WorldWideScience

Sample records for asymptotic expansion

  1. Composite asymptotic expansions

    CERN Document Server

    Fruchard, Augustin

    2013-01-01

    The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...

  2. Asymptotic expansions in nonlinear rotordynamics

    Science.gov (United States)

    Day, William B.

    1987-01-01

    This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.

  3. Asymptotic and Exact Expansions of Heat Traces

    Energy Technology Data Exchange (ETDEWEB)

    Eckstein, Michał, E-mail: michal@eckstein.pl [Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer Science (Poland); Zając, Artur, E-mail: artur.zajac@uj.edu.pl [Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)

    2015-12-15

    We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.

  4. THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS

    Institute of Scientific and Technical Information of China (English)

    Chungou Zhang; Quane Wang

    2007-01-01

    In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.

  5. Toeplitz Quantization and Asymptotic Expansions: Geometric Construction

    Directory of Open Access Journals (Sweden)

    Miroslav Englis

    2009-02-01

    Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.

  6. Asymptotic expansion of the wavelet transform with error term

    OpenAIRE

    Pathak, R.S.; Pathak, Ashish

    2014-01-01

    UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.

  7. Singular asymptotic expansions in nonlinear rotordynamics

    Science.gov (United States)

    Day, W. B.

    1985-01-01

    During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.

  8. ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS

    Institute of Scientific and Technical Information of China (English)

    ZHU Xiao-feng; LI Xiu-chun

    2006-01-01

    Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

  9. Asymptotic expansions for high-contrast linear elasticity

    KAUST Repository

    Poveda, Leonardo A.

    2015-03-01

    We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

  10. ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT

    Institute of Scientific and Technical Information of China (English)

    A.Eisinberg; G.Franzè; N.Salerno

    2001-01-01

    Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.

  11. High-order topological asymptotic expansion for Stokes equations

    Directory of Open Access Journals (Sweden)

    Mohamed Abdelwahed

    2016-06-01

    Full Text Available We use the topological sensitivity analysis method to solve various optimization problems. It consists of studying the asymptotic expansion of the objective function relative to a perturbation of the domain topology. This expansion becomes insufficient in some applications when it is limited to the first order topological derivative. We present a new topological sensitivity analysis for the Stokes equations based on a high order asymptotic expansion. The derived result is valid for different class of shape functions.

  12. Kolmogorov turbulence by matched asymptotic expansions

    Science.gov (United States)

    Lundgren, Thomas S.

    2003-04-01

    The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.

  13. Uniform Asymptotic Expansion for the Incomplete Beta Function

    Science.gov (United States)

    Nemes, Gergő; Olde Daalhuis, Adri B.

    2016-10-01

    In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.

  14. Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent

    Science.gov (United States)

    Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.

    2016-10-01

    In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.

  15. A convergence theorem for asymptotic expansions of Feynman amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Mabouisson, A.P.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

    1999-06-01

    The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to {infinity}, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)

  16. Quick asymptotic expansion aided by a variational principle

    Energy Technology Data Exchange (ETDEWEB)

    Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)

    2013-02-15

    It is shown how expanding asymptotically a variational functional can yield the asymptotic expansion of its Euler equation. The procedure is simple but novel and requires taking the variation of the expanded functional with respect to the leading order of the originally unknown function, even though the leading order of this function has already been determined in a previous order. An example is worked out that of a large aspect ratio tokamak plasma equilibrium state with relatively strong flows and high plasma beta.

  17. Asymptotic Expansions of Transition Densities for Hybrid Jump-Diffusions

    Institute of Scientific and Technical Information of China (English)

    Yuan-jin Liu; G.Yin

    2004-01-01

    A class of hybrid jump diffusions modulated by a Markov chain is considered in this work.The motivation stems from insurance risk models,and emerging applications in production planning and wireless communications.The models are hybrid in that they involve both continuous dynamics and discrete events.Under suitable conditions,asymptotic expansions of the transition densities for the underlying processes are developed.The formal expansions are validated and the error bounds obtained.

  18. Asymptotic chaos expansions in finance theory and practice

    CERN Document Server

    Nicolay, David

    2014-01-01

    Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...

  19. A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

    Institute of Scientific and Technical Information of China (English)

    Shi Wei

    2008-01-01

    In this article, the author extends the validity of a uniform asymptotic ex-pansion of the Hermite polynomials HN(√2n+1α) to include all positive values of a.His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.

  20. Asymptotic expansions for high-contrast elliptic equations

    KAUST Repository

    Calo, Victor M.

    2014-03-01

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

  1. Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

    Directory of Open Access Journals (Sweden)

    Okan Ozer

    2013-01-01

    Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

  2. Double asymptotic expansion of three-center electronic repulsion integrals

    Science.gov (United States)

    Alvarez-Ibarra, A.; Köster, A. M.

    2013-07-01

    A double asymptotic expansion for the evaluation of three-center electron repulsion integrals (ERIs) in the long-range limit is presented. For the definition of this limit, a natural division of space based on the atomic coordinates and basis function exponents in utilized. The resulting analytical expression for the calculation of three-center ERIs in the long-range limit are implemented in the density functional theory program deMon2k. Validation and benchmark calculations of n-alkanes, hydrogen saturated graphene sheets and hydrogen saturated diamond blocks are discussed. It is shown that for a sufficient large number of long-range ERIs, the linear scaling regime is reached.

  3. Renormalization and asymptotic expansion of Dirac's polarized vacuum

    CERN Document Server

    Gravejat, Philippe; Séré, Eric

    2010-01-01

    We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\\alphaph$, provided that the ultraviolet cut-off behaves as $\\Lambda\\sim e^{3\\pi(1-Z_3)/2\\alphaph}\\gg1$. The renormalization parameter $0

  4. On the asymptotic expansion of complete Ricci-flat Kahler metrics on quasi-projective manifolds

    CERN Document Server

    Santoro, Bianca

    2012-01-01

    In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler metrics with special approximating properties. Using those metrics as starting point, we are able to work out the asymptotic behavior of the solutions given in the work of Tian-Yau, in particular obtaining their full asymptotic expansion.

  5. MULTISCALE ASYMPTOTIC EXPANSION FOR A CLASS OF HYPERBOLIC-PARABOLIC TYPE EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Li-qun Cao; De-chao Zhu; Jian-Lan Luo

    2002-01-01

    In this paper, we will discuss the asymptotic behaviour for a class of hyper bolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.

  6. Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories

    CERN Document Server

    Linhares, C A; Roditi, I

    2007-01-01

    Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished for both convergent and renormalized amplitudes.

  7. On the ambiguity of field correlators represented by asymptotic perturbation expansions

    Energy Technology Data Exchange (ETDEWEB)

    Caprini, Irinel [National Institute of Physics and Nuclear Engineering, Bucharest POB MG-6, R-077125 Romania (Romania); Fischer, Jan [Institute of Physics, Academy of Sciences of the Czech Republic, CZ-182 21 Prague 8 (Czech Republic); Vrkoc, Ivo [Mathematical Institute, Academy of Sciences of the Czech Republic, CZ-115 67 Prague 1 (Czech Republic)

    2009-10-02

    Starting from the divergence pattern of perturbation expansions in quantum field theory and the (assumed) asymptotic character of the series, we address the problem of ambiguity of a function determined by the perturbation expansion. We consider functions represented by an integral of the Laplace-Borel type along a general contour in the Borel complex plane. Proving a modified form of Watson's lemma, we obtain a large class of functions having the same asymptotic perturbation expansion. Some remarks on perturbative QCD are made, using the particular case of the Adler function.

  8. Homogenization-Based Numerical Mathods, Homogenization, Asymptotic Analysis, Asymptotic Expansion, Numerical Simulation

    OpenAIRE

    Frenod, Emmanuel

    2013-01-01

    In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.

  9. SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

    Institute of Scientific and Technical Information of China (English)

    李大鸣; 张红萍; 高永祥

    2002-01-01

    A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.

  10. Asymptotic expansions for large closed and loss queueing networks

    Directory of Open Access Journals (Sweden)

    Kogan Yaakov

    2002-01-01

    Full Text Available Loss and closed queueing network models have long been of interest to telephone and computer engineers and becoming increasingly important as models of data transmission networks. This paper describes a uniform approach that has been developed during the last decade for asymptotic analysis of large capacity networks with product form of the stationary probability distribution. Such a distribution has an explicit form up to the normalization constant, or the partition function. The approach is based on representing the partition function as a contour integral in complex space and evaluating the integral using the saddle point method and theory of residues. This paper provides an introduction to the area and a review of recent work.

  11. On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection

    DEFF Research Database (Denmark)

    De, Amit

    We establish that the Hitchin connection is a perturbation of the $L_{2}$-connection. We notice that such a formulation of the Hitchin connection does not necessarily require the manifold in question possessing a rigid family of Kähler structures. We then proceed to calculate the asymptotic...... expansion of general perturbations of the $L_{2}$-connection, and see when under certain assumptions such perturbations are flat and projectively flat. During the calculations we also found an asymptotic expansion of the projection operator $\\pi_{\\sigma}^{\\left(k\\right)}$ which projects onto the holomorphic...

  12. Distributional asymptotic expansions of spectral functions and of the associated Green kernels

    Directory of Open Access Journals (Sweden)

    R. Estrada

    1999-03-01

    Full Text Available Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and more precisely determined by means of tools from distribution theory and summability theory. (These are the same, insofar as recently the classic Cesaro--Riesz theory of summability of series and integrals has been given a distributional interpretation. When applied to the spectral analysis of Green functions (which are then to be expanded as series in a parameter, usually the time,these methods show: (1 The ``local'' or ``global'' dependence of the expansion coefficients on the background geometry, etc., is determined by the regularity of the asymptotic expansion of the integrand at the origin (in ``frequency space''; this marks the difference between a heat kernel and a Wightman two-point function, for instance. (2 The behavior of the integrand at infinity determines whether the expansion of the Green function is genuinely asymptotic in the literal, pointwise sense, or is merely valid in a distributional (Cesaro-averaged sense; this is the difference between the heat kernel and the Schrodinger kernel. (3 The high-frequency expansion of the spectral density itself is local in a distributional sense (but not pointwise. These observations make rigorous sense out of calculations in the physics literature that are sometimes dismissed as merely formal.

  13. An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures

    DEFF Research Database (Denmark)

    Christensen, Claus Dencker; Byskov, Esben

    2010-01-01

    A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...

  14. A note on asymptotic expansions for Markov chains using operator theory

    DEFF Research Database (Denmark)

    Jensen, J.L.

    1987-01-01

    We consider asymptotic expansions for sums Sn on the form Sn = fhook0(X0) + fhook(X1, X0) + ... + fhook(Xn, Xn-1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on fhook(Xi, Xi-1), a simple representation...

  15. Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction

    NARCIS (Netherlands)

    Veldman, AEP

    2001-01-01

    The paper presents a personal view on the history of viscous-inviscid interaction methods, a history closely related to the evolution of the method of matched asymptotic expansions. The main challenge in solving Prandtl's boundary-layer equations has been to overcome the singularity at a point of st

  16. The renormalization method based on the Taylor expansion and applications for asymptotic analysis

    CERN Document Server

    Liu, Cheng-shi

    2016-01-01

    Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...

  17. Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time

    Institute of Scientific and Technical Information of China (English)

    G Yin; Dung Tien Nguyen

    2009-01-01

    This work develops asymptotic expansions for solutions of systems of backward equations of timeinhomogeneons Markov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Markov chains often have large state spaces, which make the computational tasks infeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε> 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Markov chains including also transient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions are constructed. Then error bounds are obtained.

  18. On the high-order topological asymptotic expansion for shape functions

    Directory of Open Access Journals (Sweden)

    Maatoug Hassine

    2016-04-01

    Full Text Available This article concerns the topological sensitivity analysis for the Laplace operator with respect to the presence of a Dirichlet geometry perturbation. Two main results are presented in this work. In the first result we discuss the influence of the considered geometry perturbation on the Laplace solution. In the second result we study the high-order topological derivatives. We derive a high-order topological asymptotic expansion for a large class of shape functions.

  19. Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings

    Institute of Scientific and Technical Information of China (English)

    Ze Qing LIU; Shin Min KANG

    2004-01-01

    A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established.The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).

  20. Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas

    Science.gov (United States)

    Davies, Ian; Truman, Aubrey

    1982-11-01

    Imitating Schilder's results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{-TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(-ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.

  1. Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells

    Science.gov (United States)

    Kunte, M. V.; Sarkar, Abhijit; Sonti, Venkata R.

    2010-12-01

    Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order ( n). The shallow shell theory (which is more accurate at higher frequencies) is used to model the cylinder. Initially, the in vacuo shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high- and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter μ, we find solutions for the limiting cases of small and large μ. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases, Poisson's ratio ν is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory ( in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders ( n).

  2. Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

    Energy Technology Data Exchange (ETDEWEB)

    Kamiński, Wojciech, E-mail: wkaminsk@fuw.edu.pl [Wydział Fizyki, Uniwersytet Warszawski, Hoża 69, 00-681, Warsaw (Poland); Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany); Steinhaus, Sebastian, E-mail: steinhaus.sebastian@gmail.com [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany)

    2013-12-15

    We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

  3. Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

    CERN Document Server

    Kaminski, Wojciech

    2013-01-01

    We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

  4. Evaluation of the Fokker-Planck probability by Asymptotic Taylor Expansion Method

    Science.gov (United States)

    Firat, Kenan; Ozer, Okan

    2017-02-01

    The one-dimensional Fokker-Planck equation is solved by the Asymptotic Taylor Expansion Method for the time-dependent probability density of a particle. Using an ansatz wave function, one obtains the series expansion of the solution for the Schrödinger and it allows one to find out the eigen functions and eigen energies of the states to the evaluation of the probability. The eigen energies of some certain kind of Bistable potentials are calculated for some certain potential parameters. The probability function is determined and graphed for potential parameters. The numerical results are compared with existing literature, and a conclusion about the advantages and disadvantages on the method is given.

  5. A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes

    CERN Document Server

    Gorbonos, Dan; Gorbonos, Dan; Kol, Barak

    2004-01-01

    No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The nex...

  6. A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes

    Science.gov (United States)

    Gorbonos, Dan; Kol, Barak

    2004-06-01

    No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic ``mirrors'', and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the ``Archimedes effect''. The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d geq 5, where the system of equations can be reduced to ``a master equation'' — a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.

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

    CERN Document Server

    Borot, Gaëtan; Kozlowski, Karol K

    2016-01-01

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

  8. Derivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions

    CERN Document Server

    Berninger, Heiko; Gander, Martin; Liebendorfer, Mathias; Michaud, Jerome

    2012-01-01

    We present Chapman--Enskog and Hilbert expansions applied to the $\\BigO(v/c)$ Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman-Enskog or Hilbert expansions with reaction and collision scaling. We also give asymptotically sharp results obtained by the use of an additional time scaling. The diffusion limit determines the diffusion source in the Isotropic Diffusion Source Approximation (IDSA) of Boltzmann's equation for which the free streaming limit and the reaction limit serve as limiters. Here, we derive the reaction limit as well as the free streaming limit by truncation of Chapman-Enskog or Hilbert expansions using reaction and collision scaling as well as time scaling, respectively. Finally, we motivate why limiters are a good choice for the definition of the source term i...

  9. Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order

    CERN Document Server

    Gorbonos, Dan; Gorbonos, Dan; Kol, Barak

    2005-01-01

    The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.

  10. Asymptotic expansion based equation of state for hard-disk fluids offering accurate virial coefficients

    CERN Document Server

    Tian, Jianxiang; Mulero, A

    2016-01-01

    Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...

  11. Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem

    Directory of Open Access Journals (Sweden)

    Lubomir Dechevski

    2012-01-01

    Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.

  12. The Riesz energy of the $N$-th roots of unity: an asymptotic expansion for large $N$

    CERN Document Server

    Brauchart, J S; Saff, E B

    2008-01-01

    We derive the complete asymptotic expansion in terms of powers of $N$ for the Riesz $s$-energy of $N$ equally spaced points on the unit circle as $N\\to \\infty$. For $s\\ge -1$, such points form optimal energy $N$-point configurations with respect to the Riesz potential $1/r^{s}$, $s\

  13. Asymptotic expansions of the error for hyper-singular integrals with an interval variable

    Directory of Open Access Journals (Sweden)

    Chong Chen

    2016-01-01

    Full Text Available Abstract In this paper, we present high accuracy quadrature formulas for hyper-singular integrals ∫ a b g ( x q α ( x , t d x $\\int_{a}^{b}g(xq^{\\alpha}(x,t\\, dx$ , where q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ , t ∈ ( a , b $t\\in(a,b$ , and α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ . If g ( x $g(x$ is 2 m + 1 $2m+1$ times differentiable on [ a , b ] $[a,b]$ , the asymptotic expansions of the error show that the convergence order is O ( h 2 μ + 1 + α $O(h^{2\\mu+1+\\alpha}$ with q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ for α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ and α being non-integer, and the error power is O ( h η $O(h^{\\eta}$ with q ( x , t = x − t $q(x,t=x-t$ for α being integers less than −1, where η = min ( 2 μ , 2 μ + 2 + α $\\eta =\\min(2\\mu,2\\mu+2+\\alpha$ and μ = 1 , … , m $\\mu=1,\\ldots,m$ . Since the derivatives of the density function g ( x $g(x$ in the quadrature formulas can be eliminated by means of the extrapolation method, the formulas can easily be applied to solving corresponding hyper-singular boundary integral equations. The reliability and efficiency of the proposed formulas in this paper are demonstrated by some numerical examples.

  14. Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories

    CERN Document Server

    Ryttov, T A

    2016-01-01

    We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero in the beta function at $\\alpha_{IR}$. We present general formulas for scheme-independent series expansions of quantities, evaluated at $\\alpha_{IR}$, as powers of an $N_f$-dependent expansion parameter, $\\Delta_f$. First, we apply these to calculate the derivative $d\\beta/d\\alpha$ evaluated at $\\alpha_{IR}$, denoted $\\beta'_{IR}$, which is equal to the anomalous dimension of the ${\\rm Tr}(F_{\\mu\

  15. Solving singular perturbation problem of second order ordinary differential equation using the method of matched asymptotic expansion (MMAE)

    Science.gov (United States)

    Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd

    2015-10-01

    Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.

  16. An asymptotic analysis for an integrable variant of the Lotka–Volterra prey–predator model via a determinant expansion technique

    Directory of Open Access Journals (Sweden)

    Masato Shinjo

    2015-12-01

    Full Text Available The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.

  17. Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry

    Science.gov (United States)

    Ritchie, R.H.; Sakakura, A.Y.

    1956-01-01

    The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

  18. A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

    Science.gov (United States)

    Zhang, Yongcun; Shang, Shipeng; Liu, Shutian

    2017-01-01

    Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

  19. Asymptotic expansions of the solutions for nonautonomous systems and applications in quantum mechanics

    Directory of Open Access Journals (Sweden)

    Bezyaev Vladimir Ivanovich

    2014-09-01

    Full Text Available The authors present an efficient algorithm different from the previously known to construct the asymptotics of solutions of nonautonomous systems of ordinary differential equations with meromorphic matrix. Schrödinger equation, Dirac system, Lippman-Schwinger equation and other equations of quantum mechanics with spherically symmetric and meromorphic potentials may be reduced to such systems. The Schrödinger equation and the Dirac system describe the stationary states of an electron in a Coulomb field with a fixed point charge in the description of the relativistic and nonrelativistic hydrogen atom. The Lippman-Schwinger equation of scattering theory describes the results of collision and interaction of quantum-mechanical particles in mathematical language after these particles have already diverged a long way from one another and ceased to interact. The observed algorithm supplements the known results and allows you to approach the analysis of the problems of this type with a fairly simple and at the same time, a universal point of view.

  20. Asymptotic expansion of beta matrix models in the one-cut regime

    CERN Document Server

    Borot, Gaëtan

    2011-01-01

    We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus, the coefficients of the expansion can be obtained recursively by the "topological recursion" of Chekhov and Eynard. Our method relies on the combination of a priori bounds on the correlators and the study of Schwinger-Dyson equations, thanks to the uses of classical complex analysis techniques. These a priori bounds can be derived following Boutet de Monvel, Pastur and Shcherbina, or for strictly convex potentials by using concentration of measure. Doing so, we extend the strategy of Guionnet and Maurel-Segala, from the hermitian models (beta = 2) and perturbative potentials, to general beta models. The existence of the first correction in 1/N has been considered previously by Johansson and more recently by Kriecherbauer and Shcherbina. Here, by taking similar hypotheses, we extend the result to all orders in 1/N.

  1. A novel asymptotic expansion homogenization analysis for 3-D composite with relieved periodicity in the thickness direction

    KAUST Repository

    Nasution, Muhammad Ridlo Erdata

    2014-06-01

    A new asymptotic expansion homogenization analysis is proposed to analyze 3-D composite in which thermomechanical and finite thickness effects are considered. Finite thickness effect is captured by relieving periodic boundary condition at the top and bottom of unit-cell surfaces. The mathematical treatment yields that only 2-D periodicity (i.e. in in-plane directions) is taken into account. A unit-cell representing the whole thickness of 3-D composite is built to facilitate the present method. The equivalent in-plane thermomechanical properties of 3-D orthogonal interlock composites are calculated by present method, and the results are compared with those obtained by standard homogenization method (with 3-D periodicity). Young\\'s modulus and Poisson\\'s ratio obtained by present method are also compared with experiments whereby a good agreement is particularly found for the Young\\'s modulus. Localization analysis is carried out to evaluate the stress responses within the unit-cell of 3-D composites for two cases: thermal and biaxial tensile loading. Standard finite element (FE) analysis is also performed to validate the stress responses obtained by localization analysis. It is found that present method results are in a good agreement with standard FE analysis. This fact emphasizes that relieving periodicity in the thickness direction is necessary to accurately simulate the real free-traction condition in 3-D composite. © 2014 Elsevier Ltd.

  2. Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results

    Institute of Scientific and Technical Information of China (English)

    E. M. E. ZAYED

    2003-01-01

    The asymptotic expansions of the trace of the heat kernel Θ(t) = ∑∞ν=1 exp(-tλν) for smallpositive t, where {λν} are the eigenvalues of the negative Laplacian -△n = - ∑n i=1 ( / xi )2 in Rn(n= 2or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary (e)Ω1 and asmooth outer boundary (e)Ω2, where a finite number of piecewise smooth Robin boundary conditions((e)/(e)nj+rj)φ=0 on the components γj(j = 1, ..., k)of (e)Ω1 and on teh components γj(j = 1, ..., m) of (e)Ω2 are considered such that( (e)Ω1+ukj=1 Fj and (e)Ω2=Umj=k+1Fj )and where the coefficients (rj(j=1,…,m))are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gasenclosed in the general annular bounded domain Ω are given. Further results are also obtained.

  3. Linear Approximation and Asymptotic Expansion of Solutions for a Nonlinear Carrier Wave Equation in an Annular Membrane with Robin-Dirichlet Conditions

    Directory of Open Access Journals (Sweden)

    Le Thi Phuong Ngoc

    2016-01-01

    Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.

  4. Two-loop two-point functions with masses asymptotic expansions and Taylor series, in any dimension

    CERN Document Server

    Broadhurst, D J; Tarasov, O V

    1993-01-01

    In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.

  5. Calculation of the eigenfunctions and eigenvalues of Schr\\"odinger type equations by asymptotic Taylor expansion method (ATEM)

    OpenAIRE

    Koc, Ramazan; Olgar, Eser

    2010-01-01

    A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.

  6. Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

    Science.gov (United States)

    Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

    2016-08-01

    The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the

  7. ARCH(0,1)系数中位无偏估计分布的渐近展开%Asymptotic Expansion for the Distribution of a Median Unbiased Estimator of ARCH(0,1) Coefficient

    Institute of Scientific and Technical Information of China (English)

    王德辉

    2007-01-01

    This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1) coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement,even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximatioh of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.

  8. Polynomial Asymptotes

    Science.gov (United States)

    Dobbs, David E.

    2010-01-01

    This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…

  9. Renormalization-group study of a superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations

    Science.gov (United States)

    Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.

    2014-11-01

    We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.

  10. Nonstandard asymptotic analysis

    CERN Document Server

    Berg, Imme

    1987-01-01

    This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...

  11. Study of the asymptotic expansion of multiple integrals in mathematical physics; Etudes sur les developpements asymptotiques des integrales multiples de la physique mathematique

    Energy Technology Data Exchange (ETDEWEB)

    Chako, N. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1968-07-01

    We have applied the method of stationary phase to evaluate double and multiple integrals of the type: (A) U(k) = g(x)e{sup ik{phi}}{sup (x)} d(x), (x)=(x{sub 1},..., x{sub n}) for large values of the parameter k. In the first part we have established in a rigorous manner the stationary phase method to double and multiple integrals of type (A). Furthermore we have obtained an asymptotic expansion of (A), if the amplitude and phase functions can be developed in a canonical form near the vicinity of critical or stationary points of the integral. This development contains as particular cases all those which are important in physical applications, especially, to diffraction and scattering of electromagnetic and corpuscular waves by optical systems, diffracting bodies and potential scatterers. In the second part we have considered the problem of convergence of the expansion of the principal contribution to the integral in the asymptotic sense of Poincare. The proof is based on the increasing method used in mathematical analysis. The third part is devoted to the derivation of various asymptotic series due to different types of critical or stationary points associated with the amplitude and phase functions. In the fourth part we have generalized the method to multiple integrals and to the case where the parameter k enter implicitly in the phase function The latter type of integrals extend the scope of the former type to a number of important physical problems; for instance, to the propagation of waves in dispersive and absorbing media. In the last chapter we have made a study and compared the results obtained by the application of the stationary phase method to the integrals (double) of diffraction and the results derived by using the Young-Rubinowicz method. Result of our analysis shows the equivalence of the two methods of approach to the problems of diffraction based, on one hand, on the Fresnel-Kirchhoff theory and, on the other hand, the Young-Rubinowicz theory

  12. Asymptotically hyperbolic connections

    CERN Document Server

    Fine, Joel; Krasnov, Kirill; Scarinci, Carlos

    2015-01-01

    General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...

  13. Asymptotically hyperbolic connections

    Science.gov (United States)

    Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos

    2016-09-01

    General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.

  14. Asymptotic analysis and boundary layers

    CERN Document Server

    Cousteix, Jean

    2007-01-01

    This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...

  15. A note on asymptotic expansions for sums over a weakly dependent random field with application to the Poisson and Strauss processes

    DEFF Research Database (Denmark)

    Jensen, J.L.

    1993-01-01

    Previous results on Edgeworth expansions for sums over a random field are extended to the case where the strong mixing coefficient depends not only on the distance between two sets of random variables, but also on the size of the two sets. The results are applied to the Poisson and the Strauss po...... point processes, giving rise also to local limit results. © 1993 The Institute of Statistical Mathematics....

  16. Numerical and asymptotic aspects of parabolic cylinder functions

    NARCIS (Netherlands)

    Temme, N.M.

    2000-01-01

    Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are

  17. Feasibility of Diagrammatic Monte-Carlo based on weak-coupling expansion in asymptotically free theories: case study of $O(N)$ sigma-model in the large-$N$ limit

    CERN Document Server

    Buividovich, P V

    2015-01-01

    We discuss the feasibility of applying Diagrammatic Monte-Carlo algorithms to the weak-coupling expansions of asymptotically free quantum field theories, taking the large-$N$ limit of the $O(N)$ sigma-model as the simplest example where exact results are available. We use stereographic mapping from the sphere to the real plane to set up the perturbation theory, which results in a small bare mass term proportional to the coupling $\\lambda$. Counting the powers of coupling associated with higher-order interaction vertices, we arrive at the double-series representation for the dynamically generated mass gap in powers of both $\\lambda$ and $\\log(\\lambda)$, which converges quite quickly to the exact non-perturbative answer. We also demonstrate that it is feasible to obtain the coefficients of these double series by a Monte-Carlo sampling in the space of Feynman diagrams. In particular, the sign problem of such sampling becomes milder at small $\\lambda$, that is, close to the continuum limit.

  18. Confinement versus asymptotic freedom

    CERN Document Server

    Dubin, A Yu

    2002-01-01

    I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...

  19. A Shortcut to LAD Estimator Asymptotics

    OpenAIRE

    1990-01-01

    Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...

  20. Asymptotic solution for EI Nino-southern oscillation of nonlinear model

    Institute of Scientific and Technical Information of China (English)

    MO Jia-qi; LIN Wan-tao

    2008-01-01

    A class of nonlinear coupled system for E1 Nino-Southern Oscillation (ENSO) model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.

  1. The n-th prime asymptotically

    CERN Document Server

    de Reyna, Juan Arias

    2012-01-01

    A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.

  2. Asymptotically Safe Dark Matter

    DEFF Research Database (Denmark)

    Sannino, Francesco; Shoemaker, Ian M.

    2015-01-01

    We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....

  3. Preliminary study of two-scale model for analyzing brittle rock based on asymptotic expansion method%基于渐近展开法的脆性岩石双尺度方法初步研究

    Institute of Scientific and Technical Information of China (English)

    彭从文; 朱向荣; 王金昌

    2011-01-01

    将渐近展开法与细观统计模型相结合,研究了脆性岩石双尺度计算方法.该方法在细观尺度定义材料属性,假定材料参数符合Weibull分布,采用弹性-理想脆性本构模型,脆断标准采用修正的Mohr-Coulomb准则和最大拉应力准则,通过宏细观尺度耦合计算,得到细观尺度材料损伤演化及其对结构宏观性状的影响.方法包括确定材料统计参数、确定细观尺度代表性体积单元(RVE)及求解边值方程等步骤.数值模型采用商业软件ABAQUS及其内嵌的UMAT用户子程序实现.该方法适用于岩石单轴受压或低围压应力状态,考虑到计算效率,计算时宜采用混合尺度,即模型重点(关键)部位采用双尺度,而其他区域采用单尺度计算.宏观尺度材料软化后未采用正则化方法,此时的计算结果有网格依赖性.%The asymptotic expansion method was combined with micro-based statistical model to develop a two-scale scheme for analyzing the behavior of brittle rock.The material properties were defined in micro-scale and the elastic-perfect brittle constitutive was adopted, the modified Mohr-Coulomb theory and the maximum tensile strength were selected as the fracture criterion.Through calculating in a global-local coupling way, the damage evolution of material in the micro-scale and its effects on the properties of rock in the macro-scale were derived.The scheme included three steps: determining material statistical parameters, determining representative volume element (RVE) and solving boundary equations.The numerical model was realized by the commercial software ABAQUS and its subroutine UMAT.This scheme can be used in the conditions that the rock is loaded with uniaxial compression or triaxial compression with low confining pressure.The regularization method is not used, so the result is mesh dependent after the rock is localized.

  4. Asymptotic analysis of the Nörlund and Stirling polynomials

    Directory of Open Access Journals (Sweden)

    Mark Daniel Ward

    2012-04-01

    Full Text Available We provide a full asymptotic analysis of the N{\\"o}rlund polynomials and Stirling polynomials. We give a general asymptotic expansion---to any desired degree of accuracy---when the parameter is not an integer. We use singularity analysis, Hankel contours, and transfer theory. This investigation was motivated by a need for such a complete asymptotic description, with parameter 1/2, during this author's recent solution of Wilf's 3rd (previously Unsolved Problem.

  5. Large Deviations and Asymptotic Methods in Finance

    CERN Document Server

    Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef

    2015-01-01

    Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...

  6. Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

    CERN Document Server

    Sachdev, PL

    2010-01-01

    A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions

  7. Discrete Energy Asymptotics on a Riemannian circle

    CERN Document Server

    Brauchart, J S; Saff, E B

    2009-01-01

    We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\

  8. Asymptotic estimates for generalized Stirling numbers

    NARCIS (Netherlands)

    Chelluri, R.; Richmond, L.B.; Temme, N.M.

    1999-01-01

    Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu

  9. Breaking a magnetic zero locus: asymptotic analysis

    OpenAIRE

    Raymond, Nicolas

    2014-01-01

    25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.

  10. Asymptotic Methods for Solitary Solutions and Compactons

    Directory of Open Access Journals (Sweden)

    Ji-Huan He

    2012-01-01

    Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.

  11. Semiclassical Asymptotics on Manifolds with Boundary

    CERN Document Server

    Koldan, Nilufer; Shubin, Mikhail

    2008-01-01

    We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.

  12. Asymptotics of Random Contractions

    CERN Document Server

    Hashorva, Enkelejd; Tang, Qihe

    2010-01-01

    In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.

  13. ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS

    Institute of Scientific and Technical Information of China (English)

    Klaus P(o)tzelberger

    2003-01-01

    We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.

  14. 一致凸Banach空间上渐近非扩张映象Ishikawa迭代的收敛定理%Convergence Theorms of Ishikawa Iterative for Asymptotically Non-expansive Mapping in a Uniformly Convex Banach space

    Institute of Scientific and Technical Information of China (English)

    苏永福

    2001-01-01

    文[4]把文[3]的主要结果从Hilbert空间推广到一致凸Banach空间,证明了一致凸Banach空间中文上从有界闭凸集到自身的渐近非扩张映象的迭代序列收敛定理.本文将有界闭凸集的条件减弱为闭凸集,从而推广了文[4]的相应结果.%In paper [4], the relative result of Jiirgen schu is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly conves Banach space for asymptotically non - expanstive mapping is proved.In paper [4], T is asymptotically non - expanstive mapping with sequence {Kn} in a bounded closed convex subset C of uniformly convex Banach space.In this paper, we let only C is closed convex subset of uniformlly convex Banach space. But convergence theorms of iterative sequences for asymptotically non-expanstive mapping was also proved.

  15. Weakly asymptotically hyperbolic manifolds

    CERN Document Server

    Allen, Paul T; Lee, John M; Allen, Iva Stavrov

    2015-01-01

    We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.

  16. Asymptotics of high order noise corrections

    CERN Document Server

    Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre

    1999-01-01

    We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.

  17. An All-Orders Derivative Expansion

    OpenAIRE

    Dunne, Gerald(Department of Physics, University of Connecticut, Storrs, CT, 06269, U.S.A.)

    1996-01-01

    We evaluate the exact $QED_{2+1}$ effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders derivative expansion of the effective action, and indicates that the derivative expansion is an asymptotic, rather than a convergent, expansion.

  18. Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation

    CERN Document Server

    Gadylshin, R R

    1998-01-01

    It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.

  19. Asymptotic freedom, asymptotic flatness and cosmology

    CERN Document Server

    Kiritsis, Elias

    2013-01-01

    Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.

  20. Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation

    Institute of Scientific and Technical Information of China (English)

    HUANG Qiong-Wei; TANG Jia-Shi

    2011-01-01

    Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (|∈| (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.

  1. Asymptotic Enumeration of RNA Structures with Pseudoknots

    CERN Document Server

    Jin, Emma Y

    2007-01-01

    In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for $k$-noncrossing RNA structures. Our results are based on the generating function for the number of $k$-noncrossing RNA pseudoknot structures, ${\\sf S}_k(n)$, derived in \\cite{Reidys:07pseu}, where $k-1$ denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function $\\sum_{n\\ge 0}{\\sf S}_k(n)z^n$ and obtain for $k=2$ and $k=3$ the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary $k$ singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula ${\\sf S}_3(n) \\sim \\frac{10.4724\\cdot 4!}{n(n...

  2. Hydrodynamics, resurgence and trans-asymptotics

    CERN Document Server

    Basar, Gokce

    2015-01-01

    The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...

  3. On asymptotic flatness and Lorentz charges

    Energy Technology Data Exchange (ETDEWEB)

    Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)

    2011-07-21

    In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.

  4. Asymptotic Approximation of Solutions and Eigenvalues of a Boundary Problem for a Singular Perturbated Relativistic Analog of Schroedinger Equation

    CERN Document Server

    Amirkhanov, I V; Zhidkova, I E; Vasilev, S A

    2000-01-01

    Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.

  5. Asymptotic safety guaranteed

    DEFF Research Database (Denmark)

    Litim, Daniel F.; Sannino, Francesco

    2014-01-01

    We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.......We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...

  6. Asymptotic safety guaranteed

    CERN Document Server

    Litim, Daniel F

    2014-01-01

    We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.

  7. Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions

    Institute of Scientific and Technical Information of China (English)

    A.M. Il'in; R.Z. Khasminskii; G. Yin

    2002-01-01

    This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.

  8. Asymptotics of 6j and 10j symbols

    CERN Document Server

    Freidel, L; Freidel, Laurent; Louapre, David

    2003-01-01

    It is well known that the building blocks for state sum models of quantum gravity is given by 6j and 10j symbols. In this work we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics we recover the Ponzano-Regge formula for the SU(2) 6j-symbol. We show how the asymptotics of the various Lorentzian $6j$-symbols can be obtained by the same methods. Finally we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of these behavior and a way to modify the Barrett-Crane model to cure this disease.

  9. Asymptotics of thermal spectral functions

    CERN Document Server

    Caron-Huot, S

    2009-01-01

    We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...

  10. Nonabelian Higgs models: paving the way for asymptotic freedom

    CERN Document Server

    Gies, Holger

    2016-01-01

    Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.

  11. Homogenization and asymptotics for small transaction costs

    CERN Document Server

    Soner, H Mete

    2012-01-01

    We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.

  12. ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Cheng Ouyang

    2005-01-01

    A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.

  13. Asymptotic Black Holes

    CERN Document Server

    Ho, Pei-Ming

    2016-01-01

    Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.

  14. Asymptotic black holes

    Science.gov (United States)

    Ho, Pei-Ming

    2017-04-01

    Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.

  15. Asymptotic Symmetries from finite boxes

    CERN Document Server

    Andrade, Tomas

    2015-01-01

    It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.

  16. Asymptotically Safe Grand Unification

    CERN Document Server

    Bajc, Borut

    2016-01-01

    Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

  17. Asymptotically safe grand unification

    Science.gov (United States)

    Bajc, Borut; Sannino, Francesco

    2016-12-01

    Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

  18. Selected asymptotic methods with applications to electromagnetics and antennas

    CERN Document Server

    Fikioris, George; Bakas, Odysseas N

    2013-01-01

    This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som

  19. Equivariant spectral asymptotics for h-pseudodifferential operators

    Science.gov (United States)

    Weich, Tobias

    2014-10-01

    We prove equivariant spectral asymptotics for h-pseudodifferential operators for compact orthogonal group actions generalizing results of El Houakmi and Helffer ["Comportement semi-classique en présence de symétries: Action d'un groupe de Lie compact," Asymp. Anal. 5(2), 91-113 (1991)] and Cassanas ["Reduced Gutzwiller formula with symmetry: Case of a Lie group," J. Math. Pures Appl. 85(6), 719-742 (2006)]. Using recent results for certain oscillatory integrals with singular critical sets [P. Ramacher, "Singular equivariant asymptotics and Weyl's law: On the distribution of eigenvalues of an invariant elliptic operator," J. Reine Angew. Math. (Crelles J.) (to be published)], we can deduce a weak equivariant Weyl law. Furthermore, we can prove a complete asymptotic expansion for the Gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the Hamilton flow.

  20. Inference on rare errors using asymptotic expansions and bootstrap calibration

    NARCIS (Netherlands)

    Helmers, R.

    1998-01-01

    The number of items in error in an audit population is usually quite small, whereas the error distribution is typically highly skewed to the right. For applications in statistical auditing, where line item sampling is appropriate, a new upper confidence limit for the total error amount in an audit p

  1. A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis

    Directory of Open Access Journals (Sweden)

    R. Fares

    2012-01-01

    Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.

  2. Asymptotic conditions of motion for radiating charged particles

    Science.gov (United States)

    Anderson, James L.

    1997-10-01

    Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.

  3. A Note on Asymptotic Contractions

    Directory of Open Access Journals (Sweden)

    Marina Arav

    2006-12-01

    Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.

  4. A Note on Asymptotic Contractions

    Directory of Open Access Journals (Sweden)

    Castillo Santos Francisco Eduardo

    2007-01-01

    Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .

  5. Asymptotic Dynamics of Monopole Walls

    CERN Document Server

    Cross, R

    2015-01-01

    We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.

  6. Asymptotics of the filtration problem for suspension in porous media

    Directory of Open Access Journals (Sweden)

    Kuzmina Ludmila Ivanovna

    2015-01-01

    Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.

  7. Entropy Production during Asymptotically Safe Inflation

    Directory of Open Access Journals (Sweden)

    Martin Reuter

    2011-01-01

    Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.

  8. On the accuracy of the asymptotic theory for cylindrical shells

    DEFF Research Database (Denmark)

    Niordson, Frithiof; Niordson, Christian

    1999-01-01

    We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this shell theory for a cylindrical shell with clamped ends with the results of a solution to the three......-dimensional problem. The results are also compared with those of some commonly used engineering shell theories....

  9. EDGEWORTH EXPANSION AND BOOTSTRAP APPROXIMATION FOR THE STUDENTIZED MLE FROM RANDOMLY CENSORED EXPONENTIAL SAMPLES

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In this paper,the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population.It is shown that the Edgeworth expansions and the bootstrap approximation are asymptotically close to the exact distribution of the studentized MLE with a rate.

  10. Polynomial Asymptotes of the Second Kind

    Science.gov (United States)

    Dobbs, David E.

    2011-01-01

    This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

  11. Gradient expansion for anisotropic hydrodynamics

    Science.gov (United States)

    Florkowski, Wojciech; Ryblewski, Radoslaw; Spaliński, Michał

    2016-12-01

    We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of nonhydrodynamic modes.

  12. Gradient expansion for anisotropic hydrodynamics

    CERN Document Server

    Florkowski, Wojciech; Spaliński, Michał

    2016-01-01

    We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes.

  13. Metric Dependence and Asymptotic Minimization of the Expected Number of Critical Points of Random Holomorphic Sections

    CERN Document Server

    Baugher, Benjamin

    2008-01-01

    We prove the main conjecture from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the metric dependence and asymptotic minimization of the expected number \\mathcal{N}^{crit}_{N,h} of critical points of random holomorphic sections of the Nth tensor power of a positive line bundle. The first non-topological term in the asymptotic expansion of \\mathcal{N}^{crit}_{N,h} is the the Calabi functional multiplied by the constant \\be_2(m) which depends only on the dimension of the manifold. We prove that \\be_2(m) is strictly positive in all dimensions, showing that the expansion is non-topological for all m, and that the Calabi extremal metric, when it exists, asymptotically minimizes \\mathcal{N}^{crit}_{N,h}.

  14. Edgeworth expansion for functionals of continuous diffusion processes

    DEFF Research Database (Denmark)

    Podolskij, Mark; Yoshida, Nakahiro

    2016-01-01

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

  15. ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Jiaqi MO; Wantao LIN

    2008-01-01

    A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.

  16. The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

    CERN Document Server

    Brauchart, J S; Saff, E B

    2012-01-01

    We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in $\\mathbb{R}^{d+1}$, $d\\geq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\\to \\infty$) of the optimal $s$-energy.

  17. Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients

    Directory of Open Access Journals (Sweden)

    Eleni Bisognin

    2008-03-01

    Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.

  18. Asymptotics of trimmed CUSUM statistics

    CERN Document Server

    Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318

    2012-01-01

    There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...

  19. Exact and asymptotic results for insurance risk models with surplus-dependent premiums

    CERN Document Server

    Albrecher, Hansjörg; Palmowski, Zbigniew; Regensburger, Georg; Rosenkranz, Markus

    2011-01-01

    In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.

  20. Asymptotics for dissipative nonlinear equations

    CERN Document Server

    Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A

    2006-01-01

    Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

  1. Higher dimensional nonclassical eigenvalue asymptotics

    Science.gov (United States)

    Camus, Brice; Rautenberg, Nils

    2015-02-01

    In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .

  2. Ruin problems and tail asymptotics

    DEFF Research Database (Denmark)

    Rønn-Nielsen, Anders

    The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...... by an underlying Harris recurrent Markov process some asymptotic results for the ruin probability are derived. Finally, a paper, which is separate in content from the rest of the thesis, treats a RESTART problem in the situation, where failures occur with decreasing intensity....

  3. Asymptotic Rayleigh instantaneous unit hydrograph

    Science.gov (United States)

    Troutman, B.M.; Karlinger, M.R.

    1988-01-01

    The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.

  4. Asymptotic vacua with higher derivatives

    Energy Technology Data Exchange (ETDEWEB)

    Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)

    2016-04-10

    We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.

  5. Asymptotic vacua with higher derivatives

    Directory of Open Access Journals (Sweden)

    Spiros Cotsakis

    2016-04-01

    Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.

  6. Inaccurate usage of asymptotic formulas

    CERN Document Server

    Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw

    2004-01-01

    The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.

  7. Thermodynamics of asymptotically safe theories

    DEFF Research Database (Denmark)

    Rischke, Dirk H.; Sannino, Francesco

    2015-01-01

    We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...

  8. Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points

    Institute of Scientific and Technical Information of China (English)

    Fei LIU; Fang WANG

    2016-01-01

    In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.

  9. On transfinite extension of asymptotic dimension

    OpenAIRE

    Radul, Taras

    2006-01-01

    We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.

  10. Edgeworth expansion for the pre-averaging estimator

    DEFF Research Database (Denmark)

    Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro

    In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its...... asymptotic variance. Our approach is based on martingale embedding, Malliavin calculus and stable central limit theorems for continuous diffusions. Moreover, we derive the density expansion for the studentized statistic, which might be applied to construct asymptotic confidence regions....

  11. Structure and asymptotic theory for nonlinear models with GARCH errors

    Directory of Open Access Journals (Sweden)

    Felix Chan

    2015-01-01

    Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.

  12. Asymptotic safety goes on shell

    Science.gov (United States)

    Benedetti, Dario

    2012-01-01

    It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.

  13. Composite Operators in Asymptotic Safety

    CERN Document Server

    Pagani, Carlo

    2016-01-01

    We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.

  14. Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras

    Institute of Scientific and Technical Information of China (English)

    LI Jin-xiu; WANG Qin

    2006-01-01

    We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.

  15. Supersymmetric asymptotic safety is not guaranteed

    CERN Document Server

    Intriligator, Kenneth

    2015-01-01

    It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.

  16. Asymptotic integration of differential and difference equations

    CERN Document Server

    Bodine, Sigrun

    2015-01-01

    This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...

  17. Long-time asymptotics in the one-dimensional trapping problem with large bias

    Energy Technology Data Exchange (ETDEWEB)

    Aldea, A.; Dulea, M.; Gartner, P.

    1988-08-01

    The survival probability of a particle which moves according to a biased random walk in a one-dimensional lattice containing randomly distributed deep traps is studied at large times. Exact asymptotic expansions are deduced for fields exceeding a certain threshold, using the method of images. In order to cover the whole range of fields, we also derive the behavior of the survival probability below this threshold, using the eigenvalue expansion method. The connection with the continuous diffusion model is discussed.

  18. Asymptotics of Heavy-Meson Form Factors

    CERN Document Server

    Grozin, A.G.; Grozin, Andrey G.; Neubert, Matthias

    1997-01-01

    Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\\ll |v\\cdot v'|\\ll m_Q/\\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\\cdot v'|\\gg m_Q/\\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\\cdot v'|\\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\\cdot v'\\sim m_b/\\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\\cdot v'\\sim -m_b/\\Lambda$). We obtain the evolution equations and sum rules ...

  19. ASYMPTOTIC APPROXIMATION BYBERNSTEIN-DURRMEYER OPERATORS AND THEIR DERIVATIVES

    Institute of Scientific and Technical Information of China (English)

    Abel, Ulrich

    2000-01-01

    The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators M,. We derive the complete asymptotic expansion of the operators M. and their derivatives as n tends to infinity. It turns ow that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases.Finally, we obtain a Voronovskaja-type formula for simultaneous a pproximation by linear combinations of Mn.

  20. Asymptotics for Toeplitz determinants: Perturbation of symbols with a gap

    Science.gov (United States)

    Charlier, Christophe; Claeys, Tom

    2015-02-01

    We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate. We generalize an asymptotic expansion by Widom [Indiana Univ. Math. J. 21, 277-283 (1971)], which was known for symbols supported on an arc. We highlight applications of our results in the circular unitary ensemble and in the study of Fredholm determinants associated to the sine kernel.

  1. AN ASYMPTOTIC ANALYSIS METHOD FOR THE LINEAR SHELL

    Institute of Scientific and Technical Information of China (English)

    李开泰; 张文岭; 黄艾香

    2004-01-01

    In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term uk successively. According this metnod the leading term u0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution UKT(x,ζ):=U(x)+Ⅱ1Uζ+Ⅱ2Uζ2,then we give the estimation.

  2. Gravitational entropy of cosmic expansion

    CERN Document Server

    Sussman, Roberto A

    2014-01-01

    We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\\Lambda$-CDM background model. However, the $\\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.

  3. Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

    NARCIS (Netherlands)

    Temme, N.M.

    1996-01-01

    We consider the asymptotic behavior of the incomplete gamma functions $gamma (-a,-z)$ and $Gamma (-a,-z)$ as $atoinfty$. Uniform expansions are needed to describe the transition area $z sim a$, in which case error functions are used as main approximants. We use integral representations of the incomp

  4. Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.

  5. Operator product expansion algebra

    Energy Technology Data Exchange (ETDEWEB)

    Holland, Jan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Hollands, Stefan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, Leipzig, D-04103 (Germany)

    2013-07-15

    We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE, =Σ{sub C}C{sub A{sub 1A{sub 2A{sub 3}{sup C}}}}, usually interpreted only as an asymptotic short distance expansion, actually converges at finite, and even large, distances. We further show that the factorization identity C{sub A{sub 1A{sub 2A{sub 3}{sup B}}}}=Σ{sub C}C{sub A{sub 1A{sub 2}{sup C}}}C{sub CA{sub 3}{sup B}} is satisfied for suitable configurations of the spacetime arguments. Again, the infinite sum is shown to be convergent. Our proofs rely on explicit bounds on the remainders of these expansions, obtained using refined versions, mostly due to Kopper et al., of the renormalization group flow equation method. These bounds also establish that each OPE coefficient is a real analytic function in the spacetime arguments for non-coinciding points. Our results hold for arbitrary but finite loop orders. They lend support to proposals for a general axiomatic framework of quantum field theory, based on such “consistency conditions” and akin to vertex operator algebras, wherein the OPE is promoted to the defining structure of the theory.

  6. Asymptotics of robust utility maximization

    CERN Document Server

    Knispel, Thomas

    2012-01-01

    For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.

  7. Asymptotics for Associated Random Variables

    CERN Document Server

    Oliveira, Paulo Eduardo

    2012-01-01

    The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting

  8. Asymptotics of Lagged Fibonacci Sequences

    CERN Document Server

    Mertens, Stephan

    2009-01-01

    Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.

  9. Expansive Cements

    Science.gov (United States)

    1970-10-01

    sale: is disributici is unlimited = F’)RIWRD Seior Ignacio Soto, Rrecutive President, Instituto Mexicano del Cementc y Concreto , invited Mr. Bryant... Concreto , a.c., Kwidco, D. F., Mexico. Based on info.mation largely obtained from ACT Committee 223, Expansive ’ement. Concretes, ACI Journal, August 1Q70

  10. Asymptotic accuracy of Bayesian estimation for a single latent variable.

    Science.gov (United States)

    Yamazaki, Keisuke

    2015-09-01

    In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the joint probability of the latent variables in a dataset, and we proved that the Bayes method is asymptotically more accurate than the maximum-likelihood method. However, the accuracy of the Bayes estimation for a single latent variable remains unknown. In the present paper, we derive the asymptotic expansions of the error functions, which are defined by the Kullback-Leibler divergence, for two types of single-variable estimations when the statistical regularity is satisfied. Our results indicate that the accuracies of the Bayes and maximum-likelihood methods are asymptotically equivalent and clarify that the Bayes method is only advantageous for multivariable estimations.

  11. Modeling broadband poroelastic propagation using an asymptotic approach

    Energy Technology Data Exchange (ETDEWEB)

    Vasco, Donald W.

    2009-05-01

    An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.

  12. Asymptotic safety goes on shell

    CERN Document Server

    Benedetti, Dario

    2011-01-01

    It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.

  13. Asymptotically Free Gauge Theories. I

    Science.gov (United States)

    Wilczek, Frank; Gross, David J.

    1973-07-01

    Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

  14. Asymptotic properties of the C-Metric

    CERN Document Server

    Sladek, Pavel

    2010-01-01

    The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.

  15. Supersymmetric asymptotic safety is not guaranteed

    DEFF Research Database (Denmark)

    Intriligator, Kenneth; Sannino, Francesco

    2015-01-01

    It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...

  16. Edgeworth expansion for the survival function estimator in the Koziol-Green model

    Institute of Scientific and Technical Information of China (English)

    SUN; Liuquan(孙六全); WU; Guofu(吴国富)

    2002-01-01

    In the KozioI-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studen tized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.

  17. Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind

    CERN Document Server

    Fucci, Guglielmo

    2014-01-01

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

  18. An asymptotic model of the F layer

    Science.gov (United States)

    Oliver, W. L.

    2012-01-01

    A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.

  19. Einstein Constraints on Asymptotically Euclidean Manifolds

    CERN Document Server

    Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.

    2000-01-01

    We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.

  20. PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    FEIGUIHUA; QIUQINGJIU

    1997-01-01

    The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.

  1. Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity

    CERN Document Server

    Gonzalez, John B

    2009-01-01

    We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schr\\"odinger (NLS) equations $iu_t + u_{xx} \\pm |u|^2 u = 0$ in classes of smooth functions that admit an asymptotic expansion at infinity in decreasing powers of $x$. We show that an asymptotic solution differs from a genuine solution by a Schwartz class function which solves a generalized version of the NLS equation. The latter equation is solved by discretization methods. The proofs closely follow previous work done by the author and others on the Korteweg-De Vries (KdV) equation and the modified KdV equations.

  2. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    Liu, Dayan

    2012-08-01

    Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

  3. Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

    CERN Document Server

    Navas, Luis M; Varona, Juan L

    2011-01-01

    We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\\mathcal{B}_{n}(x;\\lambda)$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. These results are transferred to the Apostol-Euler polynomials $\\mathcal{E}_{n}(x;\\lambda)$ via a simple relation linking them to the Apostol-Bernoulli polynomials.

  4. Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach

    Institute of Scientific and Technical Information of China (English)

    Dan DAI; Roderick WONG

    2007-01-01

    In this paper, we study the asymptotics of the Krawtchouk polynomials KnN(z;p,q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c ∈ (0, 1) as n →∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p;in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.

  5. On the Expansions in Spin Foam Cosmology

    CERN Document Server

    Hellmann, Frank

    2011-01-01

    We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expan- sion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.

  6. Penrose type inequalities for asymptotically hyperbolic graphs

    CERN Document Server

    Dahl, Mattias; Sakovich, Anna

    2013-01-01

    In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.

  7. Asymptotic properties of random matrices and pseudomatrices

    CERN Document Server

    Lenczewski, Romuald

    2010-01-01

    We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.

  8. Universal asymptotic umbrella for hydraulic fracture modeling

    CERN Document Server

    Linkov, Aleksandr M

    2014-01-01

    The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.

  9. Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

    Institute of Scientific and Technical Information of China (English)

    王启华; 荆炳义

    2000-01-01

    Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.

  10. Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.

  11. ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin

    2006-01-01

    Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.

  12. Asymptotic Safety, Emergence and Minimal Length

    CERN Document Server

    Percacci, R

    2010-01-01

    There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.

  13. Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials

    Directory of Open Access Journals (Sweden)

    Xin Wang

    2014-01-01

    Full Text Available An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.

  14. Asymptotic Solutions of the Kinetic Boltzmann Equation, Multicomponent Non-equilibrium Gas Dynamics and Turbulence

    CERN Document Server

    Serov, S A

    2013-01-01

    In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.

  15. Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids

    CERN Document Server

    Alho, Artur; Uggla, Claes

    2015-01-01

    We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor' solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve th...

  16. Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters

    Science.gov (United States)

    Bringmann, Kathrin; Folsom, Amanda; Milas, Antun

    2017-01-01

    Motivated by recent developments in the representation theory of vertex algebras and conformal field theory, we prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable τ tends to 0 along the imaginary axis, and the elliptic variable z is unrestricted in the complex plane. We observe that these functions exhibit Stokes' phenomenon—the asymptotic behavior of these functions sharply differs depending on where the elliptic variable z is located within the complex plane. We apply our results to study the asymptotic expansions of regularized characters and quantum dimensions of the (1, p)-singlet W-algebra modules important in logarithmic conformal field theory. This, in particular, recovers and extends several results from the work of T. Creutzig et al. [Int. Math. Res. Not. (2016); e-print arXiv:1411.3282] pertaining to regularized quantum dimensions.

  17. Langmuir probe study of plasma expansion in pulsed laser ablation

    DEFF Research Database (Denmark)

    Hansen, T.N.; Schou, Jørgen; Lunney, J.G.

    1999-01-01

    Langmuir probes were used to monitor the asymptotic expansion of the plasma produced by the laser ablation of a silver target in a vacuum. The measured angular and temporal distributions of the ion flux and electron temperature were found to be in good agreement with the self-similar isentropic...... and adiabatic solution of the gas dynamics equations describing the expansion. The value of the adiabatic index gamma was about 1.25, consistent with the ablation plume being a low temperature plasma....

  18. Asymptotic Evolution of Random Unitary Operations

    CERN Document Server

    Novotny, J; Jex, I

    2009-01-01

    We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

  19. The Lorentzian proper vertex amplitude: Asymptotics

    CERN Document Server

    Engle, Jonathan; Zipfel, Antonia

    2015-01-01

    In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.

  20. Hermite polynomials and quasi-classical asymptotics

    Energy Technology Data Exchange (ETDEWEB)

    Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)

    2014-04-15

    We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.

  1. Nonsymmetric gravity does have acceptable global asymptotics

    CERN Document Server

    Cornish, N J

    1994-01-01

    "Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.

  2. Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions

    Indian Academy of Sciences (India)

    BISWAJYOTI SAHA

    2016-08-01

    For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.

  3. Right tail expansion of Tracy-Widom beta laws

    CERN Document Server

    Borot, Gaëtan

    2011-01-01

    Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail Tracy-Widom beta laws, for all positive beta, by studying the double scaling limit.

  4. The trouble with asymptotically safe inflation

    CERN Document Server

    Fang, Chao

    2013-01-01

    In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.

  5. Asymptotic forms for hard and soft edge general $\\beta$ conditional gap probabilities

    CERN Document Server

    Forrester, Peter J

    2011-01-01

    An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \\ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\\beta$ to $4/\\beta$.

  6. Asymptotic forms for hard and soft edge general {beta} conditional gap probabilities

    Energy Technology Data Exchange (ETDEWEB)

    Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Witte, Nicholas S., E-mail: nsw@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)

    2012-06-21

    An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix {beta}-ensembles. The conditioning is that there are n eigenvalues in the gap, with n Much-Less-Than |t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating {beta} to 4/{beta}.

  7. Asymptotic forms for hard and soft edge general β conditional gap probabilities

    Science.gov (United States)

    Forrester, Peter J.; Witte, Nicholas S.

    2012-06-01

    An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix β-ensembles. The conditioning is that there are n eigenvalues in the gap, with n≪|t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions — which are for the logarithm of the gap probabilities — are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating β to 4/β.

  8. Higher order asymptotic fields for mode Ⅰ crack in functionally gradient material

    Institute of Scientific and Technical Information of China (English)

    DAI Yao; YAN Xiu-fa

    2005-01-01

    Higher order stress fields for a mode Ⅰ crack perpendicular to the direction of property variation in a functionally gradient material(FGM), which has an exponential variation of elastic modulus along the gradient direction, were obtained through an asymptotic analysis. The Poisson's ratio of the FGMs was assumed to be constant throughout the analysis. The first five terms in the asymptotic expansions of crack tip stress fields were derived to bring out the influence of nonhomogeneity on the structure of the stress field explicitly. The analysis reveals that only the higher order terms in the expansion are influenced by the material nonhomogeneity. Moreover, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for the nonhomogeneity effects on the structure of crack tip stress fields.

  9. Asymptotic Symmetries in de Sitter and Inflationary Spacetimes

    CERN Document Server

    Ferreira, Ricardo Z; Sloth, Martin S

    2016-01-01

    Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, $\\langle0| 0'\\rangle$, between the unperturbed de Sitter vacuum $|0\\rangle$, and the state $| 0'\\rangle$ obtained by acting $\\mathcal{N}$ times with the charge. We show that when $\\mathcal{N}\\to M_p^2/H^2$ this overlap receives order one corrections and $\\langle0| 0'\\rangle\\...

  10. On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations

    Science.gov (United States)

    Babin, A.; Mahalov, A.; Nicolaenko, B.; Zhou, Y.

    1997-01-01

    Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.

  11. Higher-order semiclassical energy expansions for potentials with non-integer powers

    Indian Academy of Sciences (India)

    Asiri Nanayakkara

    2003-10-01

    In this paper, we present a semiclassical eigenenergy expansion for the potential || when is a positive rational number of the form 2/ ( is a positive integer and is an odd positive integer). Remarkably, this expansion is found to be identical to the WKB expansion obtained for the potential (-even), if 2/ is replaced by . Taking the limit → 2 of the above expansion, we obtain an explicit asymptotic energy expansion of symmetric odd power potentials ||2+1 (-positive integer). We then show how to develop approximate semiclassical expansions for potentials || when is any positive real number.

  12. Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations

    Science.gov (United States)

    Bas, Erdal; Ozarslan, Ramazan

    2016-06-01

    In this study, Sturm-Liouville problem with variable coefficient, potential function q (n), for difference equation is considered. The representation of solutions is obtained by variation of parameters method for two different initial value problems and trigonometric solutions are found by means of complex characteristic roots. It is proved that these results hold the equation by using summation by parts method. Two estimations of asymptotic expansion of the solutions are established.

  13. Jacobi-Sobolev Orthogonal Polynomials: Asymptotics for N-Coherence of Measures

    Directory of Open Access Journals (Sweden)

    Marcellán Francisco

    2011-01-01

    Full Text Available Let us introduce the Sobolev-type inner product , where and , , with and for all A Mehler-Heine-type formula and the inner strong asymptotics on as well as some estimates for the polynomials orthogonal with respect to the above Sobolev inner product are obtained. Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.

  14. Relations between asymptotic and Fredholm representations

    CERN Document Server

    Manuilov, V M

    1997-01-01

    We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.

  15. The optimal homotopy asymptotic method engineering applications

    CERN Document Server

    Marinca, Vasile

    2015-01-01

    This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...

  16. Nanofluid surface wettability through asymptotic contact angle.

    Science.gov (United States)

    Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian

    2011-03-15

    This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.

  17. Asymptotic analysis of outwardly propagating spherical flames

    Institute of Scientific and Technical Information of China (English)

    Yun-Chao Wu; Zheng Chen

    2012-01-01

    Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.

  18. On generalized Nariai solutions and their asymptotics

    CERN Document Server

    Beyer, Florian

    2009-01-01

    In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.

  19. Asymptotics of a horizontal liquid bridge

    Science.gov (United States)

    Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.

    2016-04-01

    This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.

  20. Asymptotic stability of singularly perturbed differential equations

    Science.gov (United States)

    Artstein, Zvi

    2017-02-01

    Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.

  1. Topological Expansion in the Complex Cubic Log-Gas Model: One-Cut Case

    Science.gov (United States)

    Bleher, Pavel; Deaño, Alfredo; Yattselev, Maxim

    2016-09-01

    We prove the topological expansion for the cubic log-gas partition function Z_N(t)= int _Γ \\cdots int _Γ prod _{1≤ jtopological expansion for log Z_N(t) in the one-cut phase region. The proof is based on the Riemann-Hilbert approach to semiclassical asymptotic expansions for the associated orthogonal polynomials and the theory of S-curves and quadratic differentials.

  2. Asymptotic Distributions for Tests of Combined Significance.

    Science.gov (United States)

    Becker, Betsy Jane

    This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…

  3. Asymptotic symmetry algebra of conformal gravity

    CERN Document Server

    Irakleidou, M

    2016-01-01

    We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.

  4. An asymptotically optimal nonparametric adaptive controller

    Institute of Scientific and Technical Information of China (English)

    郭雷; 谢亮亮

    2000-01-01

    For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.

  5. The conformal approach to asymptotic analysis

    CERN Document Server

    Nicolas, Jean-Philippe

    2015-01-01

    This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling.

  6. Couplings and Asymptotic Exponentiality of Exit Times

    Science.gov (United States)

    Brassesco, S.; Olivieri, E.; Vares, M. E.

    1998-10-01

    The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.

  7. Asymptotically periodic solutions of Volterra integral equations

    Directory of Open Access Journals (Sweden)

    Muhammad N. Islam

    2016-03-01

    Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

  8. On the Asymptotic Distribution of Signal Fraction

    CERN Document Server

    Volobouev, Igor

    2016-01-01

    Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.

  9. Resonance asymptotics in the generalized Winter model

    CERN Document Server

    Exner, P; Exner, Pavel; Fraas, Martin

    2006-01-01

    We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.

  10. Asymptotic iteration approach to supersymmetric bistable potentials

    Institute of Scientific and Technical Information of China (English)

    H. Ciftci; O. ozer; P. Roy

    2012-01-01

    We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.

  11. First-order correction terms in the weak-field asymptotic theory of tunneling ionization in many-electron systems

    Science.gov (United States)

    Trinh, Vinh H.; Tolstikhin, Oleg I.; Morishita, Toru

    2016-10-01

    The many-electron weak-field asymptotic theory of tunneling ionization including the first-order correction terms in the asymptotic expansion of the ionization rate in field strength was highlighted in our recent fast track communication (Trinh et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 061003) by demonstrating its performance for two-electron atoms. Here we present a thorough derivation of the first-order terms omitted in the previous publication and provide additional numerical illustrations of the theory.

  12. Existence and convergence of fixed points for mappings of asymptotically nonexpansive type in uniformly convex W-hyperbolic spaces

    Directory of Open Access Journals (Sweden)

    Cui Yunan

    2011-01-01

    Full Text Available Abstract Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0 spaces. In this article, we discuss the existence of fixed points and demiclosed principle for mappings of asymptotically non-expansive type in uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity. We also obtain a Δ-convergence theorem of Krasnoselski-Mann iteration for continuous mappings of asymptotically nonexpansive type in CAT(0 spaces. MSC: 47H09; 47H10; 54E40

  13. The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

    Science.gov (United States)

    Neill, Duff

    2017-01-01

    We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

  14. INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION

    Directory of Open Access Journals (Sweden)

    A. I. Popov

    2015-09-01

    Full Text Available Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain. To find some term of the series, the non-homogeneous Sturm-Liouville problem with the inhomogeneity depending on the previous term needs to be solved. At the same time, the corresponding homogeneous problem has a non-trivial solution. Hence, the solvability problem occures for the non-homogeneous Sturm-Liouville problem for functions or formal power series. The paper deals with creation of such asymptotic expansions. Method. To prove the necessary condition, we use conventional integration technique of the whole equation and boundary conditions. To prove the sufficient condition, we create an appropriate Cauchy problem (which is always solvable and analyze its solution. We deal with the general case of power series and make no hypotheses about the series convergence. Main Result. Necessary and sufficient conditions of solvability for the non-homogeneous Sturm-Liouville problem in general case for formal power series are proved in the paper. As a particular case, the result is valid for functions instead of formal power series. Practical Relevance. The result is usable at creation of the solutions for partial differential equation in the form of power series. The result is general and is applicable to particular cases of such solutions, e.g., to asymptotic series or to functions (convergent power series.

  15. Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models

    Science.gov (United States)

    Isaacson, Samuel A.; Mauro, Ava J.; Newby, Jay

    2016-10-01

    The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013), 10.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.

  16. Perturbative expansions for area-preserving maps

    Energy Technology Data Exchange (ETDEWEB)

    Servizi, G.; Turchetti, G.

    1986-10-11

    The structure of perturbation series for area-preserving maps is investigated. A basically different behaviour is found between the Birkhoff series, which formally conjugate with circles all the orbits in a neighbourhood of the origin, and the series which map into circles the individual invariant curves with fixed diophantine winding number. The former series exhibit an asymptotic character, the latter a convergent one, as one should expect from the KAM theorem. The source of this difference is found to be the different way in which the contributions of the relevant resonances propagate. In the first case, if epsilon is the size of the divisor associated to a resonance M/N, then at each order n>N an epsilon/sup -1/ contribution occurs, in the second case subtle cancellations provide a new epsilon/sup -1/ only when a harmonic (that is n=pN) is reached. This precise asymptotic statement and the properties of the relevant resonances obtained from the continued fraction expansion allow us, in the case of quadratic irrationals, to understand the limit process which leads to divergence or convergence. In the divergent case the asymptotic properties of the series are exhaustively described.

  17. Locally Asymptotic-norming Property and Kadec Property

    Institute of Scientific and Technical Information of China (English)

    王建华

    2002-01-01

    In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.

  18. Theory of tunneling ionization of molecules: Weak-field asymptotics including dipole effects

    DEFF Research Database (Denmark)

    Tolstikhin, Oleg I.; Morishita, Toru; Madsen, Lars Bojer

    2011-01-01

    The formulation of the parabolic adiabatic expansion approach to the problem of ionization of atomic systems in a static electric field, originally developed for the axially symmetric case [ Phys. Rev. A 82 023416 (2010)], is generalized to arbitrary potentials. This approach is used to rederive...... the asymptotic theory of tunneling ionization in the weak-field limit. In the atomic case, the resulting formulas for the ionization rate coincide with previously known results. In addition, the present theory accounts for the possible existence of a permanent dipole moment of the unperturbed system and, hence......, applies to polar molecules. Accounting for dipole effects constitutes an important difference of the present theory from the so-called molecular Ammosov-Delone-Krainov theory. The theory is illustrated by comparing exact and asymptotic results for a set of model polar molecules and a realistic molecular...

  19. On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

    Institute of Scientific and Technical Information of China (English)

    LIU Hong-Zhun; PAN Zu-Liang; LI Peng

    2006-01-01

    In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

  20. Asymptotical stability of stochastic neural networks with multiple time-varying delays

    Science.gov (United States)

    Zhou, Xianghui; Zhou, Wuneng; Dai, Anding; Yang, Jun; Xie, Lili

    2015-03-01

    The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

  1. Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures

    Science.gov (United States)

    Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese

    2017-04-01

    In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1-204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally, we illustrate the behavior of the model with various numerical simulations.

  2. An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit

    Science.gov (United States)

    Wang, Li; Yan, Bokai

    2016-05-01

    We present a new asymptotic-preserving scheme for the linear Boltzmann equation which, under appropriate scaling, leads to a fractional diffusion limit. Our scheme rests on novel micro-macro decomposition to the distribution function, which splits the original kinetic equation following a reshuffled Hilbert expansion. As opposed to classical diffusion limit, a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter. Our idea is, while solving the macro-micro part in a truncated velocity domain (truncation only depends on numerical accuracy), to incorporate an integrated tail over the velocity space that is beyond the truncation, and its major component can be precomputed once with any accuracy. Such an addition is essential to drive the solution to the correct asymptotic limit. Numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes.

  3. Form factor approach to the asymptotic behavior of correlation functions in critical models

    CERN Document Server

    Kitanine, N; Maillet, J M; Slavnov, N A; Terras, V

    2011-01-01

    We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Luttinger liquid approach, the conformal field theory predictions and our previous analysis of the correlation functions from their multiple integral representations. We argue that our scheme applies to a general class of non-integrable quantum critical models as well.

  4. Asymptotic dynamics of three-dimensional gravity

    CERN Document Server

    Donnay, Laura

    2016-01-01

    These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\\mathbb R)\\times SL(2,\\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.

  5. Asymptotically anti-de Sitter Proca Stars

    CERN Document Server

    Duarte, Miguel

    2016-01-01

    We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.

  6. Asymptotic Behaviour Near a Nonlinear Sink

    CERN Document Server

    Calder, Matt S

    2010-01-01

    In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.

  7. Theorems for Asymptotic Safety of Gauge Theories

    CERN Document Server

    Bond, Andrew D

    2016-01-01

    We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.

  8. Asymptotic Existence of Nearly Kirkman Systems

    Institute of Scientific and Technical Information of China (English)

    沈灏; 储文松

    1994-01-01

    It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.

  9. Asymptotic analysis of the Forward Search

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Bent

    The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made....... The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure....

  10. The self consistent expansion applied to the factorial function

    Science.gov (United States)

    Cohen, Alon; Bialy, Shmuel; Schwartz, Moshe

    2016-12-01

    Most of the interesting systems in statistical physics can be described as nonlinear stochastic field theories. A common feature in the theoretical study of such systems is that ordinary perturbation theory seldom works. On the other hand, there exists a useful tool for the study of systems of that generic nature. That tool, the Self Consistent Expansion (SCE) is technically similar to the ordinary perturbation expansion, in the sense that it is an expansion around a solvable problem. The key point which distinguishes the SCE from an ordinary perturbation expansion, is that the small parameter of the expansion is adjustable and determined inherently by optimization of the expansion. Therefore, it allows the adaptive SCE to remain accurate relative to the inflexible ordinary expansion. The goal of the present paper is to present the SCE by applying it to a well-known zero dimensional problem. We choose the evaluation of the factorial function, x!, as the test case for the SCE, because the Stirling approximation for that function is one of the best known asymptotic expansions, with a very wide use in statistical physics. We show that the SCE approximation holds for small and even negative arguments of the factorial function, where the Stirling expansion fails miserably. It does so without paying any penalty at high values of the argument, where the Stirling formula is excellent. We present numerical as well as analytic SCE approximations of the factorial function.

  11. Asymptotically flat space-times: an enigma

    Science.gov (United States)

    Newman, Ezra T.

    2016-07-01

    We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.

  12. asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.

    Science.gov (United States)

    Haller, Benjamin C; Messer, Philipp W

    2017-03-24

    The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.

  13. Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities

    Directory of Open Access Journals (Sweden)

    Xionghua Wu

    2012-01-01

    Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .

  14. Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.

    2010-12-15

    Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)

  15. Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Terras, V. [CNRS, ENS Lyon (France). Lab. de Physique

    2010-12-15

    We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)

  16. Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schr\\"{o}dinger model

    CERN Document Server

    Kozlowski, K K

    2011-01-01

    We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schr\\"{o}dinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics.

  17. On skin expansion.

    Science.gov (United States)

    Pamplona, Djenane C; Velloso, Raquel Q; Radwanski, Henrique N

    2014-01-01

    This article discusses skin expansion without considering cellular growth of the skin. An in vivo analysis was carried out that involved expansion at three different sites on one patient, allowing for the observation of the relaxation process. Those measurements were used to characterize the human skin of the thorax during the surgical process of skin expansion. A comparison between the in vivo results and the numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin of the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and incompressible membrane. When the skin is extended, such as with expanders, the collagen fibers are also extended and cause stiffening in the skin, which results in increasing resistance to expansion or further stretching. We observed this phenomenon as an increase in the parameters as subsequent expansions continued. The number and shape of the skin expanders used in expansions were also studied, both mathematically and experimentally. The choice of the site where the expansion should be performed is discussed to enlighten problems that can lead to frustrated skin expansions. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin by expansion. To our knowledge, this study has provided results that considerably improve our understanding of the behavior of human skin under expansion.

  18. Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size

    Directory of Open Access Journals (Sweden)

    Guy Louchard

    2017-01-01

    Full Text Available Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and Cauchy's integral formula, asymptotic results for the number $T(n,m,k$ of partitions of $n$ labeled objects with $m$ blocks of fixed size $k$. We analyze the central and non-central region. In the region $m=n/k-n^\\al,\\quad 1>\\al>1/2$, we analyze the dependence of $T(n,m,k$ on $\\al$. This paper fits within the framework of Analytic Combinatorics.

  19. Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem

    Institute of Scientific and Technical Information of China (English)

    TANG Rong-rong

    2009-01-01

    Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).

  20. A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches

    Science.gov (United States)

    Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.

    2013-10-01

    This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.

  1. An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering

    Science.gov (United States)

    He, Ji-Huan

    This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.

  2. Asymptotic key generation rates with phase-randomized coherent light by decoy method

    CERN Document Server

    Hayashi, M

    2007-01-01

    The asymptotic key generation (AKG) rates of quantum key distribution (QKD) with the decoy method are discussed in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of intensities. For this purpose, we derive a useful convex expansion of the phase-randomized coherent state. We also derive upper bounds of AKG rates on a natural and concrete channel model. Using these upper bounds, we numerically check that the AKG rates are almost saturated when the number of intensities is three.

  3. On q-Gevrey Asymptotics for Singularly Perturbed q-Difference-Differential Problems with an Irregular Singularity

    Directory of Open Access Journals (Sweden)

    Alberto Lastra

    2012-01-01

    in the complex domain which generalizes a previous result by Malek in (2011. First, we construct solutions defined in open q-spirals to the origin. By means of a q-Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the q-Gevrey asymptotic expansion (of certain type of the actual solutions.

  4. Asymptotic problems for stochastic partial differential equations

    Science.gov (United States)

    Salins, Michael

    Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

  5. Taming perturbative divergences in asymptotically safe gravity

    Energy Technology Data Exchange (ETDEWEB)

    Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)

    2010-01-01

    We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.

  6. Lectures on the asymptotic theory of ideals

    CERN Document Server

    Rees, D

    1988-01-01

    In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work

  7. BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES

    Institute of Scientific and Technical Information of China (English)

    Liu Yue; Wang Zhengping

    2007-01-01

    This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N > 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).

  8. The ADM mass of asymptotically flat hypersurfaces

    CERN Document Server

    de Lima, Levi Lopes

    2011-01-01

    We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.

  9. Asymptotics for a generalization of Hermite polynomials

    CERN Document Server

    Alfaro, M; Peña, A; Rezola, M L

    2009-01-01

    We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.

  10. Asymptotic curved interface models in piezoelectric composites

    Science.gov (United States)

    Serpilli, Michele

    2016-10-01

    We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.

  11. Vacuum Potential and its Asymptotic Variation

    Science.gov (United States)

    Dahal, Pravin

    2016-09-01

    The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.

  12. ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

    Institute of Scientific and Technical Information of China (English)

    Zeng Luchuan

    2006-01-01

    This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Ban ach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.

  13. Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation

    CERN Document Server

    Lannes, David

    2007-01-01

    A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \\cite{matsuno3} and Choi \\cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equati...

  14. Asymptotic solitons for a third-order Korteweg-de Vries equation

    Energy Technology Data Exchange (ETDEWEB)

    Marchant, T.R. E-mail: tim_marchant@uow.edu.au

    2004-10-01

    Solitary wave interaction for a higher-order version of the Korteweg-de Vries (KdV) equation is considered. The equation is obtained by retaining third-order terms in the perturbation expansion, where for the KdV equation only first-order terms are retained. The third-order KdV equation can be asymptotically transformed to the KdV equation, if the third-order coefficients satisfy a certain algebraic relationship. The third-order two-soliton solution is derived using the transformation. The third-order phase shift corrections are found and it is shown that the collision is asymptotically elastic. The interaction of two third-order solitary waves is also considered numerically. Examples of an elastic and an inelastic collision are both considered. For the elastic collision (which satisfies the algebraic relationship) the numerical results confirm the theoretical predictions, in particular there is good agreement found when comparing the third-order phase shift corrections. For the inelastic collision (which does not satisfy the algebraic relationship) an oscillatory wavetrain is produced by the interacting solitary waves. Also, the third-order phase shift corrections are found numerically for a range of solitary wave amplitudes. An asymptotic mass-conservation law is used to test the finite-difference scheme for the numerical solutions. In general, mass is not conserved by the third-order KdV equation, but varies during the interaction of the solitary waves.

  15. Vacuum polarization in asymptotically Lifshitz black holes

    CERN Document Server

    Quinta, Gonçalo M; Lemos, José P S

    2016-01-01

    There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to...

  16. Vacuum polarization in asymptotically Lifshitz black holes

    Science.gov (United States)

    Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.

    2016-06-01

    There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.

  17. Asymptotic behaviour of electro-$\\Lambda$ spacetimes

    CERN Document Server

    Saw, Vee-Liem

    2016-01-01

    We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...

  18. Lattice Quantum Gravity and Asymptotic Safety

    CERN Document Server

    Laiho, J; Coumbe, D; Du, D; Neelakanta, J T

    2016-01-01

    We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but not identical to, four-dimensional diffeomorphism invariance. After introducing and fine-tuning a non-trivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue tha...

  19. Relaxing the parity conditions of asymptotically flat gravity

    Science.gov (United States)

    Compère, Geoffrey; Dehouck, François

    2011-12-01

    Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.

  20. Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity

    Science.gov (United States)

    Higuera, F. J.; Jimenez, J.; Linan, A.

    1996-01-01

    The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.

  1. Liapunov structure and asymptotic expressions of linear differential systems

    Institute of Scientific and Technical Information of China (English)

    高维新

    1996-01-01

    With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.

  2. Coulomb string tension, asymptotic string tension, and the gluon chain

    Science.gov (United States)

    Greensite, Jeff; Szczepaniak, Adam P.

    2015-02-01

    We compute, via numerical simulations, the nonperturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.

  3. Asymptotic variance of grey-scale surface area estimators

    DEFF Research Database (Denmark)

    Svane, Anne Marie

    Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....

  4. Expansion by eigenvectors in case of simple eigenvalues of singular differential operator

    Directory of Open Access Journals (Sweden)

    O. V. Makhnei

    2011-06-01

    Full Text Available The asymptotic formulas with large values of parameter for solutions of singular differential equation allow us to estimate Green's function of the boundary-value problem. With the help of this estimation the expansion of singular dierential operator by eigenvectors in the case of simple eigenvalues is constructed.

  5. The Nonlinear Asymptotic Stage of the Rayleigh-Taylor Instability with Wide Bubbles and Narrowing Spikes

    CERN Document Server

    Cherniavski, V M

    2013-01-01

    The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The asymptotic solution describes the flow in which a bubble rises with constant speed and the "tongue" is in free fall. The outer expansion is stationary, but the inner one depends on time. It is shown that the solution exists within the same range of Froude number obtained previously by Vanden-Broeck (1984a,b). The Froude number and the solution depend on the initial energy of the disturbance. At the top of the bubble, the derivative of the free-surface curvature has a discontinuity when the Froude number is not equal to 0.23. This makes it possible to identify the choice of the solution obtained in a number of studies with the presence of an artificial numerical surface tension. The first correction term in the neighborhood of the tongue is obtained when large surface tensio...

  6. Introduction to Asymptotic Giant Branch Stars

    Science.gov (United States)

    El Eid, Mounib F.

    2016-04-01

    A brief introduction on the main characteristics of the asymptotic giant branch stars (briefly: AGB) is presented. We describe a link to observations and outline basic features of theoretical modeling of these important evolutionary phases of stars. The most important aspects of the AGB stars is not only because they are the progenitors of white dwarfs, but also they represent the site of almost half of the heavy element formation beyond iron in the galaxy. These elements and their isotopes are produced by the s-process nucleosynthesis, which is a neutron capture process competing with the β- radioactive decay. The neutron source is mainly due to the reaction 13C(α,n)16O reaction. It is still a challenging problem to obtain the right amount of 13 C that can lead to s-process abundances compatible with observation. Some ideas are presented in this context.

  7. Dimensionally reduced gravity theories are asymptotically safe

    Energy Technology Data Exchange (ETDEWEB)

    Niedermaier, Max E-mail: max@phys.univ-tours.fr

    2003-11-24

    4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the 'area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.

  8. Asymptotic stability of steady compressible fluids

    CERN Document Server

    Padula, Mariarosaria

    2011-01-01

    This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...

  9. Asymptotic Linear Stability of Solitary Water Waves

    Science.gov (United States)

    Pego, Robert L.; Sun, Shu-Ming

    2016-12-01

    We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.

  10. Holographic Renormalization of Asymptotically Flat Gravity

    CERN Document Server

    Park, Miok

    2012-01-01

    We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.

  11. Asymptotic sampling formulae for Lambda-coalescents

    CERN Document Server

    Berestycki, Julien; Limic, Vlada

    2012-01-01

    We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.

  12. Asymptotic analysis of ultra-relativistic charge

    CERN Document Server

    Burton, D A; Tucker, R W; Burton, David A.; Gratus, Jonathan; Tucker, Robin W.

    2006-01-01

    This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneo...

  13. Universality and asymptotic scaling in drilling percolation

    Science.gov (United States)

    Grassberger, Peter

    2017-01-01

    We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.

  14. Asymptotic Behavior of Excitable Cellular Automata

    CERN Document Server

    Durrett, R; Durrett, Richard; Griffeath, David

    1993-01-01

    Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...

  15. The asymptotic safety scenario in quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)

    2011-07-01

    Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.

  16. Asymptotic methods in mechanics of solids

    CERN Document Server

    Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi

    2015-01-01

    The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...

  17. Grassmann scalar fields and asymptotic freedom

    Energy Technology Data Exchange (ETDEWEB)

    Palumbo, F. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)

    1996-03-01

    The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.

  18. Modeling of nanoplastic by asymptotic homogenization method

    Institute of Scientific and Technical Information of China (English)

    张为民; 何伟; 李亚; 张平; 张淳源

    2008-01-01

    The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.

  19. Chiral fermions in asymptotically safe quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)

    2016-05-15

    We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)

  20. Asymptotic representation of relaxation oscillations in lasers

    CERN Document Server

    Grigorieva, Elena V

    2017-01-01

    In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

  1. Motion Parallax is Asymptotic to Binocular Disparity

    CERN Document Server

    Stroyan, Keith

    2010-01-01

    Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.

  2. Chiral fermions in asymptotically safe quantum gravity

    CERN Document Server

    Meibohm, Jan

    2016-01-01

    We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.

  3. Asymptotically thermal responses for smoothly switched detectors

    CERN Document Server

    Fewster, Christopher J; Louko, Jorma

    2015-01-01

    Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.

  4. Foundation and generalization of the expansion by regions

    CERN Document Server

    Jantzen, Bernd

    2011-01-01

    The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole integration domain. This method has been applied successfully to many complicated loop integrals, but a general proof for its correctness has still been missing. This paper shows how the expansion by regions manages to reproduce the exact result correctly in an expanded form and clarifies the conditions on the choice and completeness of the considered regions. A generalized expression for the full result is presented that involves additional overlap contributions. These extra pieces normally yield scaleless integrals which are consistently set to zero, but they may be needed depending on the choice of the regularization scheme. While the main proofs and formulae are presented in a general and concise form, a large portion of the paper is filled with simple, pedagogical one-loo...

  5. An asymptotic solution of large-N QCD

    Directory of Open Access Journals (Sweden)

    Bochicchio Marco

    2014-01-01

    Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.

  6. Asymptotic symmetries of de Sitter space-time

    Energy Technology Data Exchange (ETDEWEB)

    Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)

    1981-01-01

    The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.

  7. Asymptotic Hyperstability of Dynamic Systems with Point Delays

    Directory of Open Access Journals (Sweden)

    M. De la Sen

    2005-01-01

    Full Text Available It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.

  8. Error estimates in horocycle averages asymptotics: challenges from string theory

    NARCIS (Netherlands)

    Cardella, M.A.

    2010-01-01

    For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth

  9. Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System

    Directory of Open Access Journals (Sweden)

    Yue-Wen Cheng

    2013-01-01

    Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.

  10. Small-x asymptotics of structure function $g_2$

    CERN Document Server

    Ermolaev, B I

    1997-01-01

    Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.

  11. Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

    Institute of Scientific and Technical Information of China (English)

    Wei Shi-long; Guo Wei-ping

    2015-01-01

    The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.

  12. Global asymptotic stability of cellular neural networks with multiple delays

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.

  13. Spatial assortment of mixed propagules explains the acceleration of range expansion.

    Science.gov (United States)

    Ramanantoanina, Andriamihaja; Ouhinou, Aziz; Hui, Cang

    2014-01-01

    Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

  14. Spatial assortment of mixed propagules explains the acceleration of range expansion.

    Directory of Open Access Journals (Sweden)

    Andriamihaja Ramanantoanina

    Full Text Available Range expansion of spreading organisms has been found to follow three types: (i linear expansion with a constant rate of spread; (ii bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

  15. Asymptotic admissibility of priors and elliptic differential equations

    CERN Document Server

    Hartigan, J A

    2010-01-01

    We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.

  16. Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

    CERN Document Server

    Hod, Shahar

    2015-01-01

    The spheroidal harmonics $S_{lm}(\\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues $\\{A_{lm}(c)\\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\\to\\infty$ with a fixed value of $c$, or to the complementary regime $|c|\\to\\infty$ with a fixed value of $m$. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both $m$ and $c$. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit $m\\to\\infty$ and $|c|\\to\\infty$ with a fixed $m/c$ ratio.

  17. On the asymptotics of the α-Farey transfer operator

    Science.gov (United States)

    Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.

    2015-01-01

    We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.

  18. Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.

  19. Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

    Science.gov (United States)

    Hod, Shahar

    2015-06-01

    The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.

  20. Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals

    CERN Document Server

    Pan, Chi-Ruei; Chai, Jeng-Da

    2013-01-01

    Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is sig...

  1. Negative thermal expansion

    Energy Technology Data Exchange (ETDEWEB)

    Barrera, G D [Departamento de QuImica, Universidad Nacional de la Patagonia SJB, Ciudad Universitaria, 9000 Comodoro Rivadavia (Argentina); Bruno, J A O [Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de QuImica Inorganica, AnalItica y QuImica FIsica, Pabellon 2, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Barron, T H K [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom); Allan, N L [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom)

    2005-02-02

    There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW{sub 2}O{sub 8} contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials. (topical review)

  2. Thermal Expansion "Paradox."

    Science.gov (United States)

    Fakhruddin, Hasan

    1993-01-01

    Describes a paradox in the equation for thermal expansion. If the calculations for heating a rod and subsequently cooling a rod are determined, the new length of the cool rod is shorter than expected. (PR)

  3. Truly Minimal Unification Asymptotically Strong Panacea ?

    CERN Document Server

    Aulakh, Charanjit S

    2002-01-01

    We propose Susy GUTs have a UV {\\it{attractor}} at $E\\sim \\Lambda_{cU} \\sim 10^{17} GeV $ where gauge symmetries ``confine'' forming singlet condensates at scales $E\\sim\\Lambda_{cU}$. The length $l_U\\sim \\Lambda_{cU}^{-1}$ characterizies the {\\it{size}} of gauge non- singlet particles yielding a picture dual to the Dual Standard model of Vachaspati. This Asymptotic Slavery (AS) fixed point is driven by realistic Fermion Mass(FM) Higgs content which implies AS. This defines a dynamical morphogenetic scenario dependent on the dynamics of UV strong N=1 Susy Gauge-Chiral(SGC) theories. Such systems are already understood in the AF case but ignored in the AS case. Analogy to the AFSGC suggests the perturbative SM gauge group of the Grand Desert confines at GUT scales i.e GUT symmetry is ``non-restored''. Restoration before confinement and self-inconsistency are the two other (less likely) logical possibilities. Truly Minimal (TM) SU(5) and SO(10) models with matter and FM Higgs only are defined; AM (adjoint multip...

  4. Asymptotic dynamics of inertial particles with memory

    CERN Document Server

    Langlois, Gabriel Provencher; Haller, George

    2014-01-01

    Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $\\mathcal O(\\epsilon)$-close to the fluid velocity, where $0<\\epsilon\\ll 1$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of existence and uniqueness of global solutions to the Maxey--Riley equation, a nonlinear system of fractional-order differential equ...

  5. Asymptotic Solutions of Serial Radial Fuel Shuffling

    Directory of Open Access Journals (Sweden)

    Xue-Nong Chen

    2015-12-01

    Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.

  6. Qualitative and Asymptotic Theory of Detonations

    KAUST Repository

    Faria, Luiz

    2014-11-09

    Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.

  7. Asymptotics, structure, and integration of sound-proof atmospheric flow equations

    Science.gov (United States)

    Klein, Rupert

    2009-07-01

    Relative to the full compressible flow equations, sound-proof models filter acoustic waves while maintaining advection and internal waves. Two well-known sound-proof models, an anelastic model by Bannon and Durran’s pseudo-incompressible model, are shown here to be structurally very close to the full compressible flow equations. Essentially, the anelastic model is obtained by suppressing ∂ t ρ in the mass continuity equation and slightly modifying the gravity term, whereas the pseudo-incompressible model results from dropping ∂ t p from the pressure equation. For length scales small compared to the density and pressure scale heights, the anelastic model reduces to the Boussinesq approximation, while the pseudo-incompressible model approaches the zero Mach number, variable density flow equations. Thus, for small scales, both models are asymptotically consistent with the full compressible flow equations, yet the pseudo-incompressible model is more general in that it remains valid in the presence of large density variations. For the relatively small density variations found in typical atmosphere-ocean flows, both models are found to yield very similar results, with deviations between models much smaller than deviations obtained when using different numerical schemes for the same model. This in agreement with Smolarkiewicz and Dörnbrack (Int J Numer Meth Fluids 56:1513-1519, 2007). Despite these useful properties, neither model can be derived by a low-Mach number asymptotic expansion for length scales comparable to the pressure scale height, i.e., for the regime they were originally designed for. Derivations of these models via scale analysis ignore an asymptotic time scale separation between advection and internal waves. In fact, only the classical Ogura and Phillips model, which assumes weak stratification of the order of the Mach number squared, can be obtained as a leading-order model from systematic low Mach number asymptotic analysis. Issues of formal

  8. Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries

    CERN Document Server

    Holst, Michael

    2014-01-01

    In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on S, similar to those analyzed previously by Dain (2004), by Maxwell (2004, 2005), and by Holst and Tsogtgerel (2013) as a model of black holes in various CMC settings, and by Holst, Meier, and Tsogtgerel (2013) in the setting of far-from-CMC solutions on compact manifolds with boundary. These "marginally trapped surface" Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region S are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assumi...

  9. A theoretical study of asymptotic boundary conditions for the numerical solutions of open-boundary static electromagnetic-field problems

    Institute of Scientific and Technical Information of China (English)

    马西奎; 韩社教

    2002-01-01

    Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.

  10. Asymptotic Solution of the Theory of Shells Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    I. V. Andrianov

    2007-01-01

    Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

  11. Asymptotic failure rate of a continuously monitored system

    Energy Technology Data Exchange (ETDEWEB)

    Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr

    2006-02-01

    This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.

  12. ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL

    Institute of Scientific and Technical Information of China (English)

    CUI Hengjian

    2005-01-01

    This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.

  13. Max-Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low Complexity Transceivers

    KAUST Repository

    Sifaou, Houssem

    2016-12-28

    This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with M antennas communicates with K single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which M and K grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per- UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.

  14. All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials

    CERN Document Server

    Borot, Gaëtan

    2012-01-01

    We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of the colored Jones polynomial is a the formal wave function of an integrable system whose semiclassical spectral curve S would be the SL_2(C) character variety of the knot (the A-polynomial), and is formulated in the framework of the topological recursion. It takes as starting point the proposal made recently by Dijkgraaf, Fuji and Manabe (who kept only the perturbative part of the wave function, and found some discrepancies), but it also contains the non-perturbative parts, and solves the discrepancy problem. These non-perturbative corrections are derivatives of Theta functions associated to S, but the expansion is still in powers of 1/N due to the special properties of A-polynomials. We provide a detailed check for the figure-eight knot and the once-punctured torus bundle...

  15. Novel Foraminal Expansion Technique

    Science.gov (United States)

    Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer

    2016-01-01

    The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460

  16. Robust methods and asymptotic theory in nonlinear econometrics

    CERN Document Server

    Bierens, Herman J

    1981-01-01

    This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

  17. Asymptotical Properties for Parabolic Systems of Neutral Type

    Institute of Scientific and Technical Information of China (English)

    CUI Bao-tong; HAN Mao-an

    2005-01-01

    Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.

  18. Semilocal density functional theory with correct surface asymptotics

    Science.gov (United States)

    Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio

    2016-03-01

    Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.

  19. Research on temperature profiles of honeycomb regenerator with asymptotic analysis

    Institute of Scientific and Technical Information of China (English)

    AI Yuan-fang; MEI Chi; HUANG Guo-dong; JIANG Shao-jian; CHEN Hong-rong

    2006-01-01

    An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.

  20. Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2016-01-01

    textabstractThe paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical

  1. Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds

    CERN Document Server

    An, Ok Song; Papadimitriou, Ioannis

    2016-01-01

    The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associat...

  2. Asymptotic distributions in the projection pursuit based canonical correlation analysis

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.

  3. Uniform gradient expansions

    Energy Technology Data Exchange (ETDEWEB)

    Giovannini, Massimo, E-mail: massimo.giovannini@cern.ch [Department of Physics, Theory Division, CERN, 1211 Geneva 23 (Switzerland); INFN, Section of Milan-Bicocca, 20126 Milan (Italy)

    2015-06-30

    Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.

  4. Uniform gradient expansions

    Directory of Open Access Journals (Sweden)

    Massimo Giovannini

    2015-06-01

    Full Text Available Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.

  5. Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems

    OpenAIRE

    Jouan, Philippe; Naciri, Said

    2012-01-01

    We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...

  6. Relaxing the Parity Conditions of Asymptotically Flat Gravity

    OpenAIRE

    Compère, Geoffrey; Dehouck, François

    2011-01-01

    Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincar\\'e transformations as well as supertranslations and logarithmic translations are associated wi...

  7. High frequency asymptotics of antenna/structure interactions

    OpenAIRE

    Coats, J.

    2002-01-01

    This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illuminat...

  8. Asymptotic freedom of Yang-Mills theory with gravity

    CERN Document Server

    Folkerts, Sarah; Pawlowski, Jan M

    2011-01-01

    We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.

  9. Asymptotic freedom of Yang-Mills theory with gravity

    Energy Technology Data Exchange (ETDEWEB)

    Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)

    2012-03-19

    We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.

  10. An asymptotically exact theory of smart sandwich shells

    CERN Document Server

    Le, Khanh Chau

    2016-01-01

    An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.

  11. Asymptotic behaviour for a diffusion equation governed by nonlocal interactions

    CERN Document Server

    Ovono, Armel Andami

    2010-01-01

    In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.

  12. An asymptotically exact theory of functionally graded piezoelectric shells

    CERN Document Server

    Le, Khanh Chau

    2016-01-01

    An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.

  13. ASYMPTOTIC BEHAVIOR OF ECKHOFF'S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined.Asymptotic behavior of approximate calculation of the so-called "jumps" is studied and asymptotic L2 constants of the rate of convergence of the method are computed.

  14. Asymptotical stability analysis of linear fractional differential systems

    Institute of Scientific and Technical Information of China (English)

    LI Chang-pin; ZHAO Zhen-gang

    2009-01-01

    It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts,electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.

  15. Asymptotic-induced numerical methods for conservation laws

    Science.gov (United States)

    Garbey, Marc; Scroggs, Jeffrey S.

    1990-01-01

    Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

  16. Asymptotic symmetries and charges in de Sitter space

    Energy Technology Data Exchange (ETDEWEB)

    Anninos, Dionysios; Ng, Gim Seng; Strominger, Andrew, E-mail: gng@fas.harvard.edu [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA 02138 (United States)

    2011-09-07

    The asymptotic symmetry group (ASG) at future null infinity (I{sup +}) of asymptotically four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I{sup +}. Finite charges are constructed for each choice of ASG generator together with a two-surface on I{sup +}. A conservation equation is derived relating the evolution of the charges with the radiation flux through I{sup +}.

  17. Asymptotic behaviour of extinction probability of interacting branching collision processes

    OpenAIRE

    Chen, Anyue; Li, Junping; Chen, Yiqing; Zhou, Dingxuan

    2014-01-01

    Although the exact expressions for the extinction probabilities of the Interacting Branching Collision Processes (IBCP) were very recently given by Chen et al. [4], some of these expressions are very complicated; hence, useful information regarding asymptotic behaviour, for example, is harder to obtain. Also, these exact expressions take very different forms for different cases and thus seem lacking in homogeneity. In this paper, we show that the asymptotic behaviour of these extr...

  18. Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

    Directory of Open Access Journals (Sweden)

    Zhinan Xia

    2014-01-01

    Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.

  19. Random attractors for asymptotically upper semicompact multivalue random semiflows

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.

  20. Asymptotic Analysis of Transport Equation in Annulus

    Science.gov (United States)

    Wu, Lei; Yang, Xiongfeng; Guo, Yan

    2016-09-01

    We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem in Bensoussan et al. (Publ Res Inst Math Sci 15:53-157, 1979) states that the solution can be approximated in L^{∞} by the sum of the interior solution and Knudsen layer derived from Milne problem. However, this result was disproved in Wu and Guo (Commun Math Phys 336:1473-1553, 2015) in a plate via a different boundary layer expansion with geometric correction. In this paper, we established the diffusive limit and provide a counterexample to Bensoussan et al. (1979) in non-convex domains.

  1. Small-time asymptotics of stopped L\\'evy bridges and simulation schemes with controlled bias

    CERN Document Server

    Figueroa-López, José E

    2012-01-01

    We characterize the small-time asymptotic behavior of the exit probability of a L\\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are given in the form of a first order term and a precise computable error bound. As an important application of these formulas, we develop a novel adaptive discretization scheme for the Monte Carlo computation of functionals of killed L\\'evy processes with controlled bias. The considered functionals appear in several domains of mathematical finance (e.g. structural credit risk models, pricing of barrier options, and contingent convertible bonds) as well as in natural sciences. The proposed algorithm works by adding discretization points sampled from the L\\'evy bridge density to the skeleton of the process until the overall error for a given trajectory becomes smaller than the maximum tolerance given by the user. As another contribution of particular interest on its own, we also ...

  2. The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts

    CERN Document Server

    Neill, Duff

    2016-01-01

    We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS...

  3. Long-Time Asymptotics of a Bohmian Scalar Quantum Field in de Sitter Space-Time

    CERN Document Server

    Tumulka, Roderich

    2015-01-01

    We consider a model quantum field theory with a scalar quantum field in de Sitter space-time in a Bohmian version with a field ontology, i.e., an actual field configuration $\\varphi({\\bf x},t)$ guided by a wave function on the space of field configurations. We analyze the asymptotics at late times ($t\\to\\infty$) and provide reason to believe that for more or less any wave function and initial field configuration, every Fourier coefficient $\\varphi_{\\bf k}(t)$ of the field is asymptotically of the form $c_{\\bf k}\\sqrt{1+{\\bf k}^2 \\exp(-2Ht)/H^2}$, where the limiting coefficients $c_{\\bf k}=\\varphi_{\\bf k}(\\infty)$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode $\\varphi_{\\bf k}$ possesses a limit as $t\\to\\infty$ and thus "freezes." This result is relevant to the question whether Boltzmann brains form in the late universe according to this theory, and supports that they do not.

  4. Multi-layer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity

    CERN Document Server

    Budd, Christopher J

    2015-01-01

    We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \\theta_t = (D(\\theta)\\theta_x)_x, where the diffusivity is an exponential function D({\\theta}) = D_o exp(\\beta\\theta). This problem arises in the study of unsaturated flow in porous media where {\\theta} represents the liquid saturation. For the physical parameters corresponding to actual porous media, the diffusivity at the residual saturation is D(0) = D_o << 1 so that the diffusion problem is nearly degenerate. Such problems are characterised by wetting fronts that sharply delineate regions of saturated and unsaturated flow, and that propagate with a well-defined speed. Using matched asymptotic expansions in the limit of large {\\beta}, we derive an analytical description of the solution that is uniformly valid throughout the wetting front. This is in contrast with most other related analyses that instead truncate the solution at some specific wetting front location, which is then calculated as part...

  5. Some properties of Riesz means and spectral expansions

    Directory of Open Access Journals (Sweden)

    S. A. Fulling

    1999-03-01

    Full Text Available It is well known that short-time expansions of heat kernels correlate to formal high-frequency expansions of spectral densities. It is also well known that the latter expansions are generally not literally true beyond the first term. However, the terms in the heat-kernel expansion correspond rigorously to quantities called Riesz means of the spectral expansion, which damp out oscillations in the spectral density at high frequencies by dint of performing an average over the density at all lower frequencies. In general, a change of variables leads to new Riesz means that contain different information from the old ones. In particular, for the standard second-order elliptic operators, Riesz means with respect to the square root of the spectral parameter correspond to terms in the asymptotics of elliptic and hyperbolic Green functions associated with the operator, and these quantities contain ``nonlocal'' information not contained in the usual Riesz means and their correlates in the heat kernel. Here the relationship between these two sets of Riesz means is worked out in detail; this involves just classical one-dimensional analysis and calculation, with no substantive input from spectral theory or quantum field theory. This work provides a general framework for calculations that are often carried out piecemeal (and without precise understanding of their rigorous meaning in the physics literature.

  6. Asymptotic behaviour of two-point functions in multi-species models

    Directory of Open Access Journals (Sweden)

    Karol K. Kozlowski

    2016-05-01

    Full Text Available We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU(3-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

  7. A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula

    KAUST Repository

    Hale, Nicholas

    2014-02-06

    A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.

  8. Asymptotic Cosmological Behavior of Scalar-Torsion Mode in Poincare Gauge Theory

    CERN Document Server

    Geng, Chao-Qiang; Tseng, Huan-Hsin

    2013-01-01

    We study the cosmological effect of the simple scalar-torsion ($0^+$) mode in Poincar\\'{e} gauge theory of gravity. We find that for the non-constant (affine) curvature case, the early evolution of the torsion density $\\rho_T$ has a radiation-like asymptotic behavior of $a^{-4}$ with $a$ representing the scale factor, along with the stable point of the torsion pressure ($P_T$) and density ratio $P_T/\\rho_T\\rightarrow 1/3$ in the high redshift regime $(z \\gg 0)$, which is different from the previous result in the literature. We use the Laurent expansion to resolve the solution. We also illustrate our result by the execution of numerical computations.

  9. A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators

    Science.gov (United States)

    Hagstrom, T.; Hariharan, S. I.

    1998-01-01

    In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.

  10. Asymptotic behaviour of two-point functions in multi-species models

    Science.gov (United States)

    Kozlowski, Karol K.; Ragoucy, Eric

    2016-05-01

    We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU (3)-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

  11. QCD Condensates and Holographic Wilson Loops for Asymptotically AdS Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Quevedo, R. Carcasses [Instituto Balseiro, Centro Atomico Bariloche, 8400 San Carlos de Bariloche (Argentina); CONICET, Rivadavia 1917, 1033 Buenos Aires (Argentina); Goity, Jose L. [Hampton University, Hampton, VA 23668 (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Trinchero, Roberto C. [Instituto Balseiro, Centro Atomico Bariloche, 8400 San Carlos de Bariloche (Argentina); CONICET, Rivadavia 1917, 1033 Buenos Aires (Argentina)

    2014-02-01

    The minimization of the Nambu-Goto (NG) action for a surface whose contour defines a circular Wilson loop of radius a placed at a finite value of the coordinate orthogonal to the border is considered. This is done for asymptotically AdS spaces. The condensates of dimension n = 2, 4, 6, 8, and 10 are calculated in terms of the coefficients in the expansion in powers of the radius a of the on-shell subtracted NG action for small a->0. The subtraction employed is such that it presents no conflict with conformal invariance in the AdS case and need not introduce an additional infrared scale for the case of confining geometries. It is shown that the UV value of the gluon condensates is universal in the sense that it only depends on the first coefficients of the difference with the AdS case.

  12. Sieve in expansion

    CERN Document Server

    Kowalski, Emmanuel

    2010-01-01

    This is a survey report for the Bourbaki Seminar (Exp. no. 1028, November 2010) concerning sieve and expanders, in particular the recent works of Bourgain, Gamburd and Sarnak introducing "sieve in orbits", and the related developments concerning expansion properties of Cayley graphs of finite linear groups.

  13. Expansion of Pannes

    Science.gov (United States)

    For the Long Island, New Jersey, and southern New England region, one facet of marsh drowning as a result of accelerated sea level rise is the expansion of salt marsh ponds and pannes. Over the past century, marsh ponds and pannes have formed and expanded in areas of poor drainag...

  14. Schrödinger operators on the half line: Resolvent expansions and the Fermi Golden Rule at threshold

    DEFF Research Database (Denmark)

    Jensen, Arne; Nenciu, Gheorghe

    2005-01-01

    We consider Schr\\"odinger operators $H = -d^2 \\slash dr^2 + V$ on $L^2 ([0,\\infty))$ with the Dirichlet boundary condition. The potential $V$ may be local or non-local, with polynomial decay at infinity. The point zero in the spectrum of $H$ is classified, and asymptotic expansions of the resolvent...

  15. Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size

    Science.gov (United States)

    King, Richard B.

    2016-01-01

    Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID

  16. Asymptotics of bivariate generating functions with algebraic singularities

    Science.gov (United States)

    Greenwood, Torin

    Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

  17. Bigravity from gradient expansion

    Energy Technology Data Exchange (ETDEWEB)

    Yamashita, Yasuho [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Tanaka, Takahiro [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Department of Physics, Kyoto University,606-8502, Kyoto (Japan)

    2016-05-04

    We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.

  18. Operator product expansion algebra

    Energy Technology Data Exchange (ETDEWEB)

    Holland, Jan [CPHT, Ecole Polytechnique, Paris-Palaiseau (France)

    2014-07-01

    The Operator Product Expansion (OPE) is a theoretical tool for studying the short distance behaviour of products of local quantum fields. Over the past 40 years, the OPE has not only found widespread computational application in high-energy physics, but, on a more conceptual level, it also encodes fundamental information on algebraic structures underlying quantum field theories. I review new insights into the status and properties of the OPE within Euclidean perturbation theory, addressing in particular the topics of convergence and ''factorisation'' of the expansion. Further, I present a formula for the ''deformation'' of the OPE algebra caused by a quartic interaction. This formula can be used to set up a novel iterative scheme for the perturbative computation of OPE coefficients, based solely on the zeroth order coefficients (and renormalisation conditions) as initial input.

  19. Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation.

    Science.gov (United States)

    Traytak, Sergey D

    2014-06-14

    The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.

  20. Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation

    Energy Technology Data Exchange (ETDEWEB)

    Traytak, Sergey D., E-mail: sergtray@mail.ru [Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071 Orléans (France); Le STUDIUM (Loire Valley Institute for Advanced Studies), 3D av. de la Recherche Scientifique, 45071 Orléans (France); Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow (Russian Federation)

    2014-06-14

    The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.

  1. Singularities in asymptotically anti-de Sitter spacetimes

    CERN Document Server

    Ishibashi, Akihiro

    2012-01-01

    We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's singularity theorem are satisfied, a singularity must appear in asymptotically AdS spacetime. The recent observations of turbulent instability of asymptotically AdS spacetimes indicate that AdS spacetimes are generically singular even if a closed trapped surface, which is one of the main conditions of the Hawking and Penrose theorem, does not exist in the initial hypersurface. This may lead one to expect to obtain a singularity theorem without imposing the existence of a trapped set in asymptotically AdS spacetimes. This, however, does not appear to be the case. We consider, within the use of global methods, two such attempts and discuss difficulties in eliminating conditions concerning a trapped set from singularity theorems in asymptotically AdS spacetimes. Then in the second...

  2. Superradiant instabilities of asymptotically anti-de Sitter black holes

    Science.gov (United States)

    Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.

    2016-06-01

    We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.

  3. Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

    Science.gov (United States)

    An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

    2016-03-01

    The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for {N}=2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification.

  4. asymptotics for open-loop window flow control

    Directory of Open Access Journals (Sweden)

    Arthur W. Berger

    1994-01-01

    Full Text Available An open-loop window flow-control scheme regulates the flow into a system by allowing at most a specified window size W of flow in any interval of length L. The sliding window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L. To better understand how these window control schemes perform for stationary sources, we describe for a large class of stochastic input processes the asymptotic behavior of the maximum flow in such window intervals over a time interval [0,T] as T and Lget large, with T substantially bigger than L. We use strong approximations to show that when T≫L≫logT an invariance principle holds, so that the asymptotic behavior depends on the stochastic input process only via its rate and asymptotic variability parameters. In considerable generality, the sliding and jumping windows are asymptotically equivalent. We also develop an approximate relation between the two maximum window sizes. We apply the asymptotic results to develop approximations for the means and standard deviations of the two maximum window contents. We apply computer simulation to evaluate and refine these approximations.

  5. Thermal expansion of glassy polymers.

    Science.gov (United States)

    Davy, K W; Braden, M

    1992-01-01

    The thermal expansion of a number of glassy polymers of interest in dentistry has been studied using a quartz dilatometer. In some cases, the expansion was linear and therefore the coefficient of thermal expansion readily determined. Other polymers exhibited non-linear behaviour and values appropriate to different temperature ranges are quoted. The linear coefficient of thermal expansion was, to a first approximation, a function of both the molar volume and van der Waal's volume of the repeating unit.

  6. Detailed ultraviolet asymptotics for AdS scalar field perturbations

    CERN Document Server

    Evnin, Oleg

    2016-01-01

    We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.

  7. The unitary conformal field theory behind 2D Asymptotic Safety

    CERN Document Server

    Nink, Andreas

    2015-01-01

    Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a...

  8. Asymptotics of a singularly perturbed GUE partition function

    CERN Document Server

    Mezzadri, F

    2010-01-01

    We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.

  9. A new class of asymptotically non-chaotic vacuum singularities

    Energy Technology Data Exchange (ETDEWEB)

    Klinger, Paul, E-mail: paul.klinger@univie.ac.at

    2015-12-15

    The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.

  10. Scalar hairy black holes and solitons in asymptotically flat spacetimes

    CERN Document Server

    Nucamendi, U; Nucamendi, Ulises; Salgado, Marcelo

    2003-01-01

    A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\\phi)$ of the theory is ``finetuned'' such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.

  11. Contact mechanics of articular cartilage layers asymptotic models

    CERN Document Server

    Argatov, Ivan

    2015-01-01

    This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...

  12. Fast evaluation of asymptotic waveforms from gravitational perturbations

    CERN Document Server

    Benedict, Alex G; Lau, Stephen R

    2012-01-01

    In the context of blackhole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user's standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equa...

  13. Asymptotic symmetries of QED and Weinberg's soft photon theorem

    CERN Document Server

    Campiglia, Miguel

    2015-01-01

    Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.

  14. Asymptotics of the QMLE for General ARCH(q) Models

    DEFF Research Database (Denmark)

    Kristensen, Dennis; Rahbek, Anders Christian

    2009-01-01

    Asymptotics of the QMLE for Non-Linear ARCH Models Dennis Kristensen, Columbia University Anders Rahbek, University of Copenhagen Abstract Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log......-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption...... that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identification, for a wide range of leading specific ARCH models....

  15. Holography of 3D Asymptotically Flat Black Holes

    CERN Document Server

    Fareghbal, Reza

    2014-01-01

    We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking flat-space limit (zero cosmological constant limit) of New Massive Gravity (NMG). We propose that the dual field theory of the flat-space limit of NMG can be described by a Contracted Conformal Field Theory (CCFT). Using Flat/CCFT correspondence we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. Furthermore, by taking appropriate limit of the Cardy formula in the parent CFT, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.

  16. Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials

    CERN Document Server

    Gómez-Ullate, David; Milson, Robert

    2012-01-01

    The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two classes: the regular zeros, which lie in the interval of orthogonality and the exceptional zeros, which lie outside that interval. We show that the regular zeros have two interlacing properties: one is the natural interlacing between consecutive polynomials as a consequence of their Sturm-Liouville character, while the other one shows interlacing between the zeros of exceptional and classical polynomials. A generalization of the classical Heine-Mehler formula is provided for the exceptional polynomials, which allows to derive the asymptotic behaviour of their regular zeros. We also describe the location and the asymptotic behaviour of the exceptional zeros, which converge for large n to fixed values.

  17. Spherical convective dynamos in the rapidly rotating asymptotic regime

    CERN Document Server

    Aubert, Julien; Fournier, Alexandre

    2016-01-01

    Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...

  18. Holography of 3D asymptotically flat black holes

    Science.gov (United States)

    Fareghbal, Reza; Hosseini, Seyed Morteza

    2015-04-01

    We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS3 group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.

  19. Exact and Asymptotic Measures of Multipartite Pure State Entanglement

    CERN Document Server

    Bennett, C H; Rohrlich, D E; Smolin, J A; Thapliyal, A V; Bennett, Charles H.; Popescu, Sandu; Rohrlich, Daniel; Smolin, John A.; Thapliyal, Ashish V.

    1999-01-01

    In an effort to simplify the classification of pure entangled states of multi (m) -partite quantum systems, we study exactly and asymptotically (in n) reversible transformations among n'th tensor powers of such states (ie n copies of the state shared among the same m parties) under local quantum operations and classical communication (LOCC). With regard to exact transformations, we show that two states whose 1-party entropies agree are either locally-unitarily (LU) equivalent or else LOCC-incomparable. Asymptotic transformations result in a simpler classification than exact transformations. We show that m-partite pure states having an m-way Schmidt decomposition are simply parameterizable, with the partial entropy across any nontrivial partition representing the number of standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the state in question. For general m-partite states, partial entropies across different partitions need not be equal, and since partial entropies are conserved by asymp...

  20. On the oscillation-driven cosmological expansion at the post-inflation stage

    CERN Document Server

    Koutvitsky, Vladimir A

    2016-01-01

    Dynamics of the inflaton scalar field oscillating around a minimum of the singular potentials in the expanding Universe is investigated. Asymptotic formulas are obtained describing the cosmological expansion at the late times. The problem of stability of the oscillations considered and the related phenomenon of the field fragmentation are briefly discussed. PACS numbers: 98.80.Jk, 98.80.Cq, 04.25.-g, 04.40.-b

  1. Large-j Expansion Method for Two-Body Dirac Equation

    Directory of Open Access Journals (Sweden)

    Askold Duviryak

    2006-02-01

    Full Text Available By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state problem. Linear-plus-Coulomb potentials of different spin structure are examined in order to describe the asymptotic degeneracy and fine splitting of light meson spectra.

  2. Foundation and generalization of the expansion by regions

    Science.gov (United States)

    Jantzen, Bernd

    2011-12-01

    The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole integration domain. This method has been applied successfully to many complicated loop integrals, but a general proof for its correctness has still been missing. This paper shows how the expansion by regions manages to reproduce the exact result correctly in an expanded form and clarifies the conditions on the choice and completeness of the considered regions. A generalized expression for the full result is presented that involves additional overlap contributions. These extra pieces normally yield scaleless integrals which are consistently set to zero, but they may be needed depending on the choice of the regularization scheme. While the main proofs and formulae are presented in a general and concise form, a large portion of the paper is filled with simple, pedagogical one-loop examples which illustrate the peculiarities of the expansion by regions, explain its application and show how to evaluate contributions within this method.

  3. On an Asymptotic Behavior of Exponential Functional Equation

    Institute of Scientific and Technical Information of China (English)

    Soon Mo JUNG

    2006-01-01

    The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex)normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ‖x‖ + ‖y‖→∞ under some suitable conditions.

  4. Vacuum energy in asymptotically flat 2 + 1 gravity

    Science.gov (United States)

    Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj

    2017-04-01

    We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.

  5. Asymptotic heat transfer model in thin liquid films

    CERN Document Server

    Chhay, Marx; Gisclon, Marguerite; Ruyer-Quil, Christian

    2015-01-01

    In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided against the resolution of the full Fourier equations in a steady state frame.

  6. The Asymptotic Limit for the 3D Boussinesq System

    Institute of Scientific and Technical Information of China (English)

    LI Lin-rui; WANG Ke; HONG Ming-li

    2016-01-01

    In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosityν=0 or zero diffusivityη=0) in 2D case separately.

  7. Asymptotic zero distribution of a class of hypergeometric polynomials

    OpenAIRE

    Driver, K.A.; Johnston, S. J.

    2011-01-01

    We prove that the zeros of ${}_2F_1(-n,\\frac{n+1}{2};\\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\\{z: |z(1-z)^2|=4/27; \\textrm{Re}(z)>1/3\\}$ as $n\\rightarrow \\infty$. In recent papers (cf. \\cite{KMF}, \\cite{orive}), Mart\\'inez-Finkelshtein and Kuijlaars and their co-authors have used Riemann-Hilbert methods to derive the asymptotic zero distribution of Jacobi polynomials $P_n^{(\\alpha_n,\\beta_n)}$ when the limits $\\ds A=\\lim_{n\\rightarrow \\infty}\\frac{\\alpha_n}{n}...

  8. Asymptotic traveling wave solution for a credit rating migration problem

    Science.gov (United States)

    Liang, Jin; Wu, Yuan; Hu, Bei

    2016-07-01

    In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

  9. Asymptotic Marginal Tax Rate of Individual Income Tax in China

    Institute of Scientific and Technical Information of China (English)

    ZHENYA; LIU; WU; YANG; DAVID; DICKINSON

    2014-01-01

    This paper examines the asymptotic marginal rate of individual income tax which maximizes China’s social welfare through numerical simulation based on the elasticity of China’s labor supply, income distribution and the social objectives of redistribution in accordance with the optimal direct taxation theory. Taking advantage of the optimal direct taxation model with consideration of the income effect, it comes to the conclusion that combined with China’s reality, the asymptotic marginal rate of individual labor income tax in China should be between 35% and 40%.

  10. Counting spanning trees on fractal graphs and their asymptotic complexity

    Science.gov (United States)

    Anema, Jason A.; Tsougkas, Konstantinos

    2016-09-01

    Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.

  11. Conformal Phase Diagram of Complete Asymptotically Free Theories

    CERN Document Server

    Pica, Claudio; Sannino, Francesco

    2016-01-01

    We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.

  12. Scalar and Asymptotic Scalar Derivatives Theory and Applications

    CERN Document Server

    Isac, George

    2008-01-01

    This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds. This book is

  13. The Asymptotic Limits of Zero Modes of Massless Dirac Operators

    Science.gov (United States)

    Saitō, Yoshimi; Umeda, Tomio

    2008-01-01

    Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q( x) are discussed, where α = (α1, α2, α3) is the triple of 4 × 4 Dirac matrices, D = 1/i nabla_x, and Q( x) = ( q jk ( x)) is a 4 × 4 Hermitian matrix-valued function with | q jk ( x) | ≤ C -ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of | x|2 f ( x) as | x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q( x) f ( x).

  14. Asymptotic distributions for a class of generalized $L$-statistics

    CERN Document Server

    Borovskikh, Yuri V; 10.3150/09-BEJ240

    2010-01-01

    We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.

  15. Asymptotic control theory for a system of linear oscillators

    OpenAIRE

    Fedorov, Aleksey; Ovseevich, Alexander

    2013-01-01

    We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the...

  16. Asymptotic Distribution of the Jump Change-Point Estimator

    Institute of Scientific and Technical Information of China (English)

    Changchun TAN; Huifang NIU; Baiqi MIAO

    2012-01-01

    The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] < i ≤n} + εi,where εi (i =1,…,n) are independent identically distributed random variables with Eεi=0 and Var(εi) < oo,with the help of the slip window method,the asymptotic distribution of the jump change-point estimator (T) is studied under the condition of the local alternative hypothesis.

  17. Asymptotic teleportation scheme as a universal programmable quantum processor.

    Science.gov (United States)

    Ishizaka, Satoshi; Hiroshima, Tohya

    2008-12-12

    We consider a scheme of quantum teleportation where a receiver has multiple (N) output ports and obtains the teleported state by merely selecting one of the N ports according to the outcome of the sender's measurement. We demonstrate that such teleportation is possible by showing an explicit protocol where N pairs of maximally entangled qubits are employed. The optimal measurement performed by a sender is the square-root measurement, and a perfect teleportation fidelity is asymptotically achieved for a large N limit. Such asymptotic teleportation can be utilized as a universal programmable processor.

  18. Vacuum energy in asymptotically flat 2+1 gravity

    CERN Document Server

    Miskovic, Olivera; Roy, Debraj

    2016-01-01

    We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincare group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.

  19. EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.

  20. Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian

    CERN Document Server

    Pushnitski, Alexander; Villegas-Blas, Carlos

    2011-01-01

    We consider the Landau Hamiltonian (i.e. the 2D Schroedinger operator with constant magnetic field) perturbed by an electric potential V which decays sufficiently fast at infinity. The spectrum of the perturbed Hamiltonian consists of clusters of eigenvalues which accumulate to the Landau levels. Applying a suitable version of the anti-Wick quantization, we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity. We obtain an explicit description of the asymptotic density of the eigenvalues in terms of the Radon transform of the perturbation potential V.

  1. On a new approach to asymptotic stabilization problems

    Science.gov (United States)

    Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V.

    2009-12-01

    A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.

  2. Asymptotic dynamics, large gauge transformations and infrared symmetries

    CERN Document Server

    Gomez, Cesar

    2016-01-01

    Infrared finite S matrices enjoy an infinite family of symmetries, namely decoupling of asymptotic soft modes with arbitrary direction. The infrared structure of the theory manifests itself in the form of vacuum degeneracy and in nontrivial asymptotic dynamics. These two ingredients are unified in the infrared finite S matrix symmetries and can be disentangled as soft and hard components of corresponding charges. When these two components are disentangled, the nontrivial role of large gauge transformations becomes manifest. The soft decoupling symmetry of the physical S matrix leads to relations between the corresponding soft/hard decompositions for the in and out states that can encode crucial nontrivial information about the scattering process.

  3. Phases of (Asymptotically) Safe Chiral Theories with(out) Scalars

    CERN Document Server

    Molgaard, Esben

    2016-01-01

    We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.

  4. Precise Asymptotics for Random Matrices and Random Growth Models

    Institute of Scientific and Technical Information of China (English)

    Zhong Gen SU

    2008-01-01

    The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.

  5. Gravitational waves in general relativity XIV. Bondi expansions and the ``polyhomogeneity'' of \\Scri

    CERN Document Server

    Chrúsciel, P T; Singleton, D B; Chrusciel, Piotr T.; Callum, Malcolm A.H. Mac; Singleton, David B.

    1993-01-01

    The structure of polyhomogeneous space-times (i.e., space-times with metrics which admit an expansion in terms of $r^{-j}\\log^i r$) constructed by a Bondi--Sachs type method is analysed. The occurrence of some log terms in an asymptotic expansion of the metric is related to the non--vanishing of the Weyl tensor at Scri. Various quantities of interest, including the Bondi mass loss formula, the peeling--off of the Riemann tensor and the Newman--Penrose constants of motion are re-examined in this context.

  6. Two-dimensional model of a slow-mode expansion fan at Io

    Science.gov (United States)

    Krisko, P. H.; Hill, T. W.

    1991-01-01

    A 2D model for the standing slow-mode expansion fan that is expected to exist downstream of the Jovian moon Io is developed. The leading edge of the expansion fan makes an angle of 45 deg with the upstream magnetic field direction, and the fan width is about 114 deg. The plasma flow returns to its upstream direction by way of a slow-mode shock behind Io where the MHD parameters return asymptotically to their upstream conditions. The magnetic field perturbation within the fan is much smaller than that associated with the Alfven wing, which lies farther upstream.

  7. Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method

    Science.gov (United States)

    Sedighi, Hamid M.; Shirazi, Kourosh H.

    2013-04-01

    This paper presents a new asymptotic procedure to predict the nonlinear vibrational behavior of micro-beams pre-deformed by an electric field. The nonlinear equation of motion includes both even and odd nonlinearities. A powerful analytical method called Parameter Expansion Method (PEM) is employed to obtain the approximated solution and frequency-amplitude relationship. It is demonstrated that the first two terms in series expansions are sufficient to produce an acceptable solution of mentioned system. The obtained results from numerical methods verify the soundness of the analytical procedure. Finally, the influences of basic parameters on pull-in instability and natural frequency are investigated.

  8. Engineering Properties of Expansive Soil

    Institute of Scientific and Technical Information of China (English)

    DAI Shaobin; SONG Minghai; HUANG Jun

    2005-01-01

    The components of expansive soil were analyzed with EDAX, and it is shown that the main contents of expansive soil in the northern Hubei have some significant effects on engineering properties of expansive soil. Furthermore, the soil modified by lime has an obvious increase of Ca2+ and an improvement of connections between granules so as to reduce the expansibility and contractility of soil. And it also has a better effect on the modified expansive soil than the one modified by pulverized fuel ash.

  9. Testing Machine for Expansive Mortar

    CERN Document Server

    Silva, Romulo Augusto Ventura

    2011-01-01

    The correct evaluation of a material property is fundamental to, on their application; they met all expectations that were designed for. In development of an expansive cement for ornamental rocks purpose, was denoted the absence of methodologies and equipments to evaluate the expansive pressure and temperature of expansive cement during their expansive process, having that data collected in a static state of the specimen. In that paper, is described equipment designed for evaluation of pressure and temperature of expansive cements applied to ornamental rocks.

  10. Pre-Big Bang, space-time structure, asymptotic Universe

    Directory of Open Access Journals (Sweden)

    Gonzalez-Mestres Luis

    2014-04-01

    Full Text Available Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95, while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2 spinor and the Lundmark-Lemaître-Hubble (LLH expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of

  11. On the asymptotic internal path length and the asymptotic Wiener index of random split trees

    CERN Document Server

    Munsonius, G O

    2011-01-01

    The random split tree introduced by Devroye (1999) is considered. We derive a second order expansion for the mean of its internal path length and furthermore obtain a limit law by the contraction method. As an assumption we need the splitter having a Lebesgue density and mass in every neighborhood of 1. We use properly stopped homogeneous Markov chains, for which limit results in total variation distance as well as renewal theory are used. Furthermore, we extend this method to obtain the corresponding results for the Wiener index.

  12. Asymptotic Distribution of Coefficients of Skewness and Kurtosis

    Directory of Open Access Journals (Sweden)

    Narges Abbasi

    2009-01-01

    Full Text Available Problem statement: In literature, a classic method which has been used to recognize the distribution so far is the measurement of its skewedness and kurtosis. However, there remains a question: how would these measurements work for skewed normal distribution when the size of the sample is large? Approach: This research aimed to determine the asymptotic distribution of skewedness and kurtosis measures in skewed normal distribution. In conducting this research, two groups of inferential findings will help. First, skewed normal distribution which has already been studied by a lot of researchers and we apply its characteristics. Second, there is the U-statistics theory which guides us to the determining of asymptotic distribution measures for skewedness and kurtosis. The combination of these two will solve the problem of this study. Results: Asymptotic distribution of measures for skewdness and kurtosis falls in the normal families. With the size of large samples, the values of expectation of these measures are also determined. By letting zero for skewedness parameter, asymptotic distribution for normal distribution can also be obtained. Conclusion: The findings of this study show new characteristics for skew normal distribution and this results in a new way for skew normal distribution recognition.

  13. Relaxing the parity conditions of asymptotically flat gravity

    NARCIS (Netherlands)

    Compère, G.; Dehouck, F.

    2011-01-01

    Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm

  14. DISSIPATION AND DISPERSION APPROXIMATION TO HYDRODYNAMICAL EQUATIONS AND ASYMPTOTIC LIMIT

    Institute of Scientific and Technical Information of China (English)

    Hsiao Ling; Li Hailiang

    2008-01-01

    The compressible Euler equations with dissipation and/or dispersion correction are widely used in the area of applied sciences, for instance, plasma physics,charge transport in semiconductor devices, astrophysics, geophysics, etc. We consider the compressible Euler equation with density-dependent (degenerate) viscosities and capillarity, and investigate the global existence of weak solutions and asymptotic limit.

  15. Asymptotic analysis of the Carrier-Pearson problem

    Directory of Open Access Journals (Sweden)

    Chunqing Lu

    2003-02-01

    Full Text Available This paper provides a rigorous analysis of the asymptotic behavior of the solution for the boundary-value problem begin{gather*} epsilon ^2u''+u^2-1 =0,quad -1

  16. Asymptotic behaviour of the stochastic Gilpin-Ayala competition models

    Science.gov (United States)

    Lian, Baosheng; Hu, Shigeng

    2008-03-01

    In this paper, we investigate a stochastic Gilpin-Ayala competition system, which is more general and more realistic than the classical Lotka-Volterra competition system.We discuss the asymptotic behaviour in detail of the stochastic Gilpin-Ayala competition system, and comparing the classical Lotka-Volterra with Gilpin-Ayala competition system, we find that the latter has better properties.

  17. Penrose inequality for asymptotically AdS spaces

    Energy Technology Data Exchange (ETDEWEB)

    Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)

    2012-02-28

    In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.

  18. On global asymptotic controllability of planar affine nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    SUN Yimin; GUO Lei

    2005-01-01

    In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.

  19. Asymptotic stability and stabilizability of nonlinear systems with delay.

    Science.gov (United States)

    Srinivasan, V; Sukavanam, N

    2016-11-01

    This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.

  20. ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA

    Institute of Scientific and Technical Information of China (English)

    XUE Hongqi; SONG Lixin

    2002-01-01

    A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.

  1. Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

    Directory of Open Access Journals (Sweden)

    Xueping Hu

    2012-01-01

    Full Text Available By applying the moment inequality for asymptotically almost negatively associated (in short AANA random sequence and truncated method, we get the three series theorems for AANA random variables. Moreover, a strong convergence property for the partial sums of AANA random sequence is obtained. In addition, we also study strong convergence property for weighted sums of AANA random sequence.

  2. ASYMPTOTIC STABILITY OF A SINGULAR SYSTEM WITH DISTRIBUTED DELAYS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.

  3. ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.

  4. Asymptotic stability of solutions to elastic systems with structural damping

    Directory of Open Access Journals (Sweden)

    Hongxia Fan

    2014-11-01

    Full Text Available In this article, we study the asymptotic stability of solutions for the initial value problems of second order evolution equations in Banach spaces, which can model elastic systems with structural damping. The discussion is based on exponentially stable semigroups theory. Applications to the vibration equation of elastic beams with structural damping are also considered.

  5. Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)

    Institute of Scientific and Technical Information of China (English)

    WEIBOCHENG

    1996-01-01

    A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.

  6. Asymptotic freedom of gluons in the Fock space

    CERN Document Server

    Głazek, Stanisław D

    2015-01-01

    Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory.

  7. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

    CERN Document Server

    Fougeirol, Jérémie

    2016-01-01

    We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

  8. The asymptotic limits of zero modes of massless Dirac operators

    CERN Document Server

    Saito, Yoshimi

    2007-01-01

    Asymptotic behaviors of zero modes of the massless Dirac operator $H=\\alpha\\cdot D + Q(x)$ are discussed, where $\\alpha= (\\alpha_1, \\alpha_2, \\alpha_3)$ is the triple of $4 \\times 4$ Dirac matrices, $ D=\\frac{1}{i} \

  9. A Variational Model for an Asymptotic Magnetogydrodynamic System

    Institute of Scientific and Technical Information of China (English)

    JihuanHE

    1998-01-01

    In the present paper an asymptotic gas magnetohydrodynamic system is formulated in variational principles for the first time via the semi-inverse method proposed by He.Thus,a new theoretical basis for the finite element method is founded and a new versatile way to deal with discontinuity(shock)is suggested.

  10. Causality violation in asymptotically flat space-times

    Energy Technology Data Exchange (ETDEWEB)

    Tipler, F.J.

    1976-10-04

    It is shown that a region containing closed timelike lines cannot evolve from regular initial data in a singularity-free asymptotically flat space-time. Furthermore, the causality assumption made in the black-hole uniqueness proofs is justified: It is demonstrated that no physically realistc nonsingular black hole can have a causality-violating exterior. (AIP)

  11. Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative

    OpenAIRE

    2011-01-01

    This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.

  12. Asymptotic Formulae for Multivariate Kantorovich Type Generalized Sampling Series

    Institute of Scientific and Technical Information of China (English)

    Carlo BARDARO; Ilaria MANTELLINI

    2011-01-01

    In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given.Moreover a quantitative version in terms of some moduli of smoothness is established.Finally some particular examples of kernels are discussed,as the Bochner-Riesz kernel and the multivariate splines.

  13. Strong asymptotics for Lp extremal polynomials off a complex curve

    Directory of Open Access Journals (Sweden)

    Rabah Khaldi

    2004-01-01

    Full Text Available We study the asymptotic behavior of Lp(σ extremal polynomials with respect to a measure of the form σ=α+γ, where α is a measure concentrated on a rectifiable Jordan curve in the complex plane and γ is a discrete measure concentrated on an infinite number of mass points.

  14. Geometry of exponential family nonlinear models and some asymptotic inference

    Institute of Scientific and Technical Information of China (English)

    韦博成

    1995-01-01

    A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.

  15. Asymptotically optimal feedback control for a system of linear oscillators

    Science.gov (United States)

    Ovseevich, Alexander; Fedorov, Aleksey

    2013-12-01

    We consider problem of damping of an arbitrary number of linear oscillators under common bounded control. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large.

  16. Tail asymptotics for dependent subexponential differences

    DEFF Research Database (Denmark)

    Albrecher, H; Asmussen, Søren; Kortschak, D.

    We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic co...

  17. Unified asymptotic theory for all partial directed coherence forms.

    Science.gov (United States)

    Baccalá, L A; de Brito, C S N; Takahashi, D Y; Sameshima, K

    2013-08-28

    This paper presents a unified mathematical derivation of the asymptotic behaviour of the three main forms of partial directed coherence (PDC). Numerical examples are used to contrast PDC, gPDC (generalized PDC) and iPDC (information PDC) as to meaning and applicability and, more importantly, to show their essential statistical equivalence insofar as connectivity inference is concerned.

  18. Asymptotics for the Korteweg-de Vries-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    Nakao HAYASHI; Pavel I. NAUMKIN

    2006-01-01

    We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut + uux - uxx + uxxx = 0, x ∈ R, t > 0.We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that ifthe initial data u0 ∈ Hs (R) ∩L1 (R), where s > -1/2,then there exists a uniquesolution u (t,x) ∈ C∞ ((0, ∞);H∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u (t) = t-1/2fM((·)t-1/2) + o(t-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L1 (R),then the asymptotics are true u (t) = t-1/2fM((·)t-1/2) + O(t-1/2-γ),where γ∈ (0,1/2).

  19. MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.

  20. Assessment of density functional methods with correct asymptotic behavior

    CERN Document Server

    Tsai, Chen-Wei; Li, Guan-De; Chai, Jeng-Da

    2012-01-01

    Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including the asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems, and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys. 136, 154109 (2012)], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and f...

  1. Asymptotic Properties of Unbounded Quadrature Domains in the Plane

    OpenAIRE

    Karp, Lavi

    2013-01-01

    We prove that if $\\Omega$ is a simply connected quadrature domain for a distribution with compact support and the infinity point belongs the boundary, then the boundary has an asymptotic curve that is either a straight line or a parabola or an infinite ray. In other words, unbounded quadrature domains in the plane are perturbations of null quadrature domains.

  2. Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

    CERN Document Server

    de Lima, Levi Lopes

    2012-01-01

    We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\\mathbb H^{n+1}$ whose boundary has constant mean curvature $n-1$.

  3. ASYMPTOTIC BEHAVIOR OF DELAY DISCRETETIME NEURAL NETWORKS WITH CRITICAL THRESHOLD

    Institute of Scientific and Technical Information of China (English)

    ZhangHongqiang; LiuKaiyu

    2005-01-01

    This paper is concerned with a delay discrete-time system arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity. We obtain the asymptotic behaviors of the solutions of the system for some cases.The results obtained improve and extend the corresponding results established recently by Zhou, Yu and Huang [1].

  4. Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories

    CERN Document Server

    Nanopoulos, Dimitri

    2010-01-01

    In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.

  5. Asymptotic behaviour near extinction of continuous-state branching processes

    OpenAIRE

    Pardo, Juan Carlos; Berzunza, Gabriel

    2016-01-01

    In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a continuous state branching process whose branching mechanism satisfies a given condition and its reflected process at its infimum.

  6. $\\alpha_s$ at LHC: Challenging asymptotic freedom

    CERN Document Server

    Sannino, Francesco

    2015-01-01

    Several extensions of the standard model feature new colored states that besides modifying the running of the QCD coupling could even lead to the loss of asymptotic freedom. Such a loss would potentially diminish the Wilsonian fundamental value of the theory. However, the recent discovery of complete asymptotically safe vector-like theories \\cite{Litim:2014uca}, i.e. featuring an interacting UV fixed point in all couplings, elevates these theories to a fundamental status and opens the door to alternative UV completions of (parts of) the standard model. If, for example, QCD rather than being asymptotically free becomes asymptotically safe there would be consequences on the early time evolution of the Universe (the QCD plasma would not be free). It is therefore important to test, both directly and indirectly, the strong coupling running at the highest possible energies. I will review here the attempts made in \\cite{Becciolini:2014lya} to use pure QCD observables at the Large Hadron Collider (LHC) to place bound...

  7. The Asymptotic Behavior for Numerical Solution of a Volterra Equation

    Institute of Scientific and Technical Information of China (English)

    Da Xu

    2003-01-01

    Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.

  8. AN ASYMPTOTIC ORDER OF FOURIER TRANSFORM ON SL(2,R)

    Institute of Scientific and Technical Information of China (English)

    Wang Xinsong; Zheng Weixing

    2003-01-01

    In this paper, a better asymptotic order of Fourier transform on SL(2 ,R) is obtained by using classicalanalysis and Lie analysis comparing with that of [5]、 [6], and the Plancherel theorem on Cc2 (SL (2, R)) isalso obtained as an application.

  9. Superradiant instabilities of asymptotically anti-de Sitter black holes

    CERN Document Server

    Green, Stephen R; Ishibashi, Akihiro; Wald, Robert M

    2015-01-01

    We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ...

  10. Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Saeidi Shahram

    2010-01-01

    Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.

  11. Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

    DEFF Research Database (Denmark)

    Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael

    This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors...

  12. Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure

    Science.gov (United States)

    Kalamkarov, Alexander L.; Andrianov, Igor V.; Pacheco, Pedro M. C. L.; Savi, Marcelo A.; Starushenko, Galina A.

    2016-08-01

    The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.

  13. Asymptotic analysis of laminated plates and shallow shells

    Science.gov (United States)

    Skoptsov, K. A.; Sheshenin, S. V.

    2011-02-01

    It was noted long ago [1] that the material strength theory develops both by improving computational methods and by widening the physical foundations. In the present paper, we develop a computational technique based on asymptotic methods, first of all, on the homogenization method [2, 3]. A modification of the homogenization method for plates periodic in the horizontal projection was proposed in [4], where the bending of a homogeneous plate with periodically repeating inhomogeneities on its surface was studied. A more detailed asymptotic analysis of elastic plates periodic in the horizontal projection can be found, e.g., in [5, 6]. In [6], three asymptotic approximations were considered, local problems on the periodicity cell were obtained for them, and the solvability of these problems was proved. In [7], it was shown that the techniques developed for plates periodic in the horizontal projection can also be used for laminated plates. In [7], this was illustrated by an example of asymptotic analysis of an isotropic plate symmetric with respect to the midplane. In what follows, these methods are generalized to the case of combined bending and extension of a longitudinal laminated plate up to the third approximation, which permits finding all components of the stress tensor. The study of the plate behavior is based on the method of homogenization of the three-dimensional problem of linear elasticity and does not use any hypotheses. It turns out that the Kirchhoff-Love hypothesis for the entire packet of layers is simply a consequence of the method in the zeroth approximation, and the bending stresses corresponding to the classical theory of laminated plates [8] are obtained in the first approximation. The successive approximations describe the behavior of the normal and the stress more precisely. In the present paper, the results obtained in [7] are refined, and the asymptotic solution is compared with the direct analysis of a laminated plate by the finite

  14. Optical imaging. Expansion microscopy.

    Science.gov (United States)

    Chen, Fei; Tillberg, Paul W; Boyden, Edward S

    2015-01-30

    In optical microscopy, fine structural details are resolved by using refraction to magnify images of a specimen. We discovered that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification. By covalently anchoring specific labels located within the specimen directly to the polymer network, labels spaced closer than the optical diffraction limit can be isotropically separated and optically resolved, a process we call expansion microscopy (ExM). Thus, this process can be used to perform scalable superresolution microscopy with diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer lateral resolution in both cultured cells and brain tissue, performing three-color superresolution imaging of ~10(7) cubic micrometers of the mouse hippocampus with a conventional confocal microscope.

  15. Rethinking expansive learning

    DEFF Research Database (Denmark)

    Kolbæk, Ditte; Lundh Snis, Ulrika

    Abstract: This paper analyses an online community of master’s students taking a course in ICT and organisational learning. The students initiated and facilitated an educational design for organisational learning called Proactive Review in the organisation where they are employed. By using an online...... discussion forum on Google groups, they created new ways of reflecting and learning. We used netnography to select qualitative postings from the online community and expansive learning concepts for data analysis. The findings show how students changed practices of organisational learning...... in their professional organisation and how they developed their identity to become more skilled practitioners. We discuss the effects of the written discussions and reflections on the students’ endeavour to become authors in practice. Our contribution to the research consists of considerations of changing the spoken...

  16. Conformal expansions and renormalons

    CERN Document Server

    Gardi, E; Gardi, Einan; Grunberg, Georges

    2001-01-01

    The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the fixed-point has a perturbative realization, all-order perturbative relations exist between the conformal coefficients, which are renormalon-free, and the standard perturbative coefficients, which contain renormalons. Therefore, an explicit cancellation of renormalons should occur in these relations. The absence of renormalons in the conformal limit can thus be seen as a constraint on the structure of the QCD perturbative expansion. We show that the conformal constraint is non-trivial: a generic model for the large-order behaviour violates it. We also analyse a specific example, based on a renormalon-type integral over the two-loop running-coupling, where the required cancellation does occur.

  17. ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY

    Institute of Scientific and Technical Information of China (English)

    WU Jingbo

    2000-01-01

    In this note a generalization of the concept of similarity called asymptotic similarity for infinite-dimensional linear systems is introduced. We show that this asymptotic similarity preserves the spectrum and the exponential growth bound.

  18. Burial Ground Expansion Hydrogeologic Characterization

    Energy Technology Data Exchange (ETDEWEB)

    Gaughan , T.F.

    1999-02-26

    Sirrine Environmental Consultants provided technical oversight of the installation of eighteen groundwater monitoring wells and six exploratory borings around the location of the Burial Ground Expansion.

  19. Asymptotic stability properties of θ-methods for delay differential equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ > 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.

  20. The exact asymptotic for the stationary distribution of some unreliable systems

    CERN Document Server

    Lorek, Pawel

    2011-01-01

    In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and matrix geometric approach, we also investigate the asymptotic when breakdown intensity is small. In particular, two different asymptotic regimes for small breakdown intensity suggest two different patterns of large deviations, which is confirmed by simulation study.

  1. Self-similar asymptotic optical beams in semiconductor waveguides doped with quantum dots

    Science.gov (United States)

    He, Jun-Rong; Yi, Lin; Li, Hua-Mei

    2017-01-01

    The self-similar propagation of asymptotic optical beams in semiconductor waveguides doped with quantum dots is reported. The possibility of controlling the shape of output asymptotic optical beams is demonstrated. The analytical results are confirmed by numerical simulations. We give a possible experimental protocol to generate the obtained asymptotic parabolic beams in realistic waveguides. As a generalization to the present work, the self-similar propagation of asymptotic optical beams is proposed in a power-law nonlinear medium.

  2. Asymptotic behaviour of H~p (R~n×R_+) (1

    Institute of Scientific and Technical Information of China (English)

    刘尚平

    1995-01-01

    Asymptotic behaviour of Hp (Rn×R+) (1asymptotic behaviour of Hp functions in each class is given, and the asymptotic behaviour of EHp functions is also done in general terms.

  3. MODE I AND MODE II CRACK TIP ASYMPTOTIC FIELDS WITH STRAIN GRADIENT EFFECTS

    Institute of Scientific and Technical Information of China (English)

    陈少华; 王自强

    2001-01-01

    The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l,typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field,the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields,respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

  4. Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material

    Institute of Scientific and Technical Information of China (English)

    WANG Zhen-qing; ZHAO Qi-cheng; LIANG Wen-yan; FU Zhang-jian

    2003-01-01

    Adopting an elastic-viscoplastic, the asymptotic problem of mode I propagating crack-tip field is investigated. Various asymptotic solutions resulting from the analysis of crack growing programs are presented. The analysis results show that the quasi-statically growing crack solutions are the special case of the dynamic propagating solutions. Therefore these two asymptotic solutions can be unified.

  5. Asymptotic symmetry and conservation laws in 2d Poincaré gauge theory of gravity

    CERN Document Server

    Blagojevic, M; Vukasinac, T

    1996-01-01

    The structure of the asymptotic symmetry in the Poincar\\'e gauge theory of gravity in 2d is clarified by using the Hamiltonian formalism. The improved form of the generator of the asymptotic symmetry is found for very general asymptotic behaviour of phase space variables, and the related conserved quantities are explicitly constructed.

  6. Lattice harmonics expansion revisited

    Science.gov (United States)

    Kontrym-Sznajd, G.; Holas, A.

    2017-04-01

    The main subject of the work is to provide the most effective way of determining the expansion of some quantities into orthogonal polynomials, when these quantities are known only along some limited number of sampling directions. By comparing the commonly used Houston method with the method based on the orthogonality relation, some relationships, which define the applicability and correctness of these methods, are demonstrated. They are verified for various sets of sampling directions applicable for expanding quantities having the full symmetry of the Brillouin zone of cubic and non-cubic lattices. All results clearly show that the Houston method is always better than the orthogonality-relation one. For the cubic symmetry we present a few sets of special directions (SDs) showing how their construction and, next, a proper application depend on the choice of various sets of lattice harmonics. SDs are important mainly for experimentalists who want to reconstruct anisotropic quantities from their measurements, performed at a limited number of sampling directions.

  7. Orthogonal Query Expansion

    CERN Document Server

    Ackerman, Margareta; Lopez-Ortiz, Alejandro

    2011-01-01

    Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries. One of the main remaining challenges is to satisfy the users' needs when they provide a poorly formulated query. When the pages matching the user's original keywords are judged to be unsatisfactory, query expansion techniques are used to alter the result set. These techniques find keywords that are similar to the keywords given by the user, which are then appended to the original query leading to a perturbation of the result set. However, when the original query is sufficiently ill-posed, the user's informational need is best met using entirely different keywords, and a small perturbation of the original result set is bound to fail. We propose a novel approach that is not based on the keywords of the original query. We intentionally seek out orthogonal queries, which are r...

  8. Asymptotic Formulas for Thermography Based Recovery of Anomalies

    Institute of Scientific and Technical Information of China (English)

    Habib Ammari; Anastasia Kozhemyak; Darko Volkov

    2009-01-01

    We start from a realistic half space model for thermal imaging, which we then use to develop a mathematical asymptotic analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design nonit-erative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.AMS subject classifications: 35R20, 35B30

  9. Asymptotic fingerprinting capacity for non-binary alphabets

    CERN Document Server

    Boesten, Dion

    2011-01-01

    We compute the channel capacity of non-binary fingerprinting under the Marking Assumption, in the limit of large coalition size c. The solution for the binary case was found by Huang and Moulin. They showed that asymptotically, the capacity is $1/(c^2 2\\ln 2)$, the interleaving attack is optimal and the arcsine distribution is the optimal bias distribution. In this paper we prove that the asymptotic capacity for general alphabet size q is $(q-1)/(c^2 2\\ln q)$. Our proof technique does not reveal the optimal attack or bias distribution. The fact that the capacity is an increasing function of q shows that there is a real gain in going to non-binary alphabets.

  10. Asymptotic Reissner-Nordstr\\"om solution within nonlinear electrodynamics

    CERN Document Server

    Kruglov, S I

    2016-01-01

    A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at $r\\rightarrow 0$ and $r\\rightarrow \\infty$. The asymptotic at $r\\rightarrow 0$ is shown, and we find corrections to the Reissner-Nordstr\\"om solution and Coulomb's law at $r\\rightarrow\\infty$. The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.

  11. Asymptotic behavior of subradiant states in homonuclear diatomic molecules

    CERN Document Server

    McGuyer, Bart H; Iwata, Geoffrey Z; Tarallo, Marco G; Skomorowski, Wojciech; Moszynski, Robert; Zelevinsky, Tanya

    2014-01-01

    Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in the formation of two-body superradiant and subradiant excited states. While superradiance has been demonstrated in a variety of systems, subradiance is more elusive due to the inherently weak interaction with the environment. Transition mechanisms that are strictly forbidden for atoms become allowed just below the dissociation asymptote due to new selection rules associated with the subradiant states. Here we directly probe deeply subradiant states in ultracold diatomic strontium molecules and characterize their properties near the intercombination atomic asymptote via optical spectroscopy of doubly-forbidden transitions with intrinsic quality factors exceeding 10^(13). This precision measurement of subradiance is made possible by tightly trapping the molecules in a state-insensitive optical lattice and ach...

  12. On Asymptotic Freedom and Confinement from Type-IIB Supergravity

    CERN Document Server

    Kehagias, A A

    1999-01-01

    We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS^5\\times S^5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, area-law behaviour for large separations.

  13. On asymptotic freedom and confinement from type-IIB supergravity

    Science.gov (United States)

    Kehagias, A.; Sfetsos, K.

    1999-06-01

    We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS5xS5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, an area-law behaviour for large separations.

  14. Quantum gravity on foliated spacetime - asymptotically safe and sound

    CERN Document Server

    Biemans, Jorn; Saueressig, Frank

    2016-01-01

    Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover...

  15. Asymptotic Analysis of Mixed Modes in Red Giant Stars

    CERN Document Server

    Jiang, C

    2014-01-01

    High precision space observations, such as made by the kepler and corot missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 $M_{sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense.

  16. Gravitational Two-Loop Counterterm Is Asymptotically Safe

    Science.gov (United States)

    Gies, Holger; Knorr, Benjamin; Lippoldt, Stefan; Saueressig, Frank

    2016-05-01

    Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gaussian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gaussian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the long-standing criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.

  17. Asymptotic zero distribution of a class of hypergeometric polynomials

    CERN Document Server

    Driver, K A

    2011-01-01

    We prove that the zeros of ${}_2F_1(-n,\\frac{n+1}{2};\\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\\{z: |z(1-z)^2|=4/27; \\textrm{Re}(z)>1/3\\}$ as $n\\rightarrow \\infty$. In recent papers (cf. \\cite{KMF}, \\cite{orive}), Mart\\'inez-Finkelshtein and Kuijlaars and their co-authors have used Riemann-Hilbert methods to derive the asymptotic zero distribution of Jacobi polynomials $P_n^{(\\alpha_n,\\beta_n)}$ when the limits $\\ds A=\\lim_{n\\rightarrow \\infty}\\frac{\\alpha_n}{n}$ and $\\ds B=\\lim_{n\\rightarrow \\infty}\\frac{\\beta_n}{n}$ exist and lie in the interior of certain specified regions in the $AB$-plane. Our result corresponds to one of the transitional or boundary cases for Jacobi polynomials in the Kuijlaars Mart\\'inez-Finkelshtein classification.

  18. First-order asymptotic corrections to the meanfield limit

    Energy Technology Data Exchange (ETDEWEB)

    Christandl, Matthias [Institute for Theoretical Physics, ETH Zuerich, Wolfgang-Pauli-Strasse 27, CH-8093 Zuerich (Switzerland); Matjeschk, Robert; Werner, Reinhard [Leibniz Universitaet Hannover (Germany); Trimborn, Friederike [Leibniz Universitaet Hannover (Germany); Bundesministerium fuer Bildung und Forschung (Germany)

    2014-07-01

    We derive a complete algebraic theory for treating permutation invariant problems beyond separability to first order in the asymptotics. Our work builds on a C{sup *}-algebraic theory for permutation invariant operators on n-particles, with an algebraic description of the limit n→∞ (the mean-field limit). We use the fluctuation ansatz, a version of a non-commutative central limit, and derive a continuous-variable algebra (the fluctuation algebra) that asymptotically describes the 1/n-corrections to this meanfield limit. Using the fluctuation algebra, we derive a method for estimating the ground-state energy of mean-field models up to first order, and for estimating the time-evolution of correlations between different particles. Moreover, we show that the mean-field ground-state problem is closely related to the finite de Finetti problem and therefore obtain a lower bound, complementing recent results in this direction.

  19. Asymptotic Reissner-Nordström solution within nonlinear electrodynamics

    Science.gov (United States)

    Kruglov, S. I.

    2016-08-01

    A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at r →0 and r →∞ . The asymptotic at r →0 is shown, and we find corrections to the Reissner-Nordström solution and Coulomb's law at r →∞ . The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.

  20. Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems

    DEFF Research Database (Denmark)

    Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

    2011-01-01

    is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...