Asymptotic expansions of Jacobi functions
International Nuclear Information System (INIS)
The author presents an asymptotic expansion of the Jacobi polynomials which is based on the fact, that these polynomials are special hypergeometric functions. He uses an integral representation of these functions and expands the integrand in a power series. He derives explicit error bounds on this expansion. (HSI)
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.
Asymptotic behaviour of firmly non expansive sequences
International Nuclear Information System (INIS)
We introduce the notion of firmly non expansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafir. Applications to averaged mappings are also given. (author). 16 refs
Zero bias transformation and asymptotic expansions
Jiao, Ying
2012-01-01
Let W be a sum of independent random variables. We apply the zero bias transformation to deduce recursive asymptotic expansions for $\\mathbb {E}[h(W)]$ in terms of normal expectations, or of Poisson expectations for integer-valued random variables. We also discuss the estimates of remaining errors.
Asymptotic expansion of the wavelet transform with error term
R. S. Pathak; 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.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean and...
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.
Asymptotic expansions for high-contrast linear elasticity
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.
Extended Analytic Device Optimization Employing Asymptotic Expansion
Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred
2013-01-01
Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.
Spectral Expansion for the Asymptotically Spectral Periodic Differential Operators
O. A. Veliev
2016-01-01
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
Asymptotic chaos expansions in finance theory and practice
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...
Zero bias transformation and asymptotic expansions II : the Poisson case
Jiao, Ying
2009-01-01
We apply a discrete version of the methodology in \\cite{gauss} to obtain a recursive asymptotic expansion for $\\esp[h(W)]$ in terms of Poisson expectations, where $W$ is a sum of independent integer-valued random variables and $h$ is a polynomially growing function. We also discuss the remainder estimations.
Generalized heat kernel coefficients for a new asymptotic expansion
International Nuclear Information System (INIS)
The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified
Asymptotic expansions of Mellin convolution integrals: An oscillatory case
López, José L.; Pagola, Pedro
2010-01-01
In a recent paper [J.L. López, Asymptotic expansions of Mellin convolution integrals, SIAM Rev. 50 (2) (2008) 275-293], we have presented a new, very general and simple method for deriving asymptotic expansions of for small x. It contains Watson's Lemma and other classical methods, Mellin transform techniques, McClure and Wong's distributional approach and the method of analytic continuation used in this approach as particular cases. In this paper we generalize that idea to the case of oscillatory kernels, that is, to integrals of the form , with c[set membership, variant]R, and we give a method as simple as the one given in the above cited reference for the case c=0. We show that McClure and Wong's distributional approach for oscillatory kernels and the summability method for oscillatory integrals are particular cases of this method. Some examples are given as illustration.
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.
Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge
Linhares, C. A.; Malbouisson, A. P. C.; Roditi, I.
2006-01-01
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar fi...
Asymptotic expansion and statistical description of turbulent systems
International Nuclear Information System (INIS)
A new approach to studying turbulent systems is presented in which an asymptotic expansion of the general dynamical equations is performed prior to the application of statistical methods for describing the evolution of the system. This approach has been applied to two specific systems: anomalous drift wave turbulence in plasmas and homogeneous, isotropic turbulence in fluids. For the plasma case, the time and length scales of the turbulent state result in the asymptotic expansion of the Vlasov/Poisson equations taking the form of nonlinear gyrokinetic theory. Questions regarding this theory and modern Hamiltonian perturbation methods are discussed and resolved. A new alternative Hamiltonian method is described. The Eulerian Direct Interaction Approximation (EDIA) is slightly reformulated and applied to the equations of nonlinear gyrokinetic theory. Using a similarity transformation technique, expressions for the thermal diffusivity are derived from the EDIA equations for various geometries, including a tokamak. In particular, the unique result for generalized geometry may be of use in evaluating fusion reactor designs and theories of anomalous thermal transport in tokamaks. Finally, a new and useful property of the EDIA is pointed out. For the fluid case, an asymptotic expansion is applied to the Navier-Stokes equation and the results lead to the speculation that such an approach may resolve the problem of predicting the Kolmogorov inertial range energy spectrum for homogeneous, isotropic turbulence. 45 refs., 3 figs
Asymptotic expansions for high-contrast elliptic equations
Calo, Victor M.
2014-03-01
In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.
Asymptotic expansion of the multi-orientable random tensor model
Fusy, Eric
2014-01-01
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expansion in N, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.
Relativistic Stars in Starobinsky gravity matched asymptotic expansion
Arapoğlu, Savaş; Ekşi, K Yavuz
2016-01-01
We study the structure of relativistic stars in $\\mathcal{R}+\\alpha \\mathcal{R}^{2}$ theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by $\\alpha$, for uniform density stars matching to the Schwarzschild solution outside the star. We obtain the mass-radius relations and study the dependence of maximum mass on $\\alpha$. We find that $M_{\\max} \\propto \\alpha^{-3/2}$ for values of $\\alpha$ larger than $10~{\\rm km^2}$. For each $\\alpha$ the maximum mass configuration has the biggest compactness parameter ($\\eta = GM/Rc^2$) and we argue that the general relativistic stellar configuration corresponding to $\\alpha=0$ is the most compact among these.
Renormalization and asymptotic expansion of Dirac's polarized vacuum
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
Non-LTE transfer - 3. Asymptotic expansion for small epsilon
International Nuclear Information System (INIS)
Radiative transfer with complete frequency redistribution in the full- or half-space with interior sources is considered in the limit of small epsilon (probability of collisional destruction). It is shown that a suitably scaled source function satisfied for epsilon → a singular equation. In the full-space case with a Doppler profile this reads S(tau) - B(au) =-(-Δ)sup(1/2)S(tau) where S and B are the (scaled) source function and thermal source function, (-Δ)sup(1/2) is the square-root of the negative of the Laplacian; this equation replaces the classical diffusion equation for coherent scattering. In the half-space case, the asymptotic expansion gives only the interior source function (vanishing at the surface) and there is an additional boundary layer. The numerical aspects are considered in a companion paper. (author)
Solution of internal erosion equations by asymptotic expansion
Directory of Open Access Journals (Sweden)
Dubujet P.
2012-07-01
Full Text Available One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.
Naoto Kunitomo; Akihiko Takahashi
2003-01-01
This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arised in nance. As illustrations we use three major problems in nance and give some useful formulae and new results including numerical analyses.
International Nuclear Information System (INIS)
For the free models of statistical mechanics on torus, including the Ising model, dimer model and Gaussian model, exact asymptotic expansions of free energy, internal energy and specific heat in the vicinity of the critical point are found. It is shown that there is a direct relation between the terms of the expansion and Kronecker's double series. The latter can be expressed in terms of the elliptic θ-functions in all orders of the asymptotic expansion. (author)
On the ambiguity of field correlators represented by asymptotic perturbation expansions
Caprini, Irinel; Fischer, Jan; Vrkoč, Ivo
2009-01-01
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 the Watson lemma, we obtain a large class of functions having the same asymptotic perturbation expansion. Som...
Allaire, Grégoire; Briane, Marc; Vanninathan, Muthusamy
2016-01-01
in press International audience In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is well-known that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogenized equation [5] where the homogenized equation can be improve...
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.
Institute of Scientific and Technical Information of China (English)
HUANG; Yunqing; SHU; Shi; YU; Haiyuan
2004-01-01
In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the approximate derivatives.
A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach
Matsuoka, Ryosuke; Takahashi, Akihiko; Uchida, Yoshihiko
2005-01-01
We developed a new scheme for computing "Greeks"of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and Vegas of plain vanilla and av-erage European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes con?rmed the validity...
Asymptotic expansions of integral means and applications to the ratio of gamma functions
Elezović, Neven; Vukšić, Lenka
2013-01-01
Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form $B(A(x))=C(x)$, where $B$ and $C$ have known asymptotic expansions. The results are illustrated by calculation of some important integral means connected with gamma and digamma functions.
Asymptotic Expansions in the CLT in Free Probability
Chistyakov, G P
2011-01-01
We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution. We apply these results to the expansion of densities to derive expansions for the free entropic distance of sums to the Wigner law.
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
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...
THE HIGHER ASYMPTOTIC EXPANSIONS FINDING FOR BOUNDARY VALUE PROBLEM OF THE ZOM MODEL
Directory of Open Access Journals (Sweden)
Kovalenko A. V.
2013-12-01
Full Text Available In this article authors propose the asymptotic solution of the boundary value problem modeling the transport of salt ions in the cell electrodialysis desalination unit. The domain of the camera desalting broken into two subdomains: electroneutrality and space charge. Subdomains has own asymptotic expansion. The subdomain of the space charge has unique solvability of the current approach used by the solvability condition of the next approximation
On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection
Amit
2013-01-01
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 e...
Asymptotic expansions for large closed and loss queueing networks
Directory of Open Access Journals (Sweden)
Yaakov Kogan
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.
Borisov, D
2009-01-01
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant but can rotate along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We also show that for sufficiently thin rod this set contains any prescribed number of the first eigenvalues and give the complete asymptotic expansions for the associated eigenfunctions in C^k-norms.
Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction
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
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...... with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions. The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions...
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
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...
Honkonen, J; Nalimov, M Yu
2002-01-01
Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the $\\phi ^4$ $(4-\\epsilon)$ theory is discussed. Well-known results of the asymptotic $4-\\epsilon $ expansion of critical indices are shown to be far from the large order asymptotic value. A {\\em convergent} series for the model $\\phi ^4$ $(4-\\epsilon)$ is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the $4-\\epsilon $ scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed.
International Nuclear Information System (INIS)
Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the φ4 (4 - ε) theory is discussed. Well-known results of the asymptotic 4 - ε expansion of critical indices are shown to be far from the large order asymptotic value. A convergent series for the model φ4 (4 - ε) is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the 4 - ε scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed (Authors)
Guoping Xu; Harry Zheng
2010-01-01
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is...
APPLICATION OF A HIGH-ORDER ASYMPTOTIC EXPANSION SCHEME TO LONG-TERM CURRENCY OPTIONS
Kohta Takehara; Masashi Toda; Akihiko Takahashi
2011-01-01
Recently, not only academic researchers but also many practitioners have used the methodology so-called ``an asymptotic expansion method" in their proposed techniques for a variety of financial issues. e.g. pricing or hedging complex derivatives under high-dimensional stochastic environments. This methodology is mathematically justified by Watanabe theory (Watanabe [1987], Yoshida [1992a,b]) in Malliavin calculus and essentially based on the framework initiated by Kunitomo and Takahashi [2003...
Fujikoshi, Yasunori; Shimizu, Ryoichi
1989-01-01
This paper deals with the distribution of $\\mathbf{X} = \\sum^{1/2}\\mathbf{Z}$, where $\\mathbf{Z}: p \\times 1$ is distributed as $N_p(0, I_p), \\sum$ is a positive definite random matrix and $\\mathbf{Z}$ and $\\sum$ are independent. Assuming that $\\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\\mathbf{X}$ and its error bound, which is useful in the situation where $\\sum$ tends to $I_p$. A stronger version of the expansion is also given. The results are appl...
Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells
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).
Vijay Prakash, S.; Sonti, Venkata R.
2016-02-01
Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrödinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions.
Calise, Anthony J.; Melamed, Nahum
1993-01-01
In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
International Nuclear Information System (INIS)
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
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 of the cha...... characteristic function of Sn is obtained. The representation is in term of the maximal eigenvalue of the linear operator sending a function g(x) into the function x → E(g(Xi)exp[itfhook(Xi, x)]|Xi-1 = x). © 1987....
The asymptotic expansion of Tracy-Widom GUE law and symplectic invariants
Borot, Gaetan; Eynard, Bertrand
2010-01-01
We establish the relation between two objects: an integrable system related to Painlev\\'e II equation, and the symplectic invariants of a certain plane curve S(TW). This curve describes the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This shows that the s -> -infinity asymptotic expansion of Tracy-Widow law F_{GUE}(s), governing the distribution of the maximal eigenvalue in hermitian random matrices, is given by sympl...
Dissipative dynamics of fission in the framework of asymptotic expansion of Fokker-Planck equation
International Nuclear Information System (INIS)
The dynamics of fission has been formulated by generalising the asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuations where the diffusion coefficients depend on the stochastic variables explicitly. The prescission neutron multiplicities and mean kinetic energies of the evaporated neutrons have been calculated and compared with the respective experimental data over a wide range of excitation energy and compound nuclear mass. The mean and the variance of the total kinetic energies of the fission fragments have been calculated and compared with the experimental values. (orig.)
International Nuclear Information System (INIS)
A formal asymptotic expansion of a solution of the initial problem for a singularly perturbed differential-operational nonlinear equation in a small parameter has been constructed in the critical case. Splash functions of and boundary functions have been estimated of found and assessment of the residual member of the expansion has been obtained
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...
Matched asymptotic expansion for caged black holes: regularization of the post-Newtonian order
International Nuclear Information System (INIS)
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 analysed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension-a dimension where the transition turns second order
Cardone, G; Panasenko, G P
2012-01-01
The Stokes equation with the varying viscosity is considered in a thin tube structure, i.e. in a connected union of thin rectangles with heights of order $\\varepsilon<<1 $ and with bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed: it contains some Poiseuille type flows in the channels (rectangles) with some boundary layers correctors in the neighborhoods of the bifurcations of the channels. The estimates for the difference of the exact solution and its asymptotic approximation are proved.
Datta, Nilanjana; Hsieh, Min-Hsiu; Oppenheim, Jonathan
2016-05-01
State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.
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.
Long-range asymptotic expansion of the diagonal Born–Oppenheimer correction
International Nuclear Information System (INIS)
Graphical abstract: We derived formulas for coefficients A6, A8, A10 determining long-range asymptotic behavior of the adiabatic correction to the potential energy. The formulas were used to compute the coefficients for hydrogen molecule and helium dimers. Abstract: Formulas for the coefficients A6, A8, and A10 determining the long-range asymptotic behavior Ead(R)∼-A6R-6-A8R-8-A10R-10 of the diagonal Born–Oppenheimer (adiabatic) correction Ead(R) to the potential energy of a diatomic molecule are derived using two standard definitions of Ead(R). The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born–Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.
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 expan...
Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach
Cyril Grunspan
2011-01-01
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the ?rst 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in terms of a power series in call price.
Bao, Zhigang
2011-01-01
We study the renormalized real sample covariance matrix $H=X^TX/\\sqrt{MN}-\\sqrt{M/N}$ with $N/M\\rightarrow0$ in this paper, where $X=[X_{jk}]_{M\\times N}$ is an $M\\times N$ real random matrix with entries sharing the same first five order moments, and we assume $\\mathbb{E}|X_{jk}|^5\\leq\\infty$. The Stieltjes transform $m_N(z)=N^{-1}Tr(H-z)^{-1}$ and the linear eigenvalue statistics of $H$ are considered. We mainly focus on the asymptotic expansion of $\\mathbb{E}\\{m_N(z)\\}$, different from the Wigner matrix case, it is shown that the order of the first order term of the remainder may depend on the ratio $N/M$. Then for some fine test function, a central limit theorem for the linear eigenvalue statistics of $H$ is established. We show that the variance of the limiting normal distribution coincides with the case of a real Gaussian Wigner matrix, under the effect of central limit theorem and asymptotic independence for the matrix entries.
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.
International Nuclear Information System (INIS)
We consider one-dimensional Fokker–Planck and Schrödinger equations with a potential that approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be applicable to such asymptotically periodic cases. Using this method, we study the low-energy behavior of the Green function. (paper)
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.
Dettmann, Carl P.
2002-01-01
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...
Directory of Open Access Journals (Sweden)
Mirela Kohr
2004-09-01
Full Text Available We study the low Reynolds number flow of an incompressible Newtonian fluid of infinite expanse past a cylinder of arbitrary cross section by using the method of matched asymptotic expansions. The analysis that will be made in this paper is equivalent to that developed by Power (1990 in order to solve the resulting inner (or Stokes problems with the completed double-layer boundary integral equation method (CDLBIEM due to Power and Miranda (1987. We will solve these problems by the boundary integral method developed by Hsiao and Kress (1985.
Czech Academy of Sciences Publication Activity Database
Profant, T.; Klusák, Jan; Ševeček, O.; Kotoul, M.; Hrstka, M.; Marcián, P.
Zurich : Trans Tech Publications, 2014 - (Šandera, P.), s. 745-748 ISBN 978-3-03785-934-6. ISSN 1013-9826. - (Key Engineering Materials. 592-593). [MSMF 7 - International Conference on Materials Structure & Micromechanics of Fracture /7./. Brno (CZ), 01.07.2013-03.07.2013] Institutional support: RVO:68081723 Keywords : Orthotropic bi-material notch * two-state integral * non-singular stress terms * T-stress * matched asymptotic expansion Subject RIV: JL - Materials Fatigue, Friction Mechanics http://www.scientific.net/KEM.592-593.745
Two-loop two-point functions with masses asymptotic expansions and Taylor series, in any dimension
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 $d=4$.
International Nuclear Information System (INIS)
In this paper we apply to gravitational waves (GW) from the inspiral phase of binary systems a recently derived frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. We use expansions of the covariance and the bias of a maximum likelihood estimate in terms of inverse powers of the signal-to-noise ration (SNR)s where the square root of the first order in the covariance expansion is the Cramer Rao lower bound (CRLB). We evaluate the expansions, for the first time, for GW signals in noises of GW interferometers. The examples are limited to a single, optimally oriented, interferometer. We also compare the error estimates using the first two orders of the expansions with existing numerical Monte Carlo simulations. The first two orders of the covariance allow us to get error predictions closer to what is observed in numerical simulations than the CRLB. The methodology also predicts a necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties, SNR, dimension of the parameter space and estimation errors. For example the timing match filtering can achieve the CRLB only if the SNR is larger than the Kurtosis of the gravitational wave spectrum and the necessary SNR is much larger if other physical parameters are also unknown.
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.
International Nuclear Information System (INIS)
A powerful new technique, using a two-dimensional position-sensitive multichannel plate detector coupled with a spherical-sector electron analyzer, allows rapid data collection of doubly- and triply-differential electron spectra. This device is used to collect spectra, doubly differential in electron energy and emission angle, for the electron loss to the continuum cross section, where an electron originally bound to the incoming projectile is excited just over the ionization limit into the continuum of the ion, for O5+ projectiles incident on helium and argon gas targets at energies of 41, 82, and 105 MeV at the Holifield Heavy Ion Research Facility at Oak Ridge National Laboratory. By making a multipole expansion of the cross section in the projectile frame, and appropriately including the effects of the electron analyzer, a general characterization of the electron loss to the continuum cusp (ELC) shape is made. These results are directly compared with the recent theory of J. Burgdoerfer, which derives the multipole content for the ELC cross section, and excellent agreement is found for the case of argon targets at the highest two energies, where the theory is expected to be more reliable. The lack of good agreement with helium target data suggests the need for better treatment of electron-electron interactions within the theoretical framework
Nonstandard asymptotic analysis
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...
Numerical Asymptotic Solutions Of Differential Equations
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
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
Asymptotic behavior of atomic momentals
Thakkar, Ajit J.
1987-05-01
Knowledge of the large and small momentum transfer behavior of the electron momentum distribution is an important ingredient in the analysis of experimental isotropic Compton profiles. This behavior ultimately rests upon the asymptotic behavior of atomic momentals (momentum space orbitals). The small momentum Maclaurin expansion and the large momentum asymptotic expansion of atomic momentals with arbitrary angular momentum quantum number are derived in this paper. Their implications for momentum densities and Compton profiles are derived and discussed.
Asymptotically hyperbolic connections
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...
Exponential asymptotics and gravity waves
Chapman, S. J.; Vanden-Broeck, J.
2006-01-01
The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves acro...
Asymptotic analysis and boundary layers
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...
Asymptotically flat and regular Cauchy data
Dain, S
2002-01-01
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
8. Asymptotically Flat and Regular Cauchy Data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
EMC effect: asymptotic freedom with nuclear targets
International Nuclear Information System (INIS)
General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references
Dirichlet eigenvalues of asymptotically flat triangles
Ourmières-Bonafos, Thomas
2015-01-01
This paper is devoted to the study of the eigenpairs of the Dirichlet Laplacian on a family of triangles where two vertices are fixed and the altitude associated with the third vertex goes to zero. We investigate the dependence of the eigenvalues on this altitude. For the first eigenvalues and eigenfunctions, we obtain an asymptotic expansion at any order at the scale cube root of this altitude due to the influence of the Airy operator. Asymptotic expansions of the eigenpairs are provided, ex...
Asymptotic perturbation theory of waves
Ostrovsky, Lev
2014-01-01
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theor
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.
Exponential asymptotics of the Voigt functions
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Large degree asymptotics of generalized Bessel polynomials
López, J.L.; Temme, N.M.
2011-01-01
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in t
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Asymptotic safety: A simple example
International Nuclear Information System (INIS)
We use the Gross-Neveu model in 2f expansion where the model is known to be renormalizable to all orders. In this limit, the fixed-point action as well as all universal critical exponents can be computed analytically. As asymptotic safety has become an important scenario for quantizing gravity, our description of a well-understood model is meant to provide for an easily accessible and controllable example of modern nonperturbative quantum field theory.
Asymptotically hyperbolic black holes in Horava gravity
Janiszewski, Stefan
2014-01-01
Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.
Institute of Scientific and Technical Information of China (English)
陈刚; 王梦婕
2014-01-01
通过对χ2分布概率密度函数的自变量进行标准化变换,将其展开成如下形式：2nχ2( x；n)=1+r1(t)n +r2(t)n +r3(t)n n +r4(t)n2éëùûφ(t)+o 1n2(),其中n为自由度,φ(t)为标准正态分布的密度函数,ri(t)(1≤i≤4)均为关于t的多项式。从该展开式得到χ2分布密度函数的一个近似计算公式。进一步建立φ( t)的幂系数积分递推关系,得到χ2分布函数的渐近展开式。最后通过数值计算验证了这些结果在实际应用中的有效性。%Through the transformation of the independent variable of χ2 distribution probability density function,degree of freedom of which is n,the equation can be expanded as follows: 2nχ2(x;n)=f(t;n)= 1+r1(t)n +r2(t)n +r3(t)n n +r4(t)n2éë ùûφ(t)+o 1n2( ) ,here,φ(t) is a density function of standard normal distribution;ri(t) is a 3i order polynomial of t(1≤i≤4). An approximate formula can be obtained from the expansion of the distribution density function. We further establish the integral recurrence relations of the power coefficients of the standard normal density function and obtain the asymptotic expansion of the distribution function ofχ2 . Finally,the effectiveness of these results in practical application was verified by the numerical calculations.
Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case
Zhang JM; Cao LH
2010-01-01
We discuss in detail the error bounds for asymptotic solutions of second-order linear difference equation where and are integers, and have asymptotic expansions of the form , , for large values of , , and .
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.
Extended asymptotic theory of unstable resonator modes.
Li, Y Q; Sung, C C
1990-10-20
The modes in an unstable resonator can be computed within the limit of a large Fresnel number using the asymptotic expansion of the diffraction integral, as shown by Horwitz, Butts, and Avizonis. The expansion is not valid for the points of interest around or beyond the shadow boundary of the output light. We use a better numerical representation, which extends the regions of use. The comparison of several cases with earlier work shows that the asymptotic theory can be successfully applied for all parameters without restrictions. PMID:20577410
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....
Large Degree Asymptotics of Generalized Bessel Polynomials
López, J. L.; Temme, Nico
2011-01-01
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\\pm i/n$ are derived, and a new expansion in terms of modified Bessel fu...
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.
Large Deviations and Asymptotic Methods in Finance
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...
Asymptotic analysis, Working Note No. 1: Basic concepts and definitions
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universite Claude Bernard Lyon 1, 69 - Villeurbanne (France). Lab. d`Analyse Numerique; Kaper, H.G. [Argonne National Lab., IL (United States)
1993-07-01
In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, Nico
2000-01-01
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 including the classical integral domain.
Asymptotic estimates for generalized Stirling numbers
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
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
On asymptotic extension dimension
Repovš, Dušan; Zarichnyi, Mykhailo
2011-01-01
The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.
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.
Asymptotic Resource Usage Bounds
Albert E.; Alonso D.; Arenas P.; Genaim S.; Puebla G.
2009-01-01
When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by ...
Bousso, Raphael
2016-01-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the Quantum Null Energy Condition, of the Generalized Second Law, and of the Quantum Bousso Bound.
Asymptotically Safe Dark Matter
Sannino, Francesco
2014-01-01
We introduce a new paradigm for dark matter interactions according to which the interaction strength is asymptotically safe. In models of this type, the interaction strength is small at low energies but increases at higher energies towards a finite constant value of the coupling. The net effect is to partially offset direct detection constraints without affecting thermal freeze-out at higher energies. High-energy collider and indirect annihilation searches are the primary ways to constrain or discover asymptotically safe dark matter.
Asymptotic properties of difference schemes of maximum odd accuracy
International Nuclear Information System (INIS)
The asymptotic estimates of the difference Green function and difference step function are obtained for difference schemes of maximum odd accuracy (2k-1), k = 0(1nh-1), h is step of the net. The problem is reduced to construction of asymptotic expansion of some integrals. Principal estimates are obtained by application of the saddle point method. The saddle points determining asymptotic expansion are situated near finite radius circle and they become close to each other when h → 0. These asymptotic estimates give that the numerical solution convergences to the solution of the continuous problem with the rate 0(hsup(N+α) 1n1nh-1). The width of zone over which an isolated discontinuity spreads out is proportional to 1nh-1
Quasi-extended asymptotic functions
International Nuclear Information System (INIS)
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
Theory of asymptotic operation. A summary of basic principles
Tkachov, Fyodor V.
1997-01-01
This summary of several talks given in 1990-1993 discusses the problem of asymptotic expansions of multiloop Feynman diagrams in masses and external momenta - a central problem in perturbative quantum field theory. Basic principles of the theory of asymptotic operation -- the most powerful tool for that purpose -- are discussed. Its connection with the conventional methods is explained (the BPHZ theory, the method of leading logarithmic approximation etc.). The problem of non-euclidean asympt...
Berezin-Toeplitz quantization and its kernel expansion
Ma, Xiaonan
2012-01-01
We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.
Puschnigg, Michael
1996-01-01
The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.
Skin Effect in Electromagnetism and Asymptotic Behaviour of Skin Depth for High Conductivity
Péron, Victor; Caloz, Gabriel; Dauge, Monique; Faou, Erwan
2010-01-01
International audience We study a three-dimensional model for the skin effect in electromagnetism. The 3-D case of the Maxwell equations in harmonic regime on a domain composed of a dielectric and of a highly conducting material is considered. We derive an asymptotic expansion with respect to a small parameter related to high conductivity. This expansion is theoretically justified at any order. The asymptotic expansion and numerical simulations in axisymmetric geometry exhibit the influenc...
International Nuclear Information System (INIS)
A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
Asymptotics for spherical needlets
Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.
Asymptotic freedom, asymptotic flatness and cosmology
International Nuclear Information System (INIS)
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 β-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, naturalness and other problems of such inflationary models
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 ...
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Asymptotic Enumeration of RNA Structures with Pseudoknots
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...
Hydrodynamics, resurgence and trans-asymptotics
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...
Optimistic Agents are Asymptotically Optimal
Sunehag, Peter; Hutter, Marcus
2012-01-01
We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic case we provide finite error bounds.
Asymptotic Flatness in Rainbow Gravity
Hackett, Jonathan
2005-01-01
A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.
Coarse geometry and asymptotic dimension
Grave, Bernd
2006-01-01
We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively curved spaces, e.g. for complete, simply connected manifolds with bounded, strictly negative sectional curvature.
Another Asymptotic Notation : "Almost"
Mondal, Nabarun; Ghosh, Partha P.
2013-01-01
Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the various existing notations a new notation is proposed. This notation has similarities with the other heavily used notations like Big-Oh, Big Theta, while being more accurate when describing the order relationship. It has been argued that this notation is more su...
Higher order asymptotics for the Hirota equation via Deift–Zhou higher order theory
Energy Technology Data Exchange (ETDEWEB)
Huang, Lin, E-mail: huangl12@fudan.edu.cn [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China); Xu, Jian, E-mail: jianxu02@gmail.com [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China); Fan, En-gui, E-mail: faneg@fudan.edu.cn [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China)
2015-01-02
In this paper, the Deift–Zhou higher order asymptotic theory is used to further establish the full asymptotic expansion for the solution of the Hirota equation to all order, as t→∞. The method is rigorous and does not rely on an a priori ansatz for the form of the solution. - Highlights: • Give RHP for Hirota equation. • Systemically apply Deift–Zhou theory. • Give full asymptotics for Hirota equation.
Gulisashvili, A.; Stein, E. M.
2009-01-01
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas f...
Local heat kernel asymptotics for nonminimal differential operators
International Nuclear Information System (INIS)
The method for computing the local coefficients in the asymptotical heat kernel expansion is extended to the case of nonminimal differential operators. The lowest expansion coefficients are calculated for the second-order nonminimal operators on oneforms over a riemannian space in arbitrary dimensions. Unlike the coefficients for the minimal second-order operators those for nonminimal ones turn out to be essentially dependent on the space dimension. (orig.)
Asymptotic freedom in Horava-Lifshitz gravity
D'Odorico, Giulio; Schutten, Marrit
2014-01-01
We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.
The asymptotic safety scenario and scalar field inflation
Rahmede, Christoph
2013-01-01
We study quantum gravity corrections to early universe cosmology as resulting within the asymptotic safety scenario. We analyse if it is possible to obtain accelerated expansion in the regime of the renormalisation group fixed point in a theory with Einstein-Hilbert gravity and a scalar field. We show how this phase impacts cosmological perturbations observed in the cosmic microwave background.
Gap asymptotics in a weakly bent leaky quantum wire
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Kondej, S.
2015-01-01
Roč. 48, č. 49 (2015), s. 495301. ISSN 1751-8113 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : singular Schroedinger operators * delta interaction * leaky quantum wires * weak perturbation * asymptotic expansion Subject RIV: BE - Theoretical Physics Impact factor: 1.583, year: 2014
Mathematical justification of Kelvin-Voigt beam models by asymptotic methods
Rodríguez-Arós, Á. D.; Viaño, J. M.
2012-06-01
The authors derive and justify two models for the bending-stretching of a viscoelastic rod by using the asymptotic expansion method. The material behaviour is modelled by using a general Kelvin-Voigt constitutive law.
Duality and asymptotic geometries
Boonstra, H J; Skenderis, K
1997-01-01
We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \\xx E^l \\xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed.
On the asymptotic distribution of the mean absolute deviation about the mean
Segers, Johan
2014-01-01
The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the sample mean absolute deviation is proposed. The expansion yields the asymptotic distribution of the sample mean absolute deviation under a wide range of settings, allowing for serial dependence or an infinite second moment. Key words: central limit theorem;...
On the asymptotic distribution of the mean absolute deviation about the mean
Segers, Johan
2014-01-01
The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the sample mean absolute deviation is proposed. The expansion yields the asymptotic distribution of the sample mean absolute deviation under a wide range of settings, allowing for serial dependence or an infinite second moment.
Asymptotic analysis and numerical modeling of mass transport in tubular structures
Cardone, G; Sirakov, Y
2009-01-01
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This expansion is used further for justification of an asymptotic domain decomposition strategy essentially reducing the memory and the time of the code. A numerical solution obtained by this strategy is compared to the numerical solution obtained by a direct FEM computation.
Asymptotic Symmetries from finite boxes
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.
Asymptotic symmetries from finite boxes
Andrade, Tomás; Marolf, Donald
2016-01-01
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 Poincaré 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 AdS3 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.
Regular Variation and Smile Asymptotics
Benaim, Shalom; Friz, Peter
2006-01-01
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.
Extended asymptotic functions - some examples
International Nuclear Information System (INIS)
Several examples of extended asymptotic functions are exposed. These examples will illustrate the notions introduced in another paper but at the same time they have a significance as realizations of some Schwartz disctibutions: delta(x), H(x), P(1/xsup(n)), etc. The important thing is that the asymptotic functions of these examples (which, on their part, are realizations of the above-mentioned distributions) can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. Some properties of the set of all extended asymptotic functions are considered which are essential for the next step of this approach
Spectral asymptotics of a strong δ′ interaction supported by a surface
International Nuclear Information System (INIS)
Highlights: • Attractive δ′ interactions supported by a smooth surface are considered. • Surfaces can be either infinite and asymptotically planar, or compact and closed. • Spectral asymptotics is determined by the geometry of the interaction support. - Abstract: We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive δ′ interaction supported by a smooth surface in R3, either infinite and asymptotically planar, or compact and closed. Its second term is found to be determined by a Schrödinger type operator with an effective potential expressed in terms of the interaction support curvatures
Asymptotic Efficiency in OLEDS
Nelson, Mitchell C
2015-01-01
Asymptotic efficiency (high output without droop) was recently reported for OLEDS in which a thin emitter layer is located at the anti-node in a resonant microcavity. Here we extend our theoretical analysis to treat multi-mode devices with isotropic emitter orientation. We recover our efficiency equations for the limiting cases with an isotropic emitter layer located at the anti-node where output is linear in current, and for an isotropic emitter located at the node where output can exhibit second order losses with an overall efficiency coefficient that depends on loss terms in competition with a cavity factor. Additional scenarios are described where output is driven by spontaneous emission, or mixed spontaneous and stimulated emission, with stimulated emission present in a loss mode, potentially resulting in cavity driven droop or output clamping, and where the emitter layer is a host-guest system.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Selected asymptotic methods with applications to electromagnetics and antennas
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
On the charge density and asymptotic tail of a monopole
Harland, Derek
2015-01-01
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions.
Asymptotic Phase for Stochastic Oscillators
Thomas, Peter J.; Lindner, Benjamin
2014-12-01
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density's approach to its steady state.
Asymptotic Expansion and the LG/(Fano, General Type) Correspondence
Acosta, Pedro
2014-01-01
The celebrated LG/CY correspondence asserts that the Gromov-Witten theory of a Calabi-Yau (CY) hypersurface in weighted projective space is equivalent to its corresponding FJRW-theory (LG) via analytic continuation. It is well known that this correspondence fails in non-Calabi-Yau cases. The main obstruction is a collapsing or dimensional reduction of the state space of the Landau-Ginzburg model in the Fano case, and a similar collapsing of the state space of Gromov-Witten theory in the general type case. We state and prove a modified version of the cohomological correspondence that describes this collapsing phenomenon at the level of state spaces. This result confirms a physical conjecture of Witten-Hori-Vafa. The main purpose of this article is to provide a quantum explanation for the collapsing phenomenon. A key observation is that the corresponding Picard-Fuchs equation develops irregular singularities precisely at the points where the collapsing occurs. Our main idea is to replace analytic continuation w...
Toeplitz quantization and asymptotic expansions for real bounded symmetric domains
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Upmeier, H.
2011-01-01
Roč. 268, 3-4 (2011), s. 931-967. ISSN 0025-5874 R&D Projects: GA ČR(CZ) GA201/06/0128 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded symmetric domain * Toeplitz operator * star product Subject RIV: BA - General Mathematics Impact factor: 0.749, year: 2011 http://rd.springer.com/article/10.1007/s00209-010-0702-9
Asymptotic completeness and multiparticle structure in field theories
International Nuclear Information System (INIS)
Previous proofs of asymptotic completeness and related results on scattering in field theories are restricted to P(φ)2 models in the 2- and 3-particle regions. In this paper, new cluster expansions that are well adapted to more direct proofs and generalizations of these results are presented. In contrast to previous ones, they are designed to provide direct graphical definitions of general irreducible kernels satisfying structure equations recently proposed and shown to be closely linked with asymptotic completeness and with the multiparticle structure of Green functions and collision amplitudes in general energy regions. The method can be applied as previously to P(φ)2 and can also be extended to theories involving renormalization which are controlled by phase-space analysis. It is here illustrated in detail for the Bethe-Salpeter kernel in φ24, in which case a new proof of its 4-particle decay (which yields asymptotic completeness in the 2-particle region) is given. (orig.)
Asymptotic corrections to the eigenvalue density of the GUE and LUE
Garoni, T. M.; Forrester, P. J.; Frankel, N. E.
2005-10-01
We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N ×N matrices, both in the bulk of the spectrum and near the spectral edge. This is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density, to which we apply the saddle point method. The main correction to the bulk density is oscillatory in N and depends on the distribution function of the limiting density, while the corrections to the Airy kernel at the soft edge are again expressed in terms of the Airy function and its first derivative. We demonstrate numerically that these expansions are very accurate. A matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk.
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
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.
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.
Gradient expansion for anisotropic hydrodynamics
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.
The 6j-symbol: recursion, correlations and asymptotics
International Nuclear Information System (INIS)
We study the asymptotic expansion of the {6j}-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third-order corrections beyond the leading order. Moreover, in the framework of spinfoam models for 3D quantum gravity, we show how these recursion relations can be used to derive Ward-Takahashi-like identities between the expectation values of graviton-like spinfoam correlations.
Strong and ratio asymptotics for Laguerre polynomials revisited
Deaño, Alfredo; Huertas, Edmundo J.; Marcellán, Francisco
2013-01-01
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the context of Krall-Laguerre or Laguerre-Sobolev-type orthogonal polynomials, are notoriously difficult to compute. In this paper, we propose the use of an alternative expansion, due to Buchholz, in terms of Bessel functions of the first kind. The coefficients in t...
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....
Two-parameter Asymptotics in Magnetic Weyl Calculus
Lein, Max
2008-01-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter \\eps, the case of small coupling $\\lambda$ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which ...
Airy asymptotics: the logarithmic derivative and its reciprocal
Energy Technology Data Exchange (ETDEWEB)
Kearney, Michael J [Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH (United Kingdom); Martin, Richard J [AHL, Man Investments Limited, Sugar Quay, Lower Thames Street, London, EC3R 6DU (United Kingdom)], E-mail: m.j.kearney@surrey.ac.uk
2009-10-23
We consider the asymptotic expansion of the logarithmic derivative of the Airy function Ai'(z)/Ai(z), and also its reciprocal Ai(z)/Ai'(z), as |z| {yields} {infinity}. We derive simple, closed-form solutions for the coefficients which appear in these expansions, which are of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transforms of given functions; this fact, together with the methods employed, suggests further avenues for research.
Two-parameter Asymptotics in Magnetic Weyl Calculus
Lein, Max
2008-01-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter $\\eps$, the case of small coupling $\\lambda$ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two H\\"ormander class symbols are proven: (i) $\\eps \\ll 1$ and $\\lambda \\ll 1$, (ii) $\\eps \\ll 1$ and $\\lambda = 1$ as well as (iii) $\\eps = 1$ and $\\lambda \\ll 1$. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and ...
Two-parameter asymptotics in magnetic Weyl calculus
Lein, Max
2010-12-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ɛ, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hörmander class symbols are proven as (i) ɛ ≪ 1 and λ ≪ 1, (ii) ɛ ≪ 1 and λ = 1, as well as (iii) ɛ = 1 and λ ≪ 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
Two-parameter asymptotics in magnetic Weyl calculus
International Nuclear Information System (INIS)
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
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...... 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....
Edgeworth expansion for functionals of continuous diffusion processes
DEFF Research Database (Denmark)
Podolskij, Mark; Yoshida, Nakahiro
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes....... Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations....
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.
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.
A Semigroup Expansion for Pricing Barrier Options
Directory of Open Access Journals (Sweden)
Takashi Kato
2014-01-01
Full Text Available This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develop a semigroup expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.
Baez, J C; Egan, G F; Baez, John C.; Egan, Greg
2002-01-01
The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a `degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of R^3. We conjecture formulas for the asymptotics of a large class of Riemannian and Lorentzian spin networks, including the Lorentzian 10j symbols, in terms of these degenerate spin networks.
Asymptotics for restricted integer compositions
Malandro, Martin E
2011-01-01
We study the compositions of an integer n where the part sizes of the compositions are restricted to lie in a finite set. We obtain asymptotic formulas for the number of such compositions, the total and average number of parts among all such compositions, and the total and average number of times a particular part size appears among all such compositions. Several of our asymptotics have the additional property that their absolute errors---not just their percentage errors---go to 0 as n goes to infinity. Along the way we also obtain recurrences and generating functions for calculating several of these quantities. Our asymptotic formulas come from the meromorphic analysis of our generating functions. Our results also apply to questions about certain kinds of tilings and rhythm patterns.
International Nuclear Information System (INIS)
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.
Exact and asymptotic results for insurance risk models with surplus-dependent premiums
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.
Asymptotic risks of Viterbi segmentation
Kuljus, Kristi
2010-01-01
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.
ASYMPTOTIC METHODS OF STATISTICAL CONTROL
Directory of Open Access Journals (Sweden)
Orlov A. I.
2014-10-01
Full Text Available Statistical control is a sampling control based on the probability theory and mathematical statistics. The article presents the development of the methods of statistical control in our country. It discussed the basics of the theory of statistical control – the plans of statistical control and their operational characteristics, the risks of the supplier and the consumer, the acceptance level of defectiveness and the rejection level of defectiveness. We have obtained the asymptotic method of synthesis of control plans based on the limit average output level of defectiveness. We have also developed the asymptotic theory of single sampling plans and formulated some unsolved mathematical problems of the theory of statistical control
Asymptotic freedom for nonrelativistic confinement
International Nuclear Information System (INIS)
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle nonrelativistic confining potential model. In this model, asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given, and explicit examples are given for the case of a harmonic oscillator
Comment on Asymptotically Safe Inflation
Tye, S -H Henry
2010-01-01
We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuning is necessary to get enough efolds of infflation in the asymptotically safe inflationary scenario.
Asymptotically free SU(5) models
International Nuclear Information System (INIS)
The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles
International Nuclear Information System (INIS)
Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
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. An...
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...
Cherniavski, V. M.; Shtemler, Yu. 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 n...
Non-Fefferman-Graham asymptotics and holographic renormalization in New Massive Gravity
Cunliff, Colin
2013-01-01
The asymptotic behavior of new massive gravity (NMG) is analyzed for all values of the mass parameter satisfying the Breitenlohner-Freedman bound. The traditional Fefferman-Graham expansion fails to capture the dynamics of NMG, and new terms in the asymptotic expansion are needed to include the massive graviton modes. New boundary conditions are discovered for a range of values $-1<2m^2l^2<1$ at which non-Einstein modes decay more slowly than the Brown-Henneaux boundary conditions. The holographically renormalized stress tensor is computed for these modes, and the relevant counterterms are identified up to unphysical ambiguities.
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....
On Asymptotically Efficient Estimation in Semiparametric Models
Schick, Anton
1986-01-01
A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.
On transfinite extension of asymptotic dimension
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.
Born expansions for charged particle scattering
International Nuclear Information System (INIS)
High-order terms in Born expansions of scattering amplitudes in powers of charge are frequently divergent when long-range Coulomb interactions are present asymptotically. Expansions which are free from these logarithmic divergences have been constructed recently. This paper illustrates these expansions with the simplest example, namely the non-relativistic Rutherford scattering of two charged particles. This approach represents an adequate framework for the calculation of transition amplitudes and a comprehensive starting point for the development of consistent perturbation approximations in multi-channel descriptions of strongly interacting atomic systems
Asymptotic functions and multiplication of distributions
International Nuclear Information System (INIS)
Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory
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.
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)
Asymptotic safety goes on shell
International Nuclear Information System (INIS)
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. (paper)
Asymptotic safety goes on shell
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.
Asymptotic analysis of Hoppe trees
Leckey, Kevin
2012-01-01
We introduce and analyze a random tree model associated to Hoppe's urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight $\\vartheta>0$, a given fixed parameter, all other nodes have weight 1. This resembles the stochastic dynamic of Hoppe's urn. For $\\vartheta=1$ the resulting tree is the well-studied random recursive tree. We analyze the height, internal path length and number of leaves of the Hoppe tree with $n$ nodes as well as the depth of the last inserted node asymptotically as $n\\to \\infty$. Mainly expectations, variances and asymptotic distributions of these parameters are derived.
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.
Exponential asymptotics and capillary waves
Chapman, S. J.; Vanden-Broeck, J.
2002-01-01
Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows....
Asymptotic algebra for charged particles and radiation
International Nuclear Information System (INIS)
A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss' law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish-Faddeev treatment of electrically charged asymptotic fields. (orig.)
Renormalization constants and asymptotic behaviour in quantum electrodynamics
International Nuclear Information System (INIS)
Using dimensional regularization a field theory contains at least one parameter less than the dimension of a mass. The Callan-Symanzik equations for the renormalization constants then become soluble entirely in terms of the coefficient functions. Explicit expressions are obtained for all the renormalization constants in Quantum Electrodynamics. At nonexceptional momenta the infrared behaviour and the three leading terms in the asymptotic expansion of any Greens function are controlled by the Callan-Symanzik equations. For the propagators the three leading terms are computed explicitly in terms of functions of α only. The gauge dependence of the electron propagator in momentum space is solved explicitly in all orders of perturbation theory. (Auth.)
Asymptotic scaling corrections in QCD with Wilson fermions from the 3-loop average plaquette
Alles, B.; FEO, A; Panagopoulos, H.
1998-01-01
We calculate the 3-loop perturbative expansion of the average plaquette in lattice QCD with N_f massive Wilson fermions and gauge group SU(N). The corrections to asymptotic scaling in the corresponding energy scheme are also evaluated. We have also improved the accuracy of the already known pure gluonic results at 2 and 3 loops.
Loss asymptotics for the single-server queue with complete rejection
Zwart, A.P.
2015-01-01
Consider the single-server queue in which customers are rejected if their total sojourn time would exceed a certain level K. A basic performance measure of this system is the probability PK that a customer gets rejected in steady state. This paper presents asymptotic expansions for PK as K ... If
International Nuclear Information System (INIS)
Full text: Calculational methods and Reduce software are described for determining polyhomogeneous asymptotic expansions of solutions of Einstein's equations in null characteristic transport form. As an example, results concerning peeling of gravitational radiation in Null Quasi-Spherical (NQS) spacetimes are presented
Synchronization of complex chaotic systems in series expansion form
International Nuclear Information System (INIS)
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Synchronization of complex chaotic systems in series expansion form
Energy Technology Data Exchange (ETDEWEB)
Ge Zhengming [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)]. E-mail: zmg@cc.nctu.edu.tw; Yang Chenghsiung [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)
2007-12-15
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy.
Asymptotic black hole quasinormal frequencies
Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d greater than or equal to 4 and Reissner-Nordstrom black holes in d = 4, in the limit of infinite damping. For Schwarzschild in d greater than or equal to 4 we find that the asymptotic real part is THawkinglog(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d = 4. For Reissner-Nordstrom in d = 4 w...
Asymptotics of robust utility maximization
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.
Asymptotics for Associated Random Variables
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
S, Vijay Prakash; Sonti, Venkata R.
2016-07-01
Structural-acoustic waveguides of two different geometries are considered: a 2-D rectangular and a circular cylindrical geometry. The objective is to obtain asymptotic expansions of the fluid-structure coupled wavenumbers. The required asymptotic parameters are derived in a systematic way, in contrast to the usual intuitive methods used in such problems. The systematic way involves analyzing the phase change of a wave incident on a single boundary of the waveguide. Then, the coupled wavenumber expansions are derived using these asymptotic parameters. The phase change is also used to qualitatively demarcate the dispersion diagram as dominantly structure-originated, fluid-originated or fully coupled. In contrast to intuitively obtained asymptotic parameters, this approach does not involve any restriction on the material and geometry of the structure. The derived closed-form solutions are compared with the numerical solutions and a good match is obtained.
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.
Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept
International Nuclear Information System (INIS)
The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)
Caustics, counting maps and semi-classical asymptotics
Ercolani, N M
2009-01-01
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitean random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion, (and its derivatives) are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are in fact specific rational functions of a distinguished irrational (algebraic) function of the generating function parameters. This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of parameter). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. These results in turn provide new information about the asymptotics of ...
Asymptotic black hole quasinormal frequencies
Motl, L; Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a simple derivation of the quasinormal frequencies of Schwarzschild black holes in d>=4 and non-extremal Reissner-Nordstrom black holes in d=4, in the limit of infinite damping. For Schwarzschild in d=4 the asymptotic real part of the frequency is (T_Hawking)log(1+2cos(pi.j)), where j is the spin of the perturbation; this confirms a result previously obtained by other means. For Schwarzschild in d>4 we find that the asymptotic real part is (T_Hawking)log(3) for scalar perturbations. For non-extremal Reissner-Nordstrom in d=4 we find a specific but generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for axial electromagnetic-gravitational perturbations; there is nevertheless a hint that the value (T_Hawking)log(2) may be special in this case. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane.
Asymptotically Free Gauge Theories. I
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.
The maximum drag reduction asymptote
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotic safety goes on shell
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.
Asymptotic conservation laws in field theory
Anderson, Ian M.; Torre, Charles G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation...
Asymptotically Plane Wave Spacetimes and their Actions
Witt, Julian Le; Ross, Simon F.
2008-01-01
We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff condi...
Asymptotics of near unit roots (in Russian)
Stanislav Anatolyev; Nikolay Gospodinov
2012-01-01
Sometimes the conventional asymptotic theory yields that the limiting distribution changes discontinuously, or that the asymptotic distribution does not approximate accurately the actual finite-sample distribution. In such situations one finds useful an asymptotic tool of drifting parameterizations where certain parameters are allowed to depend explicitly on the sample size. It proves useful, among other things, for impulse response analysis and forecasting of strongly dependent processes at ...
Asymptotic independence and a network traffic model
Maulik, Krishanu; Resnick, Sidney; Rootzén, Holger
2002-01-01
The usual concept of asymptotic independence, as discussed in the context of extreme value theory, requires the distribution of the coordinatewise sample maxima under suitable centering and scaling to converge to a product measure. However, this definition is too broad to conclude anything interesting about the tail behavior of the product of two random variables that are asymptotically independent. Here we introduce a new concept of asymptotic independence which allows u...
Exponential asymptotic stability for linear volterra equations
John A. D. Appleby
2000-01-01
This note studies the exponential asymptotic stability of the zero solution of the linear Volterra equation x˙ (t) = Ax(t) + t 0 K(t − s)x(s) ds by extending results in the paper of Murakami “Exponential Asymptotic Stability for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991. In particular, when K isi ntegrable and has entries which do not change sign, and the equation has a uniformly asymptotically stable solution, exponential asympto...
International Nuclear Information System (INIS)
We consider a two-dimensional model Schroedinger equation with logarithmic integral non-linearity. We find asymptotic expansions for its solutions (Airy polarons) that decay exponentially at the 'semi-infinity' and oscillate along one direction. These solutions may be regarded as new special functions, which are somewhat similar to the Airy function. We use them to construct global asymptotic solutions of Schroedinger equations with a small parameter and with integral non-linearity of Hartree type
Nikonov, Anatolij Viktorovič; Zakharov, D.D.
2015-01-01
Asymptotically accurate low-frequency models for isotropic elastic coatings and interlayers are developed. The main constraint is the requirement on contact conditions for the layer and the base that at least one of the boundary conditions must include the displacement component in an explicit form. The displacement and stress fields in the three-dimensional elastic system are sought in the form of asymptotic expansion into power series of a small parameter - the ratio between the half-thickn...
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
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...
Why are tensor field theories asymptotically free?
Rivasseau, Vincent
2015-01-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.
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.
Thermodynamics of asymptotically safe theories
Rischke, Dirk H
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 at a constant and calculable value in the ultraviolet, their values can even be made arbitrarily small for an appropriate choice of the ratio $N_c/N_f$ of fermion colours and flavours in the Veneziano limit. Thus, a perturbative treatment can be justified. We compute the pressure, entropy density, and thermal degrees of freedom of these theories to next-to-next-to-leading order in the coupling constants.
An Edgeworth expansion for symmetric statistics
Bentkus, V.; Götze, F.; van Zwet, W. R.
1997-01-01
We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder $O(N^{-1})$ under Cramér's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder $o(N^{-1})$ without imposing additional assumptions on the...
Asymptotic spectral theory for nonlinear time series
Shao, Xiaofeng; Wu, Wei Biao
2007-01-01
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.
Asymptotics of implied volatility far from maturity
Michael R., Tehranchi
2009-01-01
This note explores the behaviour of the implied volatility of a European call option far from maturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.
Complete WKB asymptotics of high frequency vibrations in a stiff problem
Babych, N
2008-01-01
Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and vanishes as epsilon tends to zero on a subinterval, we prove the existence of low and high frequency resonance vibrations. The low frequency vibrations admit the power series expansions on epsilon but this method is not applicable to the description of high frequency vibrations. However, the nonclassical asymptotics on epsilon of the high frequency vibrations were constructed using the WKB method.
International Nuclear Information System (INIS)
Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense
Non-asymptotic fractional order differentiators via an algebraic parametric method
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.
Universal asymptotic umbrella for hydraulic fracture modeling
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.
Penrose type inequalities for asymptotically hyperbolic graphs
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.
1/N-expansion for the anharmonic oscillator
International Nuclear Information System (INIS)
The properties of the 1/N-expansion for the anharmonic oscillator in quantum mechanics have been investigated. The first seven terms of the expansion for the energy of ground and first excited levels are obtained analytically. The high-order behaviour of the 1/N-expansion coefficients in closed form was found, the asymptotic series obtained being Borel summable. The formulae derived was used to find the first seven coefficients of the perturbative expansion in powers of the coupling constant in the case of the double-well potential for arbitrary number of components N. These exact expressions enable us to guess the large-order behaviour of the perturbative coefficients for N=0, 1, ... 4. An example of summing the asymptotic series in powers of 1/N applying the Pade-Borel method is given
Asymptotics of phase and wave functions
Zhaba, V I
2016-01-01
For single and twochannel nucleon-nucleon scattering the asymptotic form of the phase function for r->0 were taken into account for the asymptotic behavior of the wave function. Asymptotics of the wave function will not r^(l+1), and will have a more complex view and be also determined by the behavior of the potential near the origin. Have examined the cases for nonsingular (weakly singular) and strongly singular potentials. Were the numerical calculations of phase, amplitude and wave functions for the nucleon-nucleon potential Argonne v18. Considered 1S0-, 3P0-, 3P1- states of the np- system.
Asymptotic study of subcritical graph classes
Drmota, Michael; Kang, Mihyun; Kraus, Veronika; Rué, Juanjo
2010-01-01
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical"$ $ graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works both in the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp. $g_n$) of labelled (resp. unlabelled) graphs on $n$ vertices from a subcritical graph class ${\\cG}=\\cup_n {\\cG_n}$ satisfies asymptotically the universal behaviour
Energy Technology Data Exchange (ETDEWEB)
Belov, P. A., E-mail: pavelbelov@gmail.com; Yakovlev, S. L., E-mail: yakovlev@cph10.phys.spbu.ru [St. Petersburg State University, Department of Computational Physics (Russian Federation)
2013-02-15
The process of neutron-deuteron scattering at energies above the deuteron-breakup threshold is described within the three-body formalism of Faddeev equations. Use is made of the method of solving Faddeev equations in configuration space on the basis of expanding wave-function components in the asymptotic region in bases of eigenfunctions of specially chosen operators. Asymptotically, wave-function components are represented in the form of an expansion in an orthonormalized basis of functions depending on the hyperangle. This basis makes it possible to orthogonalize the contributions of elastic-scattering and breakup channels. The proposed method permits determining scattering and breakup parameters from the asymptotic representation of the wave function without reconstructing it over the entire configuration space. The scattering and breakup amplitudes for states of total spin S = 1/2 and 3/2 were obtained for the s-wave Faddeev equation.
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...
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.
Asymptotic-group analysis of algebraic equations
Shamrovskii, A. D.; I. V. Andrianov; J. Awrejcewicz
2004-01-01
Both the method of asymptotic analysis and the theory of extension group are applied to study the Descates equation. The proposed algorithm allows to obtain various variants of simplification and can be easily generalized to their algebraic and differential equations.
The Lorentzian proper vertex amplitude: Asymptotics
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.
Asymptotic Likelihood Distribution for Correlated & Constrained Systems
Agarwal, Ujjwal
2016-01-01
It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.
A quantum kinematics for asymptotically flat spacetimes
Campiglia, Miguel
2014-01-01
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\\em states} and the background electric fields which label the {\\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We...
Asymptotic fixed points for nonlinear contractions
Directory of Open Access Journals (Sweden)
Yong-Zhuo Chen
2005-06-01
Full Text Available Recently, W. A. Kirk proved an asymptotic fixed point theorem for nonlinear contractions by using ultrafilter methods. In this paper, we prove his theorem under weaker assumptions. Furthermore, our proof does not use ultrafilter methods.
Negative dimension in general and asymptotic topology
Maslov, V. P.
2006-01-01
We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.
Kinematical bound in asymptotically translationally invariant spacetimes
Shiromizu, T; Tomizawa, S; Shiromizu, Tetsuya; Ida, Daisuke; Tomizawa, Shinya
2004-01-01
We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.
Precise Asymptotics for Lévy Processes
Institute of Scientific and Technical Information of China (English)
Zhi Shui HU; Chun SU
2007-01-01
Let {X(t), t ≥ 0} be a Lévy process with EX(1)=0 and EX2(1)＜∞. In this paper, we shall give two precise asymptotic theorems for {X(t), t≥0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d.random variables.
Asymptotic representation theorems for poverty indices
Lo, Gane Samb; Sall, Serigne Touba
2010-01-01
We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotics of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.
AGB (asymptotic giant branch): Star evolution
Energy Technology Data Exchange (ETDEWEB)
Becker, S.A.
1987-01-01
Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs.
Loop Quantum Gravity and Asymptotically Flat Spaces
Arnsdorf, Matthias
2000-01-01
After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be interpreted as describing fluctuations around fiducial fixed backgrounds. When the backgr...
General smile asymptotics with bounded maturity
Francesco Caravenna; Jacopo Corbetta
2014-01-01
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance 19 (2009), 1-12]. We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion ...
AGB [asymptotic giant branch]: Star evolution
International Nuclear Information System (INIS)
Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs
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.
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.
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Renormalization and asymptotic safety in truncated quantum Einstein gravity
International Nuclear Information System (INIS)
A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be achieved in a space of lagrangians differing only by a field dependent conformal factor. In particular the Noether currents and the quantum constraints can be defined as finite composite operators. The form of the field-dependence in the conformal factor changes with the renormalization scale and a closed formula is obtained for the beta functional governing its flow. The flow possesses a unique fixed point at which the trace anomaly is shown to vanish. The approach to the fixed point adheres to Weinberg's 'asymptotic safety' scenario, both in the gravitational wave/cosmological sector and in the stationary sector. (author)
Asymptotic Energies and QED Shifts for Rydberg States of Helium
Drake, G.W.F.
2007-01-01
This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.
Diagrammatic and asymptotic approaches to the origins of radiative transport theory: tutorial.
Cazé, A; Schotland, John C
2015-08-01
The radiative transport equation (RTE) is used widely to describe the propagation of multiply scattered light in disordered media. In this tutorial, we present two derivations of the RTE for scalar wave fields. The first derivation is based on diagrammatic perturbation theory, while the second stems from an asymptotic multiscale expansion. Although the two approaches are quite distinct mathematically, some common ground can be found and is discussed. PMID:26367292
Asymptotic Analysis of the Load Transfer on Double-Lap Bolted Joints
KRATOCHVIL, Jan
2012-01-01
In this thesis, the complex potential method along with the method of compound asymptotic expansions is applied to the analysis of selected problems of plane elasticity related to double-lap bolted joints. The contribution to the thesis lies in the construction of several closed-form approximations of solutions to the considered problems. After a brief introduction of the basic theoretical concepts in Chapter 2, a mathematical model of a double-lap bolted joint is presented in Chapter 3....
Variational asymptotics for rotating shallow water near geostrophy: a transformational approach
Oliver, Marcel
2006-03-01
We introduce a unified variational framework in which the classical balance models for nearly geostrophic shallow water as well as several new models can be derived. Our approach is based on consistently truncating an asymptotic expansion of a near-identity transformation of the rotating shallow-water Lagrangian. Model reduction is achieved by imposing either degeneracy (for models in a semi-geostrophic scaling) or incompressibility (for models in a quasi-geostrophic scaling) with respect to the new coordinates.
Crack propagation from bi-material notches – matched asymptotic procedure
Czech Academy of Sciences Publication Activity Database
Klusák, Jan; Profant, T.; Ševeček, O.; Kotoul, M.
488-489, - (2012), s. 416-419. ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics - FDM 2011 /10./. Dubrovník, 19.09.2011-21.09.2011] R&D Projects: GA ČR GAP108/10/2049 Institutional research plan: CEZ:AV0Z20410507 Keywords : Orthotropic bi-material notch * two-state integral * matched asymptotic expansion Subject RIV: JL - Materials Fatigue, Friction Mechanics
International Nuclear Information System (INIS)
Many results of theoretical physics are expressed in terms of integrals depending on one or more parameters. Of considerable interest in the behavior of these integrals near those values of parameters which are singular points of the integrals. Corresponding behavior is expressed usually by an asymptotic expansion in Poincare sense. However such an expansion may not exhaust all the qualitative information about the integral behavior near the singularity; in this case it plays only dominant role. The asymptotic expansion of integral near singularity may contain some more terms of series which are exponentially small compared with the dominant series and are called recessive (dingle terminology). These terms not only make more precise the quantitative value of the integral near singularity, reducing the remainder term, but contain essentially new information on its behavior, which in physics describes qualitatively different phenomenon then that described by dominant series. In this paper, using as an example the parabolic cylinder functions, given by contour integrals and depending on two parameters (order and variable), we show that valuable information on their asymptotic behavior is contained in the knowledge of form of integration contour drawn along the steepest descent line (s) (SDL) from passes of the integrand, defined on Riemann surface
Fisher–Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain
International Nuclear Information System (INIS)
Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher–Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlevé equations. We present explicit results up to the 11th order and compare them with a numerical example. (paper)
Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation.
Heller, Michal P; Spaliński, Michał
2015-08-14
Consistent formulations of relativistic viscous hydrodynamics involve short-lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Müller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation. This requires careful accounting for the short-lived modes which leads to an intricate mathematical structure known from the theory of resurgence. PMID:26317715
A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection
Directory of Open Access Journals (Sweden)
Clément Marteau
2016-01-01
Full Text Available We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach and the minimax separation rate (asymptotic approach that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa. In order to enhance our understanding of these two minimax signal detection paradigms, we bring into light hitherto unknown similarities and links between non-asymptotic and asymptotic approaches.
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
The optimal homotopy asymptotic method engineering applications
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...
Light-Cone Expansion of the Dirac Sea with Light Cone Integrals
Finster, Felix
1997-01-01
The Dirac sea is calculated in an expansion around the light cone. The method is to analyze the perturbation expansion for the Dirac sea in position space. This leads to integrals over expressions containing distributions which are singular on the light cone. We derive asymptotic formulas for these "light cone integrals" in terms of line integrals over the external potential and its partial derivatives. The calculations are based on the perturbation expansion for the Dirac sea in the preprint...
Statistical tests of nonparametric hypotheses asymptotic theory
Pons, Odile
2013-01-01
An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the
Asymptotic Regime in N Random Interacting Species
Fiasconaro, A; Valenti, D
2005-01-01
The asymptotic regime of a complex ecosystem with N random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the i_th density species, the extinction of species and the local field acting on the i_th population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the i_th species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.
Asymptotic Redundancies for Universal Quantum Coding
Krattenthaler, C; Krattenthaler, Christian; Slater, Paul
1996-01-01
We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy - the excess of the encoding cost over the source entropy - of universal data compression in a parametric setting. We study certain probability distributions for the two-level quantum systems. We are able to compute exact formulas for the corresponding redundancies, for which we find the asymptotic limits. These results are very suggestive and do indeed point towards a possible quantum extension of the result of Clarke and Barron.
Asymptotically hyperbolic manifolds with small mass
Dahl, Mattias; Sakovich, Anna
2014-01-01
For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero.
The $1/N$ expansion for $SO(N)$ lattice gauge theory at strong coupling
Chatterjee, Sourav
2016-01-01
The $1/N$ expansion is an asymptotic series expansion for certain quantities in large-$N$ lattice gauge theories. This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in $SO(N)$ lattice gauge theory in the strong coupling regime in any dimension. The terms in the expansion are expressed as sums over trajectories of strings in a lattice string theory, establishing an explicit gauge-string duality. The trajectories trace out surfaces of genus zero for the first term in the expansion, and surfaces of higher genus for the higher terms.
Drag force in asymptotically Lifshitz spacetimes
Fadafan, Kazem Bitaghsir
2009-01-01
We calculated drag force for asymptotically Lifshitz space times in (d + 2)-dimensions with arbitrary dynamical exponent $z$. We find that at zero and finite temperature the drag force has a non-zero value. Using the drag force calculations, we investigate the DC conductivity of strange metals.
Phase Spaces for asymptotically de Sitter Cosmologies
Kelly, William R
2012-01-01
We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension $d \\ge 3$. One type contains solutions asymptotic to the expanding spatially-flat ($k=0$) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic $(k=-1)$ patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For $d=3$ and $k=-1$ our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermore, we identify an interesting algebra (even larger than the ASG) containing two Virasoro algebras related by a reality condition and having imaginary central charges $\\pm i \\frac{3\\ell}{2G}$. On the appropriate phase spaces, our charges agree with those obtained previously using dS/CFT methods. Thus we provide a sense in which (some of) the dS/CFT charges act on a well-defined phase space. Along the way we show that, des...
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.
Asymptotic base loci on singular varieties
Cacciola, Salvatore
2011-01-01
We prove that the non-nef locus and the restricted base locus of a pseudoeffective divisor coincide on KLT pairs. We also extend to KLT pairs F. Russo's characterization of nef and abundant divisors by means of asymptotic multiplier ideals.
The conformal approach to asymptotic analysis
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.
Asymptotic evolution of quantum Markov chains
International Nuclear Information System (INIS)
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.
Asymptotic structure in substitution tiling spaces
Barge, Marcy
2011-01-01
Every sufficiently regular space of tilings of $\\R^d$ has at least one pair of distinct tilings that are asymptotic under translation in all the directions of some open $(d-1)$-dimensional hemisphere. If the tiling space comes from a substitution, there is a way of defining a location on such tilings at which asymptoticity `starts'. This leads to the definition of the {\\em branch locus} of the tiling space: this is a subspace of the tiling space, of dimension at most $d-1$, that summarizes the `asymptotic in at least a half-space' behavior in the tiling space. We prove that if a $d$-dimensional self-similar substitution tiling space has a pair of distinct tilings that are asymptotic in a set of directions that contains a closed $(d-1)$-hemisphere in its interior, then the branch locus is a topological invariant of the tiling space. If the tiling space is a 2-dimensional self-similar Pisot substitution tiling space, the branch locus has a description as an inverse limit of an expanding Markov map on a 1-dimens...
Contraints on Matter from Asymptotic Safety
Percacci, Roberto; Perini, Daniele
2002-01-01
Recent studies of the ultraviolet behaviour of pure gravity suggest that it admits a non-Gaussian attractive fixed point, and therefore that the theory is asymptotically safe. We consider the effect on this fixed point of massless minimally coupled matter fields. The existence of a UV attractive fixed point puts bounds on the type and number of such fields.
On the Asymptotic Accuracy of Efron's Bootstrap
Singh, Kesar
1981-01-01
In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.
Asymptotic theory of integrated conditional moment tests
Bierens, H.J.; Ploberger, W.
1995-01-01
In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network tes
Infrared studies of asymptotic giant branch stars
International Nuclear Information System (INIS)
In this thesis studies are presented of asymptotic giant branch stars, which are thought to be an important link in the evolution of the galaxy. The studies were performed on the basis of data collected by the IRAS, the infrared astronomical satelite. 233 refs.; 33 figs.; 16 tabs
On the Asymptotic Distribution of Signal Fraction
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.
Lectures on renormalization and asymptotic safety
International Nuclear Information System (INIS)
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method
Asymptotic quantum cloning is state estimation
Bae, Joonwoo; Acin, Antonio
2006-01-01
The impossibility of perfect cloning and state estimation are two fundamental results in Quantum Mechanics. It has been conjectured that quantum cloning becomes equivalent to state estimation in the asymptotic regime where the number of clones tends to infinity. We prove this conjecture using two known results of Quantum Information Theory: the monogamy of quantum correlations and the properties of entanglement breaking channels.
Asymptotic probability density functions in turbulence
Minotti, F. O.; Speranza, E.
2007-01-01
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily applied to rather general problems. Although the approximation involved cannot be ascertained a priori, we show that application of the formalism to well known problems gives the correct results.
Resonance asymptotics in the generalized Winter model
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.
Asymptotic approaches to marginally stable resonators.
Nagel, J; Rogovin, D; Avizonis, P; Butts, R
1979-09-01
We present analytical solutions valid for large Fresnel number of the Fresnel-Kirchhoff integral equation for marginally stable resonators, for the specific case of flat circular mirrors. The asymptotic approaches used for curved mirrors have been extended to the waveguide region given by m diffraction around the mirror edge. PMID:19687883
Eigenvalue asymptotics for Dirac-Bessel operators
Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.
2016-06-01
In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.
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...
Heavy axion in asymptotically safe QCD
Kobakhidze, Archil
2016-01-01
Assuming QCD exhibits an interacting fixed-point behaviour in the ultraviolet regime, I argue that the axion can be substantially heavier than in the conventional case of asymptotically free QCD due to the enhanced contribution of small size instantons to its mass.
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
Pobylitsa, P V
2004-01-01
The 1/Nc expansion is formulated for the baryon wave function in terms of a specially constructed generating functional. The leading order of this 1/Nc expansion is universal for all low lying baryons [including the O(1/Nc)and O(1)excited resonances] and for baryon-meson scattering states. A nonlinear evolution equation of Hamilton-Jacobi type is derived for the generating functional describing the baryon distribution amplitude in the large-Nc limit. In the asymptotic regime this nonlinear equation is solved analytically. The anomalous dimensions of the leading twist baryon operators diagonalizing the evolution are computed analytically up to the next-to-leading order of the 1/Nc expansion.
Asymptotics of the discrete spectrum for complex Jacobi matrices
Maria Malejki
2014-01-01
The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of infinite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in \\(l^2(\\mathbb{N})\\).
Cosmic censorship, persistent curvature and asymptotic causal pathology
International Nuclear Information System (INIS)
The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)
Solutions of special asymptotics to the Einstein constraint equations
Huang, Lan-Hsuan
2010-01-01
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.
Weak Gibbs measures as Gibbs measures for asymptotically additive sequences
Iommi, Godofredo; Yayama, Yuki
2015-01-01
In this note we prove that every weak Gibbs measure for an asymptotically additive sequences is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure for an asymptotically additive sequence. This allows, for example, to apply recent results on dimension theory of asymptotically additive sequences to study multifractal analysis for weak Gibbs measure for continuous potentials.
Asymptotic estimates and compactness of expanding gradient Ricci solitons
Deruelle, Alix
2014-01-01
We first investigate the asymptotics of conical expanding gradient Ricci solitons by proving sharp decay rates to the asymptotic cone both in the generic and the asymptotically Ricci flat case. We then establish a compactness theorem concerning nonnegatively curved expanding gradient Ricci solitons.
Supersymmetric 3D gravity with torsion: asymptotic symmetries
Cvetkovic, B.; Blagojevic, M
2007-01-01
We study the structure of asymptotic symmetries in N=1+1 supersymmetric extension of three-dimensional gravity with torsion. Using a natural generalization of the bosonic anti-de Sitter asymptotic conditions, we show that the asymptotic Poisson bracket algebra of the canonical generators has the form of two independent super-Virasoro algebras with different central charges.
Asymptotic symmetries in 3d gravity with torsion
Blagojevic, M; Vasilic, M.
2003-01-01
We study the nature of asymptotic symmetries in topological 3d gravity with torsion. After introducing the concept of asymptotically anti-de Sitter configuration, we find that the canonical realization of the asymptotic symmetry is characterized by the Virasoro algebra with classical central charge, the value of which is the same as in general relativity: c=3l/2G.
Componentwise Asymptotic Stability of Continuous-Time Interval Systems
Institute of Scientific and Technical Information of China (English)
赵胜民; 唐万生; 李光泉; 李文秀
2003-01-01
A special type of asymptotic (exponential) stability, namely componentwise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.
Robust Asymptotic Tests of Statistical Hypotheses Involving Nuisance Parameters
Wang, Paul C. C.
1981-01-01
A robust version of Neyman's optimal $C(\\alpha)$ test is proposed for contamination neighborhoods. The proposed robust test is shown to be asymptotically locally maximin among all asymptotic level $\\alpha$ tests. Asymptotic efficiency of the test procedure at the ideal model is investigated. An outlier resistant version of Student's $t$-test is proposed.
Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits
Directory of Open Access Journals (Sweden)
Nicolae Adriana
2010-01-01
Full Text Available We give fixed point results for classes of mappings that generalize pointwise contractions, asymptotic contractions, asymptotic pointwise contractions, and nonexpansive and asymptotic nonexpansive mappings. We consider the case of metric spaces and, in particular, CAT spaces. We also study the well-posedness of these fixed point problems.
Borisov, Denis; Cardone, Giuseppe
2012-01-01
We consider a magnetic Schroedinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum.
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
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.
The Asymptotic Safety Scenario in Quantum Gravity
Directory of Open Access Journals (Sweden)
Niedermaier Max
2006-12-01
Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotically Lifshitz brane-world black holes
International Nuclear Information System (INIS)
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: ► Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. ► Studying the thermodynamical behavior of asymptotically Lifshitz black holes. ► Showing that the entropy imposes the critical exponent z to be bounded from above. ► Discussing the phase transition for different spatial topologies.
Asymptotically Lifshitz Brane-World Black Holes
Ranjbar, Arash; Shahidi, Shahab
2012-01-01
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We show that although the Lifshitz space-time cannot be considered as a vacuum solution of the RSII brane-world, the asymptotically Lifshitz solution can. We then study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the condition on the positivity of entropy imposes an upper bound on the critical exponent $z$. This maximum value of $z$ corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed.
Asymptotic safety and the cosmological constant
Falls, Kevin
2016-01-01
We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, ν = 1/3, found in numerical lattice studies by Hamber. Returning to the full theory we find that by setting the cosmological constant to zero the critical exponent agrees with the conformally reduced theory. This suggests the fixed point may be physical while hinting at solution to the cosmological constant problem.
Black holes and asymptotically safe gravity
Falls, Kevin; Raghuraman, Aarti
2010-01-01
Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short distance physics is characterized by a non-trivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross sections display a threshold, are suppressed in the Planckian, and reproduce the semi-classical result in the deep...
Asymptotic dynamics of three-dimensional gravity
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.
Asymptotically anti-de Sitter Proca Stars
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.
Brane model with two asymptotic regions
Lubo, Musongela
2005-02-01
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
A Brane model with two asymptotic regions
Lubo, M
2004-01-01
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip.S.Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
Brane model with two asymptotic regions
International Nuclear Information System (INIS)
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane
Line Complexity Asymptotics of Polynomial Cellular Automata
Stone, Bertrand
2016-01-01
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial transition rules, where the symbols in the automaton are integers modulo some prime $p$. We are principally concerned with the asymptotic behavior of the line complexity sequence $a_T(k)$, which counts, for each $k$, the number of coefficient strings of length...
Asymptotic elastic energy in simple metals
International Nuclear Information System (INIS)
The asymptotic form of the elastic binding energy ΔEsup(as)(R) between two Mg atoms in Al is expressed as a product of a lattice Green function and the dipole force tensor P. The quantity P is obtained by a nearly free electron model in which the impurity effect is introduced by a screened Ashcroft pseudopotential characterized by an excess charge ΔZ and a core radius rsub(j). (author)
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J.; Bassler, S.; 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 n...
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan; Pawlowski, Jan M.
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{Christia...
Asymptotic Consensus Without Self-Confidence
Nowak, Thomas
2015-01-01
This paper studies asymptotic consensus in systems in which agents do not necessarily have self-confidence, i.e., may disregard their own value during execution of the update rule. We show that the prevalent hypothesis of self-confidence in many convergence results can be replaced by the existence of aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually store information about an agent's value distributedly in the network. Our results are applicable to systems with m...
Asymptotic linear stability of solitary water waves
Pego, Robert L.; Sun, Shu-Ming
2010-01-01
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 a...
Asymptotic completeness in QED. Pt. 1
International Nuclear Information System (INIS)
Projection operators onto the asymptotic scattering states are defined in the space of quasilocal states of QED in a Gupta-Bleuler formulation. They are obtained as weak limits for t → ±∞ of expressions formed with interacting fields, in close analogy to the LSZ expressions known from field theories without infrared problems. It is shown that these limits exist in perturbative QED and are equal to the identity. (orig.)
Asymptotic completeness in QED. Pt. 2
International Nuclear Information System (INIS)
Physical states and fields in QED are defined as limits in the sense of Wightman functions of states and composite fields of the Gupta-Bleuler formalism. A formulation of asymptotic completeness proposed in an earlier publication for the Gupta-Bleuler case is transferred to the physical state space and shown to be valid in perturbation theory. An application to the calculation of inclusive cross sections is discussed. (orig.)
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M.(Centro Multidisciplinar de Astrofísica – CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Avenida Rovisco Pais 1, Lisboa, 1049-001, Portugal); Flachi, Antonino; 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 th...
Theorems for Asymptotic Safety of Gauge Theories
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.
Variational Asymptotic Micromechanics Modeling of Composite Materials
Tang, Tian
2008-01-01
The issue of accurately determining the effective properties of composite materials has received the attention of numerous researchers in the last few decades and continues to be in the forefront of material research. Micromechanics models have been proven to be very useful tools for design and analysis of composite materials. In the present work, a versatile micromechanics modeling framework, namely, the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), has been invented a...
On the large $N$ expansion in hyperbolic sigma-models
Niedermaier, Max
2007-01-01
Invariant correlation functions for ${\\rm SO}(1,N)$ hyperbolic sigma-models are investigated. The existence of a large $N$ asymptotic expansion is proven on finite lattices of dimension $d \\geq 2$. The unique saddle point configuration is characterized by a negative gap vanishing at least like 1/V with the volume. Technical difficulties compared to the compact case are bypassed using horospherical coordinates and the matrix-tree theorem.
Asymptotics of the instantons of Painleve I
Garoufalidis, Stavros; Kapaev, Andrei; Marino, Marcos
2010-01-01
The 0-instanton solution of Painlev\\'e I is a sequence $(u_{n,0})$ of complex numbers which appears universally in many enumerative problems in algebraic geometry, graph theory, matrix models and 2-dimensional quantum gravity. The asymptotics of the 0-instanton $(u_{n,0})$ for large $n$ were obtained by the third author using the Riemann-Hilbert approach. For $k=0,1,2,...$, the $k$-instanton solution of Painlev\\'e I is a doubly-indexed sequence $(u_{n,k})$ of complex numbers that satisfies an explicit quadratic non-linear recursion relation. The goal of the paper is three-fold: (a) to compute the asymptotics of the 1-instanton sequence $(u_{n,1})$ to all orders in $1/n$ by using the Riemann-Hilbert method, (b) to present formulas for the asymptotics of $(u_{n,k})$ for fixed $k$ and to all orders in $1/n$ using resurgent analysis, and (c) to confirm numerically the predictions of resurgent analysis. We point out that the instanton solutions display a new type of Stokes behavior, induced from the tritronqu\\'ee ...
Asymptotic form of the Kohn-Sham correlation potential
International Nuclear Information System (INIS)
The density-functional correlation potential of a finite system is shown to asymptotically approach a nonzero constant along a nodal surface of the energetically highest occupied orbital and zero everywhere else. This nonuniform asymptotic form of the correlation potential exactly cancels the nonuniform asymptotic behavior of the exact exchange potential discussed by Della Sala and Goerling [Phys. Rev. Lett. 89, 33003 (2002)]. The sum of the exchange and correlation potentials therefore asymptotically tends to -1/r everywhere, consistent with the asymptotic form of the Kohn-Sham potential as analyzed by Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)
Volume expansion of a Swiss-cheese universe
International Nuclear Information System (INIS)
In order to investigate the effect of inhomogeneities on the volume expansion of the universe, we study a modified Swiss-cheese universe model. Since this model is an exact solution of Einstein's equations, we can get insight into the nonlinear dynamics of an inhomogeneous universe from it. We find that inhomogeneities make the volume expansion slower than that of the background Einstein-de Sitter universe when they can be regarded as small fluctuations in the background universe. This result is consistent with the previous studies based on the second order perturbation analysis. On the other hand, if the inhomogeneities cannot be treated as small perturbations, the volume expansion of the universe depends on the type of fluctuations. Although the volume expansion rate approaches the background value asymptotically, the volume itself can be finally arbitrarily smaller than the background one and can be larger than that of the background, but there is an upper bound on it
An asymptotic sampling formula for the coalescent with Recombination
Jenkins, Paul A; 10.1214/09-AAP646
2010-01-01
Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the population genetics community, extending the underlying random-mating model to include recombination has received much attention in the past, but no general closed-form sampling formula is currently known even for the simplest extension, that is, a model with two loci. In this paper, we show that it is possible to obtain useful closed-form results in the case the population-scaled recombination rate $\\rho$ is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formu...
Asymptotic dynamics of short-waves in nonlinear dispersive models
Manna, M A
1998-01-01
The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation can propagates short-waves. This result contradict the Benjamin hypothesis that short-waves tends not to propagate in this model and close a part of the old controversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine equations. We shown that a nonlinear (quadratic) Klein-Gordon type equation substitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation of long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon equations are understood as an all orders asymptotic behaviour of short-waves. It is proved that the antikink solution of phi-4 model which was never obtained perturbatively can be obtained by perturbation expansion in the wave-number k in the short-wave limit.
Asymptotics with a positive cosmological constant: III. The quadrupole formula
Ashtekar, Abhay; Kesavan, Aruna
2015-01-01
Almost a century ago, Einstein used a weak field approximation around Minkowski space-time to calculate the energy carried away by gravitational waves emitted by a time changing mass-quadrupole. However, by now there is strong observational evidence for a positive cosmological constant, $\\Lambda$. To incorporate this fact, Einstein's celebrated derivation is generalized by replacing Minkowski space-time with de Sitter space-time. The investigation is motivated by the fact that, because of the significant differences between the asymptotic structures of Minkowski and de Sitter space-times, many of the standard techniques, including the standard $1/r$ expansions, can not be used for $\\Lambda >0$. Furthermore since, e.g., the energy carried by gravitational waves is always positive in Minkowski space-time but can be arbitrarily negative in de Sitter space-time \\emph{irrespective of how small $\\Lambda$ is}, the limit $\\Lambda\\to 0$ can fail to be continuous. Therefore, a priori it is not clear that a small $\\Lamb...
Asymptotics with a positive cosmological constant. III. The quadrupole formula
Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna
2015-11-01
Almost a century ago, Einstein used a weak field approximation around Minkowski spacetime to calculate the energy carried away by gravitational waves emitted by a time changing mass-quadrupole. However, by now there is strong observational evidence for a positive cosmological constant, Λ . To incorporate this fact, Einstein's celebrated derivation is generalized by replacing Minkowski spacetime with de Sitter spacetime. The investigation is motivated by the fact that, because of the significant differences between the asymptotic structures of Minkowski and de Sitter spacetimes, many of the standard techniques, including the usual 1 /r expansions, cannot be used for Λ >0 . Furthermore, since, e.g., the energy carried by gravitational waves is always positive in Minkowski spacetime but can be arbitrarily negative in de Sitter spacetime irrespective of how small Λ is, the limit Λ →0 can fail to be continuous. Therefore, a priori it is not clear that a small Λ would introduce only negligible corrections to Einstein's formula. We show that, while even a tiny cosmological constant does introduce qualitatively new features, in the end, corrections to Einstein's formula are negligible for astrophysical sources currently under consideration by gravitational wave observatories.
Birk, C.; Liu, L.; Song, Ch.
2016-04-01
A high-order doubly-asymptotic open boundary for modelling scalar wave propagation in two-dimensional unbounded media is presented. The proposed method is capable of handling domains with arbitrary geometry by using a circular boundary to divide these into near field and far field. The original doubly-asymptotic continued-fraction approach for the far field is improved by introducing additional factor coefficients. Additionally, low-order modes are approximated by singly-asymptotic expansions only to increase the robustness of the formulation. The scaled boundary finite element method is employed to model wave propagation in the near field. Here, the frequency-dependent impedance of bounded subdomains is also expanded into a series of continued fractions. Only three to four terms per wavelength are required to obtain accurate results. The continued-fraction solutions for the bounded domain and the proposed high-order doubly-asymptotic open boundary are expressed in the time-domain as coupled ordinary differential equations, which can be solved by standard time-stepping schemes. Numerical examples are presented to demonstrate the accuracy and robustness of the proposed method, as well as its advantage over existing singly-asymptotic open boundaries.
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.)
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.)
A uniformly valid asymptotic solution of the surface wave problem due to underwater sources
International Nuclear Information System (INIS)
The two-dimensional linearized problem of surface waves in water of finite (or infinite) depth due to a stationary periodic source situated at a finite depth below the free surface, is considered. The formal solution of the problem is derived by using Laplace and Fourier transforms. A uniformly valid asymptotic expansion of the wave integral is obtained by using the method of Bleistein in the case of finite depth and that of Vander Waerden in the case of infinite depth. Physical interpretation of the results so derived is given. (author)
Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
Skenderis, K
2001-01-01
We consider asymtotically anti-de Sitter spacetimes in general dimensions. We review the origin of infrared divergences in the on-shell gravitational action, and the construction of the renormalized on-shell action by the addition of boundary counterterms. In odd dimensions, the renormalized on-shell action is not invariant under bulk diffeomorphisms that yield conformal transformations in the boundary (holographic Weyl anomaly). We obtain formulae for the gravitational stress energy tensor, defined as the metric variation of the renormalized on-shell action, in terms of coefficients in the asymptotic expansion of the metric near infinity. The stress energy tensor transforms anomalously under bulk diffeomorphisms broken by infrared divergences.
Energy Technology Data Exchange (ETDEWEB)
Batishchev, V.A.
1989-06-01
For large Marangoni numbers, formal asymptotic expansions are obtained for the solution to the stationary problem of thermocapillary flow of a liquid in an unbounded region with nonuniform heating of the free boundary. A nonlinear boundary layer is shown to be formed near the free surface. Self-similar solutions are obtained for the boundary layer in the vicinity of the critical point. An equation for the free boundary is obtained which is reduced to the known equation for an equilibrium free boundary of a capillary liquid when the temperature gradient becomes zero. 11 refs.
Energy Technology Data Exchange (ETDEWEB)
Borisov, D I
2003-12-31
We consider a singularly perturbed spectral boundary-value problem for the Laplace operator in a two-dimensional domain with frequently alternating non-periodic boundary conditions. Under certain very weak restrictions on the alternation structure of the boundary conditions, we obtain the first terms of the asymptotic expansions of the eigenelements of this problem. Under still weaker restrictions, we obtain estimates for the rate of convergence of the eigenvalues.
Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories
International Nuclear Information System (INIS)
An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed
An Asymptotically Free Phi4 Theory
Huang, Kerson
1993-01-01
The Phi4 theory in 4-epsilon dimensions has two fixed points, which coincide in the limit epsilon->0. One is a Gaussian UV fixed point, and the other a non-trivial IR fixed point. They lead to two different continuum field theories. The commonly adopted IR theory is ``trivial,'' behaves like perturbation theory, and suggests an upper bound on the Higgs boson mass. The UV theory is asymptotically free, and does not impose a bound on the Higgs mass. The UV continuum limit can also be reached in...
On the rate of asymptotic eigenvalue degeneracy
International Nuclear Information System (INIS)
The gap between asymptotically degenerate eigenvalues of onedimensional Schroedinger operators is estimated. The procedure is illustrated for two examples, one where the solutions of Schroedinger's equation are explicitly known and one where they are not. For the latter case a comparison theorem for ordinary differential equationsis required. An incidental result is that a semiclassical (W-K-B) method gives a much better approximation to the logarithmic derivative of a wave-function than to the wave-funtion itself; explicit error-bounds for the logarithmic derivative are given. (orig.)
Asymptotic behaviour of exclusive processes in QCD
International Nuclear Information System (INIS)
The main ideas, methods and results in the investigation of the asymptotic behaviour of exclusive processes are reviewed. We discuss power behaviour and its dependence on hadron quantum numbers, logarithmic corrections and properties of nonperturbative hadronic wave functions. Applications to meson and baryon form factors, strong, electromagnetic and weak decays of heavy mesons, elastic scattering, threshold behaviour of inclusive structure functions, etc., are described. Comparison of theoretical predictions with experimental data is made whenever possible. The review may be of interest to theoreticians, experimentalists and students specializing in elementary particle physics. The experts in this field can also find new results (nonleading logarithms, higher twist processes, novel applications, etc.). (orig.)
Asymptotic Performance for Delayed Exponential Process
Boyer, Remy; Abed-Meraim, Karim
2007-01-01
The damped and delayed sinusoidal (DDS) model can be defined as the sum of sinusoids whose waveforms can be damped and delayed. This model is suitable for compactly modeling short time events. This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this correspondence, we derive exact and approximate asymptotic Cramér–Rao bounds (CRBs) for the DDS model. This analysis shows that this model has better, or at least similar, theoretical perform...
The asymptotics of group Russian roulette
van de Brug, Tim; Kager, Wouter; Meester, Ronald
2015-01-01
We study the group Russian roulette problem, also known as the shooting problem, defined as follows. We have $n$ armed people in a room. At each chime of a clock, everyone shoots a random other person. The persons shot fall dead and the survivors shoot again at the next chime. Eventually, either everyone is dead or there is a single survivor. We prove that the probability $p_n$ of having no survivors does not converge as $n\\to\\infty$, and becomes asymptotically periodic and continuous on the ...
Energy Technology Data Exchange (ETDEWEB)
Milgram, Michael S. [P.O. Box 1484, Deep River, Ont., K0J 1P0 (Canada)]. E-mail: mike@geometrics-unlimited.com
2005-07-15
Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.
Forelli-Rudin construction and asymptotic expansion of Szegö kernel on Reinhardt domains
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Xu, H.
2015-01-01
Roč. 52, č. 4 (2015), s. 905-927. ISSN 0030-6126 Institutional support: RVO:67985840 Keywords : transformation Subject RIV: BA - General Mathematics Impact factor: 0.402, year: 2014 http://projecteuclid.org/euclid.ojm/1447856025
Asymptotically Exact Localized Expansions for Signals in Time-Frequency Domain
Muzhikyan, Aramazd H
2011-01-01
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative geometry of the time-frequency plane. Signals are visualized using graphical representation constructed.
Asymptotic Expansion of a Multiscale Numerical Scheme for Compressible Multiphase Flow
Abgrall, Remi; Perrier, Vincent
2006-01-01
32 pages International audience The simulation of compressible multiphase problems is a difficult task for modelization and mathematical reasons. Here, thanks to a probabilistic multiscale interpretation of multiphase flows, we construct a numerical scheme that provides a solution to these difficulties. Three types of terms can be identified in the scheme in addition to the temporal term. One is a conservative term, the second one plays the role of a nonconservative term that is related...
Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
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...
Lattice Quantum Gravity and Asymptotic Safety
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...
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
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...
Asymptotic properties of quantum Markov chains
International Nuclear Information System (INIS)
The asymptotic dynamics of discrete quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space in which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis of 1-forms is presented. It is applicable whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small, but it also sheds new light onto the relation between the asymptotic dynamics of discrete quantum Markov chains and fixed points of their generating quantum operations. Finally, we show that without any restriction our construction applies to all initial states whose support belongs to the so-called recurrent subspace. (paper)
Asymptotically Lifshitz brane-world black holes
Energy Technology Data Exchange (ETDEWEB)
Ranjbar, Arash, E-mail: a_ranjbar@sbu.ac.ir; Sepangi, Hamid Reza, E-mail: hr-sepangi@sbu.ac.ir; Shahidi, Shahab, E-mail: s_shahidi@sbu.ac.ir
2012-12-15
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: Black-Right-Pointing-Pointer Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. Black-Right-Pointing-Pointer Studying the thermodynamical behavior of asymptotically Lifshitz black holes. Black-Right-Pointing-Pointer Showing that the entropy imposes the critical exponent z to be bounded from above. Black-Right-Pointing-Pointer Discussing the phase transition for different spatial topologies.
Vacuum polarization in asymptotically Lifshitz black holes
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.
Vacuum polarization in asymptotically Lifshitz black holes
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...
Relaxing the parity conditions of asymptotically flat gravity
International Nuclear Information System (INIS)
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. Poincare 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 Poincare group. (paper)
Asymptotic parameterization in inverse limit spaces of dendrites
Hamilton, Brent
2012-01-01
In this paper, we study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point is periodic. Using symbolic dynamics, sufficient conditions for two rays in the inverse limit space to have asymptotic parameterizations are given. Being a topological invariant, the classification of asymptotic parameterizations would be a useful tool when d...
Singularities in asymptotically anti-de Sitter spacetimes
Ishibashi, Akihiro; Maeda, Kengo
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 surfac...
The Goldbach problem with primes having binary expansions of a special form
Eminyan, K. M.
2014-02-01
We obtain an asymptotic formula for the number of representations of an odd number N by a sum of three primes in {N}_{0}, where {N}_{0} stands for the set of positive integers whose binary expansions have evenly many 1's.
The Goldbach problem with primes having binary expansions of a special form
International Nuclear Information System (INIS)
We obtain an asymptotic formula for the number of representations of an odd number N by a sum of three primes in N0, where N0 stands for the set of positive integers whose binary expansions have evenly many 1's
On the asymptotic methods for nuclear collective models
Gheorghe, A. C.; Raduta, A. A.
2009-01-01
Contractions of orthogonal groups to Euclidean groups are applied to analytic descriptions of nuclear quantum phase transitions. The semiclassical asymptotic of multipole collective Hamiltonians are also investigated.
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....
Asymptotic stability of Riemann waves for conservation laws
Chen, G.-Q.; Frid, H.; Marta
We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L∞ . Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.
International Nuclear Information System (INIS)
The asymptotic method of post-Newtonian (PN) expansion for weak gravitational fields, recently developed, is compared with the standard method of PN expansion, in the particular case of a massive test particle moving along a geodesic line of a weak Schwarzschild field. First, the expression of the active mass in Schwarzschild's solution is given for a barotropic perfect fluid, both for general relativity (GR) and for an alternative, scalar theory. The principle of the asymptotic method is then recalled and the PN expansion of the active mass is derived. The PN correction to the active mass is made of Newtonian elastic energy, augmented, for the scalar theory, by a term due to the self-reinforcement of the gravitational field. Third, two equations, both correct to first order, are derived for the geodesic motion of a mass particle: a standard one an asymptotic one. Finally, the difference between the solutions of these two equations is numerically investigated in the case of Mercury. The asymptotic solution deviates from the standard one like the square of the time elapsed since the initial time. This is due to a practical shortcoming of the asymptotic method, which is shown to disappear if one reinitializes the asymptotic problem often enough. Thus, both methods are equivalent in the case investigated
International Nuclear Information System (INIS)
In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential vee(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is vee(r)=vee(0)+βr+O(r2), with vee(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange vx(r) and correlation vc(r) potentials. These functions also approach the nucleus linearly with the linear term of vx(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of vc(r) being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed
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...
Asymptotic Behaviour of Neutron Transport Processes
International Nuclear Information System (INIS)
The solution of the initial-value problem of the time-dependent linear Boltzmann equation corresponds to a semigroup of linear transformations: Initial-value problem: δn/δt = An n(x, v, 0) = f(x, v) Solution: n(x, v, t) = Ttf(x, v) Tt = eAt Lehner and Wing were the first to use a Laplace transform technique for the study of the asymptotic behaviour of the solution. Mika, Bednarz, Albertoni, Kaper et al. extended this technique to more general problems. The main task is always to find the spectrum of the Boltzmann operator A. Asymptotic behaviour is closely related to the point spectrum of A , if the latter exists. This paper uses a completely new approach, mean ergodic theory, the study of asymptotic properties of semigroups of bounded transformations in a Banach space. Two types of function spaces are considered; (1) The Banach space Ltm of functions integrable on the six-dimensional μ- space of statistical mechanics. The Banach norm ||f|| equals the total number of neutrons in the system; (2) The Hilbert space L2m of functions square integrable on the μ-space. The inner product (f, g) equals the totalNcount rate of the neutron distribution f due to an array of neutron detectors described by the weight function g of the space dual to that of all neutron distributions. Excluding the case of a super-critical system, the semigroup generated by the Boltzmann operator A is uniformly bounded || Tt II K, t ≥ 0. The splitting theorem of mean ergodic theory can be applied to T t . The initial distribution is split uniquely into a sum of a reversible and a flight vector. Now a special property of the semigroup generated by the Boltzmann operator A enters: there exists a characteristic time t0 > 0 depending only on the geometry and chemistry of the system such that Ttf(x,v) > 0 for all (x, v) , for all f and all t ≥ 0. From this property it is possible to deduce that an equilibrium distribution exists and is unique. Taking the Hilbert space L2m criticality of a
Narski Jacek; Negulescu Claudia; Maldarella Dario; Degond Pierre; Deluzet Fabrice; Parisot Martin
2011-01-01
International audience In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, ellip-tic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this ...
Effects of pair creation on the expansion of vacuum bubbles
International Nuclear Information System (INIS)
The real-time behavior of true-vacuum bubbles nucleated in the false-vacuum background is studied in a lambdaphi4 theory. Classically, the bubble expansion rate has been known to approach the velocity of light asymptotically. A quantum effect, creation of Higgs and fermion pairs, is studied by a semiclassical method, and is shown to lead to a slower expansion rate. Within the thin-wall approximation, several possible asymptotic behaviors are examined. A solution that behaves like the classical one but with different coefficients is shown to be stable. The first-order corrections to the coefficients are calculated approximately. The created Higgs are found to remain inside the bubble and carry an energy of approximately 10-3 lambda of the energy released from the false vacuum. The fermions that are massless in the false vacuum go out of the bubble and have energy approx.= 10-3 g2, where g is the Yukawa coupling constant. It is shown that the resulting asymptotic state is Lorentz invariant. (orig.)
Expansion for Universal Quantifiers
Lenglet, Sergueï
2012-01-01
Expansion is an operation on typings (i.e., pairs of typing environments and result types) defined originally in type systems for the lambda-calculus with intersection types in order to obtain principal (i.e., most informative, strongest) typings. In a type inference scenario, expansion allows postponing choices for whether and how to use non-syntax-driven typing rules (e.g., intersection introduction) until enough information has been gathered to make the right decision. Furthermore, these choices can be equivalent to inserting uses of such typing rules at deeply nested positions in a typing derivation, without needing to actually inspect or modify (or even have) the typing derivation. Expansion has in recent years become simpler due to the use of expansion variables (e.g., in System E). This paper extends expansion and expansion variables to systems with forall-quantifiers. We present System Fs, an extension of System F with expansion, and prove its main properties. This system turns type inference into a c...
Introduction to Asymptotic Giant Branch Stars
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.
Traversable asymptotically flat wormholes in Rastall gravity
Moradpour, H
2016-01-01
Having introduced the Rastall gravitational theory, and by virtue of the fact that this theory has two unknown parameters, we take the Newtonian limit to define a new parameter for Rastall gravitational theory; a useful dimensionless parameter for simplifying calculations in the Rastall framework. Equipped with basics of the theory, we study the properties of traversable asymptotically flat wormholes in Rastall framework. Then, we investigate the possibility of supporting such geometries by a source with the same state parameter as that of the baryonic matters. Our survey indicates that the parameters of Rastall theory affect the wormhole parameters. It also shows the weak energy condition is violated for all of the studied cases. We then come to investigate the possibility of supporting such geometries by a source of negative energy density and the same state parameter as that of dark energy. Such dark energy-like sources have positive radial and transverse pressures.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, J.; Pawlowski, J. M.
2016-05-01
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 (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.
Quantum defect theory and asymptotic methods
International Nuclear Information System (INIS)
It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)
Asymptotic safety, singularities, and gravitational collapse
International Nuclear Information System (INIS)
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
Asymptotically thermal responses for smoothly switched detectors
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.
Asymptotically Honest Confidence Regions for High Dimensional
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
While variable selection and oracle inequalities for the estimation and prediction error have received considerable attention in the literature on high-dimensional models, very little work has been done in the area of testing and construction of confidence bands in high-dimensional models. However......, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz-Zygmund inequality which in our context provides sharper bounds than Nemirovski's inequality. As opposed to van de Geer et al. (2014) we...... allow for heteroskedastic non-subgaussian error terms and covariates. Next, we desparsify the conservative Lasso estimator and derive the asymptotic distribution of tests involving an increasing number of parameters. As a stepping stone towards this, we also provide a feasible uniformly consistent...
Asymptotic theory of quantum statistical inference
Hayashi, Masahito
Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Stein's lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dénes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramèr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramèr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramèr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramèr-Rao Bound in Pure States Model: Introduction to Part III-- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure
Asymptotic linear stability of solitary water waves
Pego, Robert L
2010-01-01
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 (i.e., 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.
Black holes in Asymptotically Safe Gravity
Saueressig, Frank; D'Odorico, Giulio; Vidotto, Francesca
2015-01-01
Black holes are among the most fascinating objects populating our universe. Their characteristic features, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. In this note we observe that the renormalization group improved Schwarzschild black holes constructed by Bonanno and Reuter within Weinberg's asymptotic safety program constitute a prototypical example of a Hayward geometry used to model non-singular black holes within quantum gravity phenomenology. Moreover, they share many features of a Planck star: their effective geometry naturally incorporates the one-loop corrections found in the effective field theory framework, their Kretschmann scalar is bounded, and the black hole singularity is replaced by a regular de Sitter patch. The role of the cosmological constant in the renormalization group improvement process is briefly discussed.
Grassmann scalar fields and asymptotic freedom
International Nuclear Information System (INIS)
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 φ4 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 β-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
Motion Parallax is Asymptotic to Binocular Disparity
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.
Asymptotic methods in mechanics of solids
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...
Generalized local induction equation, elliptic asymptotics, and simulating superfluid turbulence
International Nuclear Information System (INIS)
We prove the generalized induction equation and the generalized local induction equation (GLIE), which replaces the commonly used local induction approximation (LIA) to simulate the dynamics of vortex lines and thus superfluid turbulence. We show that the LIA is, without in fact any approximation at all, a general feature of the velocity field induced by any length of a curved vortex filament. Specifically, the LIA states that the velocity field induced by a curved vortex filament is asymmetric in the binormal direction. Up to a potential term, the induced incompressible field is given by the Biot-Savart integral, where we recall that there is a direct analogy between hydrodynamics and magnetostatics. Series approximations to the Biot-Savart integrand indicate a logarithmic divergence of the local field in the binormal direction. While this is qualitatively correct, LIA lacks metrics quantifying its small parameters. Regardless, LIA is used in vortex filament methods simulating the self-induced motion of quantized vortices. With numerics in mind, we represent the binormal field in terms of incomplete elliptic integrals, which is valid for R3. From this and known expansions we derive the GLIE, asymptotic for local field points. Like the LIA, generalized induction shows a persistent binormal deviation in the local field but unlike the LIA, the GLIE provides bounds on the truncated remainder. As an application, we adapt formulae from vortex filament methods to the GLIE for future use in these methods. Other examples we consider include vortex rings, relevant for both superfluid 4He and Bose-Einstein condensates.
Uniform asymptotic estimates of transition probabilities on combs
Bertacchi, Daniela; Zucca, Fabio
2000-01-01
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting Jones-type non-Gaussian estimates.
Asymptotic Formula for Quantum Harmonic Oscillator Tunneling Probabilities
Jadczyk, Arkadiusz
2015-10-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Asymptotic formula for quantum harmonic oscillator tunneling probabilities
Jadczyk, Arkadiusz
2015-01-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
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.
Global asymptotic stability of delay BAM neural networks with impulses
Energy Technology Data Exchange (ETDEWEB)
Lou Xuyang [Research Center of Control Science and Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China); Cui Baotong [Research Center of Control Science and Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China)]. E-mail: btcui@sohu.com
2006-08-15
The global asymptotic stability of delay bi-directional associative memory neural networks with impulses are studied by constructing suitable Lyapunov functional. Sufficient conditions, which are independent to the delayed quantity, are obtained for the global asymptotic stability of the neural networks. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.
Asymptotic behavior of the number of Eulerian orientations of graphs
Isaev, Mikhail
2011-01-01
We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominance
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.
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.
Einstein-Yang-Mills theory : I. Asymptotic symmetries
Barnich, Glenn
2013-01-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four dimensional asymptotically flat case.
Asymptotic size determines species abundance in the marine size spectrum
DEFF Research Database (Denmark)
Andersen, Ken Haste; Beyer, Jan
2006-01-01
The majority of higher organisms in the marine environment display indeterminate growth; that is, they continue to grow throughout their life, limited by an asymptotic size. We derive the abundance of species as a function of their asymptotic size. The derivation is based on size-spectrum theory...
Asymptotic functions and their application in quantum theory
International Nuclear Information System (INIS)
An asymptotic function introduced as a limit for a certain class of successions has been determined. The basic properties of the functions are given: continuity, differentiability, integrability. The fields of application of the asymptotic functions in the quantum field theory are presented. The shortcomings and potentialities of further development of the theory are enumerated
Multipole expansions in magnetostatics
International Nuclear Information System (INIS)
Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out. (methodological notes)
Multipole expansions in magnetostatics
Energy Technology Data Exchange (ETDEWEB)
Agre, Mark Ya [National University of ' Kyiv-Mohyla Academy' , Kyiv (Ukraine)
2011-02-28
Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out. (methodological notes)
Weakly relativistic plasma expansion
Energy Technology Data Exchange (ETDEWEB)
Fermous, Rachid, E-mail: rfermous@usthb.dz; Djebli, Mourad, E-mail: mdjebli@usthb.dz [Theoretical Physics Laboratory, Faculty of Physics, USTHB, B.P. 32 Bab-Ezzouar, 16079 Algiers (Algeria)
2015-04-15
Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.
Treyens, Pierre-Eric
2008-01-01
We consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Then, by using Edgeworth expansions, we compute the exact errors in the rejection probability (ERPs) for all one-restriction tests (asymptotic and bootstrap) which can occur in these linear models. More precisely, we show that the ERP is the same for the asymptotic test as for the classical parametric bootstrap test it is based on as soon as the third cumulant is nonnul. On the other sid...
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
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.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
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.
International Nuclear Information System (INIS)
The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.)
Asymptotics of Entropy Rate in Special Families of Hidden Markov Chains
Han, Guangyue
2008-01-01
We derive an asymptotic formula for entropy rate of a hidden Markov chain around a "weak Black Hole". We also discuss applications of the asymptotic formula to the asymptotic behaviors of certain channels.
Infra-Red Fixed Points in an Asymptotically Non-Free Theory
Bando, Masako; Sato, Joe(Department of Physics, Saitama University, Shimo-Okubo, Sakura-ku, Saitama 355-8570, Japan); Yoshioka, Koichi
1997-01-01
We investigate the infrared fixed point structure in asymptotically free and asymptotically non-free theory. We find that the ratios of couplings converge strongly to their infrared fixed points in the asymptotically non-free theory.
International Nuclear Information System (INIS)
This discourse recounts efforts put into the SNR-2 project; specifically the development of compensation devices. The various prototypes of these compensation devices are described and the state of the development reviewed. Large Na (sodium)-heat transfer systems require a lot of valuable space if the component lay-out does not include compensation devices. So, in order to condense the spatial requirement as much as possible, expansion joints must be integrated into the pipe system. There are two basic types to suit the purpose: axial expansion joints and angular expansion joints. The expansion joints were developed on the basis of specific design criteria whereby differentiation is made between expansion joints of small and large nominal diameter. Expansion joints for installation in the sodium-filled primary piping are equipped with safety bellows in addition to the actual working bellows. Expansion joints must be designed and mounted in a manner to completely withstand seismic forces. The design must exclude any damage to the bellows during intermittent operations, that is, when sodium is drained the bellows' folds must be completely empty; otherwise residual solidified sodium could destroy the bellows when restarting. The expansion joints must be engineered on the basis of the following design data for the secondary system of the SNR project: working pressure: 16 bar; failure mode pressure: 5 events; failure mode: 5 sec., 28.5 bar, 520 deg. C; working temperature: 520 deg. C; temperature transients: 30 deg. C/sec.; service life: 200,000 h; number of load cycles: 104; material: 1.4948 or 1.4919; layer thickness of folds: 0.5 mm; angular deflection (DN 800): +3 deg. C or; axial expansion absorption (DN 600): ±80 mm; calculation: ASME class. The bellows' development work is not handled within this scope. The bellows are supplied by leading manufacturers, and warrant highest quality. Multiple bellows were selected on the basis of maximum elasticity - a property
Basis for calculations in the topological expansion
International Nuclear Information System (INIS)
Investigations aimed at putting the topological theory of particles on a more quantitative basis are described. First, the incorporation of spin into the topological structure is discussed and shown to successfully reproduce the observed lowest mass hadron spectrum. The absence of parity-doubled states represents a significant improvement over previous efforts in similar directions. This theory is applied to the lowest order calculation of elementary hadron coupling constant ratios. SU(6)/sub W/ symmetry is maintained and extended via the notions of topological supersymmetry and universality. Finally, efforts to discover a perturbative basis for the topological expansion are described. This has led to the formulation of off-shell Feynman-like rules which provide a calculational scheme for the strong interaction components of the topological expansion once the zero-entropy connected parts are known. These rules are shown to imply a topological asymptotic freedom. Even though the nonlinear zero-entropy problem cannot itself be treated perturbatively, plausible general assumptions about zero-entropy amplitudes allow immediate qualitative inferences concerning physical hadrons. In particular, scenarios for mass splittings beyond the supersymmetric level are described
Completeness relations and resonant state expansions
International Nuclear Information System (INIS)
The completeness properties of the discrete set of bound states, virtual states, and resonant states characterizing the system of a single nonrelativistic particle moving in a central cutoff potential are investigated. We do not limit ourselves to the restricted form of completeness that can be obtained from Mittag-Leffler theory in this case. Instead we will make use of the information contained in the asymptotic behavior of the discrete states to get a new approach to the question of eventual overcompleteness. Using the theory of analytic functions we derive a number of completeness relations in terms of discrete states and complex continuum states and give some criteria for how to use them to form resonant state expansions of functions, matrix elements, and Green's functions. In cases where the integral contribution vanishes, the discrete part of the expansions is of the same form as that given by Mittag-Leffler theory but with regularized inner products. We also consider the possibility of using the discrete states as basis in a matrix representation
Asymptotic dynamics of reflecting spiral waves.
Langham, Jacob; Biktasheva, Irina; Barkley, Dwight
2014-12-01
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as pointlike objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this velocity and may often result in a reflection of the drift trajectory. Such reflections have diverse characteristics and are known to be highly nonspecular in general. In this context we apply the theory of response functions, which via numerically computable integrals, reduces the reaction-diffusion equations governing the whole excitable medium to the dynamics of just the rotation center and rotation phase of a spiral wave. Spiral reflection trajectories are computed by this method for both small- and large-core spiral waves in the Barkley model. Such calculations provide insight into the process of reflection as well as explanations for differences in trajectories across parameters, including the effects of incidence angle and forcing amplitude. Qualitative aspects of these results are preserved far beyond the asymptotic limit of weak boundary effects and slow resonant drift. PMID:25615159
Truly Minimal Unification Asymptotically Strong Panacea ?
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...
Qualitative and Asymptotic Theory of Detonations
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.
On Approximate Asymptotic Solution of Integral Equations
Jikia, Vagner
2013-01-01
It is well known that multi-particle integral equations of collision theory, in general, are not compact. At the same time it has been shown that the motion of three and four particles is described with consistent integral equations. In particular, by using identical transformations of the kernel of the Lipman-Schwinger equation for certain classes of potentials Faddeev obtained Fredholm type integral equations for three-particle problems $[1]$. The motion of for bodies is described by equations of Yakubovsky and Alt-Grassberger-Sandhas-Khelashvili $[2.3]$, which are obtained as a result of two subsequent transpormations of the kernel of Lipman-Schwinger equation. in the case of $N>4$ the compactness of multi-particle equations has not been proven yet. In turn out that for sufficiently high energies the $N$-particle $\\left( {N \\ge 3} \\right)$ dynamic equations have correct asymptotic solutions satisfying unitary condition $[4]$. In present paper by using the Heitler formalism we obtain the results briefly sum...
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.
Asymptotic safety of gravity-matter systems
Meibohm, J.; Pawlowski, J. M.; Reichert, M.
2016-04-01
We study the ultraviolet stability of gravity-matter systems for general numbers of minimally coupled scalars and fermions. This is done within the functional renormalization group setup put forward in [N. Christiansen, B. Knorr, J. Meibohm, J. M. Pawlowski, and M. Reichert, Phys. Rev. D 92, 121501 (2015).] for pure gravity. It includes full dynamical propagators and a genuine dynamical Newton's coupling, which is extracted from the graviton three-point function. We find ultraviolet stability of general gravity-fermion systems. Gravity-scalar systems are also found to be ultraviolet stable within validity bounds for the chosen generic class of regulators, based on the size of the anomalous dimension. Remarkably, the ultraviolet fixed points for the dynamical couplings are found to be significantly different from those of their associated background counterparts, once matter fields are included. In summary, the asymptotic safety scenario does not put constraints on the matter content of the theory within the validity bounds for the chosen generic class of regulators.
Asymptotic Orbits in Barred Spiral Galaxies
Harsoula, Maria; Contopoulos, George
2010-01-01
We study the formation of the spiral structure of barred spiral galaxies, using an $N$-body model. The evolution of this $N$-body model in the adiabatic approximation maintains a strong spiral pattern for more than 10 bar rotations. We find that this longevity of the spiral arms is mainly due to the phenomenon of stickiness of chaotic orbits close to the unstable asymptotic manifolds originated from the main unstable periodic orbits, both inside and outside corotation. The stickiness along the manifolds corresponding to different energy levels supports parts of the spiral structure. The loci of the disc velocity minima (where the particles spend most of their time, in the configuration space) reveal the density maxima and therefore the main morphological structures of the system. We study the relation of these loci with those of the apocentres and pericentres at different energy levels. The diffusion of the sticky chaotic orbits outwards is slow and depends on the initial conditions and the corresponding Jaco...
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...
Asymptotically minimax Bayesian predictive densities for multinomial models
Komaki, Fumiyasu
2011-01-01
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of risk functions of Bayesian predictive densities based on Dirichlet priors are obtained. It is shown that a Bayesian predictive density based on a specific Dirichlet prior is asymptotically minimax. The asymptotically minimax prior is different from known objective priors such as the Jeffreys prior or the uniform prior.
Asymptotic stability of solitons for the Benjamin-Ono equation
Kenig, C. E.; Martel, Y.
2008-01-01
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [Martel, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations wit...
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.
The asymptotic distribution of maxima in bivariate samples
Campbell, J. W.; Tsokos, C. P.
1973-01-01
The joint distribution (as n tends to infinity) of the maxima of a sample of n independent observations of a bivariate random variable (X,Y) is studied. A method is developed for deriving the asymptotic distribution of the maxima, assuming that X and Y possess asymptotic extreme-value distributions and that the probability element dF(x,y) can be expanded in a canonical series. Applied both to the bivariate normal distribution and to the bivariate gamma and compound correlated bivariate Poisson distributions, the method shows that maxima from all these distributions are asymptotically uncorrelated.
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.
Dai, Hui-Hui; Chen, Zhen
2008-01-01
In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct the asymptotic solutions based on an axisymmetrical three-dimensional setting and use the results to describe the key features (in particular, instability phenomena) observed in the experiments by others. The difficult problem of the solution bifurcations of the governing nonlinear partial differential equations (PDE's) is solved through a novel approach. By using a methodology involving coupled series-asymptotic expansions, we derive the normal form equation of the original complicated system of nonlinear PDE's. By writing the normal form equation into a first-order dynamical system and with a phase-plane analysis, we manage to deduce the global bifurcation properties and to solve the boundary-value problem analytically. The asymptotic solutions (including post-bifurcation solutions) in terms of integrals are obtained. The engi...
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...
Directory of Open Access Journals (Sweden)
Narski Jacek
2011-11-01
Full Text Available In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this paper is well suited for the simulation of a plasma in the presence of a magnetic field, whose intensity may vary considerably within the simulation domain.
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...
Directory of Open Access Journals (Sweden)
Hazra Imran
2009-11-01
Full Text Available The explosive growth of the World Wide Web is making it difficult for a user to locate information that isrelevant to his/her interest. Though existing search engines work well to a certain extent but they still faceproblems like word mismatch which arises because the majority of information retrieval systemscompare query and document terms on lexical level rather than on semantic level and short query: theaverage length of queries by the user is less than two words. Short queries and the incompatibilitybetween the terms in user queries and documents strongly affect the retrieval of relevant document.Query expansion has long been suggested as a technique to increase the effectiveness of the informationretrieval. Query expansion is the process of supplementing additional terms or phrases to the originalquery to improve the retrieval performance. The central problem of query expansion is the selection ofthe expansion terms based on which user’s original query is expanded. Thesaurus helps to solve thisproblem. Thesaurus have frequently been incorporated in information retrieval system for identifying thesynonymous expressions and linguistic entities that are semantically similar. Thesaurus has been widelyused in many applications, including information retrieval and natural language processing.
OPEC future capacity expansions
International Nuclear Information System (INIS)
This conference presentation examined OPEC future capacity expansions including highlights from 2000-2004 from the supply perspective and actions by OPEC; OPEC spare capacity in 2005/2006; medium-term capacity expansion and investments; long-term scenarios, challenges and opportunities; and upstream policies in member countries. Highlights from the supply perspective included worst than expected non-OPEC supply response; non-OPEC supply affected by a number of accidents and strikes; geopolitical tensions; and higher than expected demand for OPEC crude. OPEC's actions included closer relationship with other producers and consumers; capacity expansions in 2004 and 2005/2006; and OPEC kept the market well supplied with crude in 2004. The presentation also provided data using graphical charts on OPEC net capacity additions until 2005/2006; OPEC production versus spare capacity from 2003 to 2005; OPEC production and capacity to 2010; and change in required OPEC production from 2005-2020. Medium term expansion to 2010 includes over 60 projects. Medium-term risks such as project execution, financing, costs, demand, reserves, depletion, integration of Iraq, and geopolitical tensions were also discussed. The presentation concluded that in the long term, large uncertainties remain; the peak of world supply is not imminent; and continued and enhanced cooperation is essential to market stability. tabs., figs
International Nuclear Information System (INIS)
The Am/Cm program will vitrify the americium and curium currently stored in F-canyon. A batch flowsheet has been developed (with non-radioactive surrogate feed in place of the F-canyon solution) and tested full-scale in the 5-inch Cylindrical Induction Melter (CIM) facility at TNX. During a normal process run, a small bed expansion occurs when oxygen released from reduction of cerium (IV) oxide to cerium (III) oxide is trapped in highly viscous glass. The bed expansion is characterized by a foamy layer of glass that slowly expands as the oxygen is trapped and then dissipates when the viscosity of the foam becomes low enough to allow the oxygen to escape. Severe bed expansions were noted in the 5-inch CIM when re-heating after an interlock during the calcination phase of the heat cycle, escaping the confines of the melter vessel. In order to better understand the cause of the larger than normal bed expansion and to develop mitigating techniques, a series of three crucible tests were conducted
ASYMPTOTICALLY OPTIMAL SUCCESSIVE OVERRELAXATION METHODS FOR SYSTEMS OF LINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhong-zhi Bai; Xue-bin Chi
2003-01-01
We present a class of asymptotically optimal successive overrelaxation methods forsolving the large sparse system of linear equations. Numerical computations show thatthese new methods are more efficient and robust than the classical successive overrelaxationmethod.
ASYMPTOTIC SOLUTION TO NONLINEAR ECOLOGICAL REACTION DIFFUSION SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Nonlinear ecological species group singularly perturbed initial boundary value problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities, the existence and asymptotic behavior of solution to initial boundary value problems are studied.
Asymptotically anti-de Sitter spacetimes in topologically massive gravity
International Nuclear Information System (INIS)
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter μ (μ≠0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |μl|=1 (where l is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.
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.
Asymptotic behavior of future-complete cosmological space-times
Anderson, M T
2004-01-01
This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future and which admit a foliation by compact constant mean curvature Cauchy surfaces.
Asymptotic behavior of future-complete cosmological space-times
Anderson, Michael T.
2003-01-01
This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future and which admit a foliation by compact constant mean curvature Cauchy surfaces.
Asymptotic Safety of the CARTAN Induced Four-Fermion Interaction?
Mielke, Eckehard W.
2015-01-01
The difference between Einstein's general relativity and its Cartan extension is analyzed within the scenario of asymptotic safety. In particular, the four-fermion interaction is studied which distinguishes the Einstein-Cartan theory from its Riemannian limit.
Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds
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...
Asymptotic behaviour of the number of the Eulerian circuits
Isaev, Mikhail
2011-01-01
We determine the asymptotic behaviour of the number of the Eulerian circuits in undirected simple graphs with large second eigenvalue of the Laplacian matrix (the algebraic connectivity). We also prove some new properties of the Laplacian matrix.
Robust methods and asymptotic theory in nonlinear econometrics
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 ...
Asymptotic distributions in the projection pursuit based canonical correlation analysis
Institute of Scientific and Technical Information of China (English)
无
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.
An asymptotic model in acoustics:acoustic drift equations
Vladimirov, Vladimir; Ilin, Konstantin
2013-01-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
Pseudo-random number generator based on asymptotic deterministic randomness
International Nuclear Information System (INIS)
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks
Asymptotic formula for eigenvalues of one dimensional Dirac system
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
Spherical Cap Packing Asymptotics and Rank-Extreme Detection
Zhang, Kai
2015-01-01
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors are themselves independently uniformly distributed, we further develop the extreme value distribution limit of the maximal inner product, which characterizes its uncertainty around the bound. As applications of the above asymptotic results, we derive (1) an asymptotic sharp universal uniform bound on the maximal spurious correlation, as well as its uniform convergence in distribution when the explanatory variables are independently Gaussian distributed; and (2) an asymptotic sharp universal bound on the maximum norm of a low-rank elliptically distributed vector, as well as related limiting distributions. With these results, we develop a fast detection method for a low-rank structure in high-dime...
Asymptotics for the Covariance of the Airy2 Process
Shinault, Gregory; Tracy, Craig A.
2011-04-01
In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function {P}({A}2(0)≤ s1,A2(t)≤ s2), extending the previous work of Adler and van Moerbeke (arXiv:math.PR/0302329; Ann. Probab. 33, 1326-1361, 2005) and Widom (J. Stat. Phys. 115, 1129-1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integrals of the Painlevé II function q and its derivative q'. Further, for up to tenth order we give this asymptotic approximation as a linear combination of the Tracy-Widom GUE density function f 2 and its derivatives. As a corollary to this, the asymptotic covariance is expressed up to tenth order in terms of the moments of the Tracy-Widom GUE distribution.
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.
Asymptotic normality through factorial cumulants and partitions identities
Bobecka, Konstancja; Lopez-Blazquez, Fernando; Rempala, Grzegorz; Wesolowski, Jacek
2011-01-01
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for "moments" of partitions of numbers. The general limiting result is then used to (re)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.
Unified treatment of the asymptotics of asymmetric kernel density estimators
Hoffmann, Till; Jones, Nick S.
2015-01-01
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density estimators which are subsumed under these two general classes of kernel density estimators. We demonstrate our method by deriving the asymptotic bias, variance, and mean (integrated) squared error of density estimators with gamma, log-normal, Birnbaum-Saun...
Global asymptotic stability for a class of nonlinear chemical equations
Anderson, David F.
2007-01-01
We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will consider chemical reaction systems that are weakly reversible, have a deficiency of zero, and are equipped with mass action kinetics. We show that if for each $c \\in \\R_{> 0}^m$ the intersection of the stoichiometric compatibility class $c + S$ ...
An asymptotically exact theory of functionally graded piezoelectric shells
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.
The asymptotics of an amplitude for the 4-simplex
Barrett, John W.; Williams, Ruth M.
1998-01-01
An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas. The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry.
Functional truncations in asymptotic safety for quantum gravity
Dietz, Juergen
2016-01-01
Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional, or functional, truncations of the effective action as well as the effects that can be caused by the single field approximation in this context. It begins with a comprehensive analysis of the three existing flow equations of the single field f(R) truncation...
Asymptotic State Discrimination and a Strict Hierarchy in Distinguishability Norms
Chitambar, Eric; Hsieh, Min-Hsiu
2013-01-01
In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state discrimination, and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic LOCC. We use this new criterion to prove a gap in the LOCC and separable distinguishability norms. We then turn to the operational...
Asymptotic heat transfer model in thin liquid films
Chhay, Marx; Dutykh, Denys; 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 again...
Asymptotic optimal designs under long-range dependence error structure
Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly; 10.3150/09-BEJ185
2010-01-01
We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally, the optimal designs are compared with asymptotic optimal designs which were derived by Bickel and Herzberg [Ann. Statist. 7 (1979) 77--95] for regression models with short-range dependent error.
Asymptotics for maximum score method under general conditions
Taisuke Otsu; Myung Hwan Seo
2014-01-01
Abstract. Since Manski's (1975) seminal work, the maximum score method for discrete choice models has been applied to various econometric problems. Kim and Pollard (1990) established the cube root asymptotics for the maximum score estimator. Since then, however, econometricians posed several open questions and conjectures in the course of generalizing the maximum score approach, such as (a) asymptotic distribution of the conditional maximum score estimator for a panel data dynamic discrete ch...
An asymptotically exact theory of smart sandwich shells
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.
Sharp asymptotic results for simplified mutation-selection algorithms
Bérard, J.; Bienvenüe, A
2003-01-01
We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\\sqrt{n}$ times the posi...
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
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.
Asymptotic Behavior of Mean Partitions in Consensus Clustering
Jain, Brijnesh
2015-01-01
Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic normal. To derive both results, we represent partitions as points of some geometric space, called orbit space. Then we draw on results from the theory of Fr\\'echet means and sto...
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.
CLTs and asymptotic variance of time-sampled Markov chains
Latuszynski, Krzysztof
2011-01-01
For a Markov transition kernel $P$ and a probability distribution $ \\mu$ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\\mu} = \\sum_k \\mu(k)P^k.$ In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance.
Asymptotic solutions of magnetohydrodynamics equations near the derivatives discontinuity lines
International Nuclear Information System (INIS)
Asymptotic solutions of one-dimensional and scalar magnetohydrodynamics equations near the derivatives discontinuity lines have been discussed. The equations of magnetohydrodynamics for the cases of finite and infinite conductivities are formulated and the problem of eigenvalues and eigenvectors is solved. The so called transport equations which describe the behaviour of derivatives in solutions of the quasilinear equations have been used to find the asymptotic solutions of the magnetohydrodynamics equations. (S.B.)
Mass-like invariants for asymptotically hyperbolic metrics
Cortier, Julien; Gicquaud, Romain
2016-01-01
In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example (but probably the most important one) among the two families of invariants we find. These invariants are attached to finite-dimensional representations of the group of isometries of hyperbolic space. They are then described in terms of wave harmonic polynomials and polynomial solutions to the linearized Einstein equations in Minkowski space.
Global Asymptotic Stability of Switched Neural Networks with Delays
Zhenyu Lu; Kai Li; Yan Li
2015-01-01
This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs) are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified ...
Asymptotic-induced numerical methods for conservation laws
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.
On the Number of Solutions to Asymptotic Plateau Problem
Coskunuzer, Baris
2005-01-01
We give a simple topological argument to show that the number of solutions of the asymptotic Plateau problem in hyperbolic space is generically unique. In particular, we show that the space of codimension-1 closed submanifolds of sphere at infinity, which bounds a unique absolutely area minimizing hypersurface in hyperbolic n-space, is dense in the space of all codimension-1 closed submanifolds at infinity. In dimension 3, we also prove that the set of uniqueness curves in asymptotic sphere f...
International Nuclear Information System (INIS)
The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase and Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg's (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure
International Nuclear Information System (INIS)
A detailed positivity analysis of e+e-→Hadrons and e+e-→antiproton+x is made within a framework of light-cone expansion/parton theory. A positivity bound for the asymptotic ratio between the two processes cross-sections R infinity is derived and the stability of such a bound is studied by including non-leading terms up to third order. Corresponding positivity domains for the nonasymptotic ratio, Rs, (s finite), inclusive distribution s(dsigma/dx)(e+e-→antiproton+x) and inclusive angular distribution s(dsigma/dxd cos theta)(e+e-→antiproton+x) are also estimated in the present accelerator energies and predictions are made for future energies. The extra assumption is the validity of the Gribov-Lipatov reciprocity relation for e+e-→antiproton+x in the asymptotic region. Our analysis suggests that scaling of sigma(e+e-→hadrons) will set in within the SPEAR II limit (approximately 81(GeV)2, while that of sigma(e+e-→antiproton+x) will set in beyond this limit for slow particles in the centre-of-mass frame (i.e. for the pionization region)
Small-time asymptotics of stopped L\\'evy bridges and simulation schemes with controlled bias
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 ...
Some Late-time Asymptotics of General Scalar-Tensor Cosmologies
Barrow, John D
2007-01-01
We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p=-rho vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be approach to a de Sitter spacetime at large 4-volumes the coupling function, omega(phi), which defines the scalar-tensor theory, must diverge faster than |phi_infty-phi|^(-1+epsilon) for all epsilon>0 as phi rightarrow phi_infty 0 for large values of the time. Thus, for a given theory, specified by omega(phi), there must exist some phi_infty in (0,infty) such that omega -> infty and omega' / omega^(2+epsilon) -> 0 as phi -> 0 phi_infty in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation `constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of ``Boltzmann brains'' at late cosmological t...
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...
Long-Time Asymptotics of a Bohmian Scalar Quantum Field in de Sitter Space-Time
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.
An Asymptotic Study for the Steady Model of Oxygen Diffusion in Tissue Region
Directory of Open Access Journals (Sweden)
Kartika Yulianti
2012-07-01
Full Text Available Oxygen plays an important role in cell metabolism inside a human's body. The transfer of oxygen from blood to tissues takes place in capillaries through the diffusion process. A capillary-tissue region is usually represented by so called the Krogh Cylinder arrangement in which the distribution of the oxygen concentration in a tissue region leads to a diffusion equation with oxygen consumption rates following the Michaelis-Menten kinetics. In this paper, we restrict ourselves to consider the steady case and solve the equation analytically, by means of the asymptotic expansions, for a particular limit of the oxygen consumption rate. Results show that there exists a critical ratio between supply and consumption of oxygen in tissue region in order to fulfill cell’s oxygen requirements. Above this critical ratio, we also find a critical distance in the tissue region above which the oxygen concentration vanishes. We also compare our asymptotic results with numerical simulations which are both quite in agreement.
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
Caflisch, Russel E.; Lombardo, Maria Carmela; Sammartino, Marco
2011-05-01
In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.
QCD Condensates and Holographic Wilson Loops for Asymptotically AdS Spaces
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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.
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.
Asymptotic behaviour of two-point functions in multi-species models
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.
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
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.
Asymptotic results for the semi-Markovian random walk with delay
International Nuclear Information System (INIS)
In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,SN). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ1- s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)
Heavy quark coefficient functions at asymptotic values Q$^{2}$ $>$ m$^{2}$
Buza, M; Smith, J; Migneron, R; van Neerven, W L
1996-01-01
In this paper we present the analytic form of the heavy-quark coefficient functions for deep-inelastic lepton-hadron scattering in the kinematical regime Q^2 \\gg m^2 . Here Q^2 and m^2 stand for the masses squared of the virtual photon and heavy quark respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant \\alpha_s using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition Q^2 \\gg m_c^2 is satisfied. Furthermore the analytical expressions can also be used when one applies the variable heavy flavour scheme up to next-to-leading order in \\alpha_s.
Heavy quark coefficient functions at asymptotic values Q2>>m2
International Nuclear Information System (INIS)
In this paper we present the analytic form of the heavy quark coefficient functions for deep inelastic lepton-hadron scattering in the kinematical regime Q2>>m2. Here Q2 and m2 stand for the masses squared of the virtual photon and heavy quark, respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant αs using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition Q2>>m2c is satisfied. Furthermore, the analytical expressions can also be used when one applies the variable flavour number scheme up to next-to-leading order in αs. (orig.)
On asymptotic behavior of anisotropic branes with induced gravity inspired by L(R) term
International Nuclear Information System (INIS)
The DGP brane-world scenario provides the accelerated expansion of the universe at late-time by large-distance modification of general relativity without any need for dark energy. Using the method in reference [33], we investigate the asymptotic behavior of homogeneous and anisotropic cosmologies on a generalization of DGP scenario where the effective theory of gravity induced on the brane is given by a L(R) term. We show that for a constant induced curvature term on the brane all Bianchi models except type IX isotropize, like general relativity, if the effective energy density and Eab term satisfy some energy conditions. Finally, we compare the result of the model with the result of anisotropic DGP branes and general relativity
International Nuclear Information System (INIS)
In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes
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...
The drift-flux asymptotic limit of baro-tropic two-phase two-pressure models
International Nuclear Information System (INIS)
We study the asymptotic behavior of the solutions of baro-tropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a drift-flux model with an algebraic closure law, in the spirit of Zuber-Findlay models. The example of a two-phase flow in a vertical pipe is described. (authors)
Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
2015-01-01
We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in th...
Financing electricity expansion
International Nuclear Information System (INIS)
Expansion of electricity supply is associated with economic development. The installation and enlargement of power systems in developing countries entails a huge financial burden, however. Energy consumers in such countries must pay not only for supplies but for the cost of raising the capital for expansion on the international markets. Estimates are presented for the capital expenditure for electricity supply over the period 1990 to 2020 for the major world regions, using approximations for the cost of plant and capital and for the returns earned. These data lead to the conclusion that the five regions with the lowest per capita incomes are those which will need the major part of the capital expenditure and the highest percentage of external finance. (6 tables) (UK)
Operator product expansion algebra
International Nuclear Information System (INIS)
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.
International Nuclear Information System (INIS)
The Olympic Dam orebody is the 6th largest copper and the single largest uranium orebody in the world. Mine production commenced in June 1988, at an annual production rate of around 45,000 tonnes of copper and 1,000 tonnes of uranium. Western Mining Corporation announced in 1996 a proposed $1.25 billion expansion of the Olympic Dam operation to raise the annual production capacity of the mine to 200,000 tonnes of copper, approximately 3,700 tonnes of uranium, 75,000 ounces of gold and 950,000 ounces of silver by 2001. Further optimisation work has identified a faster track expansion route, with an increase in the capital cost to $1.487 billion but improved investment outcome, a new target completion date of end 1999, and a new uranium output of 4,600 tonnes per annum from that date
International Nuclear Information System (INIS)
This report presents results of measurements of thermal expansion of concrete cores from Hanford, Washington facilities, and concrete cast at the Construction Technology Laboratories of Portland Cement Association (CTL/PCA). Thermal expansion was measured from room temperature to 16000F on 0.5 x 3.0-in. specimens heated at a rate of 100F/min. Specimens were cored from concrete cylinders cast at CTL/PCA in 1975 and 1977, and from cylindrical cores taken from the Purex Building and Waste Tank Farms at the Hanford, Washington complex. A total of 14 specimens were tested: eight tests on CTL/PCA cast concrete, two tests on material from the Purex Building, and four tests on Waste Tank Farms concrete. All tests were conducted using a commercially built dilatometer of high strain resolution
IKEA's International Expansion
Harapiak, Clayton
2013-01-01
This case concerns a global retailing firm that is dealing with strategic management and marketing issues. Applying a scenario of international expansion, this case provides a thorough analysis of the current business environment for IKEA. Utilizing a variety of methods (e.g. SWOT, PESTLE, McKinsey Matrix) the overall objective is to provide students with the opportunity to apply their research skills and knowledge regarding a highly competitive industry to develop strategic marketing strateg...
China petrochemical expansion progressing
International Nuclear Information System (INIS)
This paper reports on China's petrochemical expansion surge which is picking up speed. A worldscale petrochemical complex is emerging at Shanghai with an eye to expanding China's petrochemical exports, possibly through joint ventures with foreign companies, China Features reported. In other action, Beijing and Henan province have approved plans for a $1.2 billion chemical fibers complex at the proposed Luoyang refinery, China Daily reported
Ultraprecise thermal expansion measurements of seven low expansion materials
Berthold, J. W., III; Jacobs, S. F.
1976-01-01
We summarize a large number of ultraprecise thermal expansion measurements made on seven different low expansivity materials. Expansion coefficients in the -150-300 C temperature range are shown for Owens-Illinois Cer-Vit C-101, Corning ULE 7971 (titanium silicate) and fused silica 7940, Heraeus-Schott Zerodur low-expansion material and Homosil fused silica, Universal Cyclops Invar LR-35, and Simonds Saw and Steel Super Invar.
Exponential Decay of Expansive Constants
Sun, Peng
2011-01-01
A map $f$ on a compact metric space is expansive if and only if $f^n$ is expansive. We study the exponential rate of decay of the expansive constant of $f^n$. A major result is that this rate times box dimension bounds topological entropy.
Superradiant instabilities of asymptotically anti-de Sitter black holes
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.
Singularities in asymptotically anti-de Sitter spacetimes
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...
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
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.