the relative central intensities in the Ca II H+Hepsilon and Ca II K lines, which is shown to be constant for late-type (i.e., F, G, and K) stars, but changes drastically at earlier types. The observed Ca II H+Hepsilon/Ca II K indices in ellipticals can be reproduced by the inclusion of a small metal-poor population (as in the globular cluster M5) that contributes approx.8% of the light at 4000 A. Such a contribution is qualitatively consistent with the amount of

  4. COLORS OF ELLIPTICALS FROM GALEX TO SPITZER

    International Nuclear Information System (INIS)

    Schombert, James M.

    2016-01-01

    Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

  5. Evolution of Hot Gas in Elliptical Galaxies

    Science.gov (United States)

    Mathews, William G.

    2004-01-01

    This theory grant was awarded to study the curious nature, origin and evolution of hot gas in elliptical galaxies and their surrounding groups. Understanding the properties of this X-ray emitting gas has profound implications over the broad landscape of modern astrophysics: cosmology, galaxy formation, star formation, cosmic metal enrichment, galactic structure and dynamics, and the physics of hot gases containing dust and magnetic fields. One of our principal specific objectives was to interpret the marvelous new observations from the XMM and Chandru satellite X-ray telescopes.

  6. Neutral hydrogen in elliptical and IO galaxies

    International Nuclear Information System (INIS)

    Bottinelli, L.; Gouguenheim, L.

    1979-01-01

    New HI detections have been obtained using the Nancay radiotelescope for NGC 2974 and 3962. These results and the large scale distribution obtained for NGC 3962 indicate that the HI-rich elliptical galaxies exhibit common properties which are not easily explained by accretion of an intergalactic cloud. The field aroud NGC 1052 has been mapped and there is an HI connection with the neighbouring galaxies. The HI content of several IO galaxies indicates that the galaxies which are members of groups are relatively HI-rich; this could be produced by additional HI coming from companion galaxies [fr

  7. Instanton geometry and quantum A∞ structure on the elliptic curve

    International Nuclear Information System (INIS)

    Herbst, M.; Lerche, W.; Nemeschansky, D.

    2006-03-01

    We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the 'long-diagonal branes' on the elliptic curve. We verify that they satisfy the relevant A ∞ consistency relations at both classical and quantum levels. In particular we find that the A ∞ relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A ∞ relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields. (orig.)

  8. Magnetic X-ray measurements using the elliptical multipole wiggler

    International Nuclear Information System (INIS)

    Montano, P. A.; Li, Y.; Beno, M. A.; Jennings, G.; Kimball, C. W.

    1999-01-01

    The EMW at the BESSRC beam lines at the APS provides high photon flux at high energies with the capability of producing circular polarization on axis. The authors observe a high degree of circularly polarized x-rays at such energies. The polarization and frequency tunability of the elliptical multipole wiggler (EMW) is an ideal source for many magnetic measurements from X-ray Magnetic Circular Dichroism (XMCD) to Compton scattering experiments. They performed Compton scattering measurements to determine the polarization and photon flux at the sample as a function of the deflection parameters K y and K x . They used for their measurements a Si (220) Laue monochromator providing simultaneous photon energies at 50 keV, 100 keV and 150 keV. Magnetic Compton Profiles were determined by either switching the magnet polarity or the photon helicity. The results obtained using Fe(110) single crystals were very similar

  9. Numerical simulation of heat exchangers elliptical tubes and corrugated fins

    International Nuclear Information System (INIS)

    Borrajo Pérez, Rubén; González Bayón, Juan José; Menéndez Pérez, Alberto

    2015-01-01

    The intensified heat exchangers fins are widely used in the automotive and domestic industry. The low heat transfer coefficients on the air side are the main reason why these fins of heat exchangers need to be intensified. In this paper, the numerical simulation of a wavy fin type is made with elliptical tubes. The dimensions of the fin is in the range of those used in air conditioning equipment. The friction factor and the mass transfer coefficient as a function of the Reynolds number for this type of fin, always within the laminar regime is determined. The numerical model against experimental results published in the literature is validated. In addition the mechanisms that produce intensified heat transfer fin in such occur. (full text)

  10. A new approach to flow through a region bounded by two ellipses of the same ellipticity

    Science.gov (United States)

    Lal, K.; Chorlton, F.

    1981-05-01

    A new approach is presented to calculate steady flow of a laminar viscous incompressible fluid through a channel whose cross section is bounded by two ellipses with the same ellipticity. The Milne-Thomas approach avoids the stream function and is similar to the Rayleigh-Ritz approximation process of the calculus of variations in its first satisfying boundary conditions and then adjusting constants or multiplying functions to fit the differential equation.

  11. Thermodynamics of Inozemtsev's elliptic spin chain

    International Nuclear Information System (INIS)

    Klabbers, Rob

    2016-01-01

    We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

  12. Development of a superconducting elliptically polarized undulator

    International Nuclear Information System (INIS)

    Chen, S D; Liang, K S; Jan, J C; Hwang, C S

    2010-01-01

    A superconducting, elliptically polarized undulator (SEPU24) with a period of length 24 mm was developed to provide first-harmonic photons from a 0.8 GeV storage ring for extreme-ultraviolet (EUV) lithography experiment. In SEPU24, two layers of a magnet array structure - with and without rotated magnet arrays - are combined to generate a helical field that provides radiation with wavelength 13.5 nm in the in-band energy. The arrays of iron and aluminium poles were wound with a racetrack coil vertically as for the magnet pole array. The elliptical field is created when the up and down magnet-pole arrays pass excitation currents in alternate directions. SEPU24 is designed with a magnet of gap 6.8 mm, yielding magnetic flux density B x =B z =0.61 T of the helical field. A prototype magnet was fabricated with a diode for quench protection, and assembled in a test dewar to test the magnet performance. A cryogenic Hall-probe system with a precise linear stage was used to measure the distribution of the magnetic field. We describe the design concept and algorithm, the engineering design, the calculation of the magnetic field, the construction and testing of the 10-pole prototype magnet and related issues.

  13. On the N=1{sup ∗} gauge theory on a circle and elliptic integrable systems

    Energy Technology Data Exchange (ETDEWEB)

    Bourget, Antoine; Troost, Jan [Laboratoire de Physique Théorique, Ecole Normale Supérieure,24 rue Lhomond, 75005 Paris (France)

    2016-01-18

    We continue our study of the N=1{sup ∗} supersymmetric gauge theory on ℝ{sup 2,1}×S{sup 1} and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the classification of nilpotent orbits, as well as on the conjugacy classes of the component group of their centralizer. We demonstrate that semi-classically massless vacua can be lifted by Wilson lines in unbroken discrete gauge groups. The pseudo-Levi subalgebras that play a classifying role in the nilpotent orbit theory are also key in defining generalized Inozemtsev limits of (twisted) elliptic integrable systems. We illustrate our analysis in the N=1{sup ∗} theories with gauge algebras su(3), su(4), so(5) and for the exceptional gauge algebra G{sub 2}. We map out modular duality diagrams of the massive and massless vacua. Moreover, we provide an analytic description of the branches of massless vacua in the case of the su(3) and the so(5) theory. The description of these branches in terms of the complexified Wilson lines on the circle invokes the Eichler-Zagier technique for inverting the elliptic Weierstrass function. After fine-tuning the coupling to elliptic points of order three, we identify the Argyres-Douglas singularities of the su(3)N=1{sup ∗} theory.

  14. Magnetic properties of elliptical and stadium-shaped nanoparticles: Effect of the shape anisotropy

    Energy Technology Data Exchange (ETDEWEB)

    Corona, R.M. [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Altbir, D. [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Escrig, J., E-mail: jescrigm@gmail.com [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Avda. Ecuador 3493, 917-0124 Santiago (Chile)

    2012-11-15

    Elliptical and stadium-shaped nanoparticles as a function of their geometry have been investigated using numerical simulations. The effect of the shape anisotropy of the particles on coercivity and remanence together with the angular dependence of the remanence and coercivity are addressed. Our results demonstrate that the stadium-shaped particles have many of the outstanding properties of elliptical particles, but also have unique properties, such that the coercivity and remanence remain stable for a wide range of geometry parameters, and exhibit a peculiar angular dependence in the coercivity. These properties suggest that they can be useful for applications in the area of magnetic recording systems. - Highlights: Black-Right-Pointing-Pointer Coercivity and remanence are strongly affected by the shape anisotropy of the particles. Black-Right-Pointing-Pointer Coercivities for ellipses are nearly three times the obtained for stadium-shaped particles. Black-Right-Pointing-Pointer Elliptical particles with {delta}{<=}0.6, the hystereses resemble the square loops of wires. Black-Right-Pointing-Pointer An anhisteretic behavior appears for {theta}=90 Degree-Sign for elliptical particles, which do not appear in stadium-shaped particles. Black-Right-Pointing-Pointer Stadium-shaped particles have unique properties that allow us to suggest them for applications.

  15. Magnetic properties of elliptical and stadium-shaped nanoparticles: Effect of the shape anisotropy

    International Nuclear Information System (INIS)

    Corona, R.M.; Altbir, D.; Escrig, J.

    2012-01-01

    Elliptical and stadium-shaped nanoparticles as a function of their geometry have been investigated using numerical simulations. The effect of the shape anisotropy of the particles on coercivity and remanence together with the angular dependence of the remanence and coercivity are addressed. Our results demonstrate that the stadium-shaped particles have many of the outstanding properties of elliptical particles, but also have unique properties, such that the coercivity and remanence remain stable for a wide range of geometry parameters, and exhibit a peculiar angular dependence in the coercivity. These properties suggest that they can be useful for applications in the area of magnetic recording systems. - Highlights: ► Coercivity and remanence are strongly affected by the shape anisotropy of the particles. ► Coercivities for ellipses are nearly three times the obtained for stadium-shaped particles. ►Elliptical particles with δ≤0.6, the hystereses resemble the square loops of wires. ► An anhisteretic behavior appears for θ=90° for elliptical particles, which do not appear in stadium-shaped particles. ► Stadium-shaped particles have unique properties that allow us to suggest them for applications.

  16. Constructive Solution of Ellipticity Problem for the First Order Differential System

    Directory of Open Access Journals (Sweden)

    Vladimir E. Balabaev

    2017-01-01

    Full Text Available We built first order elliptic systems with any possible number of unknown functions and the maximum possible number of unknowns, i.e, in general. These systems provide the basis for studying the properties of any first order elliptic systems. The study of the Cauchy-Riemann system and its generalizations led to the identification of a class of elliptic systems of first-order of a special structure. An integral representation of solutions is of great importance in the study of these systems. Only by means of a constructive method of integral representations we can solve a number of problems in the theory of elliptic systems related mainly to the boundary properties of solutions. The obtained integral representation could be applied to solve a number of problems that are hard to solve, if you rely only on the non-constructive methods. Some analogues of the theorems of Liouville, Weierstrass, Cauchy, Gauss, Morera, an analogue of Green’s formula are established, as well as an analogue of the maximum principle. The used matrix operators allow the new structural arrangement of the maximum number of linearly independent vector fields on spheres of any possible dimension. Also the built operators allow to obtain a constructive solution of the extended problem ”of the sum of squares” known in algebra. 

  17. Picone-type inequalities for nonlinear elliptic equations and their applications

    Directory of Open Access Journals (Sweden)

    Takaŝi Kusano

    2001-01-01

    Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

  18. Elliptical Orbit [arrow right] 1/r[superscript 2] Force

    Science.gov (United States)

    Prentis, Jeffrey; Fulton, Bryan; Hesse, Carol; Mazzino, Laura

    2007-01-01

    Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

  19. Multiple solutions for a quasilinear (p,q-elliptic system

    Directory of Open Access Journals (Sweden)

    Seyyed Mohsen Khalkhali

    2013-06-01

    Full Text Available In this article we show the existence of three weak solutions of a Dirichlet quasilinear elliptic system of differential equations which involves a general (p,q-elliptic operator in divergence, with $1

  20. three solutions for a semilinear elliptic boundary value problem

    Indian Academy of Sciences (India)

    69

    Keywords: The Laplacian operator, elliptic problem, Nehari man- ifold, three critical points, weak solution. 1. Introduction. Let Ω be a smooth bounded domain in RN , N ≥ 3 . In this work, we show the existence of at least three solutions for the semilinear elliptic boundary- value problem: (Pλ).. −∆u = f(x)|u(x)|p−2u(x) + ...

  1. Rotational magnetization of anisotropic media: Lag angle, ellipticity and accommodation

    International Nuclear Information System (INIS)

    Kahler, G.R.; Della Torre, E.

    2006-01-01

    This paper discusses the change in the ellipticity of two-dimensional magnetization trajectories as the applied field rotates from the easy axis to the hard axis of a material. Furthermore, the impact that the reversible magnetization has on the ellipticity is discussed, including the relationship between the magnetization squareness and the reversible component of the magnetization

  2. Near-infrared photometry of bright elliptical galaxies

    NARCIS (Netherlands)

    Peletier, R. F.; Valentijn, E. A.; Jameson, R. F.

    High-quality visual-infrared color profiles have been determined for elliptical galaxies for the first time. Surface photometry in J and K is presented for 12 bright elliptical galaxies, and the results have been combined with CCD data in visual passbands. It is shown that the galaxies become bluer

  3. Vanishing viscosity limits of mixed hyperbolic–elliptic systems arising in multilayer channel flows

    International Nuclear Information System (INIS)

    Papaefthymiou, E S; Papageorgiou, D T

    2015-01-01

    This study considers the spatially periodic initial value problem of 2 × 2 quasi-linear parabolic systems in one space dimension having quadratic polynomial flux functions. These systems arise physically in the interfacial dynamics of viscous immiscible multilayer channel flows. The equations describe the spatiotemporal evolution of phase-separating interfaces with dissipation arising from surface tension (fourth-order) and/or stable stratification effects (second-order). A crucial mathematical aspect of these systems is the presence of mixed hyperbolic–elliptic flux functions that provide the only source of instability. The study concentrates on scaled spatially 2π-periodic solutions as the dissipation vanishes, and in particular the behaviour of such limits when generalized dissipation operators (spanning second to fourth-order) are considered. Extensive numerical computations and asymptotic analysis suggest that the existence (or not) of bounded vanishing viscosity solutions depends crucially on the structure of the flux function. In the absence of linear terms (i.e. homogeneous flux functions) the vanishing viscosity limit does not exist in the L ∞ -norm. On the other hand, if linear terms in the flux function are present the computations strongly suggest that the solutions exist and are bounded in the L ∞ -norm as the dissipation vanishes. It is found that the key mechanism that provides such boundedness centres on persistent spatiotemporal hyperbolic–elliptic transitions. Strikingly, as the dissipation decreases, the flux function becomes almost everywhere hyperbolic except on a fractal set of elliptic regions, whose dimension depends on the order of the regularized operator. Furthermore, the spatial structures of the emerging weak solutions are found to support an increasing number of discontinuities (measure-valued solutions) located in the vicinity of the fractally distributed elliptic regions. For the unscaled problem, such spatially

  4. Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

    Science.gov (United States)

    Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

    2018-03-01

    We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

  5. On the Behavior of Eisenstein Series Through Elliptic Degeneration

    Science.gov (United States)

    Garbin, D.; Pippich, A.-M. V.

    2009-12-01

    Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

  6. Ellipticity of near-threshold harmonics from stretched molecules.

    Science.gov (United States)

    Li, Weiyan; Dong, Fulong; Yu, Shujuan; Wang, Shang; Yang, Shiping; Chen, Yanjun

    2015-11-30

    We study the ellipticity of near-threshold harmonics (NTH) from aligned molecules with large internuclear distances numerically and analytically. The calculated harmonic spectra show a broad plateau for NTH which is several orders of magnitude higher than that for high-order harmonics. In particular, the NTH plateau shows high ellipticity at small and intermediate orientation angles. Our analyses reveal that the main contributions to the NTH plateau come from the transition of the electron from continuum states to these two lowest bound states of the system, which are strongly coupled together by the laser field. Besides continuum states, higher excited states also play a role in the NTH plateau, resulting in a large phase difference between parallel and perpendicular harmonics and accordingly high ellipticity of the NTH plateau. The NTH plateau with high intensity and large ellipticity provides a promising manner for generating strong elliptically-polarized extreme-ultraviolet (EUV) pulses.

  7. Multipacting studies in elliptic SRF cavities

    Science.gov (United States)

    Prakash, Ram; Jana, Arup Ratan; Kumar, Vinit

    2017-09-01

    Multipacting is a resonant process, where the number of unwanted electrons resulting from a parasitic discharge rapidly grows to a larger value at some specific locations in a radio-frequency cavity. This results in a degradation of the cavity performance indicators (e.g. the quality factor Q and the maximum achievable accelerating gradient Eacc), and in the case of a superconducting radiofrequency (SRF) cavity, it leads to a quenching of superconductivity. Numerical simulations are essential to pre-empt the possibility of multipacting in SRF cavities, such that its design can be suitably refined to avoid this performance limiting phenomenon. Readily available computer codes (e.g.FishPact, MultiPac,CST-PICetc.) are widely used to simulate the phenomenon of multipacting in such cases. Most of the contemporary two dimensional (2D) codes such as FishPact, MultiPacetc. are unable to detect the multipacting in elliptic cavities because they use a simplistic secondary emission model, where it is assumed that all the secondary electrons are emitted with same energy. Some three-dimensional (3D) codes such as CST-PIC, which use a more realistic secondary emission model (Furman model) by following a probability distribution for the emission energy of secondary electrons, are able to correctly predict the occurrence of multipacting. These 3D codes however require large data handling and are slower than the 2D codes. In this paper, we report a detailed analysis of the multipacting phenomenon in elliptic SRF cavities and development of a 2D code to numerically simulate this phenomenon by employing the Furman model to simulate the secondary emission process. Since our code is 2D, it is faster than the 3D codes. It is however as accurate as the contemporary 3D codes since it uses the Furman model for secondary emission. We have also explored the possibility to further simplify the Furman model, which enables us to quickly estimate the growth rate of multipacting without

  8. How Does Abundance Affect the Strength of UV Emission in Elliptical Galaxies?

    Science.gov (United States)

    Sonneborn, George (Technical Monitor); Brown, Thomas

    2005-01-01

    This program used the Far Ultraviolet Spectroscopic Explorer (FUSE) to observe elliptical galaxies with the intention of measuring the chemical abundances in their hot stellar populations. It was designed to complement an earlier FUSE program that observed elliptical galaxies with strong UV emission. The current program originally planned observations of two ellipticals with weak UV emission (M32 and M49). Once FUSE encountered pointing control problems in certain regions of the sky (particularly Virgo, which is very unfortunate for the study of ellipticals in general), M49 was replaced with the bulge of M31, which has a similar UV-to-optical flux ratio as the center of M49. As the closest elliptical galaxy and the one with the weakest UV-to-optical flux ratio, M32 was an obvious choice of target, but M49 was the ideal complementary target, because it has a very low reddening (unlike M32). With the inability of FUSE to point at Virgo, nearly all of the best elliptical galaxies (bright galaxies with low foreground extinction) were also lost, and this severely hampered three FUSE programs of the PI, all focused on the hot stellar populations of ellipticals. M31 was the best replacement for M49, but like M32, it suffers from significant foreground reddening. Strong Galactic ISM lines heavily contaminate the FUSE spectra of M31 and M32. These ISM lines are coincident with the photospheric lines from the stellar populations (whereas M49, with little foreground ISM and significant redshift, would not have suffered from this problem). We have reduced the faint (and thus difficult) data for M31 and M32, producing final co-added spectra representing all of the exposures, but we have not yet finished our analysis, due to the complication of the contaminating ISM. The silver lining here is the set of CHI lines at 1175 Angstroms, which are not significantly contaminated by the ISM. A comparison of the M31 spectrum with other galaxies observed by FEE showed a surprising result

  9. The different star formation histories of blue and red spiral and elliptical galaxies

    Science.gov (United States)

    Tojeiro, Rita; Masters, Karen L.; Richards, Joshua; Percival, Will J.; Bamford, Steven P.; Maraston, Claudia; Nichol, Robert C.; Skibba, Ramin; Thomas, Daniel

    2013-06-01

    We study the spectral properties of intermediate mass galaxies (M* ˜ 1010.7 M⊙) as a function of colour and morphology. We use Galaxy Zoo to define three morphological classes of galaxies, namely early types (ellipticals), late-type (disc-dominated) face-on spirals and early-type (bulge-dominated) face-on spirals. We classify these galaxies as blue or red according to their Sloan Digital Sky Survey (SDSS) g - r colour and use the spectral fitting code Versatile Spectral Analyses to calculate time-resolved star formation histories, metallicity and total starlight dust extinction from their SDSS fibre spectra. We find that red late-type spirals show less star formation in the last 500 Myr than blue late-type spirals by up to a factor of 3, but share similar star formation histories at earlier times. This decline in recent star formation explains their redder colour: their chemical and dust content are the same. We postulate that red late-type spirals are recent descendants of blue late-type spirals, with their star formation curtailed in the last 500 Myr. The red late-type spirals are however still forming stars ≃17 times faster than red ellipticals over the same period. Red early-type spirals lie between red late-type spirals and red ellipticals in terms of recent-to-intermediate star formation and dust content. Therefore, it is plausible that these galaxies represent an evolutionary link between these two populations. They are more likely to evolve directly into red ellipticals than red late-type spirals, which show star formation histories and dust content closer to blue late-type spirals. Blue ellipticals show similar star formation histories as blue spirals (regardless of type), except that they have formed less stars in the last 100 Myr. However, blue ellipticals have different dust content, which peaks at lower extinction values than all spiral galaxies. Therefore, many blue ellipticals are unlikely to be descendants of blue spirals, suggesting there may

  10. Young and Old X-ray Binary and IXO Populations in Spiral and Elliptical Galaxies

    Science.gov (United States)

    Colbert, E.; Heckman, T.; Ptak, A.; Strickland, D.; Weaver, K.

    2003-03-01

    We have analyzed Chandra ACIS observations of 32 nearby spiral and elliptical galaxies and present the results of 1441 X-ray point sources, which are presumed to be mostly X-ray binaries (XRBs) and Intermediate-luminosity X-ray Objects (IXOs, a.k.a. ULXs). The X-ray luminosity functions (XLFs) of the point sources show that the slope of the elliptical galaxy XLFs are significantly steeper than the spiral galaxy XLFs, indicating grossly different types of point sources, or different stages in their evolution. Since the spiral galaxy XLF is so shallow, the most luminous points sources (usually the IXOs) dominate the total X-ray point source luminosity LXP. We show that the galaxy total B-band and K-band light (proxies for the stellar mass) are well correlated with LXP for both spirals and ellipticals, but the FIR and UV emission is only correlated for the spirals. We deconvolve LXP into two components, one that is proportional to the galaxy stellar mass (pop II), and another that is proportional to the galaxy SFR (pop I). We also note that IXOs (and nearly all of the other point sources) in both spirals and ellipticals have X-ray colors that are most consistent with power-law slopes of Gamma ˜ 1.5--3.0, which is inconsistent with high-mass XRBS (HMXBs). Thus, HMXBs are not important contributors to LXP. We have also found that IXOs in spiral galaxies may have a slightly harder X-ray spectrum than those in elliptical galaxies. The implications of these findings will be discussed.

  11. Magnetic elliptical polarization of Schumann resonances

    International Nuclear Information System (INIS)

    Sentman, D.D.

    1987-01-01

    Measurements of orthogonal, horizontal components of the magnetic field in the ELF range obtained during September 1985 show that the Schumann resonance eigenfrequencies determined separately for the north-south and east-west magnetic components differ by as much as 0.5 Hz, suggesting that the underlying magnetic signal is not linearly polarized at such times. The high degree of magnetic ellipticity found suggests that the side multiplets of the Schumann resonances corresponding to azimuthally inhomogeneous normal modes are strongly excited in the highly asymmetric earth-ionosphere cavity. The dominant sense of polarization over the measurement passband is found to be right-handed during local daylight hours, and to be left-handed during local nighttime hours. 16 references

  12. Elliptic flow and incomplete equilibration at RHIC

    CERN Document Server

    Bhalerao, R S; Borghini, N; Ollitrault, Jean Yves

    2005-01-01

    We argue that RHIC data, in particular those on the anisotropic flow coefficients v_2 and v_4, suggest that the matter produced in the early stages of nucleus-nucleus collisions is incompletely thermalized. We interpret the parameter (1/S)(dN/dy), where S is the transverse area of the collision zone and dN/dy the multiplicity density, as an indicator of the number of collisions per particle at the time when elliptic flow is established, and hence as a measure of the degree of equilibration. This number serves as a control parameter which can be varied experimentally by changing the system size, the centrality or the beam energy. We provide predictions for Cu-Cu collisions at RHIC as well as for Pb-Pb collisions at the LHC.

  13. An implementation of multiple multipole method in the analyse of elliptical objects to enhance backscattering light

    Science.gov (United States)

    Jalali, T.

    2015-07-01

    In this paper, we present dielectric elliptical shapes modelling with respect to a highly confined power distribution in the resulting nanojet, which has been parameterized according to the beam waist and its beam divergence. The method is based on spherical bessel function as a basis function, which is adapted to standard multiple multipole method. This method can handle elliptically shaped particles due to the change of size and refractive indices, which have been studied under plane wave illumination in two and three dimensional multiple multipole method. Because of its fast and good convergence, the results obtained from simulation are highly accurate and reliable. The simulation time is less than minute for two and three dimension. Therefore, the proposed method is found to be computationally efficient, fast and accurate.

  14. Elliptic-cylindrical analytical flux-rope model for ICMEs

    Science.gov (United States)

    Nieves-Chinchilla, T.; Linton, M.; Hidalgo, M. A. U.; Vourlidas, A.

    2016-12-01

    We present an analytical flux-rope model for realistic magnetic structures embedded in Interplanetary Coronal Mass Ejections. The framework of this model was established by Nieves-Chinchilla et al. (2016) with the circular-cylindrical analytical flux rope model and under the concept developed by Hidalgo et al. (2002). Elliptic-cylindrical geometry establishes the first-grade of complexity of a series of models. The model attempts to describe the magnetic flux rope topology with distorted cross-section as a possible consequence of the interaction with the solar wind. In this model, the flux rope is completely described in the non-euclidean geometry. The Maxwell equations are solved using tensor calculus consistently with the geometry chosen, invariance along the axial component, and with the only assumption of no radial current density. The model is generalized in terms of the radial dependence of the poloidal current density component and axial current density component. The misalignment between current density and magnetic field is studied in detail for the individual cases of different pairs of indexes for the axial and poloidal current density components. This theoretical analysis provides a map of the force distribution inside of the flux-rope. The reconstruction technique has been adapted to the model and compared with in situ ICME set of events with different in situ signatures. The successful result is limited to some cases with clear in-situ signatures of distortion. However, the model adds a piece in the puzzle of the physical-analytical representation of these magnetic structures. Other effects such as axial curvature, expansion and/or interaction could be incorporated in the future to fully understand the magnetic structure. Finally, the mathematical formulation of this model opens the door to the next model: toroidal flux rope analytical model.

  15. Quasi-Static Transient Thermal Stresses in an Elliptical Plate due to Sectional Heat Supply on the Curved Surfaces over the Upper Face

    Directory of Open Access Journals (Sweden)

    Lalsingh Khalsa

    2018-01-01

    Full Text Available This paper is an attempt to determine quasi-static thermal stresses in a thin elliptical plate which is subjected to transient temperature on the top face with zero temperature on the lower face and the homogeneous boundary condition of the third kind on the fixed elliptical curved surface. The solution to conductivity equation is elucidated by employing a classical method. The solution of stress components is achieved by using Goodier’s and Airy’s potential function involving the Mathieu and modified functions and their derivatives. The obtained numerical results are accurate enough for practical purposes, better understanding of the underlying elliptic object, and better estimates of the thermal effect on the thermoelastic problem. The conclusions emphasize the importance of better understanding of the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect on the thermoelastic problem.

  16. Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM

    Czech Academy of Sciences Publication Activity Database

    Šolín, P.; Vejchodský, Tomáš; Araiza, R.

    2007-01-01

    Roč. 76, 1-3 (2007), s. 205-210 ISSN 0378-4754 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete nonnegativity conservation * discrete Green's function * elliptic problems * hp-FEM * higher-order finite element methods * Poisson equation * numerical experimetns Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007

  17. Multiple scattering of elliptically polarized light in two-dimensional medium with large inhomogeneities

    Energy Technology Data Exchange (ETDEWEB)

    Gorodnichev, E. E., E-mail: gorodn@theor.mephi.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (Russian Federation)

    2016-12-15

    For elliptically polarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.

  18. Asymptotic Estimates and Qualitatives Properties of an Elliptic Problem in Dimension Two

    OpenAIRE

    Mehdi, Khalil El; Grossi, Massimo

    2003-01-01

    In this paper we study a semilinear elliptic problem on a bounded domain in $\\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates which enable us to associate a "limit problem" to the initial one. Usong these estimates we prove some quantitative properties of the solution, namely characterization of level sets and nondegeneracy.

  19. On the solution of elliptic partial differential equations on regions with corners

    International Nuclear Information System (INIS)

    Serkh, Kirill; Rokhlin, Vladimir

    2016-01-01

    In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

  20. Formation of dwarf ellipticals and dwarf irregular galaxies by interaction of giant galaxies under environmental influence

    OpenAIRE

    Chattopadhyay, Tanuka; Debsarma, Suma; Karmakar, Pradip; Davoust, Emmanuel

    2014-01-01

    A model is proposed for the formation of gas-rich dwarf irregular galaxies and gas-poor, rotating dwarf elliptical galaxies following the interaction between two giant galaxies as a function of space density. The formation of dwarf galaxies is considered to depend on a random variable, the tidal index theta, an environmental parameter defined by Karachentsev et al. (2004), such that for theta less than zero, the formation of dwarf irregular galaxy is assured whereas for theta greater than zer...

  1. Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Zielinski, Lech [Universite Paris 7 (D. Diderot), Institut de Mathematiques de Paris-Jussieu UMR9994 (France)

    1999-09-15

    The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.

  2. Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

    International Nuclear Information System (INIS)

    Zielinski, Lech

    1999-01-01

    The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients

  3. On genus expansion of superpolynomials

    Energy Technology Data Exchange (ETDEWEB)

    Mironov, Andrei, E-mail: mironov@itep.ru [Lebedev Physics Institute, Moscow 119991 (Russian Federation); ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Morozov, Alexei, E-mail: morozov@itep.ru [ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Sleptsov, Alexei, E-mail: sleptsov@itep.ru [ITEP, Moscow 117218 (Russian Federation); Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk 454001 (Russian Federation); KdVI, University of Amsterdam (Netherlands); Smirnov, Andrey, E-mail: asmirnov@math.columbia.edu [ITEP, Moscow 117218 (Russian Federation); Columbia University, Department of Mathematics, New York (United States)

    2014-12-15

    Recently it was shown that the (Ooguri–Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β-deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots.

  4. Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

    KAUST Repository

    Waheed, Umair bin

    2014-05-01

    Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

  5. Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

    KAUST Repository

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2014-01-01

    Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

  6. Streamline integration as a method for two-dimensional elliptic grid generation

    Energy Technology Data Exchange (ETDEWEB)

    Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at [Institute for Ion Physics and Applied Physics, Universität Innsbruck, A-6020 Innsbruck (Austria); Held, M. [Institute for Ion Physics and Applied Physics, Universität Innsbruck, A-6020 Innsbruck (Austria); Einkemmer, L. [Numerical Analysis group, Universität Innsbruck, A-6020 Innsbruck (Austria)

    2017-07-01

    We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.

  7. High-resolution respirometry of fine-needle muscle biopsies in pre-manifest Huntington's disease expansion mutation carriers shows normal mitochondrial respiratory function.

    Directory of Open Access Journals (Sweden)

    Eva Buck

    Full Text Available Alterations in mitochondrial respiration are an important hallmark of Huntington's disease (HD, one of the most common monogenetic causes of neurodegeneration. The ubiquitous expression of the disease causing mutant huntingtin gene raises the prospect that mitochondrial respiratory deficits can be detected in skeletal muscle. While this tissue is readily accessible in humans, transgenic animal models offer the opportunity to cross-validate findings and allow for comparisons across organs, including the brain. The integrated respiratory chain function of the human vastus lateralis muscle was measured by high-resolution respirometry (HRR in freshly taken fine-needle biopsies from seven pre-manifest HD expansion mutation carriers and nine controls. The respiratory parameters were unaffected. For comparison skeletal muscle isolated from HD knock-in mice (HdhQ111 as well as a broader spectrum of tissues including cortex, liver and heart muscle were examined by HRR. Significant changes of mitochondrial respiration in the HdhQ knock-in mouse model were restricted to the liver and the cortex. Mitochondrial mass as quantified by mitochondrial DNA copy number and citrate synthase activity was stable in murine HD-model tissue compared to control. mRNA levels of key enzymes were determined to characterize mitochondrial metabolic pathways in HdhQ mice. We demonstrated the feasibility to perform high-resolution respirometry measurements from small human HD muscle biopsies. Furthermore, we conclude that alterations in respiratory parameters of pre-manifest human muscle biopsies are rather limited and mirrored by a similar absence of marked alterations in HdhQ skeletal muscle. In contrast, the HdhQ111 murine cortex and liver did show respiratory alterations highlighting the tissue specific nature of mutant huntingtin effects on respiration.

  8. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  9. Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies

    Science.gov (United States)

    Temi, P.; Brighenti, F.; Mathews, W. G.; Amblard, A.; Riguccini, L.

    2013-01-01

    Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.

  10. Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors

    Science.gov (United States)

    Chen, Long-Bin; Jiang, Jun; Qiao, Cong-Feng

    2018-04-01

    By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like {γ}^{\\ast}γ \\to Q\\overline{Q} , {e}+{e}-\\to γ +Q\\overline{Q} , and H/{Z}^0\\to γ +Q\\overline{Q} , heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.

  11. Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem

    Science.gov (United States)

    Lakshtanov, E.; Vainberg, B.

    2013-10-01

    The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).

  12. Formation Design Strategy for SCOPE High-Elliptic Formation Flying Mission

    Science.gov (United States)

    Tsuda, Yuichi

    2007-01-01

    The new formation design strategy using simulated annealing (SA) optimization is presented. The SA algorithm is useful to survey a whole solution space of optimum formation, taking into account realistic constraints composed of continuous and discrete functions. It is revealed that this method is not only applicable for circular orbit, but also for high-elliptic orbit formation flying. The developed algorithm is first tested with a simple cart-wheel motion example, and then applied to the formation design for SCOPE. SCOPE is the next generation geomagnetotail observation mission planned in JAXA, utilizing a formation flying techonology in a high elliptic orbit. A distinctive and useful heuristics is found by investigating SA results, showing the effectiveness of the proposed design process.

  13. Vertical elliptic operator for efficient wave propagation in TTI media

    KAUST Repository

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2015-01-01

    Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

  14. Topology of the elliptical billiard with the Hooke's potential

    Directory of Open Access Journals (Sweden)

    Radnović Milena

    2015-01-01

    Full Text Available Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential. [Projekat Ministarstva nauke Republike Srbije, br. 174020: Geometry and Topology of Manifolds and Integrable Dynamical Systems

  15. Vertical elliptic operator for efficient wave propagation in TTI media

    KAUST Repository

    Waheed, Umair bin

    2015-08-19

    Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

  16. Mergers of elliptical galaxies and the fundamental plane

    NARCIS (Netherlands)

    Gonzalez-Garcia, AC; van Albada, TS; AvilaReese,; Firmani, C; Frenk, CS; Allen, YC

    2003-01-01

    N-body simulations have been carried out in order to explore the final state of elliptical galaxies after encounters and more expecifically whether the Fundamental Plane (FP hereafter) relation is affected by merging.

  17. Optimal Rendezvous and Docking Simulator for Elliptical Orbits, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — It is proposed to develop and implement a simulation of spacecraft rendezvous and docking guidance, navigation, and control in elliptical orbit. The foundation of...

  18. Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)

    NARCIS (Netherlands)

    Miyamoto, Roland; Top, Jakob

    2005-01-01

    We determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.

  19. An imbedding theorem and its applications in degenerate elliptic equations

    International Nuclear Information System (INIS)

    Duong Minh Duc.

    1988-06-01

    We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs

  20. Chromatic Derivatives, Chromatic Expansions and Associated Spaces

    OpenAIRE

    Ignjatovic, Aleksandar

    2009-01-01

    This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess the best features of both the Taylor and the Shannon expansions. This makes chromatic derivatives and ...

  1. Handbook of elliptic and hyperelliptic curve cryptography

    CERN Document Server

    Cohen, Henri; Avanzi, Roberto; Doche, Christophe; Lange, Tanja; Nguyen, Kim; Vercauteren, Frederik

    2005-01-01

    … very comprehensive coverage of this vast subject area … a useful and essential treatise for anyone involved in elliptic curve algorithms … this book offers the opportunity to grasp the ECC technology with a diversified and comprehensive perspective. … This book will remain on my shelf for a long time and will land on my desk on many occasions, if only because the coverage of the issues common to factoring and discrete log cryptosystems is excellent.-IACR Book Reviews, June 2011… the book is designed for people who are working in the area and want to learn more about a specific issue. The chapters are written to be relatively independent so that readers can focus on the part of interest for them. Such readers will be grateful for the excellent index and extensive bibliography. … the handbook covers a wide range of topics and will be a valuable reference for researchers in curve-based cryptography. -Steven D. Galbraith, Mathematical Reviews, Issue 2007f.

  2. Kerr ellipticity effect in a birefringent optical fiber

    International Nuclear Information System (INIS)

    Ishiekwene, G.C.; Mensah, S.Y.; Brown, C.S.

    2004-09-01

    An intensity-dependent change in the ellipticity of an input light beam leads to a characteristic shift in polarization instability. Dichroism gives rise to a self-induced ellipticity effect in the polarization state of an intense input light oriented along the fast axis of a birefringent optical fiber. The critical power at which the fiber effective beat length becomes infinite is reduced considerably in the presence of dichroism. (author)

  3. Radial, sideward and elliptic flow at AGS energies

    Indian Academy of Sciences (India)

    the sideward flow, the elliptic flow and the radial transverse mass distribution of protons data at. AGS energies. In order to ... data on both sideward and elliptic flow, NL3 model is better at 2 A¡GeV, while NL23 model is at 4–8. A¡GeV. ... port approach RBUU which is based on a coupled set of covariant transport equations for.

  4. Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions

    Directory of Open Access Journals (Sweden)

    Sabri Bensid

    2010-04-01

    Full Text Available We study the nonlinear elliptic problem with discontinuous nonlinearity $$displaylines{ -Delta u = f(uH(u-mu quadhbox{in } Omega, cr u =h quad hbox{on }partial Omega, }$$ where $H$ is the Heaviside unit function, $f,h$ are given functions and $mu$ is a positive real parameter. The domain $Omega$ is the unit ball in $mathbb{R}^n$ with $ngeq 3$. We show the existence of a positive solution $u$ and a hypersurface separating the region where $-Delta u=0$ from the region where $-Delta u=f(u$. Our method relies on the implicit function theorem and bifurcation analysis.

  5. Thickness shear mode quartz crystal resonators with optimized elliptical electrodes

    International Nuclear Information System (INIS)

    Ma Ting-Feng; Feng Guan-Ping; Zhang Chao; Jiang Xiao-Ning

    2011-01-01

    Quartz crystal resonators (QCRs) with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin's theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

  6. Temperature expansions for magnetic systems

    International Nuclear Information System (INIS)

    Cangemi, D.; Dunne, G.

    1996-01-01

    We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, and zeta function regularization for developing the expansions. We emphasize the essential difference between even and odd dimensions, focusing on 2+1 and 3+1 dimensions. We concentrate on the high temperature limit, but we also discuss the T=0 limit with nonzero chemical potential. Copyright copyright 1996 Academic Press, Inc

  7. Elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity in Pb-Pb collisions at √s(NN) = 2.76 TeV

    NARCIS (Netherlands)

    Adam, J.; Adamova, D.; Aggarwal, M. M.; Rinella, G. Aglieri; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; Andrei, C.; Andronic, A.; Anguelov, V.; Anticic, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshaeuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badala, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnafoldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Bathen, B.; Batigne, G.; Camejo, A. Batista; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.|info:eu-repo/dai/nl/411263188; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.|info:eu-repo/dai/nl/371577810; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.|info:eu-repo/dai/nl/371578248; Bielcik, J.; Bielcikova, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.|info:eu-repo/dai/nl/355079615; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Boggild, H.; Boldizsar, L.; Bombara, M.; Bonora, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossu, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Diaz, L. Calero; Caliva, A.|info:eu-repo/dai/nl/411885812; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castellanos, J. Castillo; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Barroso, V. Chibante; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Balbastre, G. Conesa; del Valle, Z. Conesa; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Morales, Y. Corrales; Cortes Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crkovska, J.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; De Souza, R. D.; Deisting, A.; Deloff, A.; Denes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Di Ruzza, B.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divia, R.; Djuvsland, O.; Dobrin, A.|info:eu-repo/dai/nl/372618715; Domenicis Gimenez, D.; Doenigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.|info:eu-repo/dai/nl/355502488; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernandez Tellez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Fleck, M. G.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Girard, M. Fusco; Gaardhoje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, M.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glaessel, P.; Gomez Coral, D. M.; Ramirez, A. Gomez; Gonzalez, A. S.; Gonzalez, V.; Gonzalez-Zamora, P.; Gorbunov, S.; Gorlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.|info:eu-repo/dai/nl/326052577; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Gruber, L.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Haake, R.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbaer, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Isakov, V.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Bustamante, R. T. Jimenez; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kaplin, V.; Kar, S.; Uysal, A. Karasu; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.|info:eu-repo/dai/nl/370530780; Keil, M.; Khan, M. Mohisin; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, J. S.; Kim, J.; Kim, M.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein-Boesing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Meethaleveedu, G. Koyithatta; Kralik, I.; Kravcakova, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.|info:eu-repo/dai/nl/362845670; Kubera, A. M.; Kucera, V.; Kuijer, P. G.|info:eu-repo/dai/nl/074064975; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.|info:eu-repo/dai/nl/411295721; Lehner, S.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; Monzon, I. Leon; Leon Vargas, H.; Leoncino, M.; Levai, P.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; Lopez Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Marchisone, M.; Mares, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.|info:eu-repo/dai/nl/412461684; Marin, A.; Markert, C.; Marquard, M.; Martinengo, P.; Martinez, M. I.; Garcia, G. Martinez; Pedreira, M. Martinez; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzoni, M. A.; Mcdonald, D.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Perez, J. Mercado; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.|info:eu-repo/dai/nl/325781435; Mishra, A. N.; Miskowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.|info:eu-repo/dai/nl/369405870; Mohanty, B.; Molnar, L.; Montano Zetina, L.; Montes, E.; De Godoy, D. A. Moreira; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Muehlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Muenning, K.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; De Oliveira, R. A. Negrao; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.|info:eu-repo/dai/nl/07051349X; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Oleniacz, J.; Oliveira Da Silva, A. C.|info:eu-repo/dai/nl/323375618; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paic, G.; Pal, S. K.; Palni, P.; Pan, J.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.|info:eu-repo/dai/nl/304833959; Da Costa, H. Pereira; Peresunko, D.; Lezama, E. Perez; Peskov, V.; Pestov, Y.; Petracek, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Ploskon, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Rasanen, S. S.; Rascanu, B. T.; Rathee, D.; Ravasenga, I.; Read, K. F.; Redlich, K.; Reed, R. J.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.|info:eu-repo/dai/nl/413319628; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Cahuantzi, M. Rodriguez; Manso, A. Rodriguez; Roed, K.; Rogochaya, E.; Rohr, D.; Rohrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Safarik, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M.; Schuchmann, S.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Sefcik, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shangaraev, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.|info:eu-repo/dai/nl/165585781; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; Sozzi, F.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Sumbera, M.; Sumowidagdo, S.; Szabo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Munoz, G. Tejeda; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thader, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Palomo, L. Valencia; Van Der Maarel, J.|info:eu-repo/dai/nl/412860996; Van Hoorne, J. W.; van Leeuwen, M.|info:eu-repo/dai/nl/250599171; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Doce, O. Vazquez; Vechernin, V.; Veen, A. M.|info:eu-repo/dai/nl/413533751; Veldhoen, M.; Velure, A.; Vercellin, E.; Limon, S. Vergara; Vernet, R.; Vickovic, L.; Viinikainen, J.; Vilakazi, Z.; Baillie, O. Villalobos; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Voelkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrlakova, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.|info:eu-repo/dai/nl/369509307; Watanabe, D.; Watanabe, Y.; Weiser, D. F.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yalcin, S.; Yano, S.; Yokoyama, H.; Yoo, I. -K.; Yoon, J. H.; Yurchenko, V.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Zavada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, C.; Zhao, C.; Zhigareva, N.; Zhou, Z.; Zhu, H.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.

    2016-01-01

    The elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity (|y| <0.7) is measured in Pb-Pb collisions at TeV with ALICE at the LHC. The particle azimuthal distribution with respect to the reaction plane can be parametrized with a Fourier expansion, where the second coefficient

  8. Recent progress in the development of the Elliptic Blending Reynolds-stress model

    International Nuclear Information System (INIS)

    Manceau, Rémi

    2015-01-01

    Highlights: • Various modifications of the Elliptic Blending Reynolds stress model, proposed during the last decade, are revisited. • Using theoretical arguments and detailed comparison with DNS data, a reference model is formulated. • The model satisfactorily reproduces the effects of spanwise rotation on turbulence, for cases without and with separation. - Abstract: The Elliptic Blending Reynolds Stress Model (EB-RSM), originally proposed by Manceau and Hanjalić (2002) to extend standard, weakly inhomogeneous Reynolds stress models to the near-wall region, has been subject to various modifications by several authors during the last decade, mainly for numerical robustness reasons. The present work revisits all these modifications from the theoretical standpoint and investigates in detail their influence on the reproduction of the physical mechanisms at the origin of the influence of the wall on turbulence. The analysis exploits recent DNS databases for high-Reynolds number channel flows, spanwise rotating channel flows with strong rotation rates, up to complete laminarization, and the separated flow after a sudden expansion without and with system rotation. Theoretical arguments and comparison with DNS results lead to the selection of a recommended formulation for the EB-RSM model. This formulation shows satisfactory predictions for the configurations described above, in particular as regards the modification of the mean flow and turbulent anisotropy on the anticyclonic or pressure side

  9. Extension of the self-consistent-charge density-functional tight-binding method: third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction.

    Science.gov (United States)

    Yang, Yang; Yu, Haibo; York, Darrin; Cui, Qiang; Elstner, Marcus

    2007-10-25

    The standard self-consistent-charge density-functional-tight-binding (SCC-DFTB) method (Phys. Rev. B 1998, 58, 7260) is derived by a second-order expansion of the density functional theory total energy expression, followed by an approximation of the charge density fluctuations by charge monopoles and an effective damped Coulomb interaction between the atomic net charges. The central assumptions behind this effective charge-charge interaction are the inverse relation of atomic size and chemical hardness and the use of a fixed chemical hardness parameter independent of the atomic charge state. While these approximations seem to be unproblematic for many covalently bound systems, they are quantitatively insufficient for hydrogen-bonding interactions and (anionic) molecules with localized net charges. Here, we present an extension of the SCC-DFTB method to incorporate third-order terms in the charge density fluctuations, leading to chemical hardness parameters that are dependent on the atomic charge state and a modification of the Coulomb scaling to improve the electrostatic treatment within the second-order terms. These modifications lead to a significant improvement in the description of hydrogen-bonding interactions and proton affinities of biologically relevant molecules.

  10. Negative thermal expansion materials

    International Nuclear Information System (INIS)

    Evans, J.S.O.

    1997-01-01

    The recent discovery of negative thermal expansion over an unprecedented temperature range in ZrW 2 O 8 (which contracts continuously on warming from below 2 K to above 1000 K) has stimulated considerable interest in this unusual phenomenon. Negative and low thermal expansion materials have a number of important potential uses in ceramic, optical and electronic applications. We have now found negative thermal expansion in a large new family of materials with the general formula A 2 (MO 4 ) 3 . Chemical substitution dramatically influences the thermal expansion properties of these materials allowing the production of ceramics with negative, positive or zero coefficients of thermal expansion, with the potential to control other important materials properties such as refractive index and dielectric constant. The mechanism of negative thermal expansion and the phase transitions exhibited by this important new class of low-expansion materials will be discussed. (orig.)

  11. Disjoint sum expansion method in FTA

    International Nuclear Information System (INIS)

    Ruan Keqiang

    1987-01-01

    An expansion formula for transforming boolean algebraic expressions into disjoint form was proved. Based on this expansion formula, a method for transforming system failure function into disjoint form was devised. The fact that the expansion can be done for several elements simulatneously makes the method flexible and fast. Some examples from fault tree analysis (FTA) and network analysis were examined by the new method to show its algorithm and its merit. Besides, by means of the proved expansion formula some boolean algebraic relations can proved very easily

  12. Thermal expansion of L-ascorbic acid

    Science.gov (United States)

    Nicolaï, B.; Barrio, M.; Tamarit, J.-Ll.; Céolin, R.; Rietveld, I. B.

    2017-04-01

    The specific volume of vitamin C has been investigated by X-ray powder diffraction as a function of temperature from 110 K up to complete degradation around 440 K. Its thermal expansion is relatively small in comparison with other organic compounds with an expansivity α v of 1.2(3) × 10-4 K-1. The structure consists of strongly bound molecules in the ac plane through a dense network of hydrogen bonds. The thermal expansion is anisotropic. Along the b axis, the expansion has most leeway and is about 10 times larger than in the other directions.

  13. Thermal expansion of doped lanthanum gallates

    Indian Academy of Sciences (India)

    Administrator

    Since the components are in intimate mechanical contact, any stress generated due to their thermal expansion mis- match during thermal cycling could lead to catastrophic failure of the cell. The functional materials must have similar thermal expansions to avoid mechanical stresses. Hence it is useful to study the thermal ...

  14. Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Ciprian G. Gal

    2017-01-01

    Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

  15. The effects of axis ratio on laminar fluid flow around an elliptical cylinder

    International Nuclear Information System (INIS)

    Faruquee, Zakir; Ting, David S-K.; Fartaj, Amir; Barron, Ronald M.; Carriveau, Rupp

    2007-01-01

    An elliptical cylinder is a generic shape which represents a flat plate at its minor to major axis ratio (AR) limits of zero and infinity, and a circular cylinder at AR of unity. While incompressible flows over a streamwise flat plate (AR = 0), a cross-stream flat plate (AR = ∞), and a circular cylinder have been studied extensively, the role of AR on the detailed flow structure is still not well understood. Therefore, a numerical study was conducted to examine the flow field around an elliptical cylinder over a range of ARs from 0.3 to 1, with the major axis parallel to the free-stream, at a Reynolds number of 40 based on the hydraulic diameter. The control volume approach of FLUENT was used to solve the fluid flow equations, assuming the flow over the cylinder is unbounded, steady, incompressible and two-dimensional. It has been found that a pair of steady vortices forms when AR reaches a critical value of 0.34; below this value no vortices are formed behind the elliptical cylinder. Various wake parameters, drag coefficient, pressure and velocity distributions, have been characterized as functions of AR. The wake size and the drag coefficient are found to increase with the increase of AR. Quadratic correlations have been obtained to describe the relations of wake length and drag coefficient with axis ratio

  16. Combined Ultrasonic Elliptical Vibration and Chemical Mechanical Polishing of Monocrystalline Silicon

    Directory of Open Access Journals (Sweden)

    Liu Defu

    2016-01-01

    Full Text Available An ultrasonic elliptical vibration assisted chemical mechanical polishing(UEV-CMP is employed to achieve high material removal rate and high surface quality in the finishing of hard and brittle materials such as monocrystalline silicon, which combines the functions of conventional CMP and ultrasonic machining. In theultrasonic elliptical vibration aided chemical mechanical polishingexperimental setup developed by ourselves, the workpiece attached at the end of horn can vibrate simultaneously in both horizontal and vertical directions. Polishing experiments are carried out involving monocrystalline silicon to confirm the performance of the proposed UEV-CMP. The experimental results reveal that the ultrasonic elliptical vibration can increase significantly the material removal rate and reduce dramatically the surface roughness of monocrystalline silicon. It is found that the removal rate of monocrystalline silicon polished by UEV-CMP is increased by approximately 110% relative to that of conventional CMP because a passive layer on the monocrystalline silicon surface, formed by the chemical action of the polishing slurry, will be removed not only by the mechanical action of CMP but also by ultrasonic vibration action. It indicates that the high efficiency and high quality CMP of monocrystalline silicon can be performed with the proposed UEV-CMP technique.

  17. Cut contribution to momentum autocorrelation function of an impurity in a classical diatomic chain

    Science.gov (United States)

    Yu, Ming B.

    2018-02-01

    A classic diatomic chain with a mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity is a sum of contributions from two pairs of resonant poles and three branch cuts. The former results in cosine function and the latter in acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are integrals of elliptic functions in the real axis for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral is carried out for the calculation of optical branch: ∫0 ϕ dθ/√((1 - r 1 2 sin2 θ)(1 - r 2 2 sin2 θ)) = igsn -1 (sin ϕ) ( r 2 2 > r 1 2 > 1, g is a constant).

  18. Elliptical optical solitary waves in a finite nematic liquid crystal cell

    Science.gov (United States)

    Minzoni, Antonmaria A.; Sciberras, Luke W.; Smyth, Noel F.; Worthy, Annette L.

    2015-05-01

    The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the "chirp" variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.

  19. Umbilical cord blood regulatory T-cell expansion and functional effects of tumor necrosis factor receptor family members OX40 and 4-1BB expressed on artificial antigen-presenting cells

    Science.gov (United States)

    Harker-Murray, Paul; Porter, Stephen B.; Merkel, Sarah C.; Londer, Aryel; Taylor, Dawn K.; Bina, Megan; Panoskaltsis-Mortari, Angela; Rubinstein, Pablo; Van Rooijen, Nico; Golovina, Tatiana N.; Suhoski, Megan M.; Miller, Jeffrey S.; Wagner, John E.; June, Carl H.; Riley, James L.

    2008-01-01

    Previously, we showed that human umbilical cord blood (UCB) regulatory T cells (Tregs) could be expanded approximately 100-fold using anti-CD3/28 monoclonal antibody (mAb)–coated beads to provide T-cell receptor and costimulatory signals. Because Treg numbers from a single UCB unit are limited, we explored the use of cell-based artificial antigen-presenting cells (aAPCs) preloaded with anti-CD3/28 mAbs to achieve higher levels of Treg expansion. Compared with beads, aAPCs had similar expansion properties while significantly increasing transforming growth factor β (TGF-β) secretion and the potency of Treg suppressor function. aAPCs modified to coexpress OX40L or 4-1BBL expanded UCB Tregs to a significantly greater extent than bead- or nonmodified aAPC cultures, reaching mean expansion levels exceeding 1250-fold. Despite the high expansion and in contrast to studies using other Treg sources, neither OX40 nor 4-1BB signaling of UCB Tregs reduced in vitro suppression. UCB Tregs expanded with 4-1BBL expressing aAPCs had decreased levels of proapoptotic bim. UCB Tregs expanded with nonmodified or modified aAPCs versus beads resulted in higher survival associated with increased Treg persistence in a xeno-geneic graft-versus-host disease lethality model. These data offer a novel approach for UCB Treg expansion using aAPCs, including those coexpressing OX40L or 4-1BBL. PMID:18645038

  20. Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces

    KAUST Repository

    Efendiev, Yalchin

    2014-01-01

    We present a Boundary Element Method (BEM)-based FEM for mixed formulations of second order elliptic problems in two dimensions. The challenge, we would like to address, is a proper construction of H(div)-conforming vector valued trial functions on arbitrary polygonal partitions of the domain. The proposed construction generates trial functions on polygonal elements which inherit some of the properties of the unknown solution. In the numerical realization, the relevant local problems are treated by means of boundary integral formulations. We test the accuracy of the method on two model problems. © 2014 Springer-Verlag.