Kolmogorov turbulence by matched asymptotic expansions
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
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.
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
Helicopter rotor loads using matched asymptotic expansions: User's manual
Pierce, G. A.; Vaidyanathan, A. R.
1983-01-01
Computer programs were developed to implement the computational scheme arising from Van Holten's asymptotic method for calculating airloads on a helicopter rotor blade in forward flight, and a similar technique which is based on a discretized version of the method. The basic outlines of the two programs are presented, followed by separate descriptions of the input requirements and output format. Two examples illustrating job entry with appropriate input data and corresponding output are included. Appendices contain a sample table of lift coefficient data for the NACA 0012 air foil and listings of the two programs.
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
Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order
Gorbonos, Dan; Gorbonos, Dan; Kol, Barak
2005-01-01
The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
Gorbonos, Dan; Gorbonos, Dan; Kol, Barak
2004-01-01
No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The nex...
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
Gorbonos, Dan; Kol, Barak
2004-06-01
No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic ``mirrors'', and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the ``Archimedes effect''. The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d geq 5, where the system of equations can be reduced to ``a master equation'' — a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd
2015-10-01
Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.
Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.
2016-08-01
The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Expansions and Asymptotics for Statistics
Small, Christopher G
2010-01-01
Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and, includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of c
Asymptotic expansions for the Gaussian unitary ensemble
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...
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Singular asymptotic expansions in nonlinear rotordynamics
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS
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.
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
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.
High-order topological asymptotic expansion for Stokes equations
Mohamed Abdelwahed
2016-06-01
Full Text Available We use the topological sensitivity analysis method to solve various optimization problems. It consists of studying the asymptotic expansion of the objective function relative to a perturbation of the domain topology. This expansion becomes insufficient in some applications when it is limited to the first order topological derivative. We present a new topological sensitivity analysis for the Stokes equations based on a high order asymptotic expansion. The derived result is valid for different class of shape functions.
Uniform Asymptotic Expansion for the Incomplete Beta Function
Nemes, Gergő; Olde Daalhuis, Adri B.
2016-10-01
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
A convergence theorem for asymptotic expansions of Feynman amplitudes
Mabouisson, A.P.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1999-06-01
The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to {infinity}, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)
Quick asymptotic expansion aided by a variational principle
Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2013-02-15
It is shown how expanding asymptotically a variational functional can yield the asymptotic expansion of its Euler equation. The procedure is simple but novel and requires taking the variation of the expanded functional with respect to the leading order of the originally unknown function, even though the leading order of this function has already been determined in a previous order. An example is worked out that of a large aspect ratio tokamak plasma equilibrium state with relatively strong flows and high plasma beta.
Asymptotic Expansions of Transition Densities for Hybrid Jump-Diffusions
Yuan-jin Liu; G.Yin
2004-01-01
A class of hybrid jump diffusions modulated by a Markov chain is considered in this work.The motivation stems from insurance risk models,and emerging applications in production planning and wireless communications.The models are hybrid in that they involve both continuous dynamics and discrete events.Under suitable conditions,asymptotic expansions of the transition densities for the underlying processes are developed.The formal expansions are validated and the error bounds obtained.
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...
A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS
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 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.
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Galapon, Eric A; Martinez, Kay Marie L
2014-02-08
We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, [Formula: see text] as [Formula: see text], using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the asymptotic series does not terminate and is generally divergent, but is amenable to superasymptotic summation, i.e. by optimal truncation. For specific examples, we compare the accuracy of the optimally truncated asymptotic series owing to the McClure-Wong distributional method with owing to the Mellin-Barnes integral method. We find that the former is spectacularly more accurate than the latter, by, in some cases, more than 70 orders of magnitude for the same moderate value of b. Moreover, the exactification can lead to a resummation of the PAE when it is exact, with the resummed Poincaré series exhibiting again the same spectacular accuracy. More importantly, the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences.
Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching
Nakano, Hiroyuki; Campanelli, Manuela; West, Eric J
2016-01-01
We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic matching techniques to obtain a global solution that approximately satisfies the Einstein field equations. Precession effects are introduced by rotating the black hole spin direction according to the precessing equations of motion, in a way that is consistent with the global spacetime construction.
Double asymptotic expansion of three-center electronic repulsion integrals
Alvarez-Ibarra, A.; Köster, A. M.
2013-07-01
A double asymptotic expansion for the evaluation of three-center electron repulsion integrals (ERIs) in the long-range limit is presented. For the definition of this limit, a natural division of space based on the atomic coordinates and basis function exponents in utilized. The resulting analytical expression for the calculation of three-center ERIs in the long-range limit are implemented in the density functional theory program deMon2k. Validation and benchmark calculations of n-alkanes, hydrogen saturated graphene sheets and hydrogen saturated diamond blocks are discussed. It is shown that for a sufficient large number of long-range ERIs, the linear scaling regime is reached.
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
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).
On the asymptotic expansion of complete Ricci-flat Kahler metrics on quasi-projective manifolds
Santoro, Bianca
2012-01-01
In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler metrics with special approximating properties. Using those metrics as starting point, we are able to work out the asymptotic behavior of the solutions given in the work of Tian-Yau, in particular obtaining their full asymptotic expansion.
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.
Helicopter rotor loads using a matched asymptotic expansion technique
Pierce, G. A.; Vaidyanathan, A. R.
1981-01-01
The theoretical basis and computational feasibility of the Van Holten method, and its performance and range of validity by comparison with experiment and other approximate methods was examined. It is found that within the restrictions of incompressible, potential flow and the assumption of small disturbances, the method does lead to a valid description of the flow. However, the method begins to break down under conditions favoring nonlinear effects such as wake distortion and blade/rotor interaction.
Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
Linhares, C A; Roditi, I
2007-01-01
Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished for both convergent and renormalized amplitudes.
Remarks on Slater's asymptotic expansions of Kummer functions for large values of the $a-$parameter
N.M. Temme (Nico)
2013-01-01
textabstractIn Slater's 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the $a-$parameter. We show how similar
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
On the ambiguity of field correlators represented by asymptotic perturbation expansions
Caprini, Irinel [National Institute of Physics and Nuclear Engineering, Bucharest POB MG-6, R-077125 Romania (Romania); Fischer, Jan [Institute of Physics, Academy of Sciences of the Czech Republic, CZ-182 21 Prague 8 (Czech Republic); Vrkoc, Ivo [Mathematical Institute, Academy of Sciences of the Czech Republic, CZ-115 67 Prague 1 (Czech Republic)
2009-10-02
Starting from the divergence pattern of perturbation expansions in quantum field theory and the (assumed) asymptotic character of the series, we address the problem of ambiguity of a function determined by the perturbation expansion. We consider functions represented by an integral of the Laplace-Borel type along a general contour in the Borel complex plane. Proving a modified form of Watson's lemma, we obtain a large class of functions having the same asymptotic perturbation expansion. Some remarks on perturbative QCD are made, using the particular case of the Adler function.
Anisotropic matching principle for the hydrodynamic expansion
Tinti, Leonardo
2016-10-01
Following the recent success of anisotropic hydrodynamics, I propose here a new, general prescription for the hydrodynamic expansion around an anisotropic background. The anisotropic distribution fixes exactly the complete energy-momentum tensor, just like the effective temperature fixes the proper energy density in the ordinary expansion around local equilibrium. This means that momentum anisotropies are already included at the leading order, allowing for large pressure anisotropies without the need of a next-to-leading-order treatment. The first moment of the Boltzmann equation (local four-momentum conservation) provides the time evolution of the proper energy density and the four-velocity. Differently from previous prescriptions, the dynamic equations for the pressure corrections are not derived from the zeroth or second moment of the Boltzmann equation, but they are taken directly from the exact evolution given by the Boltzmann equation. As known in the literature, the exact evolution of the pressure corrections involves higher moments of the Boltzmann distribution, which cannot be fixed by the anisotropic distribution alone. Neglecting the next-to-leading-order contributions corresponds to an approximation, which depends on the chosen form of the anisotropic distribution. I check the the effectiveness of the leading-order expansion around the generalized Romatschke-Stricklad distribution, comparing with the exact solution of the Boltzmann equation in the Bjorken limit with the collisional kernel treated in the relaxation-time approximation, finding an unprecedented agreement.
Asymptotic expansions for large closed and loss queueing networks
Kogan Yaakov
2002-01-01
Full Text Available Loss and closed queueing network models have long been of interest to telephone and computer engineers and becoming increasingly important as models of data transmission networks. This paper describes a uniform approach that has been developed during the last decade for asymptotic analysis of large capacity networks with product form of the stationary probability distribution. Such a distribution has an explicit form up to the normalization constant, or the partition function. The approach is based on representing the partition function as a contour integral in complex space and evaluating the integral using the saddle point method and theory of residues. This paper provides an introduction to the area and a review of recent work.
Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations
Weishi Yin
2016-01-01
Full Text Available This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time-space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann-Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time-space fractional Kuramoto-Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method.
On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection
De, Amit
We establish that the Hitchin connection is a perturbation of the $L_{2}$-connection. We notice that such a formulation of the Hitchin connection does not necessarily require the manifold in question possessing a rigid family of Kähler structures. We then proceed to calculate the asymptotic...... expansion of general perturbations of the $L_{2}$-connection, and see when under certain assumptions such perturbations are flat and projectively flat. During the calculations we also found an asymptotic expansion of the projection operator $\\pi_{\\sigma}^{\\left(k\\right)}$ which projects onto the holomorphic...
Distributional asymptotic expansions of spectral functions and of the associated Green kernels
R. Estrada
1999-03-01
Full Text Available Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and more precisely determined by means of tools from distribution theory and summability theory. (These are the same, insofar as recently the classic Cesaro--Riesz theory of summability of series and integrals has been given a distributional interpretation. When applied to the spectral analysis of Green functions (which are then to be expanded as series in a parameter, usually the time,these methods show: (1 The ``local'' or ``global'' dependence of the expansion coefficients on the background geometry, etc., is determined by the regularity of the asymptotic expansion of the integrand at the origin (in ``frequency space''; this marks the difference between a heat kernel and a Wightman two-point function, for instance. (2 The behavior of the integrand at infinity determines whether the expansion of the Green function is genuinely asymptotic in the literal, pointwise sense, or is merely valid in a distributional (Cesaro-averaged sense; this is the difference between the heat kernel and the Schrodinger kernel. (3 The high-frequency expansion of the spectral density itself is local in a distributional sense (but not pointwise. These observations make rigorous sense out of calculations in the physics literature that are sometimes dismissed as merely formal.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
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 ...
Asymptotic expansions for Riesz fractional derivatives of Airy functions and applications
N.M. Temme (Nico); V. Varlamov
2009-01-01
textabstractRiesz fractional derivatives of a function, $D_{x}^{\\alpha}f(x)$ (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large $x$ are computed for the Riesz fractional derivatives of the Airy function of the first kind, $Ai(x)$, and
A note on asymptotic expansions for Markov chains using operator theory
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...
Inspiralling, Non-Precessing, Spinning Black Hole Binary Spacetime via Asymptotic Matching
Ireland, Brennan; Nakano, Hiroyuki; Campanelli, Manuela
2015-01-01
We construct a new global, fully analytic, approximate spacetime which accurately describes the dynamics of non-precessing, spinning black hole binaries during the inspiral phase of the relativistic merger process. This approximate solution of the vacuum Einstein's equations can be obtained by asymptotically matching perturbed Kerr solutions near the two black holes to a post-Newtonian metric valid far from the two black holes. This metric is then matched to a post-Minkowskian metric even farther out in the wave zone. The procedure of asymptotic matching is generalized to be valid on all spatial hypersurfaces, instead of a small group of initial hypersurfaces discussed in previous works. This metric is well suited for long term dynamical simulations of spinning black hole binary spacetimes prior to merger, such as studies of circumbinary gas accretion which requires hundreds of binary orbits.
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...
An improved perfectly matched layer in the eigenmode expansion technique
Gregersen, Niels; Mørk, Jesper
2008-01-01
When employing the eigenmode expansion technique (EET), parasitic reflections at the boundary of the computational domain can be suppressed by introducing a perfectly matched layer (PML). However, the traditional PML, suffers from an artificial field divergence limiting its usefulness. We propose...
Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time
G Yin; Dung Tien Nguyen
2009-01-01
This work develops asymptotic expansions for solutions of systems of backward equations of timeinhomogeneons Markov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Markov chains often have large state spaces, which make the computational tasks infeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε＞ 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Markov chains including also transient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions are constructed. Then error bounds are obtained.
Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
Davies, Ian; Truman, Aubrey
1982-11-01
Imitating Schilder's results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{-TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(-ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.
Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings
Ze Qing LIU; Shin Min KANG
2004-01-01
A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established.The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).
On the high-order topological asymptotic expansion for shape functions
Maatoug Hassine
2016-04-01
Full Text Available This article concerns the topological sensitivity analysis for the Laplace operator with respect to the presence of a Dirichlet geometry perturbation. Two main results are presented in this work. In the first result we discuss the influence of the considered geometry perturbation on the Laplace solution. In the second result we study the high-order topological derivatives. We derive a high-order topological asymptotic expansion for a large class of shape functions.
Canhanga, Betuel; Ni, Ying; Rančić, Milica; Malyarenko, Anatoliy; Silvestrov, Sergei
2017-01-01
After Black-Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multifactor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.
Yunes, Nicolas; Tichy, Wolfgang
2006-04-01
The accuracy of gravitational wave templates produced by numerical simulations is partially determined by the initial data chosen. A promising method to construct accurate data employs asymptotic matching to construct an approximate global 4-metric. In this talk, we will apply this method to a binary system of non-spinning black holes and discuss improvements. A global metric can be constructed by asymptotically matching two tidally perturbed Schwarzschild metrics in isotropic coordinates valid near each hole to an ADMTT post-Newtonian metric valid far from them. As a result, adjacent metrics agree in the matching region up to uncontrolled remainders in the approximations. We build a smooth global 4-metric with transition functions, carefully constructed to avoid introducing errors larger than those in the approximations. The main improvement arises by using metrics in similar coordinates before performing the matching. This similarity leads to adjacent metrics that are similar even near the horizons, thus allowing for a smoother transition and constraint violations. We also construct a map that takes this metric to Kerr-Schild coordinates near each hole.
Essam, J W [Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX (United Kingdom); Wu, F Y [Department of Physics, Northeastern University, Boston, MA 02115 (United States)
2009-01-16
We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions and obtain an asymptotic expansion of its exact expression for large M and N.
Jar Decoding: Non-Asymptotic Converse Coding Theorems, Taylor-Type Expansion, and Optimality
Yang, En-Hui
2012-01-01
Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with discrete or continuous output (DIMC). Along the path of non-asymptotic analysis, in this paper, it is further shown that jar decoding is actually optimal up to the second order coding performance by establishing new non-asymptotic converse coding theorems, and determining the Taylor expansion of the (best) coding rate $R_n (\\epsilon)$ of finite block length for any block length $n$ and word error probability $\\epsilon$ up to the second order. Finally, based on the Taylor-type expansion and the new converses, two approximation formulas for $R_n (\\epsilon)$ (dubbed "SO" and "NEP") are provided; they are further evaluated and compared against some of the best bounds known so far, as well as the normal approximation of $R_n (\\epsilon)$ revisited recently in the literature. It t...
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Kamiński, Wojciech; Steinhaus, Sebastian
2013-12-01
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Kamiński, Wojciech, E-mail: wkaminsk@fuw.edu.pl [Wydział Fizyki, Uniwersytet Warszawski, Hoża 69, 00-681, Warsaw (Poland); Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany); Steinhaus, Sebastian, E-mail: steinhaus.sebastian@gmail.com [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany)
2013-12-15
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Kaminski, Wojciech
2013-01-01
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Asymptotically Matched Layer (AML) for transient wave propagation in a moving frame of reference
Madsen, Stine Skov; Krenk, Steen
2017-01-01
The paper presents an Asymptotically Matched Layer (AML) formulation in a moving frame of reference for transient dynamic response of a multi-layer 2D half-space. A displacement based finite element formulation of the convected domain problem is presented together with the AML formulation in which...... the original convolution integrals are represented via two auxiliary displacement-like state-space variables. A parametric study of the AML parameters is conducted for optimizing the absorbing properties. The performance is demonstrated on a single- and a two-layered half-space for various velocities...
Feature Based Stereo Matching Using Two-Step Expansion
Liqiang Wang
2014-01-01
Full Text Available This paper proposes a novel method for stereo matching which is based on image features to produce a dense disparity map through two different expansion phases. It can find denser point correspondences than those of the existing seed-growing algorithms, and it has a good performance in short and wide baseline situations. This method supposes that all pixel coordinates in each image segment corresponding to a 3D surface separately satisfy projective geometry of 1D in horizontal axis. Firstly, a state-of-the-art method of feature matching is used to obtain sparse support points and an image segmentation-based prior is employed to assist the first region outspread. Secondly, the first-step expansion is to find more feature correspondences in the uniform region via initial support points, which is based on the invariant cross ratio in 1D projective transformation. In order to find enough point correspondences, we use a regular seed-growing algorithm as the second-step expansion and produce a quasi-dense disparity map. Finally, two different methods are used to obtain dense disparity map from quasi-dense pixel correspondences. Experimental results show the effectiveness of our method.
Dense Image Matching with Two Steps of Expansion
Zhang, Zuxun; He, Jia'nan; Huang, Shan; Duan, Yansong
2016-06-01
Dense image matching is a basic and key point of photogrammetry and computer version. In this paper, we provide a method derived from the seed-and-grow method, whose basic procedure consists of the following: First, the seed and feature points are extracted, after which the feature points around every seed point are found in the first step of expansion. The corresponding information on these feature points needs to be determined. This is followed by the second step of expansion, in which the seed points around the feature point are found and used to estimate the possible matching patch. Finally, the matching results are refined through the traditional correlation-based method. Our proposed method operates on two frames without geometric constraints, specifically, epipolar constraints. It (1) can smoothly operate on frame, line array, natural scene, and even synthetic aperture radar (SAR) images and (2) at the same time guarantees computing efficiency as a result of the seed-and-grow concept and the computational efficiency of the correlation-based method.
Evaluation of the Fokker-Planck probability by Asymptotic Taylor Expansion Method
Firat, Kenan; Ozer, Okan
2017-02-01
The one-dimensional Fokker-Planck equation is solved by the Asymptotic Taylor Expansion Method for the time-dependent probability density of a particle. Using an ansatz wave function, one obtains the series expansion of the solution for the Schrödinger and it allows one to find out the eigen functions and eigen energies of the states to the evaluation of the probability. The eigen energies of some certain kind of Bistable potentials are calculated for some certain potential parameters. The probability function is determined and graphed for potential parameters. The numerical results are compared with existing literature, and a conclusion about the advantages and disadvantages on the method is given.
Asymptotic expansion of a partition function related to the sinh-model
Borot, Gaëtan; Kozlowski, Karol K
2016-01-01
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...
Berninger, Heiko; Gander, Martin; Liebendorfer, Mathias; Michaud, Jerome
2012-01-01
We present Chapman--Enskog and Hilbert expansions applied to the $\\BigO(v/c)$ Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman-Enskog or Hilbert expansions with reaction and collision scaling. We also give asymptotically sharp results obtained by the use of an additional time scaling. The diffusion limit determines the diffusion source in the Isotropic Diffusion Source Approximation (IDSA) of Boltzmann's equation for which the free streaming limit and the reaction limit serve as limiters. Here, we derive the reaction limit as well as the free streaming limit by truncation of Chapman-Enskog or Hilbert expansions using reaction and collision scaling as well as time scaling, respectively. Finally, we motivate why limiters are a good choice for the definition of the source term i...
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-11-01
A theory and a numerical method are presented for the asymptotic matching analysis of resistive magnetohydrodynamic stability in a negative magnetic shear configuration with two rational surfaces. The theory formulates the problem of solving both the Newcomb equations in the ideal MHD region and the inner-layer equations around rational surfaces as boundary value/eigenvalue problems to which the finite element method and the finite difference method can be applied. Hence, the problem of stability analysis is solved by a numerically stable method. The present numerical method has been applied to model equations having analytic solutions in a negative magnetic shear configuration. Comparison of the numerical solutions with the analytical ones verifies the validity of the numerical method proposed. (author)
Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem
Lubomir Dechevski
2012-01-01
Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.
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...
Asymptotically Matched Spacetime Metric for Non-Precessing, Spinning Black Hole Binaries
Gallouin, Louis; Yunes, Nicolas; Campanelli, Manuela
2012-01-01
We construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the technique of asymptotic matching to join a perturbed Kerr metric in the neighborhood of each spinning black hole to a near-zone, post-Newtonian metric farther out. The latter is already naturally matched to a far-zone, post-Minkowskian metric that accounts for full temporal retardation. The result is a 4-metric that is approximately valid everywhere in space and in a small bundle of spatial hypersurfaces. We here restrict our attention to quasi- circular orbits, but the method is valid for any orbital motion or physical scenario, provided an overlapping region of validity or buffer zone exists. A simple extension of such a metric will allow for future studies of the accretion disk and jet dynamics around spinning back hole binaries.
The Riesz energy of the $N$-th roots of unity: an asymptotic expansion for large $N$
Brauchart, J S; Saff, E B
2008-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the Riesz $s$-energy of $N$ equally spaced points on the unit circle as $N\\to \\infty$. For $s\\ge -1$, such points form optimal energy $N$-point configurations with respect to the Riesz potential $1/r^{s}$, $s\
One-loop Matching and Running with Covariant Derivative Expansion
Henning, Brian; Murayama, Hitoshi
2016-01-01
We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these "mixed" one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of "integrating out" heavy fields. Lastly...
Asymptotic expansions of the error for hyper-singular integrals with an interval variable
Chong Chen
2016-01-01
Full Text Available Abstract In this paper, we present high accuracy quadrature formulas for hyper-singular integrals ∫ a b g ( x q α ( x , t d x $\\int_{a}^{b}g(xq^{\\alpha}(x,t\\, dx$ , where q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ , t ∈ ( a , b $t\\in(a,b$ , and α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ . If g ( x $g(x$ is 2 m + 1 $2m+1$ times differentiable on [ a , b ] $[a,b]$ , the asymptotic expansions of the error show that the convergence order is O ( h 2 μ + 1 + α $O(h^{2\\mu+1+\\alpha}$ with q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ for α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ and α being non-integer, and the error power is O ( h η $O(h^{\\eta}$ with q ( x , t = x − t $q(x,t=x-t$ for α being integers less than −1, where η = min ( 2 μ , 2 μ + 2 + α $\\eta =\\min(2\\mu,2\\mu+2+\\alpha$ and μ = 1 , … , m $\\mu=1,\\ldots,m$ . Since the derivatives of the density function g ( x $g(x$ in the quadrature formulas can be eliminated by means of the extrapolation method, the formulas can easily be applied to solving corresponding hyper-singular boundary integral equations. The reliability and efficiency of the proposed formulas in this paper are demonstrated by some numerical examples.
Ryttov, T A
2016-01-01
We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero in the beta function at $\\alpha_{IR}$. We present general formulas for scheme-independent series expansions of quantities, evaluated at $\\alpha_{IR}$, as powers of an $N_f$-dependent expansion parameter, $\\Delta_f$. First, we apply these to calculate the derivative $d\\beta/d\\alpha$ evaluated at $\\alpha_{IR}$, denoted $\\beta'_{IR}$, which is equal to the anomalous dimension of the ${\\rm Tr}(F_{\\mu\
An improved perfectly matched layer for the eigenmode expansion technique
Gregersen, Niels; Mørk, Jesper
2008-01-01
When performing optical simulations for rotationally symmetric geometries using the eigenmode expansion technique, it is necessary to place the geometry under investigation inside a cylinder with perfectly conducting walls. The parasitic reflections at the boundary of the computational domain can...
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.
Xiaowu Tang
2016-01-01
Full Text Available Permeability of soil plays an important role in geotechnical engineering and is commonly determined by methods combining measurements with theory. Using the double-scale asymptotic expansion method, the Navier-Stokes equation is numerically solved to calculate the permeability, based on the homogenization method and the assumption that the homogeneous microstructure of the relevant porous media is represented accurately as the Representative Elemental Volume (REV. In this study, the commonly used square model is tested in the calculation of sea clay permeability. The results show large deviations. It is suspected that the square model could not represent the flattened shape of the clay particles and the bound water film wrapping around them. Hence, the Rectangle Particle-Water Film Model (i.e., the R-W model is proposed. After determining the horizontal and vertical characteristic length of the unit cell using two pairs of initial data, the permeabilities of other different void ratios could be inversely calculated. The results of three types of clay obtained using the R-W model agree well with the experimental data. This shows the efficient feasibility and accuracy of the R-W model by providing a good representation of the clay particles when using the double-scale asymptotic expansion method to calculate clay permeability.
An Irreducible Form for the Asymptotic Expansion Coefficients of the Heat Kernel of Fermions
Yajima, S.; Fukuda, M.; Tokuo, S.; Kubota, S.-I.; Higashida, Y.; Kamo, Y.
2008-09-01
We consider the asymptotic coefficients of the heat kernel for a fermion of spin (1)/(2) interacting with all types of non-abelian boson fields, i.e. totally antisymmetric tensor fields, in even dimensional Riemannian space. The coefficients are decomposed by irreducible matrices which are the totally antisymmetric product of the γ-matrices. The form of the coefficients given in our method is useful to evaluate some fermionic anomalies.
Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
Kroon, Juan Antonio Valiente [Institut fuer Theoretische Physik, Universitaet Wien, Boltzmanngasse 5, A-1090 Vienna (Austria)
2004-07-07
We discuss expansions for the Cotton-York tensor near infinity for arbitrary slices of stationary spacetimes. From these expansions, it follows directly that a necessary condition for the existence of conformally flat slices in stationary solutions is the vanishing of a certain quantity of quadrupolar nature (obstruction). The obstruction is non-zero for the Kerr solution. Thus, the Kerr metric admits no conformally flat slices. An analysis of the next order terms in the expansions in the case of solutions such that the obstruction vanishes, suggests that the only stationary solutions admitting conformally flat slices are the Schwarzschild family of solutions.
Ritchie, R.H.; Sakakura, A.Y.
1956-01-01
The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.
Dai, Hui-Hui
2011-01-01
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical solutions of the deformations by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, ma...
Zhang, Yongcun; Shang, Shipeng; Liu, Shutian
2017-01-01
Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
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.
Izmailian, N Sh; Huang, Ming-Chang
2010-07-01
We analyze the exact formulas for the resistance between two arbitrary notes in a rectangular network of resistors under free, periodic and cylindrical boundary conditions obtained by Wu [J. Phys. A 37, 6653 (2004)]. Based on such expression, we then apply the algorithm of Ivashkevich, Izmailian, and Hu [J. Phys. A 35, 5543 (2002)] to derive the exact asymptotic expansions of the resistance between two maximally separated nodes on an M×N rectangular network of resistors with resistors r and s in the two spatial directions. Our results is 1/s (R(M×N))(r,s) = c(ρ)ln S + c(0)(ρ,ξ) + ∑(p=1)(∞) (c(2p)(ρ,ξ))/S(p) with S = MN, ρ = r/s and ξ = M/N. The all coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ξeff = square root(ρ)ξ for free and periodic boundary conditions and ξeff = square root(ρ)ξ/2 for cylindrical boundary condition and show that all finite-size correction terms are invariant under transformation ξeff→1/ξeff.
Asymptotic expansion of beta matrix models in the one-cut regime
Borot, Gaëtan
2011-01-01
We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus, the coefficients of the expansion can be obtained recursively by the "topological recursion" of Chekhov and Eynard. Our method relies on the combination of a priori bounds on the correlators and the study of Schwinger-Dyson equations, thanks to the uses of classical complex analysis techniques. These a priori bounds can be derived following Boutet de Monvel, Pastur and Shcherbina, or for strictly convex potentials by using concentration of measure. Doing so, we extend the strategy of Guionnet and Maurel-Segala, from the hermitian models (beta = 2) and perturbative potentials, to general beta models. The existence of the first correction in 1/N has been considered previously by Johansson and more recently by Kriecherbauer and Shcherbina. Here, by taking similar hypotheses, we extend the result to all orders in 1/N.
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...
Method of Matched Expansions & the Singularity Structure of the Green Function
Casals, Marc; Ottewill, Adrian C; Wardell, Barry
2010-01-01
We present the first successful application of the method of Matched Expansions for the calculation of the self-force on a point particle in a curved spacetime. We investigate the case of a scalar charge in the Nariai spacetime, which serves as a toy model for a point mass moving in the Schwarzschild black hole background. We discuss the singularity structure of the Green function beyond the normal neighbourhood and the interesting effect of caustics on null wave propagation.
E. M. E. ZAYED
2003-01-01
The asymptotic expansions of the trace of the heat kernel Θ(t) = ∑∞ν=1 exp(-tλν) for smallpositive t, where {λν} are the eigenvalues of the negative Laplacian -△n = - ∑n i=1 ( / xi )2 in Rn(n= 2or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary (e)Ω1 and asmooth outer boundary (e)Ω2, where a finite number of piecewise smooth Robin boundary conditions((e)/(e)nj+rj)φ=0 on the components γj(j = 1, ..., k)of (e)Ω1 and on teh components γj(j = 1, ..., m) of (e)Ω2 are considered such that( (e)Ω1+ukj=1 Fj and (e)Ω2=Umj=k+1Fj )and where the coefficients (rj(j=1，…，m))are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gasenclosed in the general annular bounded domain Ω are given. Further results are also obtained.
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.
Asymptotic inversion of the Erlang B formula
J. van Leeuwaarden; N.M. Temme (Nico)
2009-01-01
textabstractThe Erlang B formula represents the steady-state blocking probability in the Erlang loss model or $M/M/s/s$ queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we mak
Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
Composite Laminate With Coefficient of Thermal Expansion Matching D263 Glass
Robinson, David; Rodini, Benjamin
2012-01-01
The International X-ray Observatory project seeks to make an X-ray telescope assembly with 14,000 flexible glass segments. The glass used is commercially available SCHOTT D263 glass. Thermal expansion causes the mirror to distort out of alignment. A housing material is needed that has a matching coefficient of thermal expansion (CTE) so that when temperatures change in the X-ray mirror assembly, the glass and housing pieces expand equally, thus reducing or eliminating distortion. Desirable characteristics of this material include a high stiffness/weight ratio, and low density. Some metal alloys show promise in matching the CTE of D263 glass, but their density is high compared to aluminum, and their stiffness/weight ratio is not favorable. A laminate made from carbon fiber reinforced plastic (CFRP) should provide more favorable characteristics, but there has not been any made with the CTE matching D263 Glass. It is common to create CFRP laminates of various CTEs by stacking layers of prepreg material at various angles. However, the CTE of D263 glass is 6.3 ppm/ C at 20 C, which is quite high, and actually unachievable solely with carbon fiber and resin. A composite laminate has been developed that has a coefficient of thermal expansion identical to that of SCHOTT D263 glass. The laminate is made of a combination of T300 carbon fiber, Eglass, and RS3C resin. The laminate has 50% uni-T300 plies and 50% uni-E-glass plies, with each fiber-layer type laid up in a quasi-isotropic laminate for a total of 16 plies. The fiber volume (percent of fiber compared to the resin) controls the CTE to a great extent. Tests have confirmed that a fiber volume around 48% gives a CTE of 6.3 ppm/ C. This is a fairly simple composite laminate, following well established industry procedures. The unique feature of this laminate is a somewhat unusual combination of carbon fiber with E-glass (fiberglass). The advantage is that the resulting CTE comes out to 6.3 ppm/ C at 20 C, which matches D
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 $d=4$.
Koc, Ramazan; Olgar, Eser
2010-01-01
A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.
Koc, Ramazan; Olgar, Eser
2010-01-01
A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.
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.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.
2014-11-01
We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.
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...
Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls
无
2007-01-01
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
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
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...
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Resurgence matches quantization
Couso-Santamaría, Ricardo; Mariño, Marcos; Schiappa, Ricardo
2017-04-01
The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi–Yau background, it has been possible to give a nonperturbative definition of the topological-string partition function. On the other hand, using techniques of resurgence and transseries, it has been possible to extend the string (asymptotic) perturbative expansion into a transseries involving nonperturbative instanton sectors. Within the specific example of the local {{{P}}2} toric Calabi–Yau threefold, the present work shows how the Borel–Padé–Écalle resummation of this resurgent transseries, alongside occurrence of Stokes phenomenon, matches the string-theoretic partition function obtained via quantization of the mirror curve. This match is highly non-trivial, given the unrelated nature of both nonperturbative frameworks, signaling at the existence of a consistent underlying structure.
Resurgence Matches Quantization
Couso-Santamaría, Ricardo; Schiappa, Ricardo
2016-01-01
The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been possible to give a nonperturbative definition of the topological-string partition function. On the other hand, using techniques of resurgence and transseries, it has been possible to extend the string (asymptotic) perturbative expansion into a transseries involving nonperturbative instanton sectors. Within the specific example of the local P2 toric Calabi-Yau threefold, the present work shows how the Borel-Pade-Ecalle resummation of this resurgent transseries, alongside occurrence of Stokes phenomenon, matches the string-theoretic partition function obtained via quantization of the mirror curve. This match is highly non-trivial, given the unrelated nature of both nonperturbative frameworks, signaling at the existence of a consistent underlying structure.
Gradient expansion for anisotropic hydrodynamics
Florkowski, Wojciech; Ryblewski, Radoslaw; Spaliński, Michał
2016-12-01
We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of nonhydrodynamic modes.
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.
Asymptotics of the filtration problem for suspension in porous media
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.
Asymptotic conditions of motion for radiating charged particles
Anderson, James L.
1997-10-01
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.
Qin Jiang
2010-01-01
Full Text Available Mismatch problem has been one of important issues of matched field processing for underwater source detection. Experimental use of MFP has shown that robust range and depth localization is difficult to achieve. In many cases this is due to uncertainty in the environmental inputs required by acoustic propagation models. The paper presents that EMD (Empirical mode decomposition processing underwater acoustic signals is motivated because it is well suited for removing specific unwanted signal components that may vary spectrally. And the Karhunen-Loève expansion is applied on sample covariance matrix to gain a relatively uncorrupted signal. The EMD denoising scheme is combined with Karhunen-Loève expansion to improve underwater target localization performance of matched field processing (MFP. The robustness and effectiveness of the proposed method is tested by the benchmark cases numerical simulation when there had large environmental parameter uncertainties of the acoustic waveguide.
Jensen, J.L.
1993-01-01
Previous results on Edgeworth expansions for sums over a random field are extended to the case where the strong mixing coefficient depends not only on the distance between two sets of random variables, but also on the size of the two sets. The results are applied to the Poisson and the Strauss po...... point processes, giving rise also to local limit results. © 1993 The Institute of Statistical Mathematics....
Zhang, Zhongyang; Berti, Emanuele
2011-01-01
We study the effect of black hole spin on the accuracy of the post-Newtonian approximation. We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J. For a given dimensionless spin a=J/M^2 (in geometrical units), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r. We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v^8 beyond the quadrupole formula), generalizing previous work by two of us. The "error function" used to determine the region of validity of the post-Newtonian expansion can have two qualitatively different kinds of behavior, and we deal with these two cases separately. We find that, at any fixed post-Newtonian order, the edge of the region of validity (as measured by v/v_{ISCO}, where v_{ISCO} is the orbital velocity at the innermost stable circula...
Numerical and asymptotic aspects of parabolic cylinder functions
Temme, N.M.
2000-01-01
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic 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
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.
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
A Shortcut to LAD Estimator Asymptotics
1990-01-01
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...
de Reyna, Juan Arias
2012-01-01
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Asymptotic solution for EI Nino-southern oscillation of nonlinear model
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.
Asymptotically Safe Dark Matter
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....
Asymptotically Safe Dark Matter
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....
Asymptotic analysis of the Nörlund and Stirling polynomials
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.
彭从文; 朱向荣; 王金昌
2011-01-01
将渐近展开法与细观统计模型相结合,研究了脆性岩石双尺度计算方法.该方法在细观尺度定义材料属性,假定材料参数符合Weibull分布,采用弹性-理想脆性本构模型,脆断标准采用修正的Mohr-Coulomb准则和最大拉应力准则,通过宏细观尺度耦合计算,得到细观尺度材料损伤演化及其对结构宏观性状的影响.方法包括确定材料统计参数、确定细观尺度代表性体积单元(RVE)及求解边值方程等步骤.数值模型采用商业软件ABAQUS及其内嵌的UMAT用户子程序实现.该方法适用于岩石单轴受压或低围压应力状态,考虑到计算效率,计算时宜采用混合尺度,即模型重点(关键)部位采用双尺度,而其他区域采用单尺度计算.宏观尺度材料软化后未采用正则化方法,此时的计算结果有网格依赖性.%The asymptotic expansion method was combined with micro-based statistical model to develop a two-scale scheme for analyzing the behavior of brittle rock.The material properties were defined in micro-scale and the elastic-perfect brittle constitutive was adopted, the modified Mohr-Coulomb theory and the maximum tensile strength were selected as the fracture criterion.Through calculating in a global-local coupling way, the damage evolution of material in the micro-scale and its effects on the properties of rock in the macro-scale were derived.The scheme included three steps: determining material statistical parameters, determining representative volume element (RVE) and solving boundary equations.The numerical model was realized by the commercial software ABAQUS and its subroutine UMAT.This scheme can be used in the conditions that the rock is loaded with uniaxial compression or triaxial compression with low confining pressure.The regularization method is not used, so the result is mesh dependent after the rock is localized.
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...
Breaking a magnetic zero locus: asymptotic analysis
Raymond, Nicolas
2014-01-01
25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
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
Discrete Energy Asymptotics on a Riemannian circle
Brauchart, J S; Saff, E B
2009-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\
Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures
Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese
2017-04-01
In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1-204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally, we illustrate the behavior of the model with various numerical simulations.
Asymptotic theory of double layer and shielding of electric field at the edge of illuminated plasma
Benilov, M. S. [Departamento de Física, CCCEE, Universidade da Madeira, Largo do Município, 9000 Funchal (Portugal); Thomas, D. M. [Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)
2014-04-15
The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length λ{sub D}. A second-approximation asymptotic solution is found for the double layer positioned at the boundary of the illuminated region and for the un-illuminated plasma for the plane geometry. Numerical calculations for different values of λ{sub D} are reported and found to confirm the asymptotic results. The net integral space charge of the double layer is asymptotically small, although in the plane geometry it is just sufficient to shield the ambipolar electric field existing in the illuminated region and thus to prevent it from penetrating into the un-illuminated region. The double layer has the same mathematical nature as the intermediate transition layer separating an active plasma and a collisionless sheath, and the underlying physics is also the same. In essence, the two layers represent the same physical object: a transonic layer.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
Asymptotic Methods for Solitary Solutions and Compactons
Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Freitas, Ayres; Plehn, Tilman
2016-01-01
Effective Lagrangians are a useful tool for a data-driven approach to physics beyond the Standard Model at the LHC. However, for the new physics scales accessible at the LHC, the effective operator expansion is only relatively slowly converging at best. For tree-level processes, it has been found that the agreement between the effective Lagrangian and a range of UV-complete models depends sensitively on the appropriate definition of the matching. We extend this analysis to the one-loop level, which is relevant for electroweak precision data and Higgs decay to photons. We show that near the scale of electroweak symmetry breaking the validity of the effective theory description can be systematically improved through an appropriate matching procedure. In particular, we find a significant increase in accuracy when including suitable terms suppressed by the Higgs vacuum expectation value in the matching.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
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.
One-loop diagrams in the random Euclidean matching problem
Lucibello, Carlo; Parisi, Giorgio; Sicuro, Gabriele
2017-01-01
The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e., the optimal matching problem between points randomly distributed on a d -dimensional Euclidean space, where the cost to minimize depends on the points' pairwise distances. Using Mayer's cluster expansion we write a formal expression for the replicated action that is suitable for a saddle point computation. We give the diagrammatic rules for each term of the expansion, and we analyze in detail the one-loop diagrams. A characteristic feature of the theory, when diagrams are perturbatively computed around the mean field part of the action, is the vanishing of the mass at zero momentum. In the non-Euclidean case of uncorrelated costs instead, we predict and numerically verify an anomalous scaling for the sub-sub-leading correction to the asymptotic average cost.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models
Isaacson, Samuel A.; Mauro, Ava J.; Newby, Jay
2016-10-01
The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013), 10.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.
苏永福
2001-01-01
文[4]把文[3]的主要结果从Hilbert空间推广到一致凸Banach空间,证明了一致凸Banach空间中文上从有界闭凸集到自身的渐近非扩张映象的迭代序列收敛定理.本文将有界闭凸集的条件减弱为闭凸集,从而推广了文[4]的相应结果.%In paper [4], the relative result of Jiirgen schu is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly conves Banach space for asymptotically non - expanstive mapping is proved.In paper [4], T is asymptotically non - expanstive mapping with sequence {Kn} in a bounded closed convex subset C of uniformly convex Banach space.In this paper, we let only C is closed convex subset of uniformlly convex Banach space. But convergence theorms of iterative sequences for asymptotically non-expanstive mapping was also proved.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Asymptotic analysis of outwardly propagating spherical flames
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
On the Asymptotics of Bessel Functions in the Fresnel Regime
2014-07-10
We introduce a version of the asymptotic expansions for Bessel functions Jν(z), Yν(z) that is valid whenever |z| > ν (which is deep in the Fresnel...equations, to be reported at a later date. On the asymptotics of Bessel functions in the Fresnel regime Z. Heitman‡ , J. Bremer?⊕, V. Rokhlin‡ , B...48109 ‡ Dept. of Mathematics, Yale University, New Haven CT 06511 Approved for public release: distribution is unlimited. Keywords: Bessel Functions
Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation
Gadylshin, R R
1998-01-01
It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Hansson, Bo
2007-01-01
This paper examines crowding-out effects and the labour market match for the tertiary educated in 26 OECD countries, using attainment data and data on labour market outcomes from Education at a Glance 2006. A first-difference approach is applied on a three-period, pooled country-panel to examine the effects of changes in tertiary attainment levels…
An All-Orders Derivative Expansion
Dunne, Gerald(Department of Physics, University of Connecticut, Storrs, CT, 06269, U.S.A.)
1996-01-01
We evaluate the exact $QED_{2+1}$ effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders derivative expansion of the effective action, and indicates that the derivative expansion is an asymptotic, rather than a convergent, expansion.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
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...
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...
On asymptotic flatness and Lorentz charges
Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)
2011-07-21
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.......We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...
Litim, Daniel F
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions
A.M. Il'in; R.Z. Khasminskii; G. Yin
2002-01-01
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
Asymptotics of 6j and 10j symbols
Freidel, L; Freidel, Laurent; Louapre, David
2003-01-01
It is well known that the building blocks for state sum models of quantum gravity is given by 6j and 10j symbols. In this work we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics we recover the Ponzano-Regge formula for the SU(2) 6j-symbol. We show how the asymptotics of the various Lorentzian $6j$-symbols can be obtained by the same methods. Finally we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of these behavior and a way to modify the Barrett-Crane model to cure this disease.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.
Homogenization and asymptotics for small transaction costs
Soner, H Mete
2012-01-01
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.
ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS
Cheng Ouyang
2005-01-01
A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.
Application of AN Asymptotic Method to Transient Dynamic Problems
Fafard, M.; Henchi, K.; Gendron, G.; Ammar, S.
1997-11-01
A new method to solve linear dynamics problems using an asymptotic method is presented. Asymptotic methods have been efficiently used for many decades to solve non-linear quasistatic structural problems. Generally, structural dynamics problems are solved using finite elements for the discretization of the space domain of the differential equations, and explicit or implicit schemes for the time domain. With the asymptotic method, time schemes are not necessary to solve the discretized (space) equations. Using the analytical solution of a single degree of freedom (DOF) problem, it is demonstrated, that the Dynamic Asymptotic Method (DAM) converges to the exact solution when an infinite series expansion is used. The stability of the method has been studied. DAM is conditionally stable for a finite series expansion and unconditionally stable for an infinite series expansion. This method is similar to the analytical method of undetermined coefficients or to power series method being used to solve ordinary differential equations. For a multi-degree-of-freedom (MDOF) problem with a lumped mass matrix, no factorization or explicit inversion of global matrices is necessary. It is shown that this conditionally stable method is more efficient than other conditionally stable explicit central difference integration techniques. The solution is continuous irrespective of the time segment (step) and the derivatives are continuous up to orderN-1 whereNis the order of the series expansion.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
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.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Plummer, MD
1986-01-01
This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.
A. Hak (Tony); J. Dul (Jan)
2009-01-01
textabstractPattern matching is comparing two patterns in order to determine whether they match (i.e., that they are the same) or do not match (i.e., that they differ). Pattern matching is the core procedure of theory-testing with cases. Testing consists of matching an “observed pattern” (a pattern
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
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...
Hak, Tony; Dul, Jan
2009-01-01
textabstractPattern matching is comparing two patterns in order to determine whether they match (i.e., that they are the same) or do not match (i.e., that they differ). Pattern matching is the core procedure of theory-testing with cases. Testing consists of matching an “observed pattern” (a pattern of measured values) with an “expected pattern” (a hypothesis), and deciding whether these patterns match (resulting in a confirmation of the hypothesis) or do not match (resulting in a disconfirmat...
Equivariant spectral asymptotics for h-pseudodifferential operators
Weich, Tobias
2014-10-01
We prove equivariant spectral asymptotics for h-pseudodifferential operators for compact orthogonal group actions generalizing results of El Houakmi and Helffer ["Comportement semi-classique en présence de symétries: Action d'un groupe de Lie compact," Asymp. Anal. 5(2), 91-113 (1991)] and Cassanas ["Reduced Gutzwiller formula with symmetry: Case of a Lie group," J. Math. Pures Appl. 85(6), 719-742 (2006)]. Using recent results for certain oscillatory integrals with singular critical sets [P. Ramacher, "Singular equivariant asymptotics and Weyl's law: On the distribution of eigenvalues of an invariant elliptic operator," J. Reine Angew. Math. (Crelles J.) (to be published)], we can deduce a weak equivariant Weyl law. Furthermore, we can prove a complete asymptotic expansion for the Gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the Hamilton flow.
R. Fares
2012-01-01
Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.
ADAPTIVE STEREO MATCHING ALGORITHM BASED ON IMPROVED SEED POINTS EXPANSION%基于改进的种子点扩展自适应立体匹配算法
李鹏格; 戴本祁
2016-01-01
由于在图像中不同区域的纹理密集程度不同，因此使用固定窗口大小的算法无法兼顾纹理不同的区域，并且在视差不连续区域的匹配精度较低。针对该问题，提出一种自适应窗口和自适应权重相结合的算法，并且采用种子点扩展的方法。首先，通过交叉自适应窗口法，区分出连续点和孤立点，对于不同的分类点采用不同的处理方法。其次，针对每一个像素点，利用改进的自适应权重方法进行匹配。最后，提出一种新的种子点扩展的视差优化方法，对初始视差图进行精细化。实验结果表明，视差图中纹理密集区域和视差不连续区域的误匹配现象得到改善。该算法可以有效地处理图像中纹理分布不均的问题，提高了在视差不连续区域内匹配精度。%Since the image in different regions has different texture intensity,therefore the algorithm using a size-fixed window can’t take into account the regions with different textures,and its matching precision is low in disparity discontinuities regions.To solve these problems, in this paper we propose a new algorithm which combines adaptive window and adaptive weight,and uses the means of seed point expansion. First,we distinguish the consecutive points and isolated points with cross-adaptive window method,and use different processing approaches for different classification points.Secondly,for each pixel point we use the improved adaptive weight method to match it.Finally,we present a new disparity optimisation approach of seed points expansion to refine the raw disparity map.Experimental results show that the phenomenon of mismatching the texture intensity region and disparity discontinuities region in disparity map has been improved.The algorithm can effectively process the problem of uneven texture distribution in image,and raise the matching precision in disparity discontinuities region.
A Note on Asymptotic Contractions
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Inference on rare errors using asymptotic expansions and bootstrap calibration
Helmers, R.
1998-01-01
The number of items in error in an audit population is usually quite small, whereas the error distribution is typically highly skewed to the right. For applications in statistical auditing, where line item sampling is appropriate, a new upper confidence limit for the total error amount in an audit p
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Entropy Production during Asymptotically Safe Inflation
Martin Reuter
2011-01-01
Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.
On the accuracy of the asymptotic theory for cylindrical shells
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....
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Asymptotic Limits for Transport in Binary Stochastic Mixtures
Prinja, A. K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-01
The Karhunen-Loeve stochastic spectral expansion of a random binary mixture of immiscible fluids in planar geometry is used to explore asymptotic limits of radiation transport in such mixtures. Under appropriate scalings of mixing parameters - correlation length, volume fraction, and material cross sections - and employing multiple- scale expansion of the angular flux, previously established atomic mix and diffusion limits are reproduced. When applied to highly contrasting material properties in the small cor- relation length limit, the methodology yields a nonstandard reflective medium transport equation that merits further investigation. Finally, a hybrid closure is proposed that produces both small and large correlation length limits of the closure condition for the material averaged equations.
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.
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.
Baugher, Benjamin
2008-01-01
We prove the main conjecture from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the metric dependence and asymptotic minimization of the expected number \\mathcal{N}^{crit}_{N,h} of critical points of random holomorphic sections of the Nth tensor power of a positive line bundle. The first non-topological term in the asymptotic expansion of \\mathcal{N}^{crit}_{N,h} is the the Calabi functional multiplied by the constant \\be_2(m) which depends only on the dimension of the manifold. We prove that \\be_2(m) is strictly positive in all dimensions, showing that the expansion is non-topological for all m, and that the Calabi extremal metric, when it exists, asymptotically minimizes \\mathcal{N}^{crit}_{N,h}.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
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.
The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
Brauchart, J S; Saff, E B
2012-01-01
We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in $\\mathbb{R}^{d+1}$, $d\\geq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\\to \\infty$) of the optimal $s$-energy.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
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.
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Asymptotic aspects of Cayley graphs
Dejter, Italo J
2011-01-01
Arising from complete Cayley graphs $\\Gamma_n$ of odd cyclic groups $\\Z_n$, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equally-multicolored copies of $K_4$ in $\\Gamma_n$ with adjacency of any two such vertices whenever they are represented by copies of $K_4$ in $\\Gamma_n$ sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order $|V|^{1/3}$, properties shared by the initial member of a collection of families of Cayley graphs of degree $2m\\geq 6$ with diameter asymptotically of order $|V|^{1/m}$, where $3\\leq m\\in\\Z$.
Asymptotic vacua with higher derivatives
Spiros Cotsakis
2016-04-01
Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic vacua with higher derivatives
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
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.
Edgeworth expansion for functionals of continuous diffusion processes
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....
Edgeworth expansion for functionals of continuous diffusion processes
Podolskij, Mark; Yoshida, Nakahiro
2016-01-01
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the second order Edgeworth expansion for power variation of diffus...... of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations....
Ruin problems and tail asymptotics
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...
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
Thermodynamics of asymptotically safe theories
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...
Aguareles, M.
2014-06-01
In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.
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.
Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points
Fei LIU; Fang WANG
2016-01-01
In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
Structure and asymptotic theory for nonlinear models with GARCH errors
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.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Remarks on asymptotically safe inflation
Tye, S.-H. Henry; Xu, Jiajun
2010-12-01
We comment on Weinberg’s interesting analysis of asymptotically safe inflation [S. Weinberg, Phys. Rev. DPRVDAQ1550-7998 81, 083535 (2010).10.1103/PhysRevD.81.083535]. 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 group flow away from the fixed point towards the infrared region that reproduces the Newton’s constant and today’s cosmological constant. We follow this renormalization group 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 e folds of inflation in the asymptotically safe inflationary scenario.
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 Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
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.
Edgeworth expansion for the pre-averaging estimator
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....
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Long-time asymptotics in the one-dimensional trapping problem with large bias
Aldea, A.; Dulea, M.; Gartner, P.
1988-08-01
The survival probability of a particle which moves according to a biased random walk in a one-dimensional lattice containing randomly distributed deep traps is studied at large times. Exact asymptotic expansions are deduced for fields exceeding a certain threshold, using the method of images. In order to cover the whole range of fields, we also derive the behavior of the survival probability below this threshold, using the eigenvalue expansion method. The connection with the continuous diffusion model is discussed.
Asymptotics of Heavy-Meson Form Factors
Grozin, A.G.; Grozin, Andrey G.; Neubert, Matthias
1997-01-01
Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\\ll |v\\cdot v'|\\ll m_Q/\\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\\cdot v'|\\gg m_Q/\\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\\cdot v'|\\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\\cdot v'\\sim m_b/\\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\\cdot v'\\sim -m_b/\\Lambda$). We obtain the evolution equations and sum rules ...
Asymptotics for Toeplitz determinants: Perturbation of symbols with a gap
Charlier, Christophe; Claeys, Tom
2015-02-01
We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate. We generalize an asymptotic expansion by Widom [Indiana Univ. Math. J. 21, 277-283 (1971)], which was known for symbols supported on an arc. We highlight applications of our results in the circular unitary ensemble and in the study of Fredholm determinants associated to the sine kernel.
ASYMPTOTIC APPROXIMATION BYBERNSTEIN-DURRMEYER OPERATORS AND THEIR DERIVATIVES
Abel, Ulrich
2000-01-01
The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators M,. We derive the complete asymptotic expansion of the operators M. and their derivatives as n tends to infinity. It turns ow that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases.Finally, we obtain a Voronovskaja-type formula for simultaneous a pproximation by linear combinations of Mn.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
AN ASYMPTOTIC ANALYSIS METHOD FOR THE LINEAR SHELL
李开泰; 张文岭; 黄艾香
2004-01-01
In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term uk successively. According this metnod the leading term u0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution UKT(x,ζ):=U(x)+Ⅱ1Uζ+Ⅱ2Uζ2,then we give the estimation.
Temme, N.M.
1996-01-01
We consider the asymptotic behavior of the incomplete gamma functions $gamma (-a,-z)$ and $Gamma (-a,-z)$ as $atoinfty$. Uniform expansions are needed to describe the transition area $z sim a$, in which case error functions are used as main approximants. We use integral representations of the incomp
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
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 of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
Oehlschlägel, Jens
2007-01-01
Cluster matching by permuting cluster labels is important in many clustering contexts such as cluster validation and cluster ensemble techniques. The classic approach is to minimize the euclidean distance between two cluster solutions which induces inappropriate stability in certain settings. Therefore, we present the truematch algorithm that introduces two improvements best explained in the crisp case. First, instead of maximizing the trace of the cluster crosstable, we propose to maximize a chi-square transformation of this crosstable. Thus, the trace will not be dominated by the cells with the largest counts but by the cells with the most non-random observations, taking into account the marginals. Second, we suggest a probabilistic component in order to break ties and to make the matching algorithm truly random on random data. The truematch algorithm is designed as a building block of the truecluster framework and scales in polynomial time. First simulation results confirm that the truematch algorithm give...
Gravitational entropy of cosmic expansion
Sussman, Roberto A
2014-01-01
We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\\Lambda$-CDM background model. However, the $\\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.
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.
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.
Modeling broadband poroelastic propagation using an asymptotic approach
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 accuracy of Bayesian estimation for a single latent variable.
Yamazaki, Keisuke
2015-09-01
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the joint probability of the latent variables in a dataset, and we proved that the Bayes method is asymptotically more accurate than the maximum-likelihood method. However, the accuracy of the Bayes estimation for a single latent variable remains unknown. In the present paper, we derive the asymptotic expansions of the error functions, which are defined by the Kullback-Leibler divergence, for two types of single-variable estimations when the statistical regularity is satisfied. Our results indicate that the accuracies of the Bayes and maximum-likelihood methods are asymptotically equivalent and clarify that the Bayes method is only advantageous for multivariable estimations.
Asymptotic properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
Operator product expansion algebra
Holland, Jan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Hollands, Stefan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, Leipzig, D-04103 (Germany)
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Linearized asymptotic stability for fractional differential equations
Nguyen Cong
2016-06-01
Full Text Available We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\\{\\lambda \\in \\mathbb{C} : |\\arg \\lambda| > \\frac{\\alpha \\pi}{2}\\}$ where $\\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
1970-10-01
sale: is disributici is unlimited = F’)RIWRD Seior Ignacio Soto, Rrecutive President, Instituto Mexicano del Cementc y Concreto , invited Mr. Bryant... Concreto , a.c., Kwidco, D. F., Mexico. Based on info.mation largely obtained from ACT Committee 223, Expansive ’ement. Concretes, ACI Journal, August 1Q70
Involatile nanodroplets: an asymptotic analysis.
Jarymowycz, Lucien B; Ortoleva, Peter J
2006-06-21
The structure of nanometer-scale droplets of weakly volatile liquids arises through the interplay of strong intermolecular attraction, and core intermolecular repulsion, interfacial forces, and the large, negative chemical potential of the low density vapor with which it is in equilibrium. Using a van der Waals equation of state and a mesoscopic multiphase model, the structure of such nanodroplets is determined via an asymptotic analysis in terms of the ambient to critical temperature ratio. The structure of a spherical droplet is obtained as the solution of a simple "shooting" problem. The intradroplet pressure profile and a minimal droplet size are determined. The high pressure in the core of the droplet gives evidence for the preferred melting there for systems like water with a negative volume of melting. Our methodology can be generalized to multiphase droplets, as well as to composite structures wherein viruses or other nanoparticles are embedded.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
Term structure modeling and asymptotic long rate
Yao, Y.
1999-01-01
This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H.,
Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
Navas, Luis M; Varona, Juan L
2011-01-01
We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\\mathcal{B}_{n}(x;\\lambda)$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. These results are transferred to the Apostol-Euler polynomials $\\mathcal{E}_{n}(x;\\lambda)$ via a simple relation linking them to the Apostol-Bernoulli polynomials.
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.
Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach
Dan DAI; Roderick WONG
2007-01-01
In this paper, we study the asymptotics of the Krawtchouk polynomials KnN(z;p,q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c ∈ (0, 1) as n →∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p;in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.
Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity
Gonzalez, John B
2009-01-01
We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schr\\"odinger (NLS) equations $iu_t + u_{xx} \\pm |u|^2 u = 0$ in classes of smooth functions that admit an asymptotic expansion at infinity in decreasing powers of $x$. We show that an asymptotic solution differs from a genuine solution by a Schwartz class function which solves a generalized version of the NLS equation. The latter equation is solved by discretization methods. The proofs closely follow previous work done by the author and others on the Korteweg-De Vries (KdV) equation and the modified KdV equations.
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
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.
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.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Edgeworth expansion for the survival function estimator in the Koziol-Green model
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.
Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind
Fucci, Guglielmo
2014-01-01
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory.
On the Expansions in Spin Foam Cosmology
Hellmann, Frank
2011-01-01
We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expan- sion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.
Grava, T
2012-01-01
We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\epsilon^{2}u_{xxx}=0$ for $\\epsilon\\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.
Asymptotics of Simple Branching Populations
Huillet, Thierry; Kłopotowski, Andrzej; Porzio, Anna
1995-09-01
In this paper we study a simple deterministic tree structure: an initial individual generates a finite number of offspring, each of which has given integer valued lifetime, iterating the same procedure when dying. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the ability of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developped to reveal the multifractal nature of the mass splitting associated to our process. On considère l'itération d'une structure déterministe arborescente selon laquelle un ancêtre engendre un nombre fini de descendants dont la durée de vie (à valeurs entières) est donnée. Dans un premier temps on s'intéresse aux trois distributions asymptotiques suivantes : répartition des générations, aptitude à engendrer des descendants et répartition selon l'âge. Ensuite nous développons le formalisme thermodynamique pour mettre en évidence le caractère multifractal de la scission d'une masse unitaire associée à cette arborescence.
Ultraviolet asymptotics of glueball propagators
Bochicchio, M
2013-01-01
We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large-N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large-N limit of YM. We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/...
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
Alho, Artur; Uggla, Claes
2015-01-01
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor' solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve th...
Bringmann, Kathrin; Folsom, Amanda; Milas, Antun
2017-01-01
Motivated by recent developments in the representation theory of vertex algebras and conformal field theory, we prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable τ tends to 0 along the imaginary axis, and the elliptic variable z is unrestricted in the complex plane. We observe that these functions exhibit Stokes' phenomenon—the asymptotic behavior of these functions sharply differs depending on where the elliptic variable z is located within the complex plane. We apply our results to study the asymptotic expansions of regularized characters and quantum dimensions of the (1, p)-singlet W-algebra modules important in logarithmic conformal field theory. This, in particular, recovers and extends several results from the work of T. Creutzig et al. [Int. Math. Res. Not. (2016); e-print arXiv:1411.3282] pertaining to regularized quantum dimensions.
Serov, S A
2013-01-01
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.
Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials
Xin Wang
2014-01-01
Full Text Available An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.
Asymptotic silence in loop quantum cosmology
Mielczarek, Jakub
2012-01-01
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density $\\rho = \\rho...
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
Asymptotic Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
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.
Hermite polynomials and quasi-classical asymptotics
Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Langmuir probe study of plasma expansion in pulsed laser ablation
Hansen, T.N.; Schou, Jørgen; Lunney, J.G.
1999-01-01
Langmuir probes were used to monitor the asymptotic expansion of the plasma produced by the laser ablation of a silver target in a vacuum. The measured angular and temporal distributions of the ion flux and electron temperature were found to be in good agreement with the self-similar isentropic...... and adiabatic solution of the gas dynamics equations describing the expansion. The value of the adiabatic index gamma was about 1.25, consistent with the ablation plume being a low temperature plasma....
Asymptotic forms for hard and soft edge general β conditional gap probabilities
Forrester, Peter J.; Witte, Nicholas S.
2012-06-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix β-ensembles. The conditioning is that there are n eigenvalues in the gap, with n≪|t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions — which are for the logarithm of the gap probabilities — are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating β to 4/β.
Asymptotic forms for hard and soft edge general {beta} conditional gap probabilities
Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Witte, Nicholas S., E-mail: nsw@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2012-06-21
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix {beta}-ensembles. The conditioning is that there are n eigenvalues in the gap, with n Much-Less-Than |t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating {beta} to 4/{beta}.
Higher order asymptotic fields for mode Ⅰ crack in functionally gradient material
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.
Asymptotic forms for hard and soft edge general $\\beta$ conditional gap probabilities
Forrester, Peter J
2011-01-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \\ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\\beta$ to $4/\\beta$.
Quantum gravity on foliated spacetimes: Asymptotically safe and sound
Biemans, Jorn; Platania, Alessia; Saueressig, Frank
2017-04-01
Asymptotic safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the Arnowitt-Deser-Misner formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed-point characteristic for asymptotic safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ɛ -expansion around two dimensions, Monte Carlo simulations based on lattice quantum gravity, and the discretized Wheeler-DeWitt equation.
Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
Ferreira, Ricardo Z; Sloth, Martin S
2016-01-01
Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, $\\langle0| 0'\\rangle$, between the unperturbed de Sitter vacuum $|0\\rangle$, and the state $| 0'\\rangle$ obtained by acting $\\mathcal{N}$ times with the charge. We show that when $\\mathcal{N}\\to M_p^2/H^2$ this overlap receives order one corrections and $\\langle0| 0'\\rangle\\...
On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations
Babin, A.; Mahalov, A.; Nicolaenko, B.; Zhou, Y.
1997-01-01
Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.
Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions
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.
Right tail expansion of Tracy-Widom beta laws
Borot, Gaëtan
2011-01-01
Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail Tracy-Widom beta laws, for all positive beta, by studying the double scaling limit.
Jacobi-Sobolev Orthogonal Polynomials: Asymptotics for N-Coherence of Measures
Marcellán Francisco
2011-01-01
Full Text Available Let us introduce the Sobolev-type inner product , where and , , with and for all A Mehler-Heine-type formula and the inner strong asymptotics on as well as some estimates for the polynomials orthogonal with respect to the above Sobolev inner product are obtained. Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.
Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations
Bas, Erdal; Ozarslan, Ramazan
2016-06-01
In this study, Sturm-Liouville problem with variable coefficient, potential function q (n), for difference equation is considered. The representation of solutions is obtained by variation of parameters method for two different initial value problems and trigonometric solutions are found by means of complex characteristic roots. It is proved that these results hold the equation by using summation by parts method. Two estimations of asymptotic expansion of the solutions are established.
Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity
Eduard Marušić-Paloka
2014-01-01
Full Text Available We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique.
Higher-order semiclassical energy expansions for potentials with non-integer powers
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.
Gopinath, Ashok
1996-01-01
Analytical and numerical studies are to be carried out to examine time-averaged thermal effects which are induced by the interaction of strong acoustic fields with a rigid boundary (thermoacoustic streaming). Also of interest is the significance of a second-order thermal expansion coefficient that emerges from this analysis. The model problem to be considered is that of a sphere that is acoustically levitated such that it is effectively isolated in a high-intensity standing acoustic field. The solution technique involves matched asymptotic analysis along with numerical solution of the boundary layer equations. The objective of this study is to predict the thermoacoustic streaming behavior and fully understand the role of the associated second-order thermodynamic modulus.
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...
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 ...
Nanofluid surface wettability through asymptotic contact angle.
Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian
2011-03-15
This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
On generalized Nariai solutions and their asymptotics
Beyer, Florian
2009-01-01
In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Ackerman, Margareta; Lopez-Ortiz, Alejandro
2011-01-01
Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries. One of the main remaining challenges is to satisfy the users' needs when they provide a poorly formulated query. When the pages matching the user's original keywords are judged to be unsatisfactory, query expansion techniques are used to alter the result set. These techniques find keywords that are similar to the keywords given by the user, which are then appended to the original query leading to a perturbation of the result set. However, when the original query is sufficiently ill-posed, the user's informational need is best met using entirely different keywords, and a small perturbation of the original result set is bound to fail. We propose a novel approach that is not based on the keywords of the original query. We intentionally seek out orthogonal queries, which are r...
Filippov, A. I.; Akhmetova, O. V.; Koval‧skii, A. A.
2016-11-01
The filtration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modified asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coefficients of expansion in an asymptotic parameter. The zero expansion coefficient describes the sought plane wave, whereas the first coefficient ensures refinement of the wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confirmed by comparing the obtained asymptotic solutions and the coefficients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
Asymptotic Distributions for Tests of Combined Significance.
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
Asymptotic iteration approach to supersymmetric bistable potentials
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
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.
An asymptotically optimal nonparametric adaptive controller
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 symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
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.
Fixed Point Theorems for Asymptotically Contractive Multimappings
M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then f
Asymptotically periodic solutions of Volterra integral equations
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
On an asymptotically linear elliptic Dirichlet problem
Zhitao Zhang
2002-01-01
Full Text Available Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS sequence of the corresponding functional. Moreover, the proof is very simple.
Resonance asymptotics in the generalized Winter model
Exner, P; Exner, Pavel; Fraas, Martin
2006-01-01
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.
Topological Expansion in the Complex Cubic Log-Gas Model: One-Cut Case
Bleher, Pavel; Deaño, Alfredo; Yattselev, Maxim
2016-09-01
We prove the topological expansion for the cubic log-gas partition function Z_N(t)= int _Γ \\cdots int _Γ prod _{1≤ jtopological expansion for log Z_N(t) in the one-cut phase region. The proof is based on the Riemann-Hilbert approach to semiclassical asymptotic expansions for the associated orthogonal polynomials and the theory of S-curves and quadratic differentials.
Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
Gerhold, Stefan; Gülüm, I. Cetin; Pinter, Arpad
2016-01-01
ABSTRACT We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula. PMID:27660537
Trinh, Vinh H.; Tolstikhin, Oleg I.; Morishita, Toru
2016-10-01
The many-electron weak-field asymptotic theory of tunneling ionization including the first-order correction terms in the asymptotic expansion of the ionization rate in field strength was highlighted in our recent fast track communication (Trinh et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 061003) by demonstrating its performance for two-electron atoms. Here we present a thorough derivation of the first-order terms omitted in the previous publication and provide additional numerical illustrations of the theory.
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
The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts
Neill, Duff
2017-01-01
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.
INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION
A. I. Popov
2015-09-01
Full Text Available Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain. To find some term of the series, the non-homogeneous Sturm-Liouville problem with the inhomogeneity depending on the previous term needs to be solved. At the same time, the corresponding homogeneous problem has a non-trivial solution. Hence, the solvability problem occures for the non-homogeneous Sturm-Liouville problem for functions or formal power series. The paper deals with creation of such asymptotic expansions. Method. To prove the necessary condition, we use conventional integration technique of the whole equation and boundary conditions. To prove the sufficient condition, we create an appropriate Cauchy problem (which is always solvable and analyze its solution. We deal with the general case of power series and make no hypotheses about the series convergence. Main Result. Necessary and sufficient conditions of solvability for the non-homogeneous Sturm-Liouville problem in general case for formal power series are proved in the paper. As a particular case, the result is valid for functions instead of formal power series. Practical Relevance. The result is usable at creation of the solutions for partial differential equation in the form of power series. The result is general and is applicable to particular cases of such solutions, e.g., to asymptotic series or to functions (convergent power series.
Locally Asymptotic-norming Property and Kadec Property
王建华
2002-01-01
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
Preheating in an asymptotically safe quantum field theory
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, ...
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.
Asymptotical stability of stochastic neural networks with multiple time-varying delays
Zhou, Xianghui; Zhou, Wuneng; Dai, Anding; Yang, Jun; Xie, Lili
2015-03-01
The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Theory of tunneling ionization of molecules: Weak-field asymptotics including dipole effects
Tolstikhin, Oleg I.; Morishita, Toru; Madsen, Lars Bojer
2011-01-01
The formulation of the parabolic adiabatic expansion approach to the problem of ionization of atomic systems in a static electric field, originally developed for the axially symmetric case [ Phys. Rev. A 82 023416 (2010)], is generalized to arbitrary potentials. This approach is used to rederive...... the asymptotic theory of tunneling ionization in the weak-field limit. In the atomic case, the resulting formulas for the ionization rate coincide with previously known results. In addition, the present theory accounts for the possible existence of a permanent dipole moment of the unperturbed system and, hence......, applies to polar molecules. Accounting for dipole effects constitutes an important difference of the present theory from the so-called molecular Ammosov-Delone-Krainov theory. The theory is illustrated by comparing exact and asymptotic results for a set of model polar molecules and a realistic molecular...
LIU Hong-Zhun; PAN Zu-Liang; LI Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
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.
Asymptotic Markov inequality on Jordan arcs
Totik, V.
2017-03-01
Markov's inequality for the derivative of algebraic polynomials is considered on C^2-smooth Jordan arcs. The asymptotically best estimate is given for the kth derivative for all k=1,2,\\dots . The best constant is related to the behaviour around the endpoints of the arc of the normal derivative of the Green's function of the complementary domain. The result is deduced from the asymptotically sharp Bernstein inequality for the kth derivative at inner points of a Jordan arc, which is derived from a recent result of Kalmykov and Nagy on the Bernstein inequality on analytic arcs. In the course of the proof we shall also need to reduce the analyticity condition in this last result to C^2-smoothness. Bibliography: 21 titles.
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.
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.
Perturbative expansions for area-preserving maps
Servizi, G.; Turchetti, G.
1986-10-11
The structure of perturbation series for area-preserving maps is investigated. A basically different behaviour is found between the Birkhoff series, which formally conjugate with circles all the orbits in a neighbourhood of the origin, and the series which map into circles the individual invariant curves with fixed diophantine winding number. The former series exhibit an asymptotic character, the latter a convergent one, as one should expect from the KAM theorem. The source of this difference is found to be the different way in which the contributions of the relevant resonances propagate. In the first case, if epsilon is the size of the divisor associated to a resonance M/N, then at each order n>N an epsilon/sup -1/ contribution occurs, in the second case subtle cancellations provide a new epsilon/sup -1/ only when a harmonic (that is n=pN) is reached. This precise asymptotic statement and the properties of the relevant resonances obtained from the continued fraction expansion allow us, in the case of quadratic irrationals, to understand the limit process which leads to divergence or convergence. In the divergent case the asymptotic properties of the series are exhaustively described.
Optimization of Parameters of Asymptotically Stable Systems
Anna Guerman
2011-01-01
Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.
Asymptotic Existence of Nearly Kirkman Systems
沈灏; 储文松
1994-01-01
It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.
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.
Theorems for asymptotic safety of gauge theories
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
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 emphasised. 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. (orig.)
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
Asymptotic analysis of the Forward Search
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made....... The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure....
Asymptotic modal analysis and statistical energy analysis
Dowell, Earl H.
1988-07-01
Statistical Energy Analysis (SEA) is defined by considering the asymptotic limit of Classical Modal Analysis, an approach called Asymptotic Modal Analysis (AMA). The general approach is described for both structural and acoustical systems. The theoretical foundation is presented for structural systems, and experimental verification is presented for a structural plate responding to a random force. Work accomplished subsequent to the grant initiation focusses on the acoustic response of an interior cavity (i.e., an aircraft or spacecraft fuselage) with a portion of the wall vibrating in a large number of structural modes. First results were presented at the ASME Winter Annual Meeting in December, 1987, and accepted for publication in the Journal of Vibration, Acoustics, Stress and Reliability in Design. It is shown that asymptotically as the number of acoustic modes excited becomes large, the pressure level in the cavity becomes uniform except at the cavity boundaries. However, the mean square pressure at the cavity corner, edge and wall is, respectively, 8, 4, and 2 times the value in the cavity interior. Also it is shown that when the portion of the wall which is vibrating is near a cavity corner or edge, the response is significantly higher.
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
CONCEPT OF TISSUE EXPANSION IN RECONSTRUCTIVE SURGERY
Sheeja Rajan
2015-01-01
Full Text Available BACKGROUND: Tissue expansion is a unique reconstructive option in the armamentarium of a reconstructive surgeon whereby skin and soft tissues of our body can be stretched to large dimensions for wound coverage. The basis for such stretch ability lies in the inherent viscoelastic properties of skin. AIMS: This paper explores the prospects of using tissue expanders to reconstruct defects arising due to a kaleidoscope of pathological conditions including burns scars, post traumatic scars, congenital anomalies like hairy nevus, involutional scars in haemangioma as well as in post mastectomy breast reconstruction . MATERIALS AND METHODS: Our experience with tissue expansion in 14 patients over 24 months is presented. Tissue expanders made of silicone in sizes from 100 - 250ml, of round, rectangular or croissant (crescent shapes have been used. Areas expanded include scalp, forehead, neck, abdomen and forearm. Multiple expanders have been used when possible. Average expansion time was 8 - 12 weeks and the expanded tissue was transferred as advancement flaps. RESULTS AND CONCLUSIONS: Tissue expansion was successfully completed in 13 patients. Expansion had to be aborted in 1 paediatric patient undergoing neck expansion due to infection. Implant failure occurred in 1 patient during serial expansion. Nevertheless, in our experience tissue expan sion is an invaluable reconstructive tool to give excellent donor tissue with colour and texture match in countless situations demanding aesthetic and functional reconstruction. KEYWORDS: Burns scars, Reconstruction, Tissue expansion .
The self consistent expansion applied to the factorial function
Cohen, Alon; Bialy, Shmuel; Schwartz, Moshe
2016-12-01
Most of the interesting systems in statistical physics can be described as nonlinear stochastic field theories. A common feature in the theoretical study of such systems is that ordinary perturbation theory seldom works. On the other hand, there exists a useful tool for the study of systems of that generic nature. That tool, the Self Consistent Expansion (SCE) is technically similar to the ordinary perturbation expansion, in the sense that it is an expansion around a solvable problem. The key point which distinguishes the SCE from an ordinary perturbation expansion, is that the small parameter of the expansion is adjustable and determined inherently by optimization of the expansion. Therefore, it allows the adaptive SCE to remain accurate relative to the inflexible ordinary expansion. The goal of the present paper is to present the SCE by applying it to a well-known zero dimensional problem. We choose the evaluation of the factorial function, x!, as the test case for the SCE, because the Stirling approximation for that function is one of the best known asymptotic expansions, with a very wide use in statistical physics. We show that the SCE approximation holds for small and even negative arguments of the factorial function, where the Stirling expansion fails miserably. It does so without paying any penalty at high values of the argument, where the Stirling formula is excellent. We present numerical as well as analytic SCE approximations of the factorial function.
Statistics of polarisation matching
Naus, H.W.L.; Zwamborn, A.P.M.
2014-01-01
The reception of electromagnetic signals depends on the polarisation matching of the transmitting and receiving antenna. The practical matching differs from the theoretical one because of the noise deterioration of the transmitted and eventually received electromagnetic field. In other applications,
Xionghua Wu
2012-01-01
Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .
Holography and Conformal Anomaly Matching
Cabo-Bizet, Alejandro; Narain, K S
2013-01-01
We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding on-shell bulk action reproduces the Wess-Zumino term for the dilaton of broken conformal symmetry, with the expected coefficient aUV-aIR. Then we consider a specific 3D example of RG flow whose UV asymptotics is normalizable and admits a 6D lifting. We promote a modulus \\rho appearing in the geometry to a function of boundary coordinates. In a 6D description {\\rho} is the scale of an SU(2) instanton. We determine the smooth deformed background up to second order in the space-time derivatives of \\rho and find that the 3D on-shell action reproduces a boundary kinetic term for the massless field \\tau= log(\\rho) with the correct coefficient \\delta c=cUV-cIR. We further analyze the linearized fluctuations around the deformed background geometry and compute the one-point functions ...
Matching Through Position Auctions
Terence Johnson
2009-01-01
This paper studies how an intermediary should design two-sided matching markets when agents are privately informed about their quality as a partner and can make payments to the intermediary. Using a mechanism design approach, I derive sufficient conditions for assortative matching to be profit- or welfare-maximizing, and then show how to implement the optimal match and payments through two-sided position auctions. This sharpens our understanding of intermediated matching markets by clarifying...
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.)
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.)
He, Ji-Huan
This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size
Guy Louchard
2017-01-01
Full Text Available Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and Cauchy's integral formula, asymptotic results for the number $T(n,m,k$ of partitions of $n$ labeled objects with $m$ blocks of fixed size $k$. We analyze the central and non-central region. In the region $m=n/k-n^\\al,\\quad 1>\\al>1/2$, we analyze the dependence of $T(n,m,k$ on $\\al$. This paper fits within the framework of Analytic Combinatorics.
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
Asymptotic key generation rates with phase-randomized coherent light by decoy method
Hayashi, M
2007-01-01
The asymptotic key generation (AKG) rates of quantum key distribution (QKD) with the decoy method are discussed in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of intensities. For this purpose, we derive a useful convex expansion of the phase-randomized coherent state. We also derive upper bounds of AKG rates on a natural and concrete channel model. Using these upper bounds, we numerically check that the AKG rates are almost saturated when the number of intensities is three.
Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
Alberto Lastra
2012-01-01
in the complex domain which generalizes a previous result by Malek in (2011. First, we construct solutions defined in open q-spirals to the origin. By means of a q-Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the q-Gevrey asymptotic expansion (of certain type of the actual solutions.
On matched asymptotic analysis for laminar channel flow with a turning point
Chunqing Lu
2000-07-01
Full Text Available This paper presents a formal analysis of the asimptotic behaviour of solutions of type III for the Berman equation $$ epsilon f^{iv}=ff'''-f'f'' ,quad f(0=f''(0=f'(1=f(1-1=0,, $$ where $f$ describes a laminar flow in a channel with porous walls. A solution has a nonlinear turning point $(1-Delta $, i.e. $f(1-Delta = 0$ for some $Delta(epsilon$. It is shown that $$ f(eta sim -frac{1-Delta }{pi Delta }sin frac{pi eta }{1-Delta }, $$ as $epsilon o 0^{+}$, for $eta in [0,1-Delta $ where $Delta $ satisfies $$ frac{Delta }{epsilon } e^{Delta/epsilon }sim frac{1}{2epi^{9} epsilon ^{8}}. $$
Hierarchical model of matching
Pedrycz, Witold; Roventa, Eugene
1992-01-01
The issue of matching two fuzzy sets becomes an essential design aspect of many algorithms including fuzzy controllers, pattern classifiers, knowledge-based systems, etc. This paper introduces a new model of matching. Its principal features involve the following: (1) matching carried out with respect to the grades of membership of fuzzy sets as well as some functionals defined on them (like energy, entropy,transom); (2) concepts of hierarchies in the matching model leading to a straightforward distinction between 'local' and 'global' levels of matching; and (3) a distributed character of the model realized as a logic-based neural network.
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Asymptotics for a generalization of Hermite polynomials
Alfaro, M; Peña, A; Rezola, M L
2009-01-01
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
New asymptotically flat phantom wormhole solutions
Lobo, Francisco S N; Riazi, Nematollah
2012-01-01
A possible cause of the late-time cosmic acceleration is an exotic fluid with an equation of state lying within the phantom regime, i.e., $w=p/\\rho 0. Thus, there is no need to surgically paste the interior wormhole geometry to an exterior vacuum spacetime. We also consider the "volume integral quantifier", which provides useful information regarding the total amount of energy condition violating matter, and show that, in principle, it is possible to construct asymptotically flat wormhole solutions with an arbitrary small amount of energy condition violating matter.
Asymptotic curved interface models in piezoelectric composites
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
Lectures on the asymptotic theory of ideals
Rees, D
1988-01-01
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work
The ADM mass of asymptotically flat hypersurfaces
de Lima, Levi Lopes
2011-01-01
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.
Taming perturbative divergences in asymptotically safe gravity
Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)
2010-01-01
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
Liu Yue; Wang Zhengping
2007-01-01
This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).
Vacuum Potential and its Asymptotic Variation
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
Best matching theory & applications
Moghaddam, Mohsen
2017-01-01
Mismatch or best match? This book demonstrates that best matching of individual entities to each other is essential to ensure smooth conduct and successful competitiveness in any distributed system, natural and artificial. Interactions must be optimized through best matching in planning and scheduling, enterprise network design, transportation and construction planning, recruitment, problem solving, selective assembly, team formation, sensor network design, and more. Fundamentals of best matching in distributed and collaborative systems are explained by providing: § Methodical analysis of various multidimensional best matching processes § Comprehensive taxonomy, comparing different best matching problems and processes § Systematic identification of systems’ hierarchy, nature of interactions, and distribution of decision-making and control functions § Practical formulation of solutions based on a library of best matching algorithms and protocols, ready for direct applications and apps development. Design...
Nagib, Hassan; Monkewitz, Peter; Österlund, Jens; Christensen, Kenneth; Adrian, Ronald
2001-11-01
Tony Perry, et al. (J. Fluid Mech., v. 439, 2001) have recently contributed to the discussion concerning the reasons for systematic deviations with Re’s (Reynolds numbers) in the Princeton “Super-Pipe” data. Perry et al. demonstrate that the deviation of the constant within the “log-law” is compatible with the “Colebrook formula” for transitionally rough pipes. Since the experiments were completed, Lex Smits and the Princeton Group have argued that the pipe is smooth for at least the majority of the Re range. Here we show that the observed deviations are equally compatible with the finite Re effects obtained from a methodology based on matched asymptotic expansion techniques proposed by us (see abstract at this meeting), in which the infinite-Re limit of the “log-law”, as well as its correction for large but finite Re’s, are derived in a systematic manner. As argued by Perry et al., in these cases one cannot rely on the variation of the centerline velocity with Re to extract the log-law coefficients. The values of the “Karman constant” extracted using either interpretation is significantly lower than the 0.436 value originally proposed and it is closer to the value of 0.38 based on our recent work on boundary layers; see two publications by Österlund et al. (Phys. of Fluids, v. 12 no. 1 and no. 9, 2001). *Supported by NSF, AFOSR & ERCOFTAC.
ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS
Zeng Luchuan
2006-01-01
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Ban ach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
Pamplona, Djenane C; Velloso, Raquel Q; Radwanski, Henrique N
2014-01-01
This article discusses skin expansion without considering cellular growth of the skin. An in vivo analysis was carried out that involved expansion at three different sites on one patient, allowing for the observation of the relaxation process. Those measurements were used to characterize the human skin of the thorax during the surgical process of skin expansion. A comparison between the in vivo results and the numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin of the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and incompressible membrane. When the skin is extended, such as with expanders, the collagen fibers are also extended and cause stiffening in the skin, which results in increasing resistance to expansion or further stretching. We observed this phenomenon as an increase in the parameters as subsequent expansions continued. The number and shape of the skin expanders used in expansions were also studied, both mathematically and experimentally. The choice of the site where the expansion should be performed is discussed to enlighten problems that can lead to frustrated skin expansions. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin by expansion. To our knowledge, this study has provided results that considerably improve our understanding of the behavior of human skin under expansion.
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...
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...
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.
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...
Relaxing the parity conditions of asymptotically flat gravity
Compère, Geoffrey; Dehouck, François
2011-12-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Asymptotic Behaviour of Pion--Pion Total Cross--Sections
Greynat, David; Vulvert, Grégory
2014-01-01
We derive a sum rule which shows an inconsistency between the Lukaszuk-Martin coefficient of the Froissart-Martin bound and well known properties of $\\pi\\pi$ amplitudes in QCD. We next compute the total cross sections for $\\pi^+ \\pi^-$, $\\pi^{\\pm} \\pi^0$ and $\\pi^0 \\pi^0$ scattering within the framework of the constituent chiral quark model (C$\\chi$QM) in the limit of a large number of colours $\\mathrm{N_c}$ and discuss their asymptotic behaviours. The same $\\pi\\pi$ cross sections are also discussed within the general framework of Large-$\\mathrm{N_c}$ QCD and we show that it is possible to make an Ansatz for the isospin $I=1$ and $I=0$ spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-$\\mathrm{N_c}$ counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the $\\sigma_{\\pi^{\\pm}\\pi^0}^{\\rm total}(s)$ cross section predicted by the C...
Asymptotic dental score and prevalent coronary heart disease.
Janket, Sok-Ja; Qvarnström, Markku; Meurman, Jukka H; Baird, Alison E; Nuutinen, Pekka; Jones, Judith A
2004-03-09
Oral infections have been postulated to produce cytokines that may contribute to the pathogenesis of coronary heart disease (CHD). We hypothesized that by estimating the combined production of inflammatory mediators attributable to several oral pathologies, we might be able to explain CHD with better precision. A total of 256 consecutive Finnish cardiac patients from Kuopio University Hospital with angiographically confirmed CHD and 250 age-, gender-, and residence-matched noncardiac patients (controls) were recruited. All dental factors expected to generate inflammatory mediators, including pericoronitis, dental caries, dentate status, root remnants, and gingivitis, were examined, and an asymptotic dental score (ADS) was developed by logistic regression analyses with an appropriate weighting scheme according to the likelihood ratio. We validated the explanatory ability of ADS by comparing it to that of the Total Dental Index and examining whether the ADS was associated with known predictors of CHD. A model that included ADS, C-reactive protein, HDL, and fibrinogen offered an explanatory ability that equaled or exceeded that of the Framingham heart score (C statistic=0.82 versus 0.80). When ADS was removed from this model, the C-statistic decreased to 0.77, which indicates that the ADS was a significant contributor to the explanatory ability of a logistic model. ADS may be useful as a prescreening tool to promote proactive cardiac evaluation among individuals without overt symptoms of CHD. However, additional prospective study is needed to validate the use of an oral health score as a predictor of incident CHD.
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...
Asymptotic solitons for a third-order Korteweg-de Vries equation
Marchant, T.R. E-mail: tim_marchant@uow.edu.au
2004-10-01
Solitary wave interaction for a higher-order version of the Korteweg-de Vries (KdV) equation is considered. The equation is obtained by retaining third-order terms in the perturbation expansion, where for the KdV equation only first-order terms are retained. The third-order KdV equation can be asymptotically transformed to the KdV equation, if the third-order coefficients satisfy a certain algebraic relationship. The third-order two-soliton solution is derived using the transformation. The third-order phase shift corrections are found and it is shown that the collision is asymptotically elastic. The interaction of two third-order solitary waves is also considered numerically. Examples of an elastic and an inelastic collision are both considered. For the elastic collision (which satisfies the algebraic relationship) the numerical results confirm the theoretical predictions, in particular there is good agreement found when comparing the third-order phase shift corrections. For the inelastic collision (which does not satisfy the algebraic relationship) an oscillatory wavetrain is produced by the interacting solitary waves. Also, the third-order phase shift corrections are found numerically for a range of solitary wave amplitudes. An asymptotic mass-conservation law is used to test the finite-difference scheme for the numerical solutions. In general, mass is not conserved by the third-order KdV equation, but varies during the interaction of the solitary waves.
Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity
Higuera, F. J.; Jimenez, J.; Linan, A.
1996-01-01
The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.
Liapunov structure and asymptotic expressions of linear differential systems
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2015-02-01
We compute, via numerical simulations, the nonperturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Asymptotic variance of grey-scale surface area estimators
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....
Gal, Avigdor
2011-01-01
Schema matching is the task of providing correspondences between concepts describing the meaning of data in various heterogeneous, distributed data sources. Schema matching is one of the basic operations required by the process of data and schema integration, and thus has a great effect on its outcomes, whether these involve targeted content delivery, view integration, database integration, query rewriting over heterogeneous sources, duplicate data elimination, or automatic streamlining of workflow activities that involve heterogeneous data sources. Although schema matching research has been o
Joung, Haewon
2002-01-01
Let $\\beta>0$ and $W_\\beta (x) = \\exp (-|x|^\\beta )$, $x \\in \\mathbb{R}$. For $c>0$, define $W_{\\beta, cn} (x) = W_\\beta (x)$ if $|x| \\leq c^{1/\\beta}\\,a_{2n}$ and $W_{\\beta, cn} (x) = 0$ if $|x| > c^{1/\\beta}\\,a_{2n}$, where $a_{2n}$ denotes Mhaskar-Rahmanov-Saff number for $W_\\beta$. Let $\\gamma_n (W_{\\beta, cn})$ be the leading coefficient of the $n$th orthonormal polynomial corresponding to $W_{\\beta, cn}$ and write $\\alpha_n(W_{\\beta, cn}) = \\gamma_{n-1}(W_{\\beta, cn})/...
E. J. Farrell
1987-01-01
Full Text Available Explicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect-d matchings in the graphs, for various values of d. In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs.
Troelsen, Jens; Meincke, Peter; Breinbjerg, Olav
2000-01-01
In many radar applications it is necessary to determine the scattering from an object over a wide frequency band. The asymptotic waveform evaluation (AWE), which is a moment matching (MM) technique, constitutes a method to this end. In general, MM techniques provide a reduced-order model of a fun......In many radar applications it is necessary to determine the scattering from an object over a wide frequency band. The asymptotic waveform evaluation (AWE), which is a moment matching (MM) technique, constitutes a method to this end. In general, MM techniques provide a reduced-order model...... into account. To the knowledge of the authors the AWE technique has not previously been applied to a MoM solution based on this kind of integral equation. It is the purpose of this paper to investigate the use of the AWE technique as a tool to obtain a fast frequency sweep of the field scattered...
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Asymptotic analysis of ultra-relativistic charge
Burton, D A; Tucker, R W; Burton, David A.; Gratus, Jonathan; Tucker, Robin W.
2006-01-01
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneo...
Asymptotic charged BTZ black hole solutions
Hendi, S. H.
2012-03-01
The well-known (2 + 1)-dimensional Reissner-Nordström (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.
Modeling of nanoplastic by asymptotic homogenization method
张为民; 何伟; 李亚; 张平; 张淳源
2008-01-01
The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
Asymptotic Sharpness of Bounds on Hypertrees
Lin Yi
2017-08-01
Full Text Available The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most (nk−1$\\left( {\\matrix{n \\cr {k - 1} } } \\right$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
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...
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
Universality and asymptotic scaling in drilling percolation
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Dimensionally reduced gravity theories are asymptotically safe
Niedermaier, Max E-mail: max@phys.univ-tours.fr
2003-11-24
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the 'area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.
Holographic Renormalization of Asymptotically Flat Gravity
Park, Miok
2012-01-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Grassmann scalar fields and asymptotic freedom
Palumbo, F. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
The asymptotic safety scenario in quantum gravity
Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)
2011-07-01
Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
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.
Asymptotic Behavior of Excitable Cellular Automata
Durrett, R; Durrett, Richard; Griffeath, David
1993-01-01
Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...
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.
Ontology Matching Across Domains
2010-05-01
matching include GMO [1], Anchor-Prompt [2], and Similarity Flooding [3]. GMO is an iterative structural matcher, which uses RDF bipartite graphs to...AFRL under contract# FA8750-09-C-0058. References [1] Hu, W., Jian, N., Qu, Y., Wang, Y., “ GMO : a graph matching for ontologies”, in: Proceedings of
Caetano, Tiberio S; Cheng, Li; Le, Quoc V; Smola, Alex J
2008-01-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the `labels' are ma...
Theiler, James P [Los Alamos National Laboratory
2009-01-01
Following an analogous distinction in statistical hypothesis testing, we investigate variants of machine learning where the training set comes in matched pairs. We demonstrate that even conventional classifiers can exhibit improved performance when the input data has a matched-pair structure. Online algorithms, in particular, converge quicker when the data is presented in pairs. In some scenarios (such as the weak signal detection problem), matched pairs can be generated from independent samples, with the effect not only doubling the nominal size of the training set, but of providing the structure that leads to better learning. A family of 'dipole' algorithms is introduced that explicitly takes advantage of matched-pair structure in the input data and leads to further performance gains. Finally, we illustrate the application of matched-pair learning to chemical plume detection in hyperspectral imagery.
Expansion by eigenvectors in case of simple eigenvalues of singular differential operator
O. V. Makhnei
2011-06-01
Full Text Available The asymptotic formulas with large values of parameter for solutions of singular differential equation allow us to estimate Green's function of the boundary-value problem. With the help of this estimation the expansion of singular dierential operator by eigenvectors in the case of simple eigenvalues is constructed.
Optimal adaptive normalized matched filter for large antenna arrays
Kammoun, Abla
2016-09-13
This paper focuses on the problem of detecting a target in the presence of a compound Gaussian clutter with unknown statistics. To this end, we focus on the design of the adaptive normalized matched filter (ANMF) detector which uses the regularized Tyler estimator (RTE) built from N-dimensional observations x, · · ·, x in order to estimate the clutter covariance matrix. The choice for the RTE is motivated by its possessing two major attributes: first its resilience to the presence of outliers, and second its regularization parameter that makes it more suitable to handle the scarcity in observations. In order to facilitate the design of the ANMF detector, we consider the regime in which n and N are both large. This allows us to derive closed-form expressions for the asymptotic false alarm and detection probabilities. Based on these expressions, we propose an asymptotically optimal setting for the regularization parameter of the RTE that maximizes the asymptotic detection probability while keeping the asymptotic false alarm probability below a certain threshold. Numerical results are provided in order to illustrate the gain of the proposed detector over a recently proposed setting of the regularization parameter.
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
An asymptotic solution of large-$N$ $QCD$
Bochicchio, Marco
2014-01-01
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 $LSZ$ 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 strin...
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
Echoes of asymptotic silence in causal set quantum gravity
Eichhorn, Astrid; Mizera, Sebastian; Surya, Sumati
2017-08-01
We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behavior akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between causal set elements in the discrete analogue of a spatial hypersurface. Using numerical simulations for causal sets approximated by \
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
An asymptotic solution of large-N QCD
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.
Small-x asymptotics of structure function $g_2$
Ermolaev, B I
1997-01-01
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
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.
Asymptotic Hyperstability of Dynamic Systems with Point Delays
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.
The asymptotic variance of departures in critically loaded queues
A. Al Hanbali; M.R.H. Mandjes (Michel); Y. Nazarathy (Yoni); W. Whitt
2010-01-01
htmlabstractWe consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load rho equals 1, and prove that the asymptotic variance rate satisfies lim_t Var D(t)/t = lambda
Asymptotic symmetries of de Sitter space-time
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Global asymptotic stability of cellular neural networks with multiple delays
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-01-01
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Covariant diagrams for one-loop matching
Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-10-15
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Effective anisotropy through traveltime and amplitude matching
Wang, Hui
2014-08-05
Introducing anisotropy to seismic wave propagation reveals more realistic physics of our Earth\\'s subsurface as compared to the isotropic assumption. However wavefield modeling, the engine of seismic inverse problems, in anisotropic media still suffers from computational burdens, in particular with complex anisotropy such as transversely isotropic (TI) and Orthorhombic anisotropy. We develop effective isotropic velocity and density models to package the effects of anisotropy such that the wave propagation behavior using these effective models approximate those of the original anisotropic model. We build these effective models through the high frequency asymptotic approximation based on the eikonal and transport equations. We match the geometrical behavior of the wave-fields, given by traveltimes, from the anisotropic and isotropic eikonal equations. This matching yields the effective isotropic velocity that approximates the kinematics of the anisotropic wavefield. Equivalently, we calculate the effective densities by equating the anisotropic and isotropic transport equations. The effective velocities and densities are then fed into the isotropic acoustic variable density wave equation to obtain cheaper anisotropic wavefields. We justify our approach by testing it on an elliptical anisotropic model. The numerical results demonstrate a good matching of both traveltime and amplitude between anisotropic and effective isotropic wavefields.
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-06-01
The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.
On the asymptotics of the α-Farey transfer operator
Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.
2015-01-01
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.
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.
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
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.
Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals
Pan, Chi-Ruei; Chai, Jeng-Da
2013-01-01
Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is sig...
Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J
2009-06-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.
Jain, Anil K; Feng, Jianjiang
2011-01-01
Latent fingerprint identification is of critical importance to law enforcement agencies in identifying suspects: Latent fingerprints are inadvertent impressions left by fingers on surfaces of objects. While tremendous progress has been made in plain and rolled fingerprint matching, latent fingerprint matching continues to be a difficult problem. Poor quality of ridge impressions, small finger area, and large nonlinear distortion are the main difficulties in latent fingerprint matching compared to plain or rolled fingerprint matching. We propose a system for matching latent fingerprints found at crime scenes to rolled fingerprints enrolled in law enforcement databases. In addition to minutiae, we also use extended features, including singularity, ridge quality map, ridge flow map, ridge wavelength map, and skeleton. We tested our system by matching 258 latents in the NIST SD27 database against a background database of 29,257 rolled fingerprints obtained by combining the NIST SD4, SD14, and SD27 databases. The minutiae-based baseline rank-1 identification rate of 34.9 percent was improved to 74 percent when extended features were used. In order to evaluate the relative importance of each extended feature, these features were incrementally used in the order of their cost in marking by latent experts. The experimental results indicate that singularity, ridge quality map, and ridge flow map are the most effective features in improving the matching accuracy.
Optimal Packed String Matching
Ben-Kiki, Oren; Bille, Philip; Breslauer, Dany
2011-01-01
In the packed string matching problem, each machine word accommodates – characters, thus an n-character text occupies n/– memory words. We extend the Crochemore-Perrin constantspace O(n)-time string matching algorithm to run in optimal O(n/–) time and even in real-time, achieving a factor – speedup...... over traditional algorithms that examine each character individually. Our solution can be efficiently implemented, unlike prior theoretical packed string matching work. We adapt the standard RAM model and only use its AC0 instructions (i.e., no multiplication) plus two specialized AC0 packed string...
Limiting distribution of maximal crossing and nesting of Poissonized random matchings
Baik, Jinho
2011-01-01
The notion of r-crossing and r-nesting of a complete match- ing was introduced and a symmetry property was proved by Chen, Deng, Du, Stanley and Yan in 2007. We consider random matchings of large size and study the maximal crossing and the maximal nesting. It is known that the marginal distribution of each of them converges to the GOE Tracy-Widom distribution. We show that the maximal crossing and the maximal nesting becomes independent asymptotically, and eval- uate the joint distribution for the Poissonized random matchings explic- itly to the first correction term. This leads to an evaluation of the asymptotic of the covariance. Furthermore, we compute the explicit second correction term of the distributions function of two ob jects: (a) the length of the longest increasing subsequence of Poissonized random permutation and (b) the maximal crossing, and hence also the maximal nesting, of Poissonized random matching.
Foundation and generalization of the expansion by regions
Jantzen, Bernd
2011-01-01
The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole integration domain. This method has been applied successfully to many complicated loop integrals, but a general proof for its correctness has still been missing. This paper shows how the expansion by regions manages to reproduce the exact result correctly in an expanded form and clarifies the conditions on the choice and completeness of the considered regions. A generalized expression for the full result is presented that involves additional overlap contributions. These extra pieces normally yield scaleless integrals which are consistently set to zero, but they may be needed depending on the choice of the regularization scheme. While the main proofs and formulae are presented in a general and concise form, a large portion of the paper is filled with simple, pedagogical one-loo...
Low-Thermal-Expansion Filled Polytetrafluoroethylene
Shapiro, Sanford S.
1989-01-01
PTFE made thermally compatible with aluminum without changing dielectric constant. Manufactured with fillers and pores to reduce coefficient of thermal expansion by factor of 6 to match aluminum. Material retains 2.1 dielectric constant of pure PTFE. Combines filler and micropore concepts. Particles and voids embedded in PTFE matrix function cooperatively. Particles take up compressive stress imposed by contracting PTFE, and voids take up expanding material. Increases dielectric constant, while voids reduce it.
Spatial assortment of mixed propagules explains the acceleration of range expansion.
Ramanantoanina, Andriamihaja; Ouhinou, Aziz; Hui, Cang
2014-01-01
Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.
Spatial assortment of mixed propagules explains the acceleration of range expansion.
Andriamihaja Ramanantoanina
Full Text Available Range expansion of spreading organisms has been found to follow three types: (i linear expansion with a constant rate of spread; (ii bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.
Infographic explaining NCI-COG Pediatric MATCH, a cancer treatment clinical trial for children and adolescents, from 1 to 21 years of age, that is testing the use of precision medicine for pediatric cancers.
Data Matching Imputation System
National Oceanic and Atmospheric Administration, Department of Commerce — The DMIS dataset is a flat file record of the matching of several data set collections. Primarily it consists of VTRs, dealer records, Observer data in conjunction...
Brooks, Martin; And Others
1983-01-01
The Cognitive Levels Matching Project trains teachers to guide students' skill acquisition and problem-solving processes by assessing students' cognitive levels and adapting their teaching materials accordingly. (MLF)
LARGE SAMPLE PROPERTIES OF THE SIR IN CDMA WITH MATCHED FILTER RECEIVERS
PAN GUANGMING; MIAO BAIQI; ZHU CHUNHUA
2005-01-01
The output signal-to-interference (SIR) of conventional matched filter receiver in random environment is considered. When the number of users and the spreading factors tend to infinity with their ratio fixed, the convergence of SIR is showed to be with probability one under finite fourth.moment of the spreading sequences. The asymptotic distribution of the SIR is also obtained.
Solvable Optimal Velocity Models and Asymptotic Trajectory
Nakanishi, K; Igarashi, Y; Bando, M
1996-01-01
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic traj...
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.
Asymptotic dynamics of inertial particles with memory
Langlois, Gabriel Provencher; Haller, George
2014-01-01
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $\\mathcal O(\\epsilon)$-close to the fluid velocity, where $0<\\epsilon\\ll 1$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of existence and uniqueness of global solutions to the Maxey--Riley equation, a nonlinear system of fractional-order differential equ...
An asymptotic model of unsteady airway reopening.
Naire, S; Jensen, O E
2003-12-01
We consider a simple physical model for the reopening of a collapsed lung airway involving the unsteady propagation of a long bubble of air, driven at a prescribed flow-rate, into a liquid-filled channel formed by two flexible membranes that are held under large longitudinal tension and are confined between two parallel rigid plates. This system is described theoretically using an asymptotic approximation, valid for uniformly small membrane slopes, which reduces to a fourth-order nonlinear evolution equation for the channel width ahead of the bubble tip, from which the time-evolution of the bubble pressure pb* and bubble speed may be determined. The model shows that there can be a substantial delay between the time at which the bubble starts to grow in volume and the time at which its tip starts to move. Under certain conditions, the start of the bubble's motion is accompanied by a transient overshoot in pb*, as seen previously in experiment; the model predicts that the overshoot is greatest in narrow channels when the bubble is driven with a large volume flux. It is also shown how the threshold pressure for steady bubble propagation in wide channels has distinct contributions from the capillary pressure drop across the bubble tip and viscous dissipation in the channel ahead of the bubble.
Asymptotic Solutions of Serial Radial Fuel Shuffling
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.
Barrera, G D [Departamento de QuImica, Universidad Nacional de la Patagonia SJB, Ciudad Universitaria, 9000 Comodoro Rivadavia (Argentina); Bruno, J A O [Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de QuImica Inorganica, AnalItica y QuImica FIsica, Pabellon 2, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Barron, T H K [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom); Allan, N L [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom)
2005-02-02
There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW{sub 2}O{sub 8} contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials. (topical review)
Asymptotics, structure, and integration of sound-proof atmospheric flow equations
Klein, Rupert
2009-07-01
Relative to the full compressible flow equations, sound-proof models filter acoustic waves while maintaining advection and internal waves. Two well-known sound-proof models, an anelastic model by Bannon and Durran’s pseudo-incompressible model, are shown here to be structurally very close to the full compressible flow equations. Essentially, the anelastic model is obtained by suppressing ∂ t ρ in the mass continuity equation and slightly modifying the gravity term, whereas the pseudo-incompressible model results from dropping ∂ t p from the pressure equation. For length scales small compared to the density and pressure scale heights, the anelastic model reduces to the Boussinesq approximation, while the pseudo-incompressible model approaches the zero Mach number, variable density flow equations. Thus, for small scales, both models are asymptotically consistent with the full compressible flow equations, yet the pseudo-incompressible model is more general in that it remains valid in the presence of large density variations. For the relatively small density variations found in typical atmosphere-ocean flows, both models are found to yield very similar results, with deviations between models much smaller than deviations obtained when using different numerical schemes for the same model. This in agreement with Smolarkiewicz and Dörnbrack (Int J Numer Meth Fluids 56:1513-1519, 2007). Despite these useful properties, neither model can be derived by a low-Mach number asymptotic expansion for length scales comparable to the pressure scale height, i.e., for the regime they were originally designed for. Derivations of these models via scale analysis ignore an asymptotic time scale separation between advection and internal waves. In fact, only the classical Ogura and Phillips model, which assumes weak stratification of the order of the Mach number squared, can be obtained as a leading-order model from systematic low Mach number asymptotic analysis. Issues of formal
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...
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
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.
Asymptotic failure rate of a continuously monitored system
Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr
2006-02-01
This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.
Asymptotic Solution of the Theory of Shells Boundary Value Problem
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.
Articular Contact Mechanics From an Asymptotic Modeling Perspective: a Review
Ivan Argatov
2016-11-01
Full Text Available In the present paper we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, nonhomogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed.
Fakhruddin, Hasan
1993-01-01
Describes a paradox in the equation for thermal expansion. If the calculations for heating a rod and subsequently cooling a rod are determined, the new length of the cool rod is shorter than expected. (PR)
Approaches for Stereo Matching
Takouhi Ozanian
1995-04-01
Full Text Available This review focuses on the last decade's development of the computational stereopsis for recovering three-dimensional information. The main components of the stereo analysis are exposed: image acquisition and camera modeling, feature selection, feature matching and disparity interpretation. A brief survey is given of the well known feature selection approaches and the estimation parameters for this selection are mentioned. The difficulties in identifying correspondent locations in the two images are explained. Methods as to how effectively to constrain the search for correct solution of the correspondence problem are discussed, as are strategies for the whole matching process. Reasons for the occurrence of matching errors are considered. Some recently proposed approaches, employing new ideas in the modeling of stereo matching in terms of energy minimization, are described. Acknowledging the importance of computation time for real-time applications, special attention is paid to parallelism as a way to achieve the required level of performance. The development of trinocular stereo analysis as an alternative to the conventional binocular one, is described. Finally a classification based on the test images for verification of the stereo matching algorithms, is supplied.
Max-Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low Complexity Transceivers
Sifaou, Houssem
2016-12-28
This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with M antennas communicates with K single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which M and K grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per- UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.
Bellahsene, Zohra; Rahm, Erhard
2011-01-01
Requiring heterogeneous information systems to cooperate and communicate has now become crucial, especially in application areas like e-business, Web-based mash-ups and the life sciences. Such cooperating systems have to automatically and efficiently match, exchange, transform and integrate large data sets from different sources and of different structure in order to enable seamless data exchange and transformation. The book edited by Bellahsene, Bonifati and Rahm provides an overview of the ways in which the schema and ontology matching and mapping tools have addressed the above requirements
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which...... nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing...
Middle matching mining algorithm
GUO Ping; CHEN Li
2003-01-01
A new algorithm for fast discovery of sequential patterns to solve the problems of too many candidate sets made by SPADE is presented, which is referred to as middle matching algorithm. Experiments on a large customer transaction database consisting of customer_id, transaction time, and transaction items demonstrate that the proposed algorithm performs better than SPADE attributed to its philosophy to generate a candidate set by matching two sequences in the middle place so as to reduce the number of the candidate sets.
Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes
M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractThe paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical
Modified Ricci flow and asymptotically non-flat spaces
Chatterjee, Shubhayu
2013-01-01
The present work extends the application of a modified Ricci flow equation to an asymptotically non flat space, namely Marder's cylindrially symmetric space. It is found that the flow equation has a solution at least in a particular case.
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...
Semilocal density functional theory with correct surface asymptotics
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Research on temperature profiles of honeycomb regenerator with asymptotic analysis
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.
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 ...
Asymptotical Properties for Parabolic Systems of Neutral Type
CUI Bao-tong; HAN Mao-an
2005-01-01
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
Asymptotic distributions in the projection pursuit based canonical correlation analysis
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.
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...
Asymptotical stability analysis of linear fractional differential systems
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.
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.
ASYMPTOTIC BEHAVIOR OF ECKHOFF'S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION
无
2007-01-01
The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined.Asymptotic behavior of approximate calculation of the so-called "jumps" is studied and asymptotic L2 constants of the rate of convergence of the method are computed.
Asymptotic symmetries and charges in de Sitter space
Anninos, Dionysios; Ng, Gim Seng; Strominger, Andrew, E-mail: gng@fas.harvard.edu [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA 02138 (United States)
2011-09-07
The asymptotic symmetry group (ASG) at future null infinity (I{sup +}) of asymptotically four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I{sup +}. Finite charges are constructed for each choice of ASG generator together with a two-surface on I{sup +}. A conservation equation is derived relating the evolution of the charges with the radiation flux through I{sup +}.
Asymptotic behaviour of extinction probability of interacting branching collision processes
Chen, Anyue; Li, Junping; Chen, Yiqing; Zhou, Dingxuan
2014-01-01
Although the exact expressions for the extinction probabilities of the Interacting Branching Collision Processes (IBCP) were very recently given by Chen et al. [4], some of these expressions are very complicated; hence, useful information regarding asymptotic behaviour, for example, is harder to obtain. Also, these exact expressions take very different forms for different cases and thus seem lacking in homogeneity. In this paper, we show that the asymptotic behaviour of these extr...
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
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.
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.
Singularity-free gravitational collapse and asymptotic safety
Torres, Ramón, E-mail: ramon.torres-herrera@upc.edu
2014-06-02
A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities.
The asymptotic variance of departures in critically loaded queues
Al Hanbali, Ahmad; Mandjes, M.R.H.; Nazarathy, Y.; Whitt, W.
2011-01-01
We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies limt→∞varD(t) / t = λ(1 - 2 / π)(ca2 +
Relaxing the Parity Conditions of Asymptotically Flat Gravity
Compère, Geoffrey; Dehouck, François
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincar\\'e transformations as well as supertranslations and logarithmic translations are associated wi...
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
High frequency asymptotics of antenna/structure interactions
Coats, J.
2002-01-01
This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illuminat...
Probabilistic and asymptotic methods with the Perron Frobenius's operator
Cirier, Guy
2012-01-01
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject.Among the applications, we use new methods to compute asymptotic results of PDE like Lorenz or Navier-Stokes equations. New questions as the resonance are studied.Perron-Frobenius;resolving deviation;Julia's sets;Plancherel-Rotach'function;Lorenz andNavier-Sto kes equations;resonance;
Asymptotic behaviour for a diffusion equation governed by nonlocal interactions
Ovono, Armel Andami
2010-01-01
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah; Pawlowski, Jan M
2011-01-01
We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)
2012-03-19
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Random attractors for asymptotically upper semicompact multivalue random semiflows
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.
Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas
Godlin, Benny; Makowsky, Johann A
2008-01-01
Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
彭硕
2002-01-01
It was a Saturday morning, our school football team was going to have a match with the No. 28 Middle Schooh They were really a strong team. But we weren't afraid of them. We had many mare good players on our team, so we were stronger than ever before.
Herrnstein, R. J.
1979-01-01
The matching law for reinforced behavior solves a differential equation relating infinitesimal changes in behavior to infinitesimal changes in reinforcement. The equation expresses plausible conceptions of behavior and reinforcement, yields a simple nonlinear operator model for acquisition, and suggests a alternative to the economic law of…
Claesson, Anders
2010-01-01
We show that there are n! matchings on 2n points without, so called, left (neighbor) nestings. We also define a set of naturally labeled (2+2)-free posets, and show that there are n! such posets on n elements. Our work was inspired by Bousquet-M\\'elou, Claesson, Dukes and Kitaev [arXiv:0806.0666]. They gave bijections between four classes of combinatorial objects: matchings with no neighbor nestings (due to Stoimenow), unlabeled (2+2)-free posets, permutations avoiding a specific pattern, and so called ascent sequences. We believe that certain statistics on our matchings and posets could generalize the work of Bousquet-M\\'elou et al.\\ and we make a conjecture to that effect. We also identify natural subsets of matchings and posets that are equinumerous to the class of unlabeled (2+2)-free posets. We give bijections that show the equivalence of (neighbor) restrictions on nesting arcs with (neighbor) restrictions on crossing arcs. These bijections are thought to be of independent interest. One of the bijections...
'Wiggle matching' radiocarbon dates
Ramsey, CB; van der Plicht, J; Weninger, B
2001-01-01
This paper covers three different methods of matching radiocarbon dates to the 'wiggles' of the calibration curve in those situations where the age difference between the C-14 dates is known. These methods are most often applied to tree-ring sequences. The simplest approach is to use a classical Chi
Jeuring, J.T.
2007-01-01
The pattern matching problem can be informally specified as follows: given a pattern and a text, find all occurrences of the pattern in the text. The pattern and the text may both be lists, or they may both be trees, or they may both be multi-dimensional arrays, etc. This paper describes a general p
Matching Supernovae to Galaxies
Kohler, Susanna
2016-12-01
developed a new automated algorithm for matching supernovae to their host galaxies. Their work builds on currently existing algorithms and makes use of information about the nearby galaxies, accounts for the uncertainty of the match, and even includes a machine learning component to improve the matching accuracy.Gupta and collaborators test their matching algorithm on catalogs of galaxies and simulated supernova events to quantify how well the algorithm is able to accurately recover the true hosts.Successful MatchingThe matching algorithms accuracy (purity) as a function of the true supernova-host separation, the supernova redshift, the true hosts brightness, and the true hosts size. [Gupta et al. 2016]The authors find that when the basic algorithm is run on catalog data, it matches supernovae to their hosts with 91% accuracy. Including the machine learning component, which is run after the initial matching algorithm, improves the accuracy of the matching to 97%.The encouraging results of this work which was intended as a proof of concept suggest that methods similar to this could prove very practical for tackling future survey data. And the method explored here has use beyond matching just supernovae to their host galaxies: it could also be applied to other extragalactic transients, such as gamma-ray bursts, tidal disruption events, or electromagnetic counterparts to gravitational-wave detections.CitationRavi R. Gupta et al 2016 AJ 152 154. doi:10.3847/0004-6256/152/6/154