Elliptic hypergeometric functions associated with root systems
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).
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
Special values of the hypergeometric series
Ebisu, Akihito
2017-01-01
In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series F(a,b;c;x) and shows that values of F(a,b;c;x) at some points x can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of F(a,b;c;x) that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.
Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
International Nuclear Information System (INIS)
Spiridonov, V.P.; Vartanov, G.S.
2012-03-01
Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from SL(3, Z)-modular transformation properties of the kernels of dual indices.
Iterated elliptic and hypergeometric integrals for Feynman diagrams
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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.
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.
Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
Energy Technology Data Exchange (ETDEWEB)
Spiridonov, V.P. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-05-15
Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from SL(3, Z)-modular transformation properties of the kernels of dual indices.
SOME PROPERTIES OF HORN TYPE SECOND ORDER DOUBLE HYPERGEOMETRIC SERIES
Directory of Open Access Journals (Sweden)
Anvar Hasanov
2018-04-01
Full Text Available Horn [1931, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann.,105(1, 381-407], (corrections in Borngasser [1933, Uber hypergeometrische funkionen zweier Veranderlichen, Dissertation, Darmstadt], defined and investigated ten second order hypergeometric series of two variables. In the course of further investigation of Horn’s series, we noticed the existence of hypergeometric double series H*2 analogous to Horn’s double series H*2. The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the analogous hypergeometric double series H*2 Indeed, motivated by the important role of the Horn’s functions in several diverse fields of physics and the contributions toward the unification and generalization of the hyper-geometric functions, we establish a system of partial differential equations, integral representations, expansions, analytic continuation, transformation formulas and generating relations. Also, we discuss the links for the various results, which are presented in this paper, with known results.
Hypergeometric series recurrence relations and some new orthogonal functions
International Nuclear Information System (INIS)
Wilson, J.A.
1978-01-01
A set of hypergeometric orthogonal polynomials, a set of biorthogonal rational functions generalizing them, and some new three-term relations for hypergeometric series containing properties of these functions are exhibited. The orthogonal polynomials depend on four free parameters, and their orthogonality relations include as special or limiting cases the orthogonalities for the classical polynomials, the Hahn and dual Hahn polynomials, Pollaczek's polynomials orthogonal on an infinite interval, and the 6-j symbols of angular momentum in quantum mechanics. Their properties include a second-order difference equation and a Rodrigues-type formula involving a divided difference operator
An asymptotic formula of the divergent bilateral basic hypergeometric series
Morita, Takeshi
2012-01-01
We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.
Some New Formulas for the Generalized Hypergeometric Series
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Sumi P. Krishnan
Full Text Available The aim of this research paper is to provide some new formulas for the generalized hypergeometric series. The results are derived with the help of the extensions of Euler's and Kummer's classical transformations. As special cases, we have recovered several results due to Sharma. The results established in this paper are simple, interesting, easily obtainable and may be useful.
One loop integration with hypergeometric series by using recursion relations
International Nuclear Information System (INIS)
Watanabe, Norihisa; Kaneko, Toshiaki
2014-01-01
General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples
International Nuclear Information System (INIS)
Sanders, Sören; Holthaus, Martin
2017-01-01
We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose–Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions. (paper)
Sanders, Sören; Holthaus, Martin
2017-11-01
We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.
Symmetries of some hypergeometric series: Implications for 3j- and 6j-coefficients
International Nuclear Information System (INIS)
Louck, J.D.; Beyer, W.A.; Biedenharn, L.C.; Stein, P.R.
1986-10-01
The occurrence of generalized hypergeometric series as factors, in the Wigner-Clebsch-Gordan (3j) and Racah (6j) coefficients is well known. The recently discovered S 5 symmetry of the Saalscheutzian 4 F 3 series may be used to extend the symmetries of the 6j-coefficients to the much larger group generated by S 5 and the group of Regge symmetries. (A similar extension may be carried out for the 3j-coefficients). The required extension of the domain of definition of the 6j-coefficients and the properties of its symmetry group is developed here. 7 refs
Group theoretical basis of some identities for the generalized hypergeometric series
International Nuclear Information System (INIS)
Beyer, W.A.; Louck, J.D.; Stein, P.R.
1987-01-01
It is shown that Thomae's identity between two 3 F 2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group S 5 is an invariance group of this series. A similar result is proved for the terminating Saalschuetzian 4 F 3 series, where S 6 is shown to be the invariance group of this series (or S 5 if one parameter is eliminated by using the Saalschuetz condition). Here Bailey's identity is realized as a permutation of appropriately defined parameters. Finally, the set of three-term relations between 3 F 2 series of unit argument discovered by Thomae [J. Thomae, J. Reine Angew. Math. 87, 26 (1879)] and systematized by Whipple [F. J. Whipple, Proc. London Math. Soc. 23, 104 (1925)] is shown to be transformed into itself under the action of the group S 6 x Λ, where Λ is a two-element group. The 12 left cosets of S 6 x Λ with respect to the invariance group S 5 are the structural elements underlying the three-term relations. The symbol manipulator macsyma was used to obtain preliminary results
International Nuclear Information System (INIS)
Sanders, Sören; Holthaus, Martin
2017-01-01
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems. (paper)
Sanders, Sören; Holthaus, Martin
2017-10-01
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.
On the Behavior of Eisenstein Series Through Elliptic Degeneration
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.
Generalized hypergeometric coherent states
International Nuclear Information System (INIS)
Appl, Thomas; Schiller, Diethard H
2004-01-01
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disc and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces as well as generalized hypergeometric Husimi distributions and corresponding phase distributions
Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.
2017-03-01
Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
Stienstra, J.
2007-01-01
This text is based on lectures by the author in the Summer School Algebraic Geometry and Hypergeometric Functions in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of Gelfand, Kapranov and Zelevinsky, including Differential
L-series of elliptic curves with CM by √-3
International Nuclear Information System (INIS)
Qiu Derong; Zhang Xianke
2001-09-01
Let E:y 2 =x 3 -2 4 3 3 D 2 be elliptic curves defined over the quadratic field Q(√-3). Hecke L-series attached to E are studied, formulae for the values of the L-series at s=1 are given, and the bound of 3-adic valuations of these values are obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer, and generalize results in recent literature about elliptic curves defined over rationals. (author)
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.
A ∞-Algebra of an Elliptic Curve and Eisenstein Series
Polishchuk, Alexander
2011-02-01
We compute explicitly the A ∞-structure on the algebra {Ext^*(mathcal{O}_C oplus L, mathcal{O}_C oplus L)} , where L is a line bundle of degree 1 on an elliptic curve C. The answer involves higher derivatives of Eisenstein series.
Elliptic genera and characteristic q-series of superconformal field theory
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L. Bonora
2015-06-01
Full Text Available We analyze the characteristic series, the KO series and the series associated with the Witten genus, and their analytic forms as the q-analogs of classical special functions (in particular q-analog of the beta integral and the gamma function. q-Series admit an analytic interpretation in terms of the spectral Ruelle functions, and their relations with appropriate elliptic modular forms can be described. We show that there is a deep correspondence between the characteristic series of the Witten genus and KO characteristic series, on one side, and the denominator identities and characters of N=2 superconformal algebras, and the affine Lie (superalgebras on the other. We represent the characteristic series in the form of double series using the Hecke–Rogers modular identity.
Classification of hypergeometric identities for pi and other logarithms of algebraic numbers.
Chudnovsky, D V; Chudnovsky, G V
1998-03-17
This paper provides transcendental and algebraic framework for the classification of identities expressing pi and other logarithms of algebraic numbers as rapidly convergent generalized hypergeometric series in rational parameters. Algebraic and arithmetic relations between values of p+1Fp hypergeometric functions and their values are analyzed. The existing identities are explained, and new exhaustive classes of new ones are presented.
Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution
DEFF Research Database (Denmark)
Fog, Agner
2008-01-01
Two different probability distributions are both known in the literature as "the" noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution...... is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...... distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....
Numerically satisfactory solutions of hypergeometric recursions
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2007-01-01
textabstractEach family of Gauss hypergeometric functions $$ f_n={}_2F_1(a+\\varepsilon_1n, b+\\varepsilon_2n ;c+\\varepsilon_3n; z),\\quad n\\in {\\mathbb Z}\\,, $$ for fixed $\\varepsilon_j=0,\\pm1$ (not all $\\varepsilon_j$ equal to zero) satisfies a second order linear difference equation of the
Hypergeometric Functions with Integral Parameter Differences
DEFF Research Database (Denmark)
Karlsson, Per W.
1971-01-01
For a generalized hypergeometric function pFq(z) with positive integral differences between certain numerator and denominator parameters, a formula expressing the pFq(z) as a finite sum of lower-order functions is proved. From this formula, Minton's two summation theorems for p = q + 1, z = 1...
Rigidity of monodromies for Appell's hypergeometric functions
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Yoshishige Haraoka
2015-01-01
Full Text Available For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeometric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.
RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.
Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the
International Nuclear Information System (INIS)
Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Moch, Sven-Olaf; Hamburg Univ.
2013-12-01
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions F D of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F S of three variables. Both functions are related with one-loop Feynman diagrams.
Numerically satisfactory solutions of hypergeometric recursions
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2006-01-01
textabstractEach family of Gauss hypergeometric functions $f_n = 2F_1(a+epsilon 1n,b+epsilon 2n;c+epsilon 3n;z), nin Z$, for fixed epsilon_j = 0,pm 1$ (not all epsilon j equal to zero) satisfies a second order linear difference equation of the form $A_n f_{n-1} + B_n f_n + C_n f_{n+1} = 0$. Because
Multivariable hypergeometric solutions for three charged particles
Energy Technology Data Exchange (ETDEWEB)
Gasaneo, G.; Colavecchia, F.D.; Garibotti, C.R. [Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche]|[Consejo Nacional de Investigaciones Cientificas y Tecnicas, San Carlos de Bariloche (Argentina); Miraglia, J.E.; Macri, P. [IAFE, Consejo de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina)
1997-04-28
We present a new wavefunction which describes the ion-atom problem above the ionization threshold. This is an approximate solution of the Schrodinger equation for the three-body Coulomb problem that can be expressed in terms of a confluent hypergeometric function of two variables. The proposed wavefunction includes correlation among the motions of the three particles and verifies the correct Coulombic asymptotic behaviours. (author).
Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces
International Nuclear Information System (INIS)
Neretin, Yu A
2001-01-01
The index hypergeometric transform (also called the Olevskii transform or the Jacobi transform) generalizes the spherical transform in L 2 on rank 1 symmetric spaces (that is, real, complex, and quaternionic Lobachevskii spaces). The aim of this paper is to obtain properties of the index hypergeometric transform imitating the analysis of Berezin kernels on rank 1 symmetric spaces. The problem of the explicit construction of a unitary operator identifying L 2 and a Berezin space is also discussed. This problem reduces to an integral expression (the Λ-function), which apparently cannot be expressed in a finite form in terms of standard special functions. (Only for certain special values of the parameter can this expression be reduced to the so-called Volterra type special functions.) Properties of this expression are investigated. For some series of symmetric spaces of large rank the above operator of unitary equivalence can be expressed in terms of the determinant of a matrix of Λ-functions
Some Instructional Issues in Hypergeometric Distribution
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Anwar H. Joarder
2012-07-01
Full Text Available 800x600 Normal 0 false false false EN-US X-NONE X-NONE A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.
Fractional Fourier transform for confluent hypergeometric beams
International Nuclear Information System (INIS)
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-01-01
Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions
Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions
2007-01-01
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Energy Technology Data Exchange (ETDEWEB)
Gahramanov, Ilmar [Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Radiation Problems ANAS,B. Vahabzade 9, AZ1143 Baku (Azerbaijan); Department of Mathematics, Khazar University,Mehseti St. 41, AZ1096 Baku (Azerbaijan); Kels, Andrew P. [Institute of Physics, University of Tokyo,Komaba, Tokyo 153-8902 (Japan)
2017-02-08
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S{sub b}{sup 3}/ℤ{sub r}) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
International Nuclear Information System (INIS)
Gahramanov, Ilmar; Kels, Andrew P.
2017-01-01
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S b 3 /ℤ r ) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.
Development of sample size allocation program using hypergeometric distribution
International Nuclear Information System (INIS)
Kim, Hyun Tae; Kwack, Eun Ho; Park, Wan Soo; Min, Kyung Soo; Park, Chan Sik
1996-01-01
The objective of this research is the development of sample allocation program using hypergeometric distribution with objected-oriented method. When IAEA(International Atomic Energy Agency) performs inspection, it simply applies a standard binomial distribution which describes sampling with replacement instead of a hypergeometric distribution which describes sampling without replacement in sample allocation to up to three verification methods. The objective of the IAEA inspection is the timely detection of diversion of significant quantities of nuclear material, therefore game theory is applied to its sampling plan. It is necessary to use hypergeometric distribution directly or approximate distribution to secure statistical accuracy. Improved binomial approximation developed by Mr. J. L. Jaech and correctly applied binomial approximation are more closer to hypergeometric distribution in sample size calculation than the simply applied binomial approximation of the IAEA. Object-oriented programs of 1. sample approximate-allocation with correctly applied standard binomial approximation, 2. sample approximate-allocation with improved binomial approximation, and 3. sample approximate-allocation with hypergeometric distribution were developed with Visual C ++ and corresponding programs were developed with EXCEL(using Visual Basic for Application). 8 tabs., 15 refs. (Author)
Conformal field theory and functions of hypergeometric type
International Nuclear Information System (INIS)
Isachenkov, Mikhail
2016-03-01
Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.
Conformal field theory and functions of hypergeometric type
Energy Technology Data Exchange (ETDEWEB)
Isachenkov, Mikhail
2016-03-15
Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.
Energy Technology Data Exchange (ETDEWEB)
Bytev, Vladimir V. [Joint Inst. for Nuclear Research, Dubna (Russian Federation); Kalmykov, Mikhail Yu. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Moch, Sven-Olaf [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2013-12-15
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions F{sub D} of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F{sub S} of three variables. Both functions are related with one-loop Feynman diagrams.
Large parameter cases of the Gauss hypergeometric function
N.M. Temme (Nico)
2002-01-01
textabstractWe consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters {it a, b, c} are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and
Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions
Wroughton, Jacqueline; Cole, Tarah
2013-01-01
Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…
Finding new relationships between hypergeometric functions by evaluating Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A. [Santa Barbara Univ., CA (United States). Kavli Inst. for Theoretical Physics; Tarasov, Oleg V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2011-08-15
Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F{sub 1}. From the comparison of this expression with a previously known one, a new relation between the Appell functions F{sub 1} and F{sub 4} is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F{sub 1} function with particular arguments to the hypergeometric function {sub 3}F{sub 2} is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F{sub 1} functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F{sub 1} function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F{sub 1} function and the Gaussian hypergeometric function {sub 2}F{sub 1} whose argument is the ratio of polynomials of degree six is presented. (orig.)
Vortex beam characterization in terms of Hypergeometric- Gaussian modes
CSIR Research Space (South Africa)
Sephton, Bereneice C
2016-10-01
Full Text Available in Optics: The 100th OSA Annual Meeting and Exhibit/Laser Science XXXII , 17-21 October 2016, Rochester Riverside Convention Center, Rochester, New York United States Vortex beam characterization in terms of Hypergeometric- Gaussian modes Sephton...
International Nuclear Information System (INIS)
Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A.
2013-05-01
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions p+1 F p , and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F 1 , F 2 , F 3 , F 4 of two variables.
Fast computation of complete elliptic integrals and Jacobian elliptic functions
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.
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.
On Approximation of Hyper-geometric Function Values of a Special Class
Directory of Open Access Journals (Sweden)
P. L. Ivankov
2017-01-01
the case of the hyper-geometric series with a finite radius of convergence. Subsequently, it will be possible to consider also a case of the irrational parameters, but there are still a number of difficulties, which are specific for the problems of such type and which are to be overcome.
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... http://www.ias.ac.in/article/fulltext/pmsc/115/04/0371-0381. Keywords. Inverse binomial series; hypergeometric series; polylogarithms; integral representations. Abstract. In this paper we investigate the series ∑ k = 1 ∞ ( 3 k k ) − 1 k − n x k . Obtaining some integral representations of them, we evaluated the ...
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.
Auto-focusing accelerating hyper-geometric laser beams
International Nuclear Information System (INIS)
Kovalev, A A; Kotlyar, V V; Porfirev, A P
2016-01-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)
Reduction of Double Clausenian Hypergeometric Functions
DEFF Research Database (Denmark)
Karlsson, Per W.
1996-01-01
The reduction formulas under consideration are those for which the conditions upon the variables are other than 'fixed values'. Known results are discussed, and some new formulas are derived by series manipulations from various known summation and transformation theorems. The ten functions in thi...
From the hypergeometric differential equation to a non-linear Schrödinger one
International Nuclear Information System (INIS)
Plastino, A.; Rocca, M.C.
2015-01-01
We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.
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.)
Some results associated with a generalized basic hypergeometric function
Directory of Open Access Journals (Sweden)
Rajeev K. Gupta
2009-05-01
Full Text Available In this paper, we define a q-extension of the new generalized hypergeometric function given by Saxena et al. in [13], and have investigated the properties of the above new function such as q-differentiation and q-integral representation. The results presented are of general character and the results given earlier by Saxena and Kalla in [14], Virchenko, Kalla and Al-Zamel in [15], Al-Musallam and Kalla in [2, 3], Kobayashi in [7, 8], Saxena et al. in [13], Kumbhat et al. in [11] follow as special cases.
Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions
DEFF Research Database (Denmark)
Fog, Agner
2008-01-01
the mode, ratio-of-uniforms rejection method, and rejection by sampling in the tau domain. Methods for the multivariate distributions include: simulation of urn experiments, conditional method, Gibbs sampling, and Metropolis-Hastings sampling. These methods are useful for Monte Carlo simulation of models...... of biased sampling and models of evolution and for calculating moments and quantiles of the distributions.......Several methods for generating variates with univariate and multivariate Wallenius' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from...
Koornwinder, T.H.
2015-01-01
For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential
Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media
Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai
2018-01-01
Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.
Multivariable hypergeometric functions for ion-atom collisions
Energy Technology Data Exchange (ETDEWEB)
Gasaneo, G.; Colavecchia, F.D.; Garibotti, C.R
1999-06-03
In this work we present a correlated wave function for a three-body continuum Coulomb problem. This state is described by the two-variables PHI{sub 2} hypergeometric function. We examine the properties of this function and their differences with previous uncorrelated models. The PHI{sub 2} wave function can be considered as a final state of ion-atom ionizing collisions, giving rise to both undistorted (Born-PHI{sub 2}) and distorted (EIS-PHI{sub 2}) models. We obtain double differential cross sections with the Born-PHI{sub 2} theory for proton-helium collisions in the intermediate to high energy regime. They exhibit all the main features of the electronic emission process and agree with the experimental data.
Directory of Open Access Journals (Sweden)
Resat Yilmazer
2016-02-01
Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.
Ellipticities of Elliptical Galaxies in Different Environments
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.
Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities
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.
Factorization method for difference equations of hypergeometric type on nonuniform lattices
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Nodarse, R. [Departamento de Analisis Matematico, Universidad de Sevilla, Sevilla (Spain); Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain); Costas-Santos, R.S. [Departamento de Analisis Matematico, Universidad de Sevilla, Sevilla (Spain)
2001-07-13
We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given. (author)
Energy Technology Data Exchange (ETDEWEB)
Bytev, Vladimir V.; Kalmykov, Mikhail Yu. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute for Nuclear Research, Dubna (Russian Federation); Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2013-05-15
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions {sub p+1}F{sub p}, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F{sub 1}, F{sub 2}, F{sub 3}, F{sub 4} of two variables.
Energy Technology Data Exchange (ETDEWEB)
Silverstone, H.J.; Nakai, S.; Harris, J.G.
1985-09-01
Asymptotic expansions for Airy functions and more generally confluent hypergeometric functions, which are of fundamental importance in semiclassical quantum mechanics, are summable. The Stokes lines of the expansions are cuts of the Borel sums of the power series occurring in the expansions. At a Stokes line on which the function is continuous, the asymptotic expansions change discontinuously, but their composite sums do not: a fact that greatly clarifies the role of the Stokes line. On a Stokes line itself, it is still possible to evaluate the asymptotic expansion by Borel summation via analytic continuation, and as a consequence complex expansions may have real sums, and vice versa. This observation has important implications for the significance and use of asymptotic expansions recently derived for the resonances of the LoSurdo-Stark effect and for the energy eigenvalues of H/sub 2/ /sup +/. For both of these problems the physical values of the expansion parameters, the electric field strength and the reciprocal of the internuclear distance, lie on Stokes lines.
International Nuclear Information System (INIS)
Bytev, Vladimir V.; Kniehl, Bernd A.
2016-12-01
We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F C of three variables.
Energy Technology Data Exchange (ETDEWEB)
Bytev, Vladimir V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute for Nuclear Research, Dubna (Russian Federation); Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2016-12-15
We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F{sub C} of three variables.
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.)
International Nuclear Information System (INIS)
van Diejen, J.F.
1997-01-01
Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2010-03-15
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed. (orig.)
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.
Directory of Open Access Journals (Sweden)
Mika Tanda
2015-01-01
Full Text Available We compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.
Elliptic Determinantal Processes and Elliptic Dyson Models
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.
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.
The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, 0203 Ashtarak (Armenia); Armenian State Pedagogical University, 0010 Yerevan (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)
2016-02-15
We present an asymmetric step–barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the particle incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function. - Highlights: • We introduce an asymmetric step-barrier potential for which the 1D Schrödinger equation is exactly solved in terms of confluent hypergeometric functions. • The potential is given in terms of the Lambert-function, which is an implicitly elementary function also known as the product logarithm. • This is a four-parametric specification of a more general five-parametric potential also solvable in terms of the confluent hypergeometric functions. • There exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function.
Directory of Open Access Journals (Sweden)
Junesang Choi
2014-01-01
Full Text Available A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving the Fp(α,β(·. In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functions Fp(α,β,m(·. Some interesting special cases of our main results are also considered.
The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach
International Nuclear Information System (INIS)
Qureshi, M I; Rafat, M; Azad, S Ismail
2010-01-01
The motion of a simple pendulum of arbitrary amplitude is usually treated by approximate methods. By using generalized hypergeometric functions, it is however possible to solve the problem exactly. In this paper, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. A new and exact expression for the time of swinging of a simple pendulum from the vertical position to an arbitrary angular position θ is given by equation (3.10). The time period of such a pendulum is also exactly expressible in terms of hypergeometric functions. The exact expressions thus obtained are used to plot the graphs that compare the exact time period T(θ 0 ) with the time period T(0) (based on simple harmonic approximation). We also compare the relative difference between T(0) and T(θ 0 ) found from the exact equation of motion with the usual perturbation theory estimate. The treatment is intended for graduate students, who have acquired some familiarity with the hypergeometric functions. This approach may also be profitably used by specialists who encounter during their investigations nonlinear differential equations similar in form to the pendulum equation. Such nonlinear differential equations could arise in diverse fields, such as acoustic vibrations, oscillations in small molecules, turbulence and electronic filters, among others.
Superconducting elliptical cavities
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.
Two-dimensional steady unsaturated flow through embedded elliptical layers
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.
Anisotropic elliptic optical fibers
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.
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Nodarse, R [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo. 1160, E-41080 Sevilla (Spain); Atakishiyev, N M [Instituto de Matematicas, UNAM, Apartado Postal 273-3, CP 62210 Cuernavaca, Morelos, Mexico (Germany); Costas-Santos, R S [Departamento de Matematicas, EPS, Universidad Carlos III de Madrid, Ave. Universidad 30, E-28911, Leganes, Madrid (Spain)
2005-01-07
We argue that one can factorize the difference equation of hypergeometric type on non-uniform lattices in the general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues, this directly leads to the dynamical symmetry algebra su{sub q}(1, 1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the q-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.
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)
Uniformization of elliptic curves
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.
Elliptic partial differential equations
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
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)
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.
The demagnetizing energies of a uniformly magnetized cylinder with an elliptic cross-section
International Nuclear Information System (INIS)
Goode, D.A.; Rowlands, G.
2003-01-01
Analytic expressions for the demagnetizing energies are obtained in the form of partial series, for long elliptic cylinders and for squat ones where the ellipticity of the cross-section is unrestrained. This leaves just a small range where the demagnetizing energies are not well defined. It is found that by replacing the elliptic cylinders with rectangular blocks, a good approximation to the demagnetizing energy may be made in this small range
Elliptic curves for applications (Tutorial)
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
International Nuclear Information System (INIS)
Hoffmann, L.; Leonhardt, T.; Mesref, L.; Ruehl, W.
2001-01-01
We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U(1) Y symmetry for four-point functions
Hoffmann, L.; Leonhardt, T.; Mesref, L.; Rühl, W.
2001-09-01
We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U(1)Y symmetry for four-point functions.
Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution
Samohyl, Robert Wayne
2017-10-01
This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The
Series expansion in fractional calculus and fractional differential equations
Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao
2009-01-01
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...
Rational points on elliptic curves
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 ...
The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators
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
A bispectral q-hypergeometric basis for a class of quantum integrable models
Baseilhac, Pascal; Martin, Xavier
2018-01-01
For the class of quantum integrable models generated from the q-Onsager algebra, a basis of bispectral multivariable q-orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q-Onsager algebra, whose fundamental generators are realized in terms of the multivariable q-difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q-Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q-hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).
Energy and the Elliptical Orbit
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.
Interstellar matter within elliptical galaxies
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.
Hydrodynamic simulation of elliptic flow
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.
Elliptic net and its cryptographic application
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.
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
Newton flows for elliptic functions
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
Diffeomorphisms of elliptic 3-manifolds
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...
Elliptic curves and primality proving
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.
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
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
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
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
Elliptic Diophantine equations a concrete approach via the elliptic logarithm
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.
Detection of Buried Inhomogeneous Elliptic Cylinders by a Memetic Algorithm
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...
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
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
Directory of Open Access Journals (Sweden)
Ernest G. Kalnins
2013-10-01
Full Text Available We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2 and so(3. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.
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)
Overdetermined elliptic problems in topological disks
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.
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)
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
Elliptic-symmetry vector optical fields.
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.
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.
Dark matter in elliptical galaxies
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.
Stellar Populations in Elliptical Galaxies
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.
A transmission line model for propagation in elliptical core optical fibers
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.
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
Convex bodies with many elliptic sections
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.
Kinematically Decoupled Cores in Dwarf (Elliptical) Galaxies
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
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
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
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.)
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
Elliptical excisions: variations and the eccentric parallelogram.
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.
International Nuclear Information System (INIS)
Aizawa, N; Chakrabarti, R; Mohammed, S S Naina; Segar, J
2007-01-01
Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and is observed that they may be expressed in terms of the Q-Hahn polynomials. We next investigate representations of the quantum supergroup OSp q (1/2) which are not well defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even-dimensional representations of the quantum supergroup OSp q (1/2)
Formal degrees of unipotent discrete series representations and the exotic Fourier transform
Ciubotaru, D.; Opdam, E.
2015-01-01
We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series representations of a semisimple p-adic group and the elliptic fake
Excursion Processes Associated with Elliptic Combinatorics
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.
International Workshop on Elliptic and Parabolic Equations
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.
Spectral transformation chains and some new biorthogonal rational functions
International Nuclear Information System (INIS)
Spiridonov, V.
2000-01-01
A discrete-time chain, associated with the generalized eigenvalue problem for two Jacobi matrices, is derived. Various discrete and continuous symmetries of this integrable equation are revealed. A class of its rational, elementary and elliptic function solutions, appearing from a similarity reduction, are constructed. The latter lead to large families of biorthogonal rational functions based upon the very-well-posed balanced hypergeometric series of three types: the standard hypergeometric series 9 F 8 , basic series 10 φ 9 and its elliptic analogue 10 E 9 . For an important subclass of the elliptic biorthogonal rational functions the weight function and normalization constants are determined explicitly. (orig.)
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.
Stability Estimates for h-p Spectral Element Methods for Elliptic Problems
Dutt, Pravir; Tomar, S.K.; Kumar, B.V. Rathish
2002-01-01
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which
Partial differential operators of elliptic type
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.
Constructing elliptic curves from Galois representations
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.
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.
Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2
Bentalha, Zine el abidine
2018-06-01
Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.
Scattering by a conducting elliptic cylinder with a multilayer dielectric coating
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.
Fabrication of elliptical SRF cavities
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
Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?
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.
Hot interstellar matter in elliptical galaxies
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.
Nonlinear elliptic equations of the second order
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...
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
An application of hypergeometric functions to a problem in function theory
Directory of Open Access Journals (Sweden)
Daniel S. Moak
1984-01-01
Full Text Available In some recent work in univalent function theory, Aharonov, Friedland, and Brannan studied the series (1+xtα(1−tβ=∑n=0∞An(α,β(xtn. Brannan posed the problem of determining S={(α,β:|An(α,β(eiθ|0, β>0, n=1,2,3,…}. Brannan showed that if β≥α≥0, and α+β≥2, then (α,β∈S. He also proved that (α,1∈S for α≥1. Brannan showed that for 0|A2k(α,1(1| for k any integer. In this paper, we show that (α,β∈S for α≥1 and β≥1.
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))
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.)
Nonlinear elliptic partial differential equations an introduction
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.
Elliptic Tales Curves, Counting, and Number Theory
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
Abundance ratios in dwarf elliptical galaxies
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.
Directory of Open Access Journals (Sweden)
Jaime Castillo Pérez
2007-06-01
Full Text Available En 1991 M. Dotsenko presentó una generalización de la función hipergeométrica de Gauss denotada por 2Rτ1 (z, estableciendo además tanto su representación en serie como también su representación integral. Es importante notar que en 1999 Nina Virchenko y luego, en el 2003, Leda Galué consideraron esta función, introduciendo un conjunto de fórmulas de recurrencia y de diferenciación las cuales permiten simplificar algunos cálculos complicados. Kalla y colaboradores estudiaron esta función y presentaron una nueva forma unificada de la función Gamma, luego en el 2006, Castillo y colaboradores presentaron algunas representaciones simples para ésta función. En este trabajo se establecen algunas integrales impropias con límites de integración infinitos que involucran a la generalización τ de la función hipergeométrica de Gauss 2R1(a, b; c; τ ; z.In 1991 M. Dotsenko presented a generalization of Gauss’ hypergeometric function refered as 2Rτ1(z, and established its representation in series and integral. It is important to remark that in 1999 Nina Virchenko and, later in 2003, Leda Galu´e considered this function by introducing a set of recurrence and diﬀerentiation formulas; they permit simplify some complicated calculus. Kalla et al estudied this function and they presented a new uniﬁed form of the gamma function. Later in 2006, Castillo et al present some simple representation for this function. Along this paper work some improper integrals with integration inﬁnity limit involving generalized hypergeometric function2R1(a, b; c; τ ; z are displayed.
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.)
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.)
Index profile measurement of asymmetrical elliptical preforms or fibers
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
Elliptic genus of singular algebraic varieties and quotients
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).
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.)
Quasilinear infiltration from an elliptical cavity
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.
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
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...
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 ...
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.
Abundance Ratios in Dwarf Elliptical Galaxies
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
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
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
Hyper-and-elliptic-curve cryptography
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
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 ...
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.
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.
Elliptic Flow, Initial Eccentricity and Elliptic Flow Fluctuations in Heavy Ion Collisions at RHIC
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.
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
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 ...
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.)
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.)
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...
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.
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.
Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong
2013-01-01
As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.
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
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.
Elliptic differential equations theory and numerical treatment
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.
Nonlinear elliptic equations and nonassociative algebras
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...
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
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.
International Nuclear Information System (INIS)
Timus, D.M.; Prata, M.J.; Kalla, S.L.; Abbas, M.I.; Oner, F.; Galiano, E.
2007-01-01
A series formulation involving complete elliptic integrals of the first and second kinds for the solid angle subtended at a point by a circular disk is presented. Results from the present model were tested against data sets obtained with previous treatments for the solid angle in order to determine the degree of simplicity and speed of our calculations. 3-D graphs are presented
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
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
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}.
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.)
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)
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.
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
Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals
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.
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.
Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method
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...
Elliptic genus derivation of 4d holomorphic blocks
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.
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.
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.
Statistics about elliptic curves over finite prime fields
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.
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.
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
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.
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
Evolution of Hot Gas in Elliptical Galaxies
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.
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
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
On the asymptotic of solutions of elliptic boundary value problems in domains with edges
International Nuclear Information System (INIS)
Nkemzi, B.
2005-10-01
Solutions of elliptic boundary value problems in three-dimensional domains with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymptotic behavior of solutions of elliptic boundary value problems in general three-dimensional domains with straight edges can be investigated by means of discrete Fourier transformation. We apply this approach to time-harmonic Maxwell's equations and prove that the singular solutions can fully be described in terms of Fourier series. The representation here can easily be used to approximate three-dimensional stress intensity factors associated with edge singularities. (author)
Rugby and elliptical-shaped hohlraums experiments on the OMEGA laser facility
Tassin, Veronique; Monteil, Marie-Christine; Depierreux, Sylvie; Masson-Laborde, Paul-Edouard; Philippe, Franck; Seytor, Patricia; Fremerye, Pascale; Villette, Bruno
2017-10-01
We are pursuing on the OMEGA laser facility indirect drive implosions experiments in gas-filled rugby-shaped hohlraums in preparation for implosion plateforms on LMJ. The question of the precise wall shape of rugby hohlraum has been addressed as part of future megajoule-scale ignition designs. Calculations show that elliptical-shaped holhraum is more efficient than spherical-shaped hohlraum. There is less wall hydrodynamics and less absorption for the inner cone, provided a better control of time-dependent symmetry swings. In this context, we have conducted a series of experiments on the OMEGA laser facility. The goal of these experiments was therefore to characterize energetics with a complete set of laser-plasma interaction measurements and capsule implosion in gas-filled elliptical-shaped hohlraum with comparison with spherical-shaped hohlraum. Experiments results are discussed and compared to FCI2 radiation hydrodynamics simulations.
Ellipticity dependence of the near-threshold harmonics of H2 in an elliptical strong laser field.
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.
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
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.
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.
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.
New series of 3 D lattice integrable models
International Nuclear Information System (INIS)
Mangazeev, V.V.; Sergeev, S.M.; Stroganov, Yu.G.
1993-01-01
In this paper we present a new series of 3-dimensional integrable lattice models with N colors. The weight functions of the models satisfy modified tetrahedron equations with N states and give a commuting family of two-layer transfer-matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations and weights are parameterized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter η. 12 refs
Elliptical Orbit [arrow right] 1/r[superscript 2] Force
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]…
Newton flows for elliptic functions: A pilot study
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
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
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) + ...
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
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
Near-infrared photometry of bright elliptical galaxies
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
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...
Ellipticity of near-threshold harmonics from stretched molecules.
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.
Multipacting studies in elliptic SRF cavities
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
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
Elliptic flow and incomplete equilibration at RHIC
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.
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.
Aerodynamic Comparison of Hyper-Elliptic Cambered Span (HECS) Wings with Conventional Configurations
Lazos, Barry S.; Visser, Kenneth D.
2006-01-01
An experimental study was conducted to examine the aerodynamic and flow field characteristics of hyper-elliptic cambered span (HECS) wings and compare results with more conventional configurations used for induced drag reduction. Previous preliminary studies, indicating improved L/D characteristics when compared to an elliptical planform prompted this more detailed experimental investigation. Balance data were acquired on a series of swept and un-swept HECS wings, a baseline elliptic planform, two winglet designs and a raked tip configuration. Seven-hole probe wake surveys were also conducted downstream of a number of the configurations. Wind tunnel results indicated aerodynamic performance levels of all but one of the HECS wings exceeded that of the other configurations. The flow field data surveys indicate the HECS configurations displaced the tip vortex farther outboard of the wing than the Baseline configuration. Minimum drag was observed on the raked tip configuration and it was noted that the winglet wake lacked the cohesive vortex structure present in the wakes of the other configurations.
Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media
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.
Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media
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.
Towards Sub-Microarsecond Rigid Earth Nutation Series in the Hamiltonian Theory
National Research Council Canada - National Science Library
Souchay, Jean; Folgueira, M
2000-01-01
...) are based on the works of Kinoshita (1977) and Wahr (1979). In Kinoshita's work, the rigid Earth nutation series were calculated by the application of the Hamiltonian canonical equations to the rotation of the rigid and elliptical Earth...
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
Investigation on computation of elliptical microwave plasma cavity
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.
Multilevel quadrature of elliptic PDEs with log-normal diffusion
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.
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
Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies
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.
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
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
Multilevel quadrature of elliptic PDEs with log-normal diffusion
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
C1,1 regularity for degenerate elliptic obstacle problems
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.
Electromagnetic fields and Green functions in elliptical vacuum chambers
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...
Vertical elliptic operator for efficient wave propagation in TTI media
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.
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
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.
Vertical elliptic operator for efficient wave propagation in TTI media
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.
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.
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
Mergers of elliptical galaxies and the fundamental plane
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.
Optimal Rendezvous and Docking Simulator for Elliptical Orbits, Phase I
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...
Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)
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.
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
Handbook of elliptic and hyperelliptic curve cryptography
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.
ON ELLIPTICALLY POLARIZED ANTENNAS IN THE PRESENCE OF GROUND
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
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)
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)
Central $L$-values of elliptic curves and local polynomials
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.
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.
International Nuclear Information System (INIS)
Miller, Willard Jr
2014-01-01
We describe a contraction theory for 2nd order superintegrable systems, showing that all such systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. Analogously, all of the quadratic symmetry algebras of these systems can be obtained by a sequence of contractions starting from S9. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.This relates the scheme directly to explicitly solvable quantum mechanical systems. Amazingly, all of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2, C). The present paper concentrates on describing this intimate link between Lie algebra and superintegrable system contractions, with the detailed calculations presented elsewhere. Joint work with E. Kalnins, S. Post, E. Subag and R. Heinonen.
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
On the analyticity of Laguerre series
International Nuclear Information System (INIS)
Weniger, Ernst Joachim
2008-01-01
The transformation of a Laguerre series f(z) = Σ ∞ n=0 λ (α) n L (α) n (z) to a power series f(z) = Σ ∞ n=0 γ n z n is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a mathematically meaningless expansion containing power series coefficients that are infinite in magnitude. Simple sufficient conditions based on the decay rates and sign patterns of the Laguerre series coefficients λ (α) n as n → ∞ can be formulated which guarantee that the resulting power series represents an analytic function. The transformation produces a mathematically meaningful result if the coefficients λ (α) n either decay exponentially or factorially as n → ∞. The situation is much more complicated-but also much more interesting-if the λ (α) n decay only algebraically as n → ∞. If the λ (α) n ultimately have the same sign, the series expansions for the power series coefficients diverge, and the corresponding function is not analytic at the origin. If the λ (α) n ultimately have strictly alternating signs, the series expansions for the power series coefficients still diverge, but are summable to something finite, and the resulting power series represents an analytic function. If algebraically decaying and ultimately alternating Laguerre series coefficients λ (α) n possess sufficiently simple explicit analytical expressions, the summation of the divergent series for the power series coefficients can often be accomplished with the help of analytic continuation formulae for hypergeometric series p+1 F p , but if the λ (α) n have a complicated structure or if only their numerical values are available, numerical summation techniques have to be employed. It is shown that certain nonlinear sequence transformations-in particular the so-called delta transformation (Weniger 1989 Comput. Phys. Rep. 10 189-371 (equation (8.4-4)))-are able to
Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions
Directory of Open Access Journals (Sweden)
Ernest X. W. Xia
2012-01-01
Full Text Available Based on the theories of Ramanujan's elliptic functions and the (p, k-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006 we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identities were proved by Liu based on the fundamental theory of elliptic functions and some of them may be new. One side of each identity involves Eisenstein series, the other products of the Borweins' cubic theta functions. As applications, we evaluate some convolution sums. These evaluations are different from the formulas given by Alaca et al.
Elliptic-cylindrical analytical flux-rope model for ICMEs
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.
Relations between elliptic multiple zeta values and a special derivation algebra
International Nuclear Information System (INIS)
Broedel, Johannes; Matthes, Nils; Schlotterer, Oliver
2016-01-01
We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths. (paper)
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.
Algorithms to solve coupled systems of differential equations in terms of power series
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten
2016-08-01
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations, and that sufficiently many initial values of the integrals are given. Then there exist algorithms that decide constructively if the coefficients of their power series representations can be given within the class of nested sums over hypergeometric products. In this article we work out the calculation steps that solve this problem. First, we present a successful tactic that has been applied recently to challenging problems coming from massive 3-loop Feynman integrals. Here our main tool is to solve scalar linear recurrences within the class of nested sums over hypergeometric products. Second, we will present a new variation of this tactic which relies on more involved summation technologies but succeeds in reducing the problem to solve scalar recurrences with lower recurrence orders. The article works out the different challenges of this new tactic and demonstrates how they can be treated efficiently with our existing summation technologies.
Advanced topics in the arithmetic of elliptic curves
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...
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.
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.
International Nuclear Information System (INIS)
Kim, Jong Wook; Lee, Gyu Mahn; Jeong, Kyeong Hoon; Kim, Tae Wan; Park, Keun Bae
2001-01-01
As actual cracks found in practical structures are mostly three-dimensional surface cracks, such cracks give rise to the important problem when the structural integrity is evaluated in a viewpoint of fracture mechanics. The case of a semi-elliptical surface crack is more complicated than that of the embedded elliptical crack since the crack front intersects the free surface. Therefore, the exact expression of stress field according to the boundary condition can be the prior process for the structural integrity evaluation . The commercial code, I-DEAS does not provide the family of strain singular element for the cracked-body analysis. This means that the user cannot make use of the pre-processing function of I-DEAS effectively. But I-DEAS has the capability to hold input data in common with computational fracture mechanics program like ABAQUS. Hence, user can construct the optimized analysis method for the generation of input data of program like ABAQUS using the I-DEAS. In the present study, a procedure for the generation of input data for the optimized 3-dimensional computational fracture mechanics is developed as a series of effort to establish the structural integriyt evaluation procedure of SMART reactor vessel assembly. Input data for the finite element analysis are made using the commercial code, I-DEAS program, The stress analysis is performed using the ABAQUS. To demonstrate the validation of the developed procedure in the present sutdy, semi-elliptic surface crack in a half space subjected to uniform tension are solved, and the effects of crack configuration ratio are discussed in detail. The numerical results are presented and compared to those presented by Raju and Newman. Also, we have established the structural integrity evaluation procedure through the 3-D crack modeling
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Elliptic flow from Coulomb interaction and low density elastic scattering
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.
Iron abundance evolution in spiral and elliptical galaxies
International Nuclear Information System (INIS)
Matteucci, F.
1987-01-01
Chemical evolution models for the Galaxy and ellipticals, which take into account the most recent developments on theories of nucleosynthesis and supernova progenitors, are presented. The evolution of the abundance of iron in these systems, under the assumption that this element is mainly produced by type I SNe, originating from white dwarfs in binary systems, has been computed and the results have been compared with the observations. Overabundances of O, Si, Ne and Mg with respect to iron have been predicted for halo stars in their Galaxy. The existence of an Fe - total mass relation with a slope steeper than the corresponding relations for Mg and O has been predicted for ellipticals. The masses of Fe ejected by ellipticals of various masses into the intergalactic medium have also been computed in detail. The general agreement obtained between these theoretical models and the observations for galaxies of different morphological type supports the assumptions made about the origin of iron
Dirac Particles Emission from An Elliptical Black Hole
Directory of Open Access Journals (Sweden)
Yuant Tiandho
2017-03-01
Full Text Available According to the general theory of relativiy, a black hole is defined as a region of spacetime with super-strong gravitational effects and there is nothing can escape from it. So in the classical theory of relativity, it is safe to say that black hole is a "dead" thermodynamical object. However, by using quantum mechanics theory, Hawking has shown that a black hole may emit particles. In this paper, calculation of temperature of an elliptical black hole when emitting the Dirac particles was presented. By using the complexpath method, radiation can be described as emission process in the tunneling pictures. According to relationship between probability of outgoing particle with the spectrum of black body radiation for fermion particles, temperature of the elliptical black hole can be obtained and it depend on the azimuthal angle. This result also showed that condition on the surface of elliptical black hole is not in thermal equilibrium.
Modern cryptography and elliptic curves a beginner's guide
Shemanske, Thomas R
2017-01-01
This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the...
Applications of elliptic Carleman inequalities to Cauchy and inverse problems
Choulli, Mourad
2016-01-01
This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.
Polarization characteristics of double-clad elliptical fibers.
Zhang, F; Lit, J W
1990-12-20
A scalar variational analysis based on a Gaussian approximation of the fundamental mode of a double-clad elliptical fiber with a depressed inner cladding is studied. The polarization properties and graphic results are presented; they are given in terms of three parameters: the ratio of the major axis to the minor axis of the core, the ratio of the inner cladding major axis to the core major axis, and the difference between the core index and the inner cladding index. The variations of both the spot size and the field intensity with core ellipticity are examined. It is shown that high birefringence and dispersion-free orthogonal polarization modes can be obtained within the single-mode region and that the field intensity distribution may be more confined to the fiber center than in a single-clad elliptical fiber.
System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow
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.
Transfer coefficients for plate fin and elliptical tube heat exchangers
International Nuclear Information System (INIS)
Saboya, S.M.; Saboya, F.E.M.
1981-01-01
In order to determine transfer coefficients for plate fin and elliptical tube exchangers, mass transfer experiments have been performed using the naphthalene sublimation technique. By means of the heat-mass transfer analogy, the results can be converted to heat transfer results. The transfer coefficients were compared with those for circular tube exchangers and the comparison revealed no major differences. This is a positive outcome, since the use of elliptical tubes may reduce substantially the pressure drop, without affecting the transfer characteristics.(Author) [pt
Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus
Berglund, P.; Henningson, M.
1994-01-01
We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirr...
FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.
Coexistence of a General Elliptic System in Population Dynamics
DEFF Research Database (Denmark)
Pedersen, Michael
2004-01-01
This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross-diffusion......This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross...
UV Visibility of Moderate-Redshift Giant Elliptical Galaxies
Directory of Open Access Journals (Sweden)
Myung-Hyun Rhee
1998-06-01
Full Text Available We show quantitatively whether giant elliptical galaxies would be visible at far UV wavelengths if they were placed at moderate redshift of 0.4-0.5. On the basis of simple cosmological tests, we conclude that giant elliptical galaxies can be detectable upto the redshift of 0.4-0.5 in the proposed GALEX (Galaxy Evolution Explorer Deep Imaging Survey. We also show that obtaining UV color index such as m_1550 - V from upcoming GALEX and SDSS (Sloan Digital Sky Survey observations should be feasible.
Plasma blob generation due to cooperative elliptic instability.
Manz, P; Xu, M; Müller, S H; Fedorczak, N; Thakur, S C; Yu, J H; Tynan, G R
2011-11-04
Using fast-camera measurements the generation mechanism of plasma blobs is investigated in the linear device CSDX. During the ejection of plasma blobs the plasma is dominated by an m=1 mode, which is a counterrotating vortex pair. These flows are known to be subject to the cooperative elliptic instability, which is characterized by a cooperative disturbance of the vortex cores and results in a three-dimensional breakdown of two-dimensional flows. The first experimental evidence of a cooperative elliptic instability preceding the blob-ejection is provided in terms of the qualitative evolution of the vortex geometries and internal wave patterns.
Inflation of polymer melts into elliptic and circular cylinders
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz; Christensen, Jens Horslund; Gøttsche, Søren
2000-01-01
A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top of the infla......A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top...
Large N elliptic genus and AdS/CFT Correspondence
International Nuclear Information System (INIS)
Boer, Jan de
1998-01-01
According to one of Maldacena's dualities, type IIB string theory on AdS 3 x S 3 x K3 is equivalent to a certain N = (4, 4) superconformal field theory. In this note we compute the elliptic genus of the boundary theory in the supergravity approximation. A finite quantity is obtained once we introduce a particular exclusion principle. In the regime where the supergravity approximation is reliable, we find exact agreement with the elliptic genus of a sigma model with target space K3 N /S N
Hörmander spaces, interpolation, and elliptic problems
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
Elliptic interpretation of black holes and quantum mechanics
International Nuclear Information System (INIS)
Gibbons, G.W.
1987-01-01
The lectures as delivered contained an elementary introduction to the classical theory of black holes together with an account of Hawking's original derivation of the thermal emission from black holes in the quantum theory. Also described here is what is here called the elliptic interpretation partly because of its possible relevance to the lectures of Professor 't Hooft. A rather more detailed account of the elliptic interpretation is given and the reader is referred to the original literature for the elementary material. 22 references
An electrostatic elliptical mirror for neutral polar molecules.
González Flórez, A Isabel; Meek, Samuel A; Haak, Henrik; Conrad, Horst; Santambrogio, Gabriele; Meijer, Gerard
2011-11-14
Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compared to the outcome of trajectory simulations.
Elliptic Genera of Symmetric Products and Second Quantized Strings
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.
Event-by-Event Elliptic Flow Fluctuations from PHOBOS
Wosiek, B.; 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.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.
2009-04-01
Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in (Au+Au) collisions at sqrt {sNN}=200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.
Elliptic flow in Au+Au collisions at RHIC
Vale, Carla M.; PHOBOS Collaboration; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Budzanowski, A.; Busza, W.; Carroll, A.; Decowski, M. P.; García, E.; George, N.; Gulbrandsen, K.; Gushue, S.; Halliwell, C.; Hamblen, J.; Heintzelman, G. A.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holynski, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Katzy, J.; Khan, N.; Kucewicz, W.; Kulinich, P.; Kuo, C. M.; Lin, W. T.; Manly, S.; McLeod, D.; Mignerey, A. C.; Ngyuen, M.; Nouicer, R.; Olszewski, A.; Pak, R.; Park, I. C.; Pernegger, H.; Reed, C.; Remsberg, L. P.; Reuter, M.; Roland, C.; Roland, G.; Rosenberg, L.; Sagerer, J.; Sarin, P.; Sawicki, P.; Skulski, W.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tang, J.-L.; Tonjes, M. B.; Trzupek, A.; van Nieuwenhuizen, G. J.; Verdier, R.; Veres, G.; Wolfs, F. L. H.; Wosiek, B.; Wozniak, K.; Wuosmaa, A. H.; Wyslouch, B.
2005-04-01
Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.
Photoinduced macroscopic chiral structures in a series of azobenzene copolyesters
DEFF Research Database (Denmark)
Nedelchev, L.; Nikolova, L.; Matharu, A.
2002-01-01
A study of the propagation of elliptically polarized light and the resulting formation of macroscopic chiral structures in a series of azobenzene side-chain copolyesters, in which the morphology is varied from liquid crystalline to amorphous, is reported. Real-time measurements are presented...
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.
The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces
Chen, Yujia; Macdonald, Colin B.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general
Efficient method for finding square roots for elliptic curves over OEF
CSIR Research Space (South Africa)
Abu-Mahfouz, Adnan M
2009-01-01
Full Text Available Elliptic curve cryptosystems like others public key encryption schemes, require computing a square roots modulo a prime number. The arithmetic operations in elliptic curve schemes over Optimal Extension Fields (OEF) can be efficiently computed...
Design of an elliptical solenoid magnet for transverse beam matching to the spiral inflector
International Nuclear Information System (INIS)
Goswami, A.; Sing Babu, P.; Pandit, V.S.
2013-01-01
In this work, we present the design study of an elliptical solenoid magnet to be used for transverse beam matching at the input of a spiral inflector for efficient transmission. We have studied the dependence of axial field and gradients in the transverse directions of the elliptical solenoid magnet with ellipticity of the aperture. Using the beam envelope equations we have studied the feasibility of using an elliptical solenoid for transverse beam matching to the acceptance of a spiral inflector. (author)
Fast summation of divergent series and resurgent transseries from Meijer-G approximants
Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.
2018-05-01
We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.
Optimization of elliptic neutron guides for triple-axis spectroscopy
International Nuclear Information System (INIS)
Janoschek, M.; Boeni, P.; Braden, M.
2010-01-01
In the last decade the performance of neutron guides for the transport of neutrons has been significantly increased. The most recent developments have shown that elliptic guide systems can be used to focus neutron beams while simultaneously reducing the number of neutron reflections, hence, leading to considerable gains in neutron flux. We have carried out Monte-Carlo simulations for a new triple-axis spectrometer that will be built at the end position of the conventional cold guide NL-1 in the neutron guide hall of the research reactor FRM-II in Munich, Germany. Our results demonstrate that an elliptic guide section at the end of a conventional guide can be used to at least maintain the total neutron flux onto the sample, while significantly improving the energy resolution of the spectrometer. The simulation further allows detailed insight how the defining parameters of an elliptic guide have to be chosen to obtain optimum results. Finally, we show that the elliptic guide limits losses in the neutron flux that generally arise at the gaps, where the monochromator system of the upstream instrument is situated.
The dynamical fingerprint of core scouring in massive elliptical galaxies
International Nuclear Information System (INIS)
Thomas, J.; Saglia, R. P.; Bender, R.; Erwin, P.; Fabricius, M.
2014-01-01
The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r b , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.
Monotone difference schemes for weakly coupled elliptic and parabolic systems
P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)
2017-01-01
textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is
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.
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.
Dynamic stress intensity factors for a longitudinal semi-elliptical ...
African Journals Online (AJOL)
elliptical crack in a thick-walled cylinder subjected to transient dynamic stresses. First, the problem of dynamic elasticity in a thick-walled cylinder is solved analytically using the finite Hankel transform. Transient pressure is assumed to act on ...
Three dimensional alignment of molecules using elliptically polarized laser fields
DEFF Research Database (Denmark)
Larsen, J.J.; Bjerre, N.; Hald, K.
2000-01-01
We demonstrate, theoretically and experimentally, that an intense, elliptically polarized, nonresonant laser field can simultaneously force all three axes of a molecule to align along given axes fixed in space, thus inhibiting the free rotation in all three Euler angles. Theoretically, the effect...
Generation of Elliptically Polarized Terahertz Waves from Antiferromagnetic Sandwiched Structure.
Zhou, Sheng; Zhang, Qiang; Fu, Shu-Fang; Wang, Xuan-Zhang; Song, Yu-Ling; Wang, Xiang-Guang; Qu, Xiu-Rong
2018-04-01
The generation of elliptically polarized electromagnetic wave of an antiferromagnetic (AF)/dielectric sandwiched structure in the terahertz range is studied. The frequency and external magnetic field can change the AF optical response, resulting in the generation of elliptical polarization. An especially useful geometry with high levels of the generation of elliptical polarization is found in the case where an incident electromagnetic wave perpendicularly illuminates the sandwiched structure, the AF anisotropy axis is vertical to the wave-vector and the external magnetic field is pointed along the wave-vector. In numerical calculations, the AF layer is FeF2 and the dielectric layers are ZnF2. Although the effect originates from the AF layer, it can be also influenced by the sandwiched structure. We found that the ZnF2/FeF2/ZnF2 structure possesses optimal rotation of the principal axis and ellipticity, which can reach up to about thrice that of a single FeF2 layer.
Eliminating line of sight in elliptic guides using gravitational curving
DEFF Research Database (Denmark)
Klenø, Kaspar H.; Willendrup, Peter Kjær; Bergbäck Knudsen, Erik
2011-01-01
result in a breakdown of the geometrical focusing mechanism inherent to the elliptical shape, resulting in unwanted reflections and loss of transmission. We present a new and yet untried idea by curving a guide in such a way as to follow the ballistic curve of a neutron in the gravitational field, while...
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.
Influence of Some Variable Parameters on Horizontal Elliptic Micro ...
African Journals Online (AJOL)
The study investigates the laminar flow and heat transfer characteristics in elliptic micro-channels of varying axis ratios and with internal longitudinal fins, operating in a region that is hydrodynamically and thermally fully developed; purposely to determine the effects of some salient fluid and geometry parameters such as ...
Recombination plus fragmentation model at RHIC: elliptic flow
Energy Technology Data Exchange (ETDEWEB)
Nonaka, C [Department of Physics, Duke University, Durham, NC 27708 (United States); Fries, R J [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Mueller, B [Department of Physics, Duke University, Durham, NC 27708 (United States); Bass, S A [Department of Physics, Duke University, Durham, NC 27708 (United States); RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 (United States); Asakawa, M [Department of Physics, Osaka University, Toyonaka 560-0043 (Japan)
2005-04-01
We discuss hadron production in relativistic heavy-ion collisions in the framework of the recombination and fragmentation model. We propose elliptic flow as a useful tool for exploring final interactions of resonances, the hadron structure of exotic particles and the phase structure of the reaction.
Tearing mode stability of tokamak plasmas with elliptical cross section
International Nuclear Information System (INIS)
Carreras, B.A.; Holmes, J.A.; Hicks, H.R.; Lynch, V.E.
1981-02-01
The effect of the ellipticity of the plasma cross section on tearing mode stability is investigated. The induced coupling between modes is shown to be destabilizing; however, the modification of the equilibrium tends to stabilize the tearing modes. The net effect depends on the manner in which the equilibrium is modified as the plasma cross-section shape is changed
The shortage of long-period comets in elliptical orbits
International Nuclear Information System (INIS)
Everhart, E.
1979-01-01
Based on the number of 'new' comets seen on near-parabolic orbits, one can predict the number of comets that should be found on definitely elliptical orbits on their subsequent returns. The author shows that about three out of four of these returning comets are not observed. (Auth.)
On nonlocal semi linear elliptic problem with an indefinite term
International Nuclear Information System (INIS)
Yechoui, Akila
2007-08-01
The aim of this paper is to investigate the existence of solutions of a nonlocal semi linear elliptic equation with an indefinite term. The monotone method, the method of upper and lower solutions and the classical maximum principle are used to obtain our results. (author)
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 ...
Flexible hardware design for RSA and Elliptic Curve Cryptosystems
Batina, L.; Bruin - Muurling, G.; Örs, S.B.; Okamoto, T.
2004-01-01
This paper presents a scalable hardware implementation of both commonly used public key cryptosystems, RSA and Elliptic Curve Cryptosystem (ECC) on the same platform. The introduced hardware accelerator features a design which can be varied from very small (less than 20 Kgates) targeting wireless
Diffraction and Dirchlet problem for parameter-elliptic convolution ...
African Journals Online (AJOL)
In this paper we evaluate the difference between the inverse operators of a Dirichlet problem and of a diffraction problem for parameter-elliptic convolution operators with constant symbols. We prove that the inverse operator of a Dirichlet problem can be obtained as a limit case of such a diffraction problem. Quaestiones ...
Fast elliptic-curve cryptography on the Cell Broadband Engine
Costigan, N.; Schwabe, P.; Preneel, B.
2009-01-01
This paper is the first to investigate the power of the Cell Broadband Engine for state-of-the-art public-key cryptography. We present a high-speed implementation of elliptic-curve Diffie-Hellman (ECDH) key exchange for this processor, which needs 697080 cycles on one Synergistic Processor Unit for
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.
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 −.
Implementing parallel elliptic solver on a Beowulf cluster
Directory of Open Access Journals (Sweden)
Marcin Paprzycki
1999-12-01
Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Radial solutions to semilinear elliptic equations via linearized operators
Directory of Open Access Journals (Sweden)
Phuong Le
2017-04-01
Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.
Nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity
Directory of Open Access Journals (Sweden)
Hocine Ayadi
2018-02-01
Full Text Available In this article, we prove the existence and the regularity of distributional solutions for a class of nonlinear anisotropic elliptic equations with $p_i(x$ growth conditions, degenerate coercivity and $L^{m(\\cdot}$ data, with $m(\\cdot$ being small, in appropriate Lebesgue-Sobolev spaces with variable exponents. The obtained results extend some existing ones [8,10].
The use of MACSYMA for solving elliptic boundary value problems
Thejll, Peter; Gilbert, Robert P.
1990-01-01
A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.
An elliptic analogue of the Franklin-Schneider theorem
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
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
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.
Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs
Directory of Open Access Journals (Sweden)
Marco Calahorrano
2004-04-01
Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$
A Primer on Elliptic Functions with Applications in Classical Mechanics
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…
On the elliptic flow for nearly symmetric collisions and nuclear ...
Indian Academy of Sciences (India)
10Ne20+13Al27, 18Ar40+21Sc45, 30Zn64+28Ni58, 36Kr86+41Nb93) using the quantum molecular dynamics (QMD) model. General features of elliptic ﬂow are investigated with the help of theoretical simulations. The simulations are ...
Stellar populations as a function of radius in giant elliptical galaxies
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
Modal analysis of wake fields and its application to elliptical pill-box cavity with finite aperture
International Nuclear Information System (INIS)
Kim, S.H.; Chen, K.W.; Yang, J.S.
1990-01-01
The potential of the wake-field produced by a bunch of relativistic charged particles passing through a pill-box cavity is expressed by using Floquet's theorem, and an obvious requirement that the energy gain over all acceleration cavity of many pill boxes must be proportional to the number of pill boxes, based on the previous modal approach (BWW theory). It is found that the wake-field is consisted of two classes of modes: the longitudinal modes which are independent of the aperture and the pill-box gap, the hybrid (pill-box) modes which are dependent of the pill-box gap. The wake field is predominated by the fundamental longitudinal mode whose wavelength is on the order of the effective diameter of the cavity, and its magnitude is inversely proportional to the cross sectional area of the cavity for practical cavities with small apertures. Both longitudinal and transverse wake fields due to the longitudinal modes in an elliptical pill box cavity are expressed analytically in a closed series form by solving exactly the longitudinal eigenmode equation in the elliptical cylindrical coordinates in terms of Mathieu functions. It is found that both longitudinal and transverse wake fields whose amplitudes per driving charge are greater than 100 MV/m/μC can be generated in an elliptical cavity
Directory of Open Access Journals (Sweden)
Moussa Leblouba
2015-01-01
Full Text Available We present an enhancement to the existing elliptical leaf spring (ELS for improved damping and energy dissipation capabilities. The ELS consists of a high tensile stainless steel elliptical leaf spring with polymer or rubber compound. This device is conceived as a shock and vibration isolator for equipment and lightweight structures. The enhancement to the ELS consists of a lead spring plugged vertically between the leaves (referred to as lead-rubber elliptical leaf spring (LRELS. The lead is shown to produce hysteretic damping under plastic deformations. The LRELS isolator is shown to exhibit nonlinear hysteretic behavior. In both horizontal directions, the LRELS showed symmetrical rate independent behavior but undergoes stiffening behavior under large displacements. However, in the vertical direction, the LRELS behavior is asymmetric, exhibiting softening behavior in compression and stiffening behavior in tension. Mathematical models based on the Bouc-Wen model, describing the hysteretic behavior of the proposed isolator, are developed and numerically calibrated using a series of finite element analyses. The LRELS is found to be effective in the in-plane and vertical directions. The improved damping and energy dissipation of the LRELS is provided from the hysteretic damping of the lead spring.
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
Thick-walled anisotropic elliptic tube analyzed via curvilinear tensor calculus
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Mareš T.
2007-10-01
Full Text Available After a brief introduction into the tensor calculus, the thick-walled anisotropic elliptic tube is analyzed. A procedure of the analysis is described in a stepwise manner. A choice of the appropriate coordinate systems is the first step. The second step consists of the determination of corresponding metric tensors. Then the elasticity tensor of a local orthotropy is transformed into a global computational coordinate system. Next the appropriate Christoffel symbols of the second kind are determined and the total potential energy of the system is expressed. At the end the solution is approximated by a Fourier series and for given geometrical values and loading the numerical results are obtained and graphically represented.It must be said that throughout the calculation the free software only was used and for the numerical operations an old laptop is sufficient. The author regards both the former and the latter as a great advantage of the demonstrated method.
Elliptic Euler–Poisson–Darboux equation, critical points and integrable systems
International Nuclear Information System (INIS)
Konopelchenko, B G; Ortenzi, G
2013-01-01
The structure and properties of families of critical points for classes of functions W(z, z-bar ) obeying the elliptic Euler–Poisson–Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(β, β-bar ;1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed. (paper)
6j-symbols for symmetric representations of SO(n) as the double series
International Nuclear Information System (INIS)
Alisauskas, Sigitas
2002-01-01
The corrected triple sum expression of Alisauskas (1987 J. Phys. A: Math. Gen. 20 35) for the recoupling (Racah) coefficients (6j-symbols) of the symmetric (most degenerate) representations of the orthogonal groups SO(n) (previously derived from the fourfold sum expression of Alisauskas also related to the result of Hormess and Junker (1999 J. Phys. A: Math. Gen. 32 4249) is rearranged into three new different double sum expressions (related to the hypergeometric Kampe de Feriet type series) and a new triple sum expression with preferable summation condition. The Regge type symmetry of special 6j-symbols of the orthogonal groups SO(n) in terms of special Kampe de Feriet F 1:4 1:3 series is revealed. The recoupling coefficients for antisymmetric representations of symplectic group Sp(2n) are derived using their relation with the recoupling coefficients of the formal orthogonal group SO(-2n)
International Nuclear Information System (INIS)
Adamová, D.; Agakichiev, G.; Andronic, A.; Antończyk, D.; Appelshäuser, H.; Belaga, V.; Bielčíková, J.; Braun-Munzinger, P.; Busch, O.; Cherlin, A.; Damjanović, S.; Dietel, T.; Dietrich, L.; Drees, A.; Dubitzky, W.; Esumi, S.I.; Filimonov, K.
2012-01-01
Differential elliptic flow spectra v 2 (p T ) of π - , K S 0 , p, Λ have been measured at √(s NN )=17.3 GeV around midrapidity by the CERN-CERES/NA45 experiment in mid-central Pb + Au collisions (10% of σ geo ). The p T range extends from about 0.1 GeV/c (0.55 GeV/c for Λ) to more than 2 GeV/c. Protons below 0.4 GeV/c are directly identified by dE/dx. At higher p T , proton elliptic flow is derived as a constituent, besides π + and K + , of the elliptic flow of positive pion candidates. This retrieval requires additional inputs: (i) of the particle composition, and (ii) of v 2 (p T ) of positive pions. For (i), particle ratios obtained by NA49 are adapted to CERES conditions; for (ii), the measured v 2 (p T ) of negative pions is substituted, assuming π + and π - elliptic flow magnitudes to be sufficiently close. The v 2 (p T ) spectra are compared to ideal-hydrodynamics calculations. In synopsis of the series π - -K S 0 -p-Λ, flow magnitudes are seen to fall with decreasing p T progressively even below hydro calculations with early kinetic freeze-out (T f =160 MeV) leaving not much time for hadronic evolution. The proton v 2 (p T ) data show a downward swing towards low p T with excursions into negative v 2 values. The pion-flow isospin asymmetry observed recently by STAR at RHIC, invalidating in principle our working assumption, is found in its impact on proton flow bracketed from above by the direct proton flow data, and not to alter any of our conclusions. Results are discussed in perspective of recent viscous hydrodynamics studies which focus on late hadronic stages.
Adamová, D.; Agakichiev, G.; Andronic, A.; Antończyk, D.; Appelshäuser, H.; Belaga, V.; Bielčíková, J.; Braun-Munzinger, P.; Busch, O.; Cherlin, A.; Damjanović, S.; Dietel, T.; Dietrich, L.; Drees, A.; Dubitzky, W.; Esumi, S. I.; Filimonov, K.; Fomenko, K.; Fraenkel, Z.; Garabatos, C.; Glässel, P.; Hering, G.; Holeczek, J.; Kalisky, M.; Krobath, G.; Kushpil, V.; Maas, A.; Marín, A.; Milošević, J.; Miśkowiec, D.; Panebrattsev, Y.; Petchenova, O.; Petráček, V.; Radomski, S.; Rak, J.; Ravinovich, I.; Rehak, P.; Sako, H.; Schmitz, W.; Schuchmann, S.; Sedykh, S.; Shimansky, S.; Stachel, J.; Šumbera, M.; Tilsner, H.; Tserruya, I.; Tsiledakis, G.; Wessels, J. P.; Wienold, T.; Wurm, J. P.; Yurevich, S.; Yurevich, V.; Ceres Collaboration
Differential elliptic flow spectra v2(pT) of π-, KS0, p, Λ have been measured at √{sNN}=17.3 GeV around midrapidity by the CERN-CERES/NA45 experiment in mid-central Pb + Au collisions (10% of σgeo). The pT range extends from about 0.1 GeV/c (0.55 GeV/c for Λ) to more than 2 GeV/c. Protons below 0.4 GeV/c are directly identified by dE/dx. At higher pT, proton elliptic flow is derived as a constituent, besides π+ and K+, of the elliptic flow of positive pion candidates. This retrieval requires additional inputs: (i) of the particle composition, and (ii) of v2(pT) of positive pions. For (i), particle ratios obtained by NA49 are adapted to CERES conditions; for (ii), the measured v2(pT) of negative pions is substituted, assuming π+ and π- elliptic flow magnitudes to be sufficiently close. The v2(pT) spectra are compared to ideal-hydrodynamics calculations. In synopsis of the series π--KS0-p-Λ, flow magnitudes are seen to fall with decreasing pT progressively even below hydro calculations with early kinetic freeze-out (Tf=160 MeV) leaving not much time for hadronic evolution. The proton v2(pT) data show a downward swing towards low pT with excursions into negative v2 values. The pion-flow isospin asymmetry observed recently by STAR at RHIC, invalidating in principle our working assumption, is found in its impact on proton flow bracketed from above by the direct proton flow data, and not to alter any of our conclusions. Results are discussed in perspective of recent viscous hydrodynamics studies which focus on late hadronic stages.
Structure and Formation of Elliptical and Spheroidal Galaxies
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
Hirschman, Isidore Isaac
2014-01-01
This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the app
Random source generating far field with elliptical flat-topped beam profile
International Nuclear Information System (INIS)
Zhang, Yongtao; Cai, Yangjian
2014-01-01
Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively. (paper)
Influences of magma chamber ellipticity on ring fracturing and eruption at collapse calderas
International Nuclear Information System (INIS)
Holohan, Eoghan P; Walsh, John J; Vries, Benjamin van Wyk de; Troll, Valentin R; Walter, Thomas R
2008-01-01
Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.
Influences of magma chamber ellipticity on ring fracturing and eruption at collapse calderas
Energy Technology Data Exchange (ETDEWEB)
Holohan, Eoghan P; Walsh, John J [Fault Analysis Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4 (Ireland); Vries, Benjamin van Wyk de [Laboratoire Magmas et Volcans, 5 rue Kessler, 63038 Clermont-Ferrand (France); Troll, Valentin R [Department of Earth Sciences, Uppsala University, SE-752 36, Uppsala (Sweden); Walter, Thomas R [GFZ Potsdam, Telegrafenberg, Potsdam, D-14473 (Germany)], E-mail: Eoghan.Holohan@ucd.ie
2008-10-01
Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.
M-strings, Elliptic Genera and N=4 String Amplitudes
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.
Subcycle dynamics of Coulomb asymmetry in strong elliptical laser fields.
Li, Min; Liu, Yunquan; Liu, Hong; Ning, Qicheng; Fu, Libin; Liu, Jie; Deng, Yongkai; Wu, Chengyin; Peng, Liang-You; Peng, Liangyou; Gong, Qihuang
2013-07-12
We measure photoelectron angular distributions of noble gases in intense elliptically polarized laser fields, which indicate strong structure-dependent Coulomb asymmetry. Using a dedicated semiclassical model, we have disentangled the contribution of direct ionization and multiple forward scattering on Coulomb asymmetry in elliptical laser fields. Our theory quantifies the roles of the ionic potential and initial transverse momentum on Coulomb asymmetry, proving that the small lobes of asymmetry are induced by direct ionization and the strong asymmetry is induced by multiple forward scattering in the ionic potential. Both processes are distorted by the Coulomb force acting on the electrons after tunneling. Lowering the ionization potential, the relative contribution of direct ionization on Coulomb asymmetry substantially decreases and Coulomb focusing on multiple rescattering is more important. We do not observe evident initial longitudinal momentum spread at the tunnel exit according to our simulation.
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.
Dynamic separation of nanomagnet sublattices by orientation of elliptical elements
Yahagi, Y.; Berk, C. R.; Harteneck, B. D.; Cabrini, S. D.; Schmidt, H.
2014-04-01
We report the separation of the magnetization dynamics of densely packed nanomagnets depending on their orientation. The arrays consist of interleaved sublattices of identical nickel elliptical disks. By controlling the orientation of the elliptic disks relative to the external field in each sublattice, we simultaneously analyzed the magnetization dynamics in each sublattice using a time-resolved magnetooptic Kerr effect (TR-MOKE) microscopy system. The Fourier spectra showed clearly separated precession modes for sublattices with different orientations. The spectra were shown to be robust against the error in applied field orientation. The sublattice response can be tuned to a single collective frequency by choosing a symmetric field orientation. We analyzed the effect of the interelement coupling with various spacing between nanomagnets and found a relatively weak dependence on dipolar interactions in good agreement with micromagnetic simulations.
Nuclear limits on gravitational waves from elliptically deformed pulsars
International Nuclear Information System (INIS)
Krastev, Plamen G.; Li Baoan; Worley, Aaron
2008-01-01
Gravitational radiation is a fundamental prediction of General Relativity. Elliptically deformed pulsars are among the possible sources emitting gravitational waves (GWs) with a strain-amplitude dependent upon the star's quadrupole moment, rotational frequency, and distance from the detector. We show that the gravitational wave strain amplitude h 0 depends strongly on the equation of state of neutron-rich stellar matter. Applying an equation of state with symmetry energy constrained by recent nuclear laboratory data, we set an upper limit on the strain-amplitude of GWs produced by elliptically deformed pulsars. Depending on details of the EOS, for several millisecond pulsars at distances 0.18 kpc to 0.35 kpc from Earth, the maximalh 0 is found to be in the range of ∼[0.4-1.5]x10 -24 . This prediction serves as the first direct nuclear constraint on the gravitational radiation. Its implications are discussed
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)
Wireless OAM transmission system based on elliptical microstrip patch antenna.
Chen, Jia Jia; Lu, Qian Nan; Dong, Fei Fei; Yang, Jing Jing; Huang, Ming
2016-05-30
The multiplexing transmission has always been a focus of attention for communication technology. In this paper, the radiation characteristics of circular microstrip patch antenna was firstly analyzed based on cavity model theory, and then spiral beams carrying orbital angular momentum (OAM) were generated, using elliptical microstrip patch antenna, with a single feed probe instead of a standard circular patch with two feedpoints. Moreover, by combining the proposed elliptic microstrip patch antenna with Universal Software Radio Peripheral (USRP), a wireless OAM transmission system was established and the real-time transmission of text, image and video in a real channel environment was realized. Since the wireless OAM transmission has the advantage of good safety and high spectrum utilization efficiency, this work has theoretical significance and potential application.
A theoretical model of semi-elliptic surface crack growth
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Shi Kaikai
2014-06-01
Full Text Available A theoretical model of semi-elliptic surface crack growth based on the low cycle strain damage accumulation near the crack tip along the cracking direction and the Newman–Raju formula is developed. The crack is regarded as a sharp notch with a small curvature radius and the process zone is assumed to be the size of cyclic plastic zone. The modified Hutchinson, Rice and Rosengren (HRR formulations are used in the presented study. Assuming that the shape of surface crack front is controlled by two critical points: the deepest point and the surface point. The theoretical model is applied to semi-elliptic surface cracked Al 7075-T6 alloy plate under cyclic loading, and five different initial crack shapes are discussed in present study. Good agreement between experimental and theoretical results is obtained.
Analytical model of impedance in elliptical beam pipes
Pesah, Arthur Chalom
2017-01-01
Beam instabilities are among the main limitations in building higher intensity accelerators. Having a good impedance model for every accelerators is necessary in order to build components that minimize the probability of instabilities caused by the interaction beam-environment and to understand what piece to change in case of intensity increasing. Most of accelerator components have their impedance simulated with finite elements method (using softwares like CST Studio), but simple components such as circular or flat pipes are modeled analytically, with a decreasing computation time and an increasing precision compared to their simulated model. Elliptical beam pipes, while being a simple component present in some accelerators, still misses a good analytical model working for the hole range of velocities and frequencies. In this report, we present a general framework to study the impedance of elliptical pipes analytically. We developed a model for both longitudinal and transverse impedance, first in the case of...
Electric sail elliptic displaced orbits with advanced thrust model
Niccolai, Lorenzo; Quarta, Alessandro A.; Mengali, Giovanni
2017-09-01
This paper analyzes the performance of an Electric Solar Wind Sail for generating and maintaining an elliptic, heliocentric, displaced non-Keplerian orbit. In this sense, this paper extends and completes recent studies regarding the performances of an Electric Solar Wind Sail that covers a circular, heliocentric, displaced orbit of given characteristics. The paper presents the general equations that describe the elliptic orbit maintenance in terms of both spacecraft attitude and performance requirements, when a refined thrust model (recently proposed for the preliminary mission design) is taken into account. In particular, the paper also discusses some practical applications on particular mission scenarios in which an analytic solution of the governing equations has been found.
Halos around ellipticals and the environment dependence of Hubble type
International Nuclear Information System (INIS)
Zurek, W.H.; Quinn, P.J.; Salmon, J.K.
1985-01-01
It is not surprising that the baryonic material inside the more compact halos will tend to form a more compact, luminous elliptical. What needs to be explained is the difference in the value of the spin parameter (lambda). It might be tempting to speculate that more compact, dense halos have systematically smaller values of lambda. Such an effect is predicted by linear calculations. Our simulations show that it may exist but it appears to be too small compared to the random scatter of the values of lambda and rho to be decisive. It is more likely that the baryonic material has initially similar lambda both in the future spirals and elliptical but compact halos damp out the lambda of the dissipative, baryonic material more readily
Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus; von Hippel, Matt; Wilhelm, Matthias
2018-03-01
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.
Pressure algorithm for elliptic flow calculations with the PDF method
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.
On generalized elliptical quantiles in the nonlinear quantile regression setup
Czech Academy of Sciences Publication Activity Database
Hlubinka, D.; Šiman, Miroslav
2015-01-01
Roč. 24, č. 2 (2015), s. 249-264 ISSN 1133-0686 R&D Projects: GA ČR GA14-07234S Institutional support: RVO:67985556 Keywords : multivariate quantile * elliptical quantile * quantile regression * multivariate statistical inference * portfolio optimization Subject RIV: BA - General Mathematics Impact factor: 1.207, year: 2015 http://library.utia.cas.cz/separaty/2014/SI/siman-0434510.pdf
Triangularity effects on the collisional diffusion for elliptic tokamak plasma
International Nuclear Information System (INIS)
Martin, P.; Castro, E.
2007-01-01
In this conference the effect of ellipticity and triangularity will be analyzed for axisymmetric tokamak in the collisional regime. Analytic forms for the magnetic field cross sections are taken from those derived recently by other authors [1,2]. Analytical results can be obtained in elliptic plasmas with triangularity by using an special system of tokamak coordinates recently published [3-5]. Our results show that triangularities smaller than 0.6, increases confinement for ellipticities in the range 1.2 to 2. This behavior happens for negative and positive triangularities; however this effect is stronger for positive than for negative triangularities. The maximum diffusion velocity is not obtained for zero triangularity, but for small negative triangularities. Ellipticity is also very important in confinement, but the effect of triangularity seems to be more important. High electric inductive field increases confinement, though this field is difficult to modify once the tokamak has been built. The analytic form of the current produced by this field is like that of a weak Ware pinch with an additional factor, which weakens the effect by an order of magnitude. The dependence of the triangularity effect with the Shafranov shift is also analyzed. References 1. - L. L. Lao, S. P. Hirshman, and R. M. Wieland, Phys. Fluids 24, 1431 (1981) 2. - G. O. Ludwig, Plasma Physics Controlled Fusion 37, 633 (1995) 3. - P. Martin, Phys. Plasmas 7, 2915 (2000) 4. - P. Martin, M. G. Haines and E. Castro, Phys. Plasmas 12, 082506 (2005) 5. - P. Martin, E. Castro and M. G. Haines, Phys. Plasmas 12, 102505 (2005)
Elliptical multiple-output quantile regression and convex optimization
Czech Academy of Sciences Publication Activity Database
Hallin, M.; Šiman, Miroslav
2016-01-01
Roč. 109, č. 1 (2016), s. 232-237 ISSN 0167-7152 R&D Projects: GA ČR GA14-07234S Institutional support: RVO:67985556 Keywords : quantile regression * elliptical quantile * multivariate quantile * multiple-output regression Subject RIV: BA - General Mathematics Impact factor: 0.540, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/siman-0458243.pdf
Voltage interval mappings for an elliptic bursting model
Wojcik, Jeremy; Shilnikov, Andrey
2013-01-01
We employed Poincar\\'e return mappings for a parameter interval to an exemplary elliptic bursting model, the FitzHugh-Nagumo-Rinzel model. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally, mixed-mode oscillations and quiescence in the FitzHugh-Nagumo-Rinzel model. We illustrate the wealth of information, qualitative and quantitati...
Jacobian elliptic wave solutions in an anharmonic molecular crystal model
International Nuclear Information System (INIS)
Teh, C.G.R.; Lee, B.S.; Koo, W.K.
1997-07-01
Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig
Existence of multiple solutions for quasilinear diagonal elliptic systems
Directory of Open Access Journals (Sweden)
Marco Squassina
1999-05-01
Full Text Available Nonsmooth-critical-point theory is applied in proving multiplicity results for the quasilinear symmetric elliptic system $$ -sum_{i,j=1}^{n}D_j(a^{k}_{ij}(x,uD_iu_k+ {1over 2}sum_{i,j=1}^{n}sum_{h=1}^N D_{s_k}a^{h}_{ij}(x,uD_iu_hD_ju_h=g_k(x,u,, $$ for $k=1,..,N$.
Existence and multiplicity of solutions for divergence type elliptic equations
Directory of Open Access Journals (Sweden)
Lin Zhao
2011-03-01
Full Text Available We establish the existence and multiplicity of weak solutions of a problem involving a uniformly convex elliptic operator in divergence form. We find one nontrivial solution by the mountain pass lemma, when the nonlinearity has a $(p-1$-superlinear growth at infinity, and two nontrivial solutions by minimization and mountain pass when the nonlinear term has a $(p-1$-sublinear growth at infinity.
Stress concentration factors for pressurized elliptic crossbores in blocks
International Nuclear Information System (INIS)
Badr, Elie A.
2006-01-01
Intersecting bore geometries are used in a number of industrial applications including heavy-walled pressure vessels containing oil holes for lubrication, ports for valves and fluid ends of reciprocating pumps. The bore intersection location is a stress concentration point where the maximum hoop stress can be many times the fluid pressure in the bores. Intersecting circular holes in heavy-walled cylinders and rectangular blocks have been extensively investigated. Specifically, stress/pressure concentration curves for intersecting circular bores in rectangular blocks were presented by Sorem et al. [Sorem JR, Shadley JR, Tipton SM. Design curves for maximum stresses in blocks containing pressurized bore intersections. ASME J Mech Des 1990; 113: 427-31.]. However, stress/pressure concentrations due to intersecting elliptic bores have not been broadly investigated. With the availability of computer numerical control (CNC) machinery, bores with elliptic crosssection can be produced with relative ease. In this paper, hoop stress concentration ratios are developed for elliptic crossbores in rectangular blocks. Results indicate that introducing elliptic crossbores, rather than circular ones, significantly reduces the hoop stress concentration factor at the crossbore intersection. Also, the presence of intersecting crossbores has a major effect on the fatigue life of pressure vessels [Badr EA, Sorem JR, Jr Tipton SM. Evaluation of the autofrettage effect on fatigue lives of steel blocks with crossbores using a statistical and a strain-based method. ASTM J Test Eval 2000; 28: 181-8.] and the reduction of hoop stress concentration is expected to enhance the fatigue life of pressure vessels containing crossbores
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
On discrete maximum principles for nonlinear elliptic problems
Czech Academy of Sciences Publication Activity Database
Karátson, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 76, č. 1 (2007), s. 99-108 ISSN 0378-4754 R&D Projects: GA MŠk 1P05ME749; GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear elliptic problem * mixed boundary conditions * finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007
Elliptic equations with measure data in Orlicz spaces
Directory of Open Access Journals (Sweden)
Ge Dong
2008-05-01
Full Text Available This article shows the existence of solutions to the nonlinear elliptic problem $A(u=f$ in Orlicz-Sobolev spaces with a measure valued right-hand side, where $A(u=-mathop{ m div}a(x,u, abla u$ is a Leray-Lions operator defined on a subset of $W_{0}^{1}L_{M}(Omega$, with general $M$.
Optimal Control for the Degenerate Elliptic Logistic Equation
International Nuclear Information System (INIS)
Delgado, M.; Montero, J.A.; Suarez, A.
2002-01-01
We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results
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.
Eliminating line of sight in elliptic guides using gravitational curving
International Nuclear Information System (INIS)
Kleno, Kaspar H.; Willendrup, Peter K.; Knudsen, Erik; Lefmann, Kim
2011-01-01
Eliminating fast neutrons (λ<0.5A) by removing direct line of sight between the source and the target sample is a well established technique. This can be done with little loss of transmission for a straight neutron guide by horizontal curving. With an elliptic guide shape, however, curving the guide would result in a breakdown of the geometrical focusing mechanism inherent to the elliptical shape, resulting in unwanted reflections and loss of transmission. We present a new and yet untried idea by curving a guide in such a way as to follow the ballistic curve of a neutron in the gravitational field, while still retaining the elliptic shape seen from the accelerated reference frame of the neutron. Analytical calculations and ray-tracing simulations show that this method is useful for cold neutrons at guide lengths in excess of 100 m. We will present some of the latest results for guide optimization relevant for instrument design at the ESS, in particular an off-backscattering spectrometer which utilizes the gravitational curving, for 6.66 A neutrons over a guide length of 300 m.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-11-01
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
Major and minor axis kinematics of 22 ellipticals
International Nuclear Information System (INIS)
Franx, M.; Illingworth, G.; Heckman, T.
1989-01-01
Rotation curves and velocity dispersion profiles have been determined for the major and the minor axes of 22 elliptical galaxies. Rotation was detected in all but one galaxy, even though the sample was biased toward round ellipticals. Minor axis rotation larger than major axis rotation was measured in two galaxies, NGC 4406 and NGC 7507. Roughly 10 percent of ellipticals may show large minor axis velocities relative to those on the major axis. A simple model is used to derive a rotational axis from the observed minor and major axis velocities to a typical accuracy of 6 deg. The rotational and photometric minor axes aligned to better than 10 deg for 60 percent of the sample, implying that the direction of the angular momentum is related to the orientation of the figure of the galaxy. IC 1459 has a kinematically distinct core with its angular momentum opposite to the angular momentum of the outer parts, and NGC 4406 has a core with its angular momentum perpendicular to that of the outer parts. 46 refs
Parallelization of elliptic solver for solving 1D Boussinesq model
Tarwidi, D.; Adytia, D.
2018-03-01
In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.
TUNNEL POINT CLOUD FILTERING METHOD BASED ON ELLIPTIC CYLINDRICAL MODEL
Directory of Open Access Journals (Sweden)
N. Zhu
2016-06-01
Full Text Available The large number of bolts and screws that attached to the subway shield ring plates, along with the great amount of accessories of metal stents and electrical equipments mounted on the tunnel walls, make the laser point cloud data include lots of non-tunnel section points (hereinafter referred to as non-points, therefore affecting the accuracy for modeling and deformation monitoring. This paper proposed a filtering method for the point cloud based on the elliptic cylindrical model. The original laser point cloud data was firstly projected onto a horizontal plane, and a searching algorithm was given to extract the edging points of both sides, which were used further to fit the tunnel central axis. Along the axis the point cloud was segmented regionally, and then fitted as smooth elliptic cylindrical surface by means of iteration. This processing enabled the automatic filtering of those inner wall non-points. Experiments of two groups showed coincident results, that the elliptic cylindrical model based method could effectively filter out the non-points, and meet the accuracy requirements for subway deformation monitoring. The method provides a new mode for the periodic monitoring of tunnel sections all-around deformation in subways routine operation and maintenance.
Mechanism of unconventional aerodynamic characteristics of an elliptic airfoil
Directory of Open Access Journals (Sweden)
Sun Wei
2015-06-01
Full Text Available The aerodynamic characteristics of elliptic airfoil are quite different from the case of conventional airfoil for Reynolds number varying from about 104 to 106. In order to reveal the fundamental mechanism, the unsteady flow around a stationary two-dimensional elliptic airfoil with 16% relative thickness has been simulated using unsteady Reynolds-averaged Navier–Stokes equations and the γ-Reθt‾ transition turbulence model at different angles of attack for flow Reynolds number of 5 × 105. The aerodynamic coefficients and the pressure distribution obtained by computation are in good agreement with experimental data, which indicates that the numerical method works well. Through this study, the mechanism of the unconventional aerodynamic characteristics of airfoil is analyzed and discussed based on the computational predictions coupled with the wind tunnel results. It is considered that the boundary layer transition at the leading edge and the unsteady flow separation vortices at the trailing edge are the causes of the case. Furthermore, a valuable insight into the physics of how the flow behavior affects the elliptic airfoil’s aerodynamics is provided.
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
Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves
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.
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.
Generation of an elliptic hollow beam using Mathieu and Bessel functions.
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.
U.S. Department of Health & Human Services — The Centers for Medicare and Medicaid Services (CMS) offers several different Chart Series with data on beneficiary health status, spending, operations, and quality...
Elliptic fibrations of maximal rank on a supersingular K3 surface
International Nuclear Information System (INIS)
Shioda, Tetsuji
2013-01-01
We study a class of elliptic K3 surfaces defined by an explicit Weierstrass equation to find elliptic fibrations of maximal rank on K3 surface in positive characteristic. In particular, we show that the supersingular K3 surface of Artin invariant 1 (unique by Ogus) admits at least one elliptic fibration with maximal rank 20 in every characteristic p>7, p≠13, and further that the number, say N(p), of such elliptic fibrations (up to isomorphisms), is unbounded as p → ∞; in fact, we prove that lim p→∞ N(p)/p 2 ≥(1/12) 2 .
Elliptic Flow in Au+Au Collisions at √sNN = 130 GeV
Ackermann, K. H.; Adams, N.; Adler, C.; Ahammed, Z.; Ahmad, S.; Allgower, C.; Amsbaugh, J.; Anderson, M.; Anderssen, E.; Arnesen, H.; Arnold, L.; Averichev, G. S.; Baldwin, A.; Balewski, J.; Barannikova, O.; Barnby, L. S.; Baudot, J.; Beddo, M.; Bekele, S.; Belaga, V. V.; Bellwied, R.; Bennett, S.; Bercovitz, J.; Berger, J.; Betts, W.; Bichsel, H.; Bieser, F.; Bland, L. C.; Bloomer, M.; Blyth, C. O.; Boehm, J.; Bonner, B. E.; Bonnet, D.; Bossingham, R.; Botlo, M.; Boucham, A.; Bouillo, N.; Bouvier, S.; Bradley, K.; Brady, F. P.; Braithwaite, E. S.; Braithwaite, W.; Brandin, A.; Brown, R. L.; Brugalette, G.; Byrd, C.; Caines, H.; Calderón de La Barca Sánchez, M.; Cardenas, A.; Carr, L.; Carroll, J.; Castillo, J.; Caylor, B.; Cebra, D.; Chatopadhyay, S.; Chen, M. L.; Chen, W.; Chen, Y.; Chernenko, S. P.; Cherney, M.; Chikanian, A.; Choi, B.; Chrin, J.; Christie, W.; Coffin, J. P.; Conin, L.; Consiglio, C.; Cormier, T. M.; Cramer, J. G.; Crawford, H. J.; Danilov, V. I.; Dayton, D.; Demello, M.; Deng, W. S.; Derevschikov, A. A.; Dialinas, M.; Diaz, H.; Deyoung, P. A.; Didenko, L.; Dimassimo, D.; Dioguardi, J.; Dominik, W.; Drancourt, C.; Draper, J. E.; Dunin, V. B.; Dunlop, J. C.; Eckardt, V.; Edwards, W. R.; Efimov, L. G.; Eggert, T.; Emelianov, V.; Engelage, J.; Eppley, G.; Erazmus, B.; Etkin, A.; Fachini, P.; Feliciano, C.; Ferenc, D.; Ferguson, M. I.; Fessler, H.; Finch, E.; Fine, V.; Fisyak, Y.; Flierl, D.; Flores, I.; Foley, K. J.; Fritz, D.; Gagunashvili, N.; Gans, J.; Gazdzicki, M.; Germain, M.; Geurts, F.; Ghazikhanian, V.; Gojak, C.; Grabski, J.; Grachov, O.; Grau, M.; Greiner, D.; Greiner, L.; Grigoriev, V.; Grosnick, D.; Gross, J.; Guilloux, G.; Gushin, E.; Hall, J.; Hallman, T. J.; Hardtke, D.; Harper, G.; Harris, J. W.; He, P.; Heffner, M.; Heppelmann, S.; Herston, T.; Hill, D.; Hippolyte, B.; Hirsch, A.; Hjort, E.; Hoffmann, G. W.; Horsley, M.; Howe, M.; Huang, H. Z.; Humanic, T. J.; Hümmler, H.; Hunt, W.; Hunter, J.; Igo, G. J.; Ishihara, A.; Ivanshin, Yu. I.; Jacobs, P.; Jacobs, W. W.; Jacobson, S.; Jared, R.; Jensen, P.; Johnson, I.; Jones, P. G.; Judd, E.; Kaneta, M.; Kaplan, M.; Keane, D.; Kenney, V. P.; Khodinov, A.; Klay, J.; Klein, S. R.; Klyachko, A.; Koehler, G.; Konstantinov, A. S.; Kormilitsyne, V.; Kotchenda, L.; Kotov, I.; Kovalenko, A. D.; Kramer, M.; Kravtsov, P.; Krueger, K.; Krupien, T.; Kuczewski, P.; Kuhn, C.; Kunde, G. J.; Kunz, C. L.; Kutuev, R. Kh.; Kuznetsov, A. A.; Lakehal-Ayat, L.; Lamas-Valverde, J.; Lamont, M. A.; Landgraf, J. M.; Lange, S.; Lansdell, C. P.; Lasiuk, B.; Laue, F.; Lebedev, A.; Lecompte, T.; Leonhardt, W. J.; Leontiev, V. M.; Leszczynski, P.; Levine, M. J.; Li, Q.; Li, Q.; Li, Z.; Liaw, C.-J.; Lin, J.; Lindenbaum, S. J.; Lindenstruth, V.; Lindstrom, P. J.; Lisa, M. A.; Liu, H.; Ljubicic, T.; Llope, W. J.; Locurto, G.; Long, H.; Longacre, R. S.; Lopez-Noriega, M.; Lopiano, D.; Love, W. A.; Lutz, J. R.; Lynn, D.; Madansky, L.; Maier, R.; Majka, R.; Maliszewski, A.; Margetis, S.; Marks, K.; Marstaller, R.; Martin, L.; Marx, J.; Matis, H. S.; Matulenko, Yu. A.; Matyushevski, E. A.; McParland, C.; McShane, T. S.; Meier, J.; Melnick, Yu.; Meschanin, A.; Middlekamp, P.; Mikhalin, N.; Miller, B.; Milosevich, Z.; Minaev, N. G.; Minor, B.; Mitchell, J.; Mogavero, E.; Moiseenko, V. A.; Moltz, D.; Moore, C. F.; Morozov, V.; Morse, R.; de Moura, M. M.; Munhoz, M. G.; Mutchler, G. S.; Nelson, J. M.; Nevski, P.; Ngo, T.; Nguyen, M.; Nguyen, T.; Nikitin, V. A.; Nogach, L. V.; Noggle, T.; Norman, B.; Nurushev, S. B.; Nussbaum, T.; Nystrand, J.; Odyniec, G.; Ogawa, A.; Ogilvie, C. A.; Olchanski, K.; Oldenburg, M.; Olson, D.; Ososkov, G. A.; Ott, G.; Padrazo, D.; Paic, G.; Pandey, S. U.; Panebratsev, Y.; Panitkin, S. Y.; Pavlinov, A. I.; Pawlak, T.; Pentia, M.; Perevotchikov, V.; Peryt, W.; Petrov, V. A.; Pinganaud, W.; Pirogov, S.; Platner, E.; Pluta, J.; Polk, I.; Porile, N.; Porter, J.; Poskanzer, A. M.; Potrebenikova, E.; Prindle, D.; Pruneau, C.; Puskar-Pasewicz, J.; Rai, G.; Rasson, J.; Ravel, O.; Ray, R. L.; Razin, S. V.; Reichhold, D.; Reid, J.; Renfordt, R. E.; Retiere, F.; Ridiger, A.; Riso, J.; Ritter, H. G.; Roberts, J. B.; Roehrich, D.; Rogachevski, O. V.; Romero, J. L.; Roy, C.; Russ, D.; Rykov, V.; Sakrejda, I.; Sanchez, R.; Sandler, Z.; Sandweiss, J.; Sappenfield, P.; Saulys, A. C.; Savin, I.; Schambach, J.; Scharenberg, R. P.; Scheblien, J.; Scheetz, R.; Schlueter, R.; Schmitz, N.; Schroeder, L. S.; Schulz, M.; Schüttauf, A.; Sedlmeir, J.; Seger, J.; Seliverstov, D.; Seyboth, J.; Seyboth, P.; Seymour, R.; Shakaliev, E. I.; Shestermanov, K. E.; Shi, Y.; Shimanskii, S. S.; Shuman, D.; Shvetcov, V. S.; Skoro, G.; Smirnov, N.; Smykov, L. P.; Snellings, R.; Solberg, K.; Sowinski, J.; Spinka, H. M.; Srivastava, B.; Stephenson, E. J.; Stock, R.; Stolpovsky, A.; Stone, N.; Stone, R.; Strikhanov, M.; Stringfellow, B.; Stroebele, H.; Struck, C.; Suaide, A. A.; Sugarbaker, E.; Suire, C.; Symons, T. J.; Takahashi, J.; Tang, A. H.; Tarchini, A.; Tarzian, J.; Thomas, J. H.; Tikhomirov, V.; Szanto de Toledo, A.; Tonse, S.; Trainor, T.; Trentalange, S.; Tokarev, M.; Tonjes, M. B.; Trofimov, V.; Tsai, O.; Turner, K.; Ullrich, T.; Underwood, D. G.; Vakula, I.; van Buren, G.; Vandermolen, A. M.; Vanyashin, A.; Vasilevski, I. M.; Vasiliev, A. N.; Vigdor, S. E.; Visser, G.; Voloshin, S. A.; Vu, C.; Wang, F.; Ward, H.; Weerasundara, D.; Weidenbach, R.; Wells, R.; Wells, R.; Wenaus, T.; Westfall, G. D.; Whitfield, J. P.; Whitten, C.; Wieman, H.; Willson, R.; Wilson, K.; Wirth, J.; Wisdom, J.; Wissink, S. W.; Witt, R.; Wolf, J.; Wood, L.; Xu, N.; Xu, Z.; Yakutin, A. E.; Yamamoto, E.; Yang, J.; Yepes, P.; Yokosawa, A.; Yurevich, V. I.; Zanevski, Y. V.; Zhang, J.; Zhang, W. M.; Zhu, J.; Zimmerman, D.; Zoulkarneev, R.; Zubarev, A. N.
2001-01-01
Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at sNN = 130 GeV using the STAR Time Projection Chamber at the Relativistic Heavy Ion Collider. The elliptic flow signal, v2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.
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)
Clinical Implications of Changing Parameters on an Elliptical Trainer.
Kaplan, Yonatan; Nyska, Meir; Palmanovich, Ezequiel; Shanker, Rebecca
2014-06-01
Specific weightbearing instructions continue to be a part of routine orthopaedic clinical practice on an injured or postoperative extremity. Researchers and clinicians have struggled to define the best weightbearing strategies to maximize clinical outcomes. To investigate the average percentage body weight (APBW) values, weightbearing distribution percentages (WBDP), and cadence values on the entire foot, hindfoot, and forefoot during changing resistance and incline on an elliptical trainer, as well as to suggest clinical implications. Descriptive laboratory study. An original research study was performed consisting of 30 asymptomatic subjects (mean age, 29.54 ± 12.64 years; range, 21-69 years). The protocol included 3 consecutive tests of changing resistance and incline within a speed range of 70 to 95 steps/min. The SmartStep weightbearing gait analysis system was utilized to measure the values. The APBW values for the entire foot ranged between 70% and 81%, the hindfoot values were between 27% and 57%, and the forefoot values between 42% and 70%. With regard to WBDP, the forefoot remained planted on the pedal (stance phase) 2 to 3 times more as compared with the hindfoot raise in the swing phase. The study findings highlight the fact that elliptical training significantly reduces weightbearing in the hindfoot, forefoot, and entire foot even at higher levels of resistance and incline. Weightbearing on the hindfoot consistently displayed the lowest weightbearing values. Orthopaedic surgeons, now equipped with accurate weightbearing data, may recommend using the elliptical trainer as a weightbearing exercise early on following certain bony or soft tissue pathologies and lower limb surgical procedures.
Rayleigh wave ellipticity across the Iberian Peninsula and Morocco
Gómez García, Clara; Villaseñor, Antonio
2015-04-01
Spectral amplitude ratios between horizontal and vertical components (H/V ratios) from seismic records are useful to evaluate site effects, predict ground motion and invert for S velocity in the top several hundred meters. These spectral ratios can be obtained from both ambient noise and earthquakes. H/V ratios from ambient noise depend on the content and predominant wave types: body waves, Rayleigh waves, a mixture of different waves, etc. The H/V ratio computed in this way is assumed to measure Rayleigh wave ellipticity since ambient vibrations are dominated by Rayleigh waves. H/V ratios from earthquakes are able to determine the local crustal structure at the vicinity of the recording station. These ratios obtained from earthquakes are based on surface wave ellipticity measurements. Although long period (>20 seconds) Rayleigh H/V ratio is not currently used because of large scatter has been reported and uncertainly about whether these measurements are compatible with traditional phase and group velocity measurements, we will investigate whether it is possible to obtain stable estimates after collecting statistics for many earthquakes. We will use teleseismic events from shallow earthquakes (depth ≤ 40 km) between 2007 January 1 and 2012 December 31 with M ≥ 6 and we will compute H/V ratios for more than 400 stations from several seismic networks across the Iberian Peninsula and Morocco for periods between 20 and 100 seconds. Also H/V ratios from cross-correlations of ambient noise in different components for each station pair will be computed. Shorter period H/V ratio measurements based on ambient noise cross-correlations are strongly sensitive to near-surface structure, rather than longer period earthquake Rayleigh waves. The combination of ellipticity measurements based on earthquakes and ambient noise will allow us to perform a joint inversion with Rayleigh wave phase velocity. Upper crustal structure is better constrained by the joint inversion compared
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)
The history of the Universe is an elliptic curve
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.
Transverse magnetic scattering by parallel conducting elliptic cylinders
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.
Symbolic manipulation techniques for vibration analysis of laminated elliptic plates
Andersen, C. M.; Noor, A. K.
1977-01-01
A computational scheme is presented for the free vibration analysis of laminated composite elliptic plates. The scheme is based on Hamilton's principle, the Rayleigh-Ritz technique and symmetry considerations and is implemented with the aid of the MACSYMA symbolic manipulation system. The MACYSMA system, through differentiation, integration, and simplification of analytic expressions, produces highly-efficient FORTRAN code for the evaluation of the stiffness and mass coefficients. Multiple use is made of this code to obtain not only the frequencies and mode shapes of the plate, but also the derivatives of the frequencies with respect to various material and geometric parameters.
Dirichlet problem for quasi-linear elliptic equations
Directory of Open Access Journals (Sweden)
Azeddine Baalal
2002-10-01
Full Text Available We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x, abla u(x+mathcal{B}(x,u(x,abla u(x=0. $$ Then we define a potential theory related to this problem and we show that the sheaf of continuous solutions satisfies the Bauer axiomatic theory. Submitted April 9, 2002. Published October 2, 2002. Math Subject Classifications: 31C15, 35B65, 35J60. Key Words: Supersolution; Dirichlet problem; obstacle problem; nonlinear potential theory.
Full Alignment of Molecules Using Elliptically Polarized Light
DEFF Research Database (Denmark)
Larsen, Jakob Juul; Hald, Kasper; Seideman, Tamar
When a molecule with an anisotropic polarizability is placed in a strong nonresonant laser field the interaction occurs through the induced dipole moment. The outcome is that the molecule experiences an angular dependent potential energy. It is now well established that a linearly polarized laser...... field can be used to align molecules along their axis of highest polarizability. Here we demonstrate, theoretically and experimentally, that an elliptically polarized laser field can be used to simultaneously force two axes of a molecule into alignment through the same mechanism. Due to the rigidity...
Atomic processes in strong bichromatic elliptically polarized laser fields
Energy Technology Data Exchange (ETDEWEB)
Odžak, S., E-mail: senad.odzak@gmail.com; Hasović, E.; Gazibegović-Busuladžić, A.; Čerkić, A., E-mail: anercerkic@yahoo.com; Fetić, B. [Faculty of Science, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo (Bosnia and Herzegovina); Kramo, A. [BHANSA, Aeronautical Meteorology Department, Kurta Schorka 36, 71000 Sarajevo (Bosnia and Herzegovina); Busuladžić, M. [Medical Faculty, University of Sarajevo, Čekaluša 90, 71000 Sarajevo (Bosnia and Herzegovina); Milošević, D. B. [Faculty of Science, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo (Bosnia and Herzegovina); Academy of Sciences and Arts of Bosnia and Herzegovina, Bistrik 7, 71000 Sarajevo (Bosnia and Herzegovina); Max-Born-Institut, Max-Born-Strasse 2a, 12489 Berlin (Germany)
2016-03-25
Nonlinear quantum-mechanical phenomena in strong laser fields, such as high-order harmonic generation (HHG) and above-threshold ionization (ATI) are significantly modified if the applied laser field is bichromatic and/or elliptically polarized. Numerical results obtained within the strong-field approximation are presented for two special cases. We show results for HHG by plasma ablation in a bichromatic linearly polarized laser field. We also consider the ATI process in bicircular field which consists of two coplanar counter-rotating circularly polarized fields.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim; Xue, Guangri
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Distribution of some sequences of points on elliptic curves
DEFF Research Database (Denmark)
Lange, Tanja; Shparlinski, Igor
2007-01-01
We estimate character sums over points on elliptic curves over a finite field of q elements. Pseudorandom sequences can be constructed by taking linear combinations with small coefficients (for example, from the set {−1, 0, 1}) of a fixed vector of points, which forms the seed of the generator. We...... consider several particular cases of this general approach which are of special practical interest and have occurred in the literature. For each of them we show that the resulting sequence has good uniformity of distribution properties....
Optimization design of a 20-in. elliptical MCP-PMT
International Nuclear Information System (INIS)
Chen, Ping; Tian, Jinshou; Wei, Yonglin; Liu, Hulin; Sai, Xiaofeng; He, Jianping; Chen, Lin; Wang, Xing; Lu, Yu
2017-01-01
This paper describes the simulation work for optimizing the newly developed 20-in. elliptical MCP-PMT by enlarging the outside diameters of the two focusing electrodes and the open area of the glass bulb. Effects of biasing voltages applied to the two focusing electrodes and the MCP input facet are studied. With the new design of the 20 in. MCP-PMT, the transit time spread of the prototype can be less than 3 ns and the collection efficiency is as much as the present prototype.
Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study
International Nuclear Information System (INIS)
Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.
1985-01-01
The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures
Development of precision elliptic neutron-focusing supermirror.
Hosobata, Takuya; Yamada, Norifumi L; Hino, Masahiro; Yamagata, Yutaka; Kawai, Toshihide; Yoshinaga, Hisao; Hori, Koichiro; Takeda, Masahiro; Takeda, Shin; Morita, Shin-Ya
2017-08-21
This paper details methods for the precision design and fabrication of neutron-focusing supermirrors, based on electroless nickel plating. We fabricated an elliptic mirror for neutron reflectometry, which is our second mirror improved from the first. The mirror is a 550-millimeter-long segmented mirror assembled using kinematic couplings, with each segment figured by diamond cutting, polished using colloidal silica, and supermirror coated through ion-beam sputtering. The mirror was evaluated with neutron beams, and the reflectivity was found to be 68-90% at a critical angle. The focusing width was 0.17 mm at the full width at half maximum.
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
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)
On state estimation and fusion with elliptical constraints
Energy Technology Data Exchange (ETDEWEB)
Rao, Nageswara S. [ORNL; Liu, Qiang [ORNL
2017-11-01
We consider tracking of a target with elliptical nonlinear constraints on its motion dynamics. The state estimates are generated by sensors and sent over long-haul links to a remote fusion center for fusion. We show that the constraints can be projected onto the known ellipse and hence incorporated into the estimation and fusion process. In particular, two methods based on (i) direct connection to the center, and (ii) shortest distance to the ellipse are discussed. A tracking example is used to illustrate the tracking performance using projection-based methods with various fusers in the lossy long-haul tracking environment.
Incomplete block factorization preconditioning for indefinite elliptic problems
Energy Technology Data Exchange (ETDEWEB)
Guo, Chun-Hua [Univ. of Calgary, Alberta (Canada)
1996-12-31
The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.
Mergers in galaxy groups. I. Structure and properties of elliptical remnants
International Nuclear Information System (INIS)
Taranu, Dan S.; Dubinski, John; Yee, H. K. C.
2013-01-01
We present collisionless simulations of dry mergers in groups of 3 to 25 galaxies to test the hypothesis that elliptical galaxies form at the centers of such groups. Mock observations of the central remnants confirm their similarity to ellipticals, despite having no dissipational component. We vary the profile of the original spiral's bulge and find that ellipticals formed from spirals with exponential bulges have too low Sersic indices. Mergers of spirals with de Vaucouleurs (classical) bulges produce remnants with larger Sersic indices correlated with luminosity, as with Sloan Digital Sky Survey ellipticals. Exponential bulge mergers are better fits to faint ellipticals, whereas classical bulge mergers better match luminous ellipticals. Similarly, luminous ellipticals are better reproduced by remnants undergoing many (>5) mergers, and fainter ellipticals by those with fewer mergers. The remnants follow tight size-luminosity and velocity dispersion-luminosity (Faber-Jackson) relations (<0.12 dex scatter), demonstrating that stochastic merging can produce tight scaling relations if the merging galaxies also follow tight scaling relations. The slopes of the size-luminosity and Faber-Jackson relations are close to observations but slightly shallower in the former case. Both relations' intercepts are offset—remnants are too large but have too low dispersions at fixed luminosity. Some remnants show substantial (v/σ > 0.1) rotational support, although most are slow rotators and few are very fast rotators (v/σ > 0.5). These findings contrast with previous studies concluding that dissipation is necessary to produce ellipticals from binary mergers of spirals. Multiple, mostly minor and dry mergers can produce bright ellipticals, whereas significant dissipation could be required to produce faint, rapidly rotating ellipticals.
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
The elliptic sine-Gordon equation in a half plane
International Nuclear Information System (INIS)
Pelloni, B; Pinotsis, D A
2010-01-01
We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions
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.
MINOR MERGERS AND THE SIZE EVOLUTION OF ELLIPTICAL GALAXIES
International Nuclear Information System (INIS)
Naab, Thorsten; Johansson, Peter H.; Ostriker, Jeremiah P.
2009-01-01
Using a high-resolution hydrodynamical cosmological simulation of the formation of a massive spheroidal galaxy we show that elliptical galaxies can be very compact and massive at high redshift in agreement with recent observations. Accretion of stripped infalling stellar material increases the size of the system with time and the central concentration is reduced by dynamical friction of the surviving stellar cores. In a specific case of a spheroidal galaxy with a final stellar mass of 1.5 x 10 11 M sun we find that the effective radius r e increases from 0.7 ± 0.2 kpc at z = 3 to r e = 2.4 ± 0.4 kpc at z = 0 with a concomitant decrease in the effective density of an order of magnitude and a decrease of the central velocity dispersion by approximately 20% over this time interval. A simple argument based on the virial theorem shows that during the accretion of weakly bound material (minor mergers) the radius can increase as the square of the mass in contrast to the usual linear rate of increase for major mergers. By undergoing minor mergers compact high-redshift spheroids can evolve into present-day systems with sizes and concentrations similar to observed local ellipticals. This indicates that minor mergers may be the main driver for the late evolution of sizes and densities of early-type galaxies.
Experimental study of elliptical jet from sub to supercritical conditions
Energy Technology Data Exchange (ETDEWEB)
Muthukumaran, C. K.; Vaidyanathan, Aravind, E-mail: aravind7@iist.ac.in [Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Trivandrum, Kerala 695547 (India)
2014-04-15
The jet mixing at supercritical conditions involves fluid dynamics as well as thermodynamic phenomena. All the jet mixing studies at critical conditions to the present date have focused only on axisymmetric jets. When the liquid jet is injected into supercritical environment, the thermodynamic transition could be well understood by considering one of the important fluid properties such as surface tension since it decides the existence of distinct boundary between the liquid and gaseous phase. It is well known that an elliptical liquid jet undergoes axis-switching phenomena under atmospheric conditions due to the presence of surface tension. The experimental investigations were carried out with low speed elliptical jet under supercritical condition. Investigation of the binary component system with fluoroketone jet and N{sub 2} gas as environment shows that the surface tension force dominates for a large downstream distance, indicating delayed thermodynamic transition. The increase in pressure to critical state at supercritical temperature is found to expedite the thermodynamic transition. The ligament like structures has been observed rather than droplets for supercritical pressures. However, for the single component system with fluoroketone jet and fluoroketone environment shows that the jet disintegrates into droplets as it is subjected to the chamber conditions even for the subcritical pressures and no axis switching phenomenon is observed. For a single component system, as the pressure is increased to critical state, the liquid jet exhibits gas-gas like mixing behavior and that too without exhibiting axis-switching behavior.
Thermodynamics of Inozemtsev's elliptic spin chain
Energy Technology Data Exchange (ETDEWEB)
Klabbers, Rob, E-mail: rob.klabbers@desy.de
2016-06-15
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.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Modelling the star formation histories of nearby elliptical galaxies
Bird, Katy
Since Lick indices were introduced in 1994, they have been used as a source of observational data against which computer models of galaxy evolution have been compared. However, as this thesis demonstrates, observed Lick indices lead to mathematical ill-conditioning: small variations in observations can lead to very large differences in population synthesis models attempting to recreate the observed values. As such, limited reliance should be placed on any results currently or historically in the literature purporting to give the star formation history of a galaxy, or group of galaxies, where this is deduced from Lick observations taken from a single instrument, without separate verification from at least one other source. Within these limitations, this thesis also constrains the star formation histories of 21 nearby elliptical galaxies, finding that they formed 13.26 +0.09 -0.06 Gyrs ago, that all mergers are dry, and that galactic winds are formed from AGN activity (rather than being supernovae-driven). This thesis also finds evidence to support the established galaxy-formation theory of "downsizing". An existing galactic model from the literature is examined and evaluated, and the reasons for it being unable to establish star formation histories of individual galaxies are ascertained. A brand-new model is designed, developed, tested and used with two separate data sets, corroborated for 10 galaxies by data from a third source, and compared to results from a Single Stellar Population model from the literature, to model the star formation histories of nearby elliptical galaxies.
Development of an innovative device for ultrasonic elliptical vibration cutting.
Zhou, Ming; Hu, Linhua
2015-07-01
An innovative ultrasonic elliptical vibration cutting (UEVC) device with 1st resonant mode of longitudinal vibration and 3rd resonant mode of bending vibration was proposed in this paper, which can deliver higher output power compared to previous UEVC devices. Using finite element method (FEM), resonance frequencies of the longitudinal and bending vibrations were tuned to be as close as possible in order to excite these two vibrations using two-phase driving voltages at a single frequency, while wave nodes of the longitudinal and bending vibrations were also adjusted to be as coincident as possible for mounting the device at a single fixed point. Based on the simulation analysis results a prototype device was fabricated, then its vibration characteristics were evaluated by an impedance analyzer and a laser displacement sensor. With two-phase sinusoidal driving voltages both of 480 V(p-p) at an ultrasonic frequency of 20.1 kHz, the developed prototype device achieved an elliptical vibration with a longitudinal amplitude of 8.9 μm and a bending amplitude of 11.3 μm. The performance of the developed UEVC device is assessed by the cutting tests of hardened steel using single crystal diamond tools. Experimental results indicate that compared to ordinary cutting process, the tool wear is reduced significantly by using the proposed device. Copyright © 2015 Elsevier B.V. All rights reserved.
Experimental Validation of Elliptical Fin-Opening Behavior
Directory of Open Access Journals (Sweden)
James M. Garner
2003-01-01
Full Text Available An effort to improve the performance of ordnance has led to the consideration of the use of folding elliptical fins for projectile stabilization. A second order differential equation was used to model elliptical fin deployment history and accounts for: deployment with respect to the geometric properties of the fin, the variation in fin aerodynamics during deployment, the initial yaw effect on fin opening, and the variation in deployment speed based on changes in projectile spin. This model supports tests conducted at the Transonic Experimental Facility, Aberdeen Proving Ground examining the opening behavior of these uniquely shaped fins. The fins use the centrifugal force from the projectile spin to deploy. During the deployment, the fin aerodynamic forces vary with angle-of-attack changes to the free stream. Model results indicate that projectile spin dominates the initial opening rates and aerodynamics dominate near the fully open state. The model results are examined to explain the observed behaviors, and suggest improvements for later designs.
Gravitational waves from pulsars in the context of magnetic ellipticity
Energy Technology Data Exchange (ETDEWEB)
Araujo, Jose C.N. de; Coelho, Jaziel G.; Costa, Cesar A. [Instituto Nacional de Pesquisas Espaciais, Divisao de Astrofisica, Sao Jose dos Campos, SP (Brazil)
2017-05-15
In one of our previous articles we have considered the role of a time dependent magnetic ellipticity on the pulsars' braking indices and on the putative gravitational waves these objects can emit. Since only nine of more than 2000 known pulsars have accurately measured braking indices, it is of interest to extend this study to all known pulsars, in particular as regards gravitational wave generation. To do so, as shown in our previous article, we need to know some pulsars' observable quantities such as: periods and their time derivatives, and estimated distances to the Earth. Moreover, we also need to know the pulsars' masses and radii, for which we are adopting current fiducial values. Our results show that the gravitational wave amplitude is at best h ∝ 10{sup -28}. This leads to a pessimistic prospect for the detection of gravitational waves generated by these pulsars, even for Advanced LIGO and Advanced Virgo, and the planned Einstein Telescope, if the ellipticity has a magnetic origin. (orig.)
Gravitational waves from pulsars in the context of magnetic ellipticity
International Nuclear Information System (INIS)
Araujo, Jose C.N. de; Coelho, Jaziel G.; Costa, Cesar A.
2017-01-01
In one of our previous articles we have considered the role of a time dependent magnetic ellipticity on the pulsars' braking indices and on the putative gravitational waves these objects can emit. Since only nine of more than 2000 known pulsars have accurately measured braking indices, it is of interest to extend this study to all known pulsars, in particular as regards gravitational wave generation. To do so, as shown in our previous article, we need to know some pulsars' observable quantities such as: periods and their time derivatives, and estimated distances to the Earth. Moreover, we also need to know the pulsars' masses and radii, for which we are adopting current fiducial values. Our results show that the gravitational wave amplitude is at best h ∝ 10 -28 . This leads to a pessimistic prospect for the detection of gravitational waves generated by these pulsars, even for Advanced LIGO and Advanced Virgo, and the planned Einstein Telescope, if the ellipticity has a magnetic origin. (orig.)
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
Energy Analysis in the Elliptic Restricted Three-body Problem
Qi, Yi; de Ruiter, Anton
2018-05-01
The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.
African Journals Online (AJOL)
calciphylaxis is prevention through rigorous control of phosphate and calcium balance. We here present two ... The authors declared no conflict of interest. Introduction. Calciphylaxis is a rare but serious disorder .... were reported to resolve the calciphylaxis lesions in a chronic renal failure patient [20]. In a series of five.
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
African Journals Online (AJOL)
abp
13 oct. 2017 ... This is an Open Access article distributed under the terms of the Creative Commons Attribution ... Bifocal leg fractures pose many challenges for the surgeon due to .... Dans notre serie, le taux d'infection est reste dans un.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
African Journals Online (AJOL)
Administrator
Key words: Case report, case series, concept analysis, research design. African Health Sciences 2012; (4): 557 - 562 http://dx.doi.org/10.4314/ahs.v12i4.25. PO Box 17666 .... According to the latest version of the Dictionary of. Epidemiology ...
Elliptic flow in a hadron-string cascade model at 130 GeV energy
Indian Academy of Sciences (India)
vectors b. The elliptic flow v2 is the anisotropy of particle emission in- and out-of reaction plane. ... However, recent observation at SPS shows similar behaviour of the elliptic flow like RHIC as a ..... hadron gas [18]. Large spatial eccentricity ε is ...
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
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
Single inclusive spectra, Hanburg–Brown–Twiss and elliptic flow: A ...
Indian Academy of Sciences (India)
The constraints due to the measurements of the single particle inclusive spectra, the ... flow and HBT vs. the reaction plane with a hydro-motivated blast wave model. .... different mass particles allows the extraction of the elliptic component of the transverse ... Moreover, the details of the dependence of elliptic flow on particle.
Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
Castrillon, Julio; Nobile, Fabio; Tempone, Raul
2016-01-01
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem
L∞-error estimate for a system of elliptic quasivariational inequalities
Directory of Open Access Journals (Sweden)
M. Boulbrachene
2003-01-01
Full Text Available We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs. Under W2,p(Ω-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs.
Impact of elliptical shaped red oak logs on lumber grade and volume recovery
Patrick M. Rappold; Brian H. Bond; Janice K. Wiedenbeck; Roncs Ese-Etame
2007-01-01
This research examined the grade and volume of lumber recovered from red oak logs with elliptical shaped cross sections. The volume and grade of lumber recovered from red oak logs with low (e ≤ 0.3) and high (e ≥ 0.4) degrees of ellipticity was measured at four hardwood sawmills. There was no significant difference (...
Solitons and separable elliptic solutions of the sine-Gordon equation
International Nuclear Information System (INIS)
Bryan, A.C.; Haines, C.R.; Stuart, A.E.G.
1979-01-01
It is pointed out that the two-soliton (antisoliton) solutions of the sine-Gordon equation may be obtained as limiting cases of a separable, two-parameter family of elliptic solutions. The solitons are found on the boundary of the parameter space for the elliptic solutions when the latter are considered over their usual complex domain. (Auth.)
Jacobian elliptic wave solutions for the Wadati-Segur-Ablowitz equation
International Nuclear Information System (INIS)
Teh, C.G.R.; Koo, W.K.; Lee, B.S.
1996-07-01
Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By a mere variation of the Jacobian elliptic parameter k 2 from zero to one, these solutions are transformed from a trivial one to the known solitary wave solutions. (author). 9 refs
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 ...
Positive solutions with single and multi-peak for semilinear elliptic ...
Indian Academy of Sciences (India)
LI WANG
2018-04-24
Apr 24, 2018 ... [2] Bahri A and Lions P, On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 14(3) (1997) 365–413. [3] Cao D, and Noussair E, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN , Ann. Inst. H.
Ellipticity and twisting of the isophotes of some bright galaxies in Virgo
International Nuclear Information System (INIS)
Barbon, R.; Benacchio, L.; Capaccioli, M.
1980-01-01
Ellipticity and twisting of the isophotes of four lenticular and seven elliptical galaxies in the Virgo cluster are presented as a sample of a more complete photometric investigation. This work has been motivated by the increasing importance of this kind of information for the understanding of the spatial structure of E galaxies. The calibrated plate material from the Loiano 1.52 meter and Tautenburg Schmidt telescopes has been digitized with a PDS microdensitometer and analysed by means of the Interactive Numerical Mapping Package (INMP). Ellipticity and orientation profiles are presented in a graphical form together with a preliminary discussion. A correlation has been found between ellipticity and twisting in barred lenticulars which might help in the understanding of some E galaxies such as NGC 4406 and NGC 4374. Twisting has been detected in all of the seven ellipticals of the sample
Violent Relaxation, Dynamical Instabilities and the Formation of Elliptical Galaxies
Aguilar, L. A.
1990-11-01
RESUMEN: El problema de la formaci6n de galaxias elfpticas por medjo de colapso gravitacional sin disipaci6n de energfa es estudiado usando un gran numero de simulaciones numericas. Se muestra que este tipo de colapsos, partiendo de condiciones iniciales frfas donde la energfa cinetica inicial representa s6lo un 5%, 0 , de a potencial inicial, produce sistemas relajados de forma triaxial muy similares a las galaxias elfpticas reales en sus formas y perfiles de densidad en proyecci6i . La forina triaxial resulta de la acci6n de una inestabilidad dinamica que aparece en sistemas 'inicos dominados por movimientos radiales, mientras que el perfil de densidad final Cs debido al llamado relajamiento violento que tiende a producir una distribuci6n en espacio fase unica. Estos dos fen6menos tienden a borrar los detalles particulares sobre las condiciones iniciales y dan lugar a una evoluci6n convergente hacia sistemas realistas, esto innecesario el uso de condiciones iniciales especiales (excepto por Ia condici6i de que estas deben ser frfas). Las condiciones iniciales frfas producen los movimientos radiales y fluctuaciones de la energfa potencial requeridos por ambos fen6menos. ABSTRACT: The problem of formation of elliptical galaxies via dissipationless collapse is studied using a large set of numerical simulations. It is shown that dissipationless collapses from cold initial conditions, where the total initial kinetic energy is less than 5% ofthe initial potential energy, lead to relaxed triaxial systems ery similar to real elliptical galaxies ii projected shape and density profiles. The triaxial shape is due to the of a dynamical instability that appears on systems dominated by radial orbits, while final density profile is due to violent relaxation that tends to produce a unique distribution iii space. These two phenomena erase memory of the initial prodtice a convergent evolution toward realistic systems, thus making unnecessary use o[special initial conditions (other
Dark matter deprivation in the field elliptical galaxy NGC 7507
Lane, Richard R.; Salinas, Ricardo; Richtler, Tom
2015-02-01
Context. Previous studies have shown that the kinematics of the field elliptical galaxy NGC 7507 do not necessarily require dark matter. This is troubling because, in the context of ΛCDM cosmologies, all galaxies should have a large dark matter component. Aims: Our aims are to determine the rotation and velocity dispersion profile out to larger radii than do previous studies, and, therefore, more accurately estimate of the dark matter content of the galaxy. Methods: We use penalised pixel-fitting software to extract velocities and velocity dispersions from GMOS slit mask spectra. Using Jeans and MONDian modelling, we then produce models with the goal of fitting the velocity dispersion data. Results: NGC 7507 has a two-component stellar halo, with the outer halo counter rotating with respect to the inner halo, with a kinematic boundary at a radius of ~110'' (~12.4 kpc). The velocity dispersion profile exhibits an increase at ~70'' (~7.9 kpc), reminiscent of several other elliptical galaxies. Our best fit models are those under mild anisotropy, which include ~100 times less dark matter than predicted by ΛCDM, although mildly anisotropic models that are completely dark matter free fit the measured dynamics almost equally well. Our MONDian models, both isotropic and anisotropic, systematically fail to reproduce the measured velocity dispersions at almost all radii. Conclusions: The counter-rotating outer halo implies a merger remnant, as does the increase in velocity dispersion at ~70''. From simulations it seems plausible that the merger that caused the increase in velocity dispersion was a spiral-spiral merger. Our Jeans models are completely consistent with a no dark matter scenario, however, some dark matter can be accommodated, although at much lower concentrations than predicted by ΛCDM simulations. This indicates that NGC 7507 may be a dark matter free elliptical galaxy. Regardless of whether NGC 7507 is completely dark matter free or very dark matter poor
Stimson, Blake
2011-01-01
Reaktion Books’ Exposures series, edited by Peter Hamilton and Mark Haworth-Booth, is comprised of 13 volumes and counting, each less than 200 pages with 80 high-quality illustrations in color and black and white. Currently available titles include Photography and Australia, Photography and Spirit, Photography and Cinema, Photography and Literature, Photography and Flight, Photography and Egypt, Photography and Science, Photography and Africa, Photography and Italy, Photography and the USA, P...
Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas
Directory of Open Access Journals (Sweden)
Jin Xisong
2018-02-01
Full Text Available Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR and Expected Shortfall (ES for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1 Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2 Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3 The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4 Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5 Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6 Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.
Static elliptic minimal surfaces in AdS{sub 4}
Energy Technology Data Exchange (ETDEWEB)
Pastras, Georgios [NCSR ' ' Demokritos' ' , Institute of Nuclear and Particle Physics, Attiki (Greece)
2017-11-15
The Ryu-Takayanagi conjecture connects the entanglement entropy in the boundary CFT to the area of open co-dimension two minimal surfaces in the bulk. Especially in AdS{sub 4}, the latter are two-dimensional surfaces, and, thus, solutions of a Euclidean non-linear sigma model on a symmetric target space that can be reduced to an integrable system via Pohlmeyer reduction. In this work, we construct static minimal surfaces in AdS{sub 4} that correspond to elliptic solutions of the reduced system, namely the cosh-Gordon equation, via the inversion of Pohlmeyer reduction. The constructed minimal surfaces comprise a two-parameter family of surfaces that include helicoids and catenoids in H{sup 3} as special limits. Minimal surfaces that correspond to identical boundary conditions are discovered within the constructed family of surfaces and the relevant geometric phase transitions are studied. (orig.)
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
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
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
On the standard conjecture for complex 4-dimensional elliptic varieties
International Nuclear Information System (INIS)
Tankeev, Sergei G
2012-01-01
We prove that the Grothendieck standard conjecture B(X) of Lefschetz type on the algebraicity of operators * and Λ of Hodge theory holds for every smooth complex projective model X of the fibre product X 1 × C X 2 , where X 1 →C is an elliptic surface over a smooth projective curve C and X 2 →C is a morphism of a smooth projective threefold onto C such that one of the following conditions holds: a generic geometric fibre X 2s is an Enriques surface; all fibres of the morphism X 2 →C are smooth K3-surfaces and the Hodge group Hg(X 2s ) of the generic geometric fibre X 2s has no geometric simple factors of type A 1 (the assumption on the Hodge group holds automatically if the number 22-rankNS(X 2s ) is not divisible by 4).
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.)
Model predictive control for spacecraft rendezvous in elliptical orbit
Li, Peng; Zhu, Zheng H.
2018-05-01
This paper studies the control of spacecraft rendezvous with attitude stable or spinning targets in an elliptical orbit. The linearized Tschauner-Hempel equation is used to describe the motion of spacecraft and the problem is formulated by model predictive control. The control objective is to maximize control accuracy and smoothness simultaneously to avoid unexpected change or overshoot of trajectory for safe rendezvous. It is achieved by minimizing the weighted summations of control errors and increments. The effects of two sets of horizons (control and predictive horizons) in the model predictive control are examined in terms of fuel consumption, rendezvous time and computational effort. The numerical results show the proposed control strategy is effective.
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
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.
Radial distributions of star populations in elliptical galaxies
International Nuclear Information System (INIS)
Angeletti, Lucio; Giannone, Pietro
2010-01-01
The dynamical structure of stars in low-ellipticity early-type galaxies has been approached in a conceptually simple manner by making use of the mass structure inferred from the radial surface brightness and the stellar metal abundance as derived from that of the contracting gas mass when the stars formed. Families of models depending on three parameters can be used to fit the surface radial profiles of spectro-photometric indices. In particular, the behavior of the spectral index Mg 2 is selected, and the observations for eleven galaxies are matched with models. With the fitting values of the free parameters, we have studied the spatial (within the galaxy) and projected (on the image of the galaxy) distributions of the metal abundances. We present the results for three chosen galaxies characterized by rather different values of the fitting parameters. Our results can be of interest for the formation of stellar populations and call attention to the need for more detailed observations.
Mixing Characteristics of Elliptical Jet Control with Crosswire
Manigandan, S.; Vijayaraja, K.
2018-02-01
The aerodynamic mixing efficiency of elliptical sonic jet flow with the effect of crosswire is studied computationally and experimentally at different range of nozzle pressure ratio with different orientation along the minor axis of the exit. The cross wire of different orientation is found to reduce the strength of the shock wave formation. Due to the presence of crosswire the pitot pressure oscillation is reduced fast, which weakens the shock cell structure. When the cross wire is placed at center position we see high mixing along the major axis. Similarly, when the cross wire is placed at ¼ and ¾ position we see high mixing promotion along minor axis. It also proves, as the position of the cross wire decreased along minor axis there will be increase in the mixing ratio. In addition to that we also found that, jet spread is high in major axis compared to minor axis due to bifurcation of jet along upstream
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
Scalable Domain Decomposition Preconditioners for Heterogeneous Elliptic Problems
Directory of Open Access Journals (Sweden)
Pierre Jolivet
2014-01-01
Full Text Available Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.
Transient experimental demonstration of an elliptical thermal camouflage device.
He, Xiao; Yang, Tianzhi; Zhang, Xingwei; Wu, Linzhi; He, Xiao Qiao
2017-11-30
The camouflage phenomenon (invisibility or illusion) of thermodynamics has attracted great attentions and many experimental demonstrations have been achieved by virtue of simplified approaches or the scattering cancellation. However, all of the experiments conducted are limited in the invisibility of spheres or two-dimensional (2D) cylinders. An ellipsoid camouflage device with a homogenous and isotropic shell is firstly reported based on the idea of the neutral inclusion and a 2D elliptical thermal camouflage device is realized by a thin-layer cloak of homogeneous isotropic material firstly. The robustness of this scheme is validated in both 2D and 3D configurations. The current work may provide a new avenue to the control of the thermal signatures and we believe this work will broaden the current research and pave a new path to the control of the path of the heat transfer.
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)
Libration-Driven Elliptical Instability Experiments in Ellipsoidal Shells
Grannan, A. M.; Lemasquerier, D. G.; Favier, B.; Cebron, D.; Le Bars, M.; Aurnou, J. M.
2016-12-01
Planets and satellites can be subjected to physical libration, which consists in forced periodic variations in their rotation rate induced by gravitational interactions with nearby bodies. These librations may mechanically drive turbulence in interior liquid layers such as subsurface oceans and metallic liquid cores. One possible driving-process is called the Libration-Driven Elliptical Instability (LDEI) and refers to the resonance of two inertial modes with the libration induced base flow. LDEI has been experimentally and numerically studied in the case of a full ellipsoid (e.g. Cébron et al. [2012c], Grannan et al. [2014] and Favier et al. [2015]). In this study, we address the question of the persistence of the LDEI in the theoretically complex case of an ellipsoidal shell which is more geophysically relevant to model planetary liquid layers. We use an ellipsoidal acrylic container filled with water and add spherical inner cores of different sizes. We perform direct side-view visualizations of the flow in the librating frame using Kalliroscope particles. A Fourier analysis of the light intensity extracted from the recorded movies shows that LDEI persists in a shell geometry for a libration frequency which is 4 and 2.4 time the rotation rate, and allows an identification of the mode coupling. Particle Image Velocimetry (PIV) is performed in vertical and horizontal planes on a selected case to confirm our light intensity results. Additionaly, our survey at a fixed forcing-frequency and variable Ekman number (E) allows a comparison with a local stability analysis, and shows that the libration amplitude at the threshold of the instability varies as ≈[E0.63, E0.72]. When extrapolating to planetary interiors conditions, such a scaling leads to an easier excitation of the elliptical instability than the E0.5 scaling commonly considered.
Fast multipole preconditioners for sparse matrices arising from elliptic equations
Ibeid, Huda
2017-11-09
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.
Fast multipole preconditioners for sparse matrices arising from elliptic equations
Ibeid, Huda; Yokota, Rio; Pestana, Jennifer; Keyes, David E.
2017-01-01
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.
Invisible anti-cloak with elliptic cross section using phase complement
International Nuclear Information System (INIS)
Yang Yu-Qi; Zhang Min; Yue Jian-Xiang
2011-01-01
Based on the theory of phase complement, an anti-cloak with circular cross section can be made invisible to an object outside its domain. As the cloak with elliptic cross section is more effective to make objects invisible than that with circular cross section, a scaled coordinate system is proposed to design equivalent materials of invisible anti-cloak with elliptic cross section using phase complement. The cloaks with conventional dielectric and double negative parameters are both simulated with the geometrical transformations. The results show that the cloak with elliptic cross section through phase complement can effectively hide the outside objects. (classical areas of phenomenology)
Short-Term Comparison of Several Solutinos of Elliptic Relative Motion
Directory of Open Access Journals (Sweden)
Jung Hyun Jo
2007-12-01
Full Text Available Recently introduced, several explicit solutions of relative motion between neighboring elliptic satellite orbits are reviewed. The performance of these solutions is compared with an analytic solution of the general linearized equation of motion. The inversion solution by the Hill-Clohessy-Wiltshire equations is used to produce the initial condition of numerical results. Despite the difference of the reference orbit, the relative motion with the relatively small eccentricity shows the similar results on elliptic case and circular case. In case of the 'chief' satellite with the relatively large eccentricity, HCW equation with the circular reference orbit has relatively larger error than other elliptic equation of motion does.
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)
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.
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.
WKB approach to evaluate series of Mathieu functions in scattering problems
Hubert, Maxime; Dubertrand, Remy
2017-01-01
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when the wavelength is comparable to the obstacle size, when the most standard approximations fail. The approximations of the radial (or modified) Mathieu functions using WKB method are shown to be especially efficient, in order to precisely evaluate series of suc...
Vetrayan, Jayachandran; Othman, Suhana; Victor Paulraj, Smily Jesu Priya
2017-01-01
To assess the effectiveness and feasibility of behavioral sleep intervention for medicated children with ADHD. Six medicated children (five boys, one girl; aged 6-12 years) with ADHD participated in a 4-week sleep intervention program. The main behavioral strategies used were Faded Bedtime With Response Cost (FBRC) and positive reinforcement. Within a case-series design, objective measure (Sleep Disturbance Scale for Children [SDSC]) and subjective measure (sleep diaries) were used to record changes in children's sleep. For all six children, significant decrease was found in the severity of children's sleep problems (based on SDSC data). Bedtime resistance and mean sleep onset latency were reduced following the 4-week intervention program according to sleep diaries data. Gains were generally maintained at the follow-up. Parents perceived the intervention as being helpful. Based on the initial data, this intervention shows promise as an effective and feasible treatment.
Formation of Compact Ellipticals in the merging star cluster scenario
Urrutia Zapata, Fernanda Cecilia; Theory and star formation group
2018-01-01
In the last years, extended old stellar clusters have been observed. They are like globular clusters (GCs) but with larger sizes(a limit of Re=10 pc is currently seen as reasonable). These extended objects (EOs) cover a huge range of mass. Objects at the low mass end with masses comparable to normal globular clusters are called extended clusters or faint fuzzies Larsen & Brodie (2000) and objects at the high-mass end are called ultra compact dwarf galaxies (UCDs). Ultra compact dwarf galaxies are compact object with luminositys above the brigtest known GCs. UCDs are more compact than typical dwarf galaxies but with comparable luminosities. Usually, a lower mass limit of 2 × 10^6 Solar masses is applied.Fellhauer & Kroupa (2002a,b) demostrated that object like ECs, FFs and UCDs can be the remnants of the merger of star clusters complexes, this scenario is called the Merging Star Cluster Scenario. Amore concise study was performed by Bruens et al. (2009, 2011).Our work tries to explain the formation of compact elliptical(cE). These objects are a comparatively rare class of spheroidal galaxies, possessing very small Re and high central surface brightnesses (Faber 1973). cEs have the same parameters as extended objects but they are slightly larger than 100 pc and the luminosities are in the range of -11 to -12 Mag.The standard formation sceanrio of these systems proposes a galaxy origin. CEs are the result of tidal stripping and truncation of nucleated larger systems. Or they could be a natural extension of the class of elliptical galaxies to lower luminosities and smaller sizes.We want to propose a completely new formation scenario for cEs. In our project we try to model cEs in a similar way that UCDs using the merging star cluster scenario extended to much higher masses and sizes. We think that in the early Universe we might have produced sufficiently strong star bursts to form cluster complexes which merge into cEs. So far it is observationally unknown if cEs are
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity
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)
Unified approach to probing Coulomb effects in tunnel ionization for any ellipticity of laser light.
Landsman, A S; Hofmann, C; Pfeiffer, A N; Cirelli, C; Keller, U
2013-12-27
We present experimental data that show significant deviations from theoretical predictions for the location of the center of the electron momenta distribution at low values of ellipticity ε of laser light. We show that these deviations are caused by significant Coulomb focusing along the minor axis of polarization, something that is normally neglected in the analysis of electron dynamics, even in cases where the Coulomb correction is otherwise taken into account. By investigating ellipticity-resolved electron momenta distributions in the plane of polarization, we show that Coulomb focusing predominates at lower values of ellipticity of laser light, while Coulomb asymmetry becomes important at higher values, showing that these two complementary phenomena can be used to probe long-range Coulomb interaction at all polarizations of laser light. Our results suggest that both the breakdown of Coulomb focusing and the onset of Coulomb asymmetry are linked to the disappearance of Rydberg states with increasing ellipticity.
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)
Directory of Open Access Journals (Sweden)
Guanwei Chen
2014-01-01
Full Text Available We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.
Comparison of elliptical and spherical mirrors for the grasshopper monochromators at SSRL
International Nuclear Information System (INIS)
Waldhauer, A.P.
1989-01-01
A comparison of the performance of a spherical and elliptical mirror in the grasshopper monochromator is presented. The problem was studied by ray tracing and then tested using visible (λ=633 nm) laser light. Calculations using ideal optics yield an improvement in flux by a factor of up to 2.7, while tests with visible light show an increase by a factor of 5 because the old spherical mirror is compared to a new, perfect elliptical one. The FWHM of the measured focus is 90 μm with a spherical mirror, and 25 μm with an elliptical one. Elliptical mirrors have been acquired and are now being installed in the two grasshoppers at SSRL
Existence of solutions for some superlinear or sublinear elliptic systems on IRN
International Nuclear Information System (INIS)
Ding Yanheng; Li Shujie.
1993-10-01
The existence of solutions for some superlinear or sublinear elliptic systems on R N is demonstrated using a compact embedding lemma which enables the application of standard critical theory for such problems. 7 refs
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
Nonlinear Schrodinger elliptic systems involving exponential critical growth in R^2
Directory of Open Access Journals (Sweden)
Francisco S. B. Albuquerque Albuquerque
2014-02-01
Full Text Available This article concerns the existence and multiplicity of solutions for elliptic systems with weights, and nonlinearities having exponential critical growth. Our approach is based on the Trudinger-Moser inequality and on a minimax theorem.
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
On a class of strongly degenerate and singular linear elliptic equation
International Nuclear Information System (INIS)
Duong Minh Duc, D.M.; Le Dung.
1992-11-01
We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs
Jin, Wa; Liu, Xuejing; Jin, Wei
2017-10-01
We report the fabrication of in-line photonic microcells (PMCs) by encapsulating tapered elliptical microfibers (MFs) inside glass tubes. The encapsulation does not change the optical property of the MF but protects the elliptical MF from external disturbance and contamination and makes the micro-laboratory robust. Such micro-laboratory can be easily integrated into standard fiber-optic circuits with low loss, making the elliptical MF-based devices more practical for real-world applications. Evanescent field sensing is realized by fabricating micro-channel on the PMC for ingress/egress of sample liquids/gas. Based on the encapsulated elliptical MF PMCs, we demonstrated RI sensitivity of 2024 nm per refractive index unit (nm/RIU) in gaseous environment and 21231 nm/RIU in water.
Effects of elliptical burner geometry on partially premixed gas jet flames in quiescent surroundings
Baird, Benjamin
This study is the investigation of the effect of elliptical nozzle burner geometry and partial premixing, both 'passive control' methods, on a hydrogen/hydrocarbon flame. Both laminar and turbulent flames for circular, 3:1, and 4:1 aspect ratio (AR) elliptical burners are considered. The amount of air mixed with the fuel is varied from fuel-lean premixed flames to fuel-rich partially premixed flames. The work includes measurements of flame stability, global pollutant emissions, flame radiation, and flame structure for the differing burner types and fuel conditions. Special emphasis is placed on the near-burner region. Experimentally, both conventional (IR absorption, chemiluminecent, and polarographic emission analysis,) and advanced (laser induced fluorescence, planar laser induced fluorescence, Laser Doppler Velocimetry (LDV), Rayleigh scattering) diagnostic techniques are used. Numerically, simulations of 3-dimensional laminar and turbulent reacting flow are conducted. These simulations are run with reduced chemical kinetics and with a Reynolds Stress Model (RSM) for the turbulence modeling. It was found that the laminar flames were similar in appearance and overall flame length for the 3:1 AR elliptical and the circular burner. The laminar 4:1 AR elliptical burner flame split into two sub-flames along the burner major axis. This splitting had the effect of greatly shortening the 4:1 AR elliptical burner flame to have an overall flame length about half of that of the circular and 3:1 AR elliptical burner flames. The length of all three burners flames increased with increasing burner exit equivalence ratio. The blowout velocity for the three burners increased with increase in hydrogen mass fraction of the hydrogen/propane fuel mixture. For the rich premixed flames, the circular burner was the most stable, the 3:1 AR elliptical burner, was the least stable, and the 4:1 AR elliptical burner was intermediate to the two other burners. This order of stability was due
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-02-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage developmentof the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, mass center, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-06-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Relativistic elliptic matrix tops and finite Fourier transformations
Zotov, A.
2017-10-01
We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.
Spectral results for mixed problems and fractional elliptic operators,
DEFF Research Database (Denmark)
Grubb, Gerd
2015-01-01
In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators P a of order 2a, with type and factorization index a ∈ R +, restricted to compact sets with boundary; this includes fractional powers of the Laplace operator. The domain...... and the regularity of eigenfunctions is described. In the second part, we apply this in a study of realizations A χ,Σ+ in L 2( Ω ) of mixed problems for a second-order strongly elliptic symmetric differential operator A on a bounded smooth set Ω ⊂ R n; here the boundary ∂Ω=Σ is partioned smoothly into Σ......=Σ_∪Σ+, the Dirichlet condition γ0u=0 is imposed on Σ_, and a Neumann or Robin condition χu=0 is imposed on Σ+. It is shown that the Dirichlet-to-Neumann operator Pγ,χ is principally of type 1/2 with factorization index 1/2, relative to Σ+. The above theory allows a detailed description of D (Aχ,Σ_+) with singular...
Asymptotic expansions for high-contrast elliptic equations
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.
Aliasing errors in measurements of beam position and ellipticity
International Nuclear Information System (INIS)
Ekdahl, Carl
2005-01-01
Beam position monitors (BPMs) are used in accelerators and ion experiments to measure currents, position, and azimuthal asymmetry. These usually consist of discrete arrays of electromagnetic field detectors, with detectors located at several equally spaced azimuthal positions at the beam tube wall. The discrete nature of these arrays introduces systematic errors into the data, independent of uncertainties resulting from signal noise, lack of recording dynamic range, etc. Computer simulations were used to understand and quantify these aliasing errors. If required, aliasing errors can be significantly reduced by employing more than the usual four detectors in the BPMs. These simulations show that the error in measurements of the centroid position of a large beam is indistinguishable from the error in the position of a filament. The simulations also show that aliasing errors in the measurement of beam ellipticity are very large unless the beam is accurately centered. The simulations were used to quantify the aliasing errors in beam parameter measurements during early experiments on the DARHT-II accelerator, demonstrating that they affected the measurements only slightly, if at all
Elliptically Bent X-ray Mirrors with Active Temperature Stabilization
International Nuclear Information System (INIS)
Yuan, Sheng; Church, Matthew; Yashchuk, Valeriy V.; Goldberg, Kenneth A.; Celestre, Rich; McKinney, Wayne R.; Kirschman, Jonathan; Morrison, Greg; Noll, Tino; Warwick, Tony; Padmore, Howard A.
2010-01-01
We present details of design of elliptically bent Kirkpatrick-Baez mirrors developed and successfully used at the Advanced Light Source for submicron focusing. A distinctive feature of the mirror design is an active temperature stabilization based on a Peltier element attached directly to the mirror body. The design and materials have been carefully optimized to provide high heat conductance between the mirror body and substrate. We describe the experimental procedures used when assembling and precisely shaping the mirrors, with special attention paid to laboratory testing of the mirror-temperature stabilization. For this purpose, the temperature dependence of the surface slope profile of a specially fabricated test mirror placed inside a temperature-controlled container was measured. We demonstrate that with active mirror-temperature stabilization, a change of the surrounding temperature by more than 3K does not noticeably affect the mirror figure. Without temperature stabilization, the surface slope changes by approximately 1.5 ?mu rad rms (primarily defocus) under the same conditions.
Systematic study on the performance of elliptic focusing neutron guides
International Nuclear Information System (INIS)
Martin Rodriguez, D.; DiJulio, D.D.; Bentley, P.M.
2016-01-01
In neutron scattering experiments there is an increasing trend towards the study of smaller volume samples, which make the use of focusing optics more important. Focusing guide geometries based on conic-sections, such as those with parabolic and elliptic shapes, have been extensively used in both recently built neutron instruments and upgrades of existing hardware. A large fraction of proposed instruments at the European Spallation Source feature the requirement of good performance when measuring on small samples. The optimised design of a focusing system comes after time consuming Monte-Carlo (MC) simulations. Therefore, in order to help reduce the time needed to design such focusing systems, it is necessary to study systematically the performance of focusing guides. In the present work, we perform a theoretical analysis of the focusing properties of neutron beams, and validate them using a combination of Monte-Carlo simulations and Particle Swarm Optimisations (PSOs), where there is a close correspondence between the maximum divergence of the beam and the shape of the guide. The analytical results show that two limits can be considered, which bound a range of conic section shapes that provide optimum performance. Finally, we analyse a more realistic guide example and we give an assessment of the importance of the contribution from multiple reflections in different systems.
Comparing Chemical Compositions of Dwarf Elliptical Galaxies and Globular Clusters
Chu, Jason; Sparkman, Lea; Toloba, Elisa; Guhathakurta, Puragra
2015-01-01
Because of their abundance in cluster environments and fragility due to their low mass, dwarf elliptical galaxies (dEs) are excellent specimens for studying the physical processes that occur inside galaxy clusters. These studies can be used to expand our understanding of the process of galaxy (specifically dE) formation and the role of dark matter in the Universe. To move closer to better understanding these topics, we present a study of the relationship between dEs and globular clusters (GCs) by using the largest sample of dEs and GC satellites to date. We focus on comparing the ages and chemical compositions of dE nuclei with those of satellite GCs by analyzing absorption lines in their spectra. To better view the spectral features of these relatively dim objects, we employ a spectral co-addition process, where we add the fluxes of several objects to produce a single spectrum with high signal-to-noise ratio. Our finding that dE nuclei are younger and more metal rich than globular clusters establishes important benchmarks that future dE formation theories will consider. We also establish a means to identify GCs whose parent galaxies are uncertain, which allows us to make comparisons between this GC group and the satellite GCs.
Elliptic curves, modular forms, and their L-functions
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...
Models of steady state cooling flows in elliptical galaxies
International Nuclear Information System (INIS)
Vedder, P.W.; Trester, J.J.; Canizares, C.R.
1988-01-01
A comprehensive set of steady state models for spherically symmetric cooling flows in early-type galaxies is presented. It is found that a reduction of the supernova (SN) rate in ellipticals produces a decrease in the X-ray luminosity of galactic cooling flows and a steepening of the surface brightness profile. The mean X-ray temperature of the cooling flow is not affected noticeably by a change in the SN rate. The external pressure around a galaxy does not markedly change the luminosity of the gas within the galaxy but does change the mean temperature of the gas. The presence of a dark matter halo in a galaxy only changes the mean X-ray temperature slightly. The addition of a distribution of mass sinks which remove material from the general accretion flow reduces L(X) very slightly, flattens the surface brightness profile, and reduces the central surface brightness level to values close to those actually observed. A reduction in the stellar mass-loss rate only slightly reduces the X-ray luminosity of the cooling flow and flattens the surface brightness by a small amount. 37 references
Asymptotic expansions for high-contrast elliptic equations
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.
Elliptical superconducting RF cavities for FRIB energy upgrade
Ostroumov, P. N.; Contreras, C.; Plastun, A. S.; Rathke, J.; Schultheiss, T.; Taylor, A.; Wei, J.; Xu, M.; Xu, T.; Zhao, Q.; Gonin, I. V.; Khabiboulline, T.; Pischalnikov, Y.; Yakovlev, V. P.
2018-04-01
The multi-physics design of a five cell, βG = 0 . 61, 644 MHz superconducting elliptical cavity being developed for an energy upgrade in the Facility for Rare Isotope Beams (FRIB) is presented. The FRIB energy upgrade from 200 MeV/u to 400 MeV/u for heaviest uranium ions will increase the intensities of rare isotope beams by nearly an order of magnitude. After studying three different frequencies, 1288 MHz, 805 MHz, and 644 MHz, the 644 MHz cavity was shown to provide the highest energy gain per cavity for both uranium and protons. The FRIB upgrade will include 11 cryomodules containing 5 cavities each and installed in 80-meter available space in the tunnel. The cavity development included extensive multi-physics optimization, mechanical and engineering analysis. The development of a niobium cavity is complete and two cavities are being fabricated in industry. The detailed design of the cavity sub-systems such as fundamental power coupler and dynamic tuner are currently being pursued. In the overall design of the cavity and its sub-systems we extensively applied experience gained during the development of 650 MHz low-beta cavities at Fermi National Accelerator Laboratory (FNAL) for the Proton Improvement Plan (PIP) II.
Dark halos and elliptical galaxies as marginally stable dynamical systems
Energy Technology Data Exchange (ETDEWEB)
El Zant, A. A. [Centre for Theoretical Physics, Zewail City of Science and Technology, Sheikh Zayed, 12588 Giza (Egypt); The British University in Egypt, Sherouk City, Cairo 11837 (Egypt)
2013-12-10
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions—a context in which subtle spurious effects originating from the singularity in the two-body potential become particularly clear. We focus on the case of spherical systems, which support only regular orbits in the collisionless limit, despite the persistence of local exponential instability of N-body trajectories in the anomalous case of discrete point particle representation even as N → ∞. When the singularity in the potential is removed, this apparent contradiction disappears. In the absence of fluctuations, equilibrium configurations generally correspond to positive scalar curvature and thus support stable trajectories. A null scalar curvature is associated with an effective, averaged equation of state describing dynamically relaxed equilibria with marginally stable trajectories. The associated configurations are quite similar to those of observed elliptical galaxies and simulated cosmological halos and are necessarily different from the systems dominated by isothermal cores, expected from entropy maximization in the context of the standard theory of violent relaxation. It is suggested that this is the case because a system starting far from equilibrium does not reach a 'most probable state' via violent relaxation, but that this process comes to an end as the system finds and (settles in) a configuration where it can most efficiently wash out perturbations. We explicitly test this interpretation by means of direct simulations.
Elliptically Bent X-Ray Mirrors with Active Temperature Stabilization
International Nuclear Information System (INIS)
Yuan, S.; Church, M.; Yashchuk, V.V.; Celestre, R.S.; McKinney, W.R.; Morrison, G.; Warwick, T.; Padmore, H.A.; Goldberg, K.A.; Kirschman, J.; Noll, T.
2010-01-01
We present details of design of elliptically bent Kirkpatrick-Baez mirrors developed and successfully used at the advanced light source for submicron focusing. A distinctive feature of the mirror design is an active temperature stabilization based on a Peltier element attached directly to the mirror body. The design and materials have been carefully optimized to provide high heat conductance between the mirror body and substrate. We describe the experimental procedures used when assembling and precisely shaping the mirrors, with special attention paid to laboratory testing of the mirror-temperature stabilization. For this purpose, the temperature dependence of the surface slope profile of a specially fabricated test mirror placed inside a temperature-controlled container was measured. We demonstrate that with active mirror-temperature stabilization, a change of the surrounding temperature by more than 3 K does not noticeably affect the mirror figure. Without temperature stabilization, the rms slope error is changed by approximately 1.5 μrad (primarily defocus) under the same conditions
Aliasing errors in measurements of beam position and ellipticity
Ekdahl, Carl
2005-09-01
Beam position monitors (BPMs) are used in accelerators and ion experiments to measure currents, position, and azimuthal asymmetry. These usually consist of discrete arrays of electromagnetic field detectors, with detectors located at several equally spaced azimuthal positions at the beam tube wall. The discrete nature of these arrays introduces systematic errors into the data, independent of uncertainties resulting from signal noise, lack of recording dynamic range, etc. Computer simulations were used to understand and quantify these aliasing errors. If required, aliasing errors can be significantly reduced by employing more than the usual four detectors in the BPMs. These simulations show that the error in measurements of the centroid position of a large beam is indistinguishable from the error in the position of a filament. The simulations also show that aliasing errors in the measurement of beam ellipticity are very large unless the beam is accurately centered. The simulations were used to quantify the aliasing errors in beam parameter measurements during early experiments on the DARHT-II accelerator, demonstrating that they affected the measurements only slightly, if at all.
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.
Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M
2005-11-01
The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.
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.
1974-09-07
ellipticity filter. The source waveforms are recreated by an inverse transform of those complex ampli- tudes associated with the same azimuth...terms of the three complex data points and the ellipticity. Having solved the equations for all frequency bins, the inverse transform of...Transform of those complex amplitudes associated with Source 1, yielding the signal a (t). Similarly, take the inverse Transform of all
Directed and Elliptic Flow in 158 GeV/Nucleon Pb + Pb Collisions
Appelshäuser, H; Bailey, S J; Barnby, L S; Bartke, J; Barton, R A; Bialkowska, H; Blyth, C O; Bock, R; Bormann, C; Brady, F P; Brockmann, R; Buncic, N; Buncic, P; Caines, H L; Cebra, D; Cooper, G E; Cramer, J G; Csató, P; Dunn, J; Eckardt, V; Eckardt, F; Ferguson, M I; Fischer, H G; Flier, D; Fodor, Z; Foka, P; Freund, P; Friese, V; Fuchs, M; Gabler, F; Gál, J; Gazdzicki, M; Gladysz-Dziadus, E; Grebieszkow, J; Günther, J; Harris, J W; Hegyi, S; Henkel, T; Hill, L A; Huang, I; Hümmler, H; Igo, G; Irmscher, D; Jacobs, P; Jones, P G; Kadija, K; Kolesnikov, V I; Kowalski, M; Lasiuk, B; Lévai, Peter; Malakhov, A I; Margetis, S; Markert, C; Melkumov, G L; Mock, A; Molnár, J; Nelson, J M; Odyniec, Grazyna Janina; Pálla, G; Panagiotou, A D; Petridis, A; Piper, A; Porter, R J; Poskanzer, A M; Poziombka, S; Prindle, D J; Pühlhofer, F; Rauch, W; Reid, J G; Rendfort, R; Retyk, W; Ritter, H G; Röhrich, D; Roland, C; Roland, G; Rudolph, H; Rybicki, A; Sandoval, A; Sann, H; Semenov, A Yu; Schäfer, E; Scjmischke, D; Schmitz, N; Schönfelder, S; Seyboth, P; Seyerlein, J; Siklér, F; Skrzypczak, E; Squier, G T A; Stock, R; Ströbele, H; Szentpétery, I; Sziklay, J; Toy, M; Trainor, T A; Trentalage, S; Ullrich, T; Vassiliou, M; Veztergombi, G; Voloshin, S; Vranic, D; Wang, F; Weerasundara, D D; Wenig, S; Whitten, C; Wienold, T; Wood, L; Yates, T A; Zimányi, J; Zybert, R
1998-01-01
The directed and elliptic flow of protons and charged pions has been observed from the semi-central collisions of a 158 GeV/nucleon Pb beam with a Pb target. The rapidity and transverse momentum dependence of the flow has been measured. The directed flow of the pions is opposite to that of the protons but both exhibit negative flow at low pt. The elliptic flow of both is fairly independent of rapidity but rises with pt.