Showing papers on "Asymptotic analysis published in 2004"
TL;DR: In this paper, the authors present asymptotic analysis of an eigenvalue problem for the Helmholtz operator in a periodic structure involving split-ring resonators, where the eigensolutions are obtained in the form of Bloch waves.
Abstract: The paper presents asymptotic analysis of an eigenvalue problem for the Helmholtz operator in a periodic structure involving split-ring resonators [originally proposed in J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)]. The eigensolutions are sought in the form of Bloch waves. The main emphasis is given to the study of localized modes within such a structure and to the control of low-frequency bandgaps on the corresponding dispersion diagram. Asymptotic results are explicit and are in good agreement with numerical simulations.
143 citations
TL;DR: It is proved that the method of moments is compatible with the non-equilibrium regime and the Rankine–Hugoniot relations are studied.
Abstract: This work addresses some asymptotic regimes for the coupling of radiation and hydrodynamics, and is inspired by the still non-answered need of high resolution and robust schemes for the numerical solutions of these problems. Using a simple characterization of the isotropy of the scattering in the comobile reference frame, we derive various asymptotic regimes. Among them is the non-equilibrium regime. Then we prove that the method of moments is compatible with the non-equilibrium regime. We also study the Rankine–Hugoniot relations.
123 citations
TL;DR: In this paper, the authors provided a mathematical proof of the existence of traveling vortex rings solutions to the Gross-Pitaevskii (GP) equation in dimension N ≥ 3.
Abstract: . We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension N ≥ 3. We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg– Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if N = 3).
111 citations
TL;DR: In this paper, a linearized model for fluid-structure interaction in one space dimension is considered and a spectral asymptotic analysis on high frequencies for the underlying semigroup is presented, showing that the semigroup governed by the system can be split into a parabolic and a hyperbolic projection.
106 citations
TL;DR: For non-linear difference equations an inclusion theorem is set up which guarantees the existence of solutions in a given asymptotic stripe as discussed by the authors, which is the limit case of the inclusion theorem for a boundary value problem in a finite interval.
Abstract: For non-linear difference equations an inclusion theorem is set up which guarantees the existence of solutions in a given asymptotic stripe. This theorem is the limit case of an inclusion theorem for a boundary value problem in a finite interval. Different applications to rational difference equations of order two are given.
75 citations
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TL;DR: In this article, omnibus and directional tests for testing the goodness-of-fit of a parametric regression time series model are proposed, based on a general class of residual marked empirical processes as the building-blocks for estimation and testing of such models.
Abstract: This paper proposes omnibus and directional tests for testing the goodness-of-fit of a parametric regression time series model. We use a general class of residual marked empirical processes as the building-blocks for estimation and testing of such models. First, we establish a weak convergence theorem under mild assumptions, which allows us to study in a unified way the asymptotic null distribution of the test statistics and their asymptotic behavior against Pitman's local alternatives. To approximate the asymptotic null distribution of test statistics we justify theoretically a bootstrap procedure. Also, some asymptotic theory for the estimation of the principal components of the residual marked processes is considered. This asymptotic theory is used to derive optimal directional tests and efficient estimation of regression parameters. Finally, a Monte Carlo study shows that the bootstrap and the asymptotic results provide good approximations for small sample sizes and an empirical application to the Canadian lynx data set is considered.
63 citations
TL;DR: In this article, the authors derived the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmology constant near the de Sitter equilibrium state at late times, and near the flat FL state at early times.
Abstract: In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium state at late times, and near the flat FL equilibrium state at early times. Our results show that there exists an open set of solutions approaching the de Sitter state at late times, consistent with the cosmic no-hair conjecture. On the other hand, solutions that approach the flat FL state at early times are special and admit a so-called isotropic initial singularity. For both classes of models the asymptotic expansion of the line element contains an arbitrary spatial metric at leading order, indicating asymptotic spatial inhomogeneity. We show, however, that in the asymptotic regimes this spatial inhomogeneity is significant only at super-horizon scales.
60 citations
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TL;DR: Through an embedding in a continuous time model, the asymptotic analysis of the binary search tree (BST) under the random permutation model gets new results, in particular the asylptotic behavior of the profile.
Abstract: We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.
50 citations
TL;DR: A degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide is introduced and qualitative behavior of the solutions for large times is investigated, and a numerical verification of this asymptotics is given.
Abstract: We introduce a degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide. For this system, we present some finite element and finite difference schemes to approximate its solutions. Numerical stability is given under suitable CFL conditions. Finally, by means of a formal scaling, the qualitative behavior of the solutions for large times is investigated, and a numerical verification of this asymptotics is given. Our results are in qualitative agreement with the experimental behavior observed in the chemical literature.
47 citations
TL;DR: In this article, a general systematic procedure for defining incremental field contributions is presented, based on the incremental theory of diffraction (ITD) localization process for uniform cylindrical, local canonical problems with elementary source illumination and arbitrary observation aspects.
Abstract: In this paper, a general systematic procedure is presented for defining incremental field contributions. They may provide effective tools to describe a wide class of scattering and diffraction phenomena at any aspect, within a unitary, self-consistent framework. This procedure is based on a generalization of the incremental theory of diffraction (ITD) localization process for uniform cylindrical, local canonical problems with elementary source illumination and arbitrary observation aspects. In particular, it is shown that the spectral integral formulation of the exact solution for the local canonical problem may also be represented as a spatial integral convolution along the longitudinal coordinates of the cylindrical configuration. Its integrand is then directly used to define the relevant incremental field contribution. For the sake of convenience, but without loss of generality, this procedure is illustrated for the case of local wedge configurations. Also, a specific suitable asymptotic analysis is developed to derive new closed form high-frequency expressions from the spectral integral formulation. These expressions for the incremental field contributions explicitly satisfy reciprocity and are applicable at any incidence and observation aspect. This generalization of the ITD localization process together with its more accurate asymptotic analysis provides a definite improvement of the method.
45 citations
TL;DR: In this paper a numerical method is suggested to solve a class of boundary value problems for a weakly coupled system of singularly perturbed second order ordinary differential equations of reaction-diffusion type using an asymptotic expansion approximation of the solution of the boundary value problem.
TL;DR: In this article, the authors show how to model thin layers and interfaces by asymptotic techniques, including visco-elasticity (Maxwell, Kelvin-Voigt, Norton), Mohr-Coulomb non-associated elastoplasticity and non-monotone relationship in the strain-stress diagram.
TL;DR: In this paper, the authors proved asymptotic stability of trapped solitons in the generalized nonlinear Schrodinger equation with a potential in dimension 1 and for even potential and even initial conditions.
Abstract: We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrodinger equation with a potential in dimension 1 and for even potential and even initial conditions.
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TL;DR: In this article, the authors review the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance and discuss its power and usefulness to solve important problems arising in finance.
Abstract: This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arisen in finance. As illustrations we use three major problems in finance and give some useful formulae and new results including numerical analyses.
TL;DR: In this article, the steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied, and error estimates are proved by using a boundary layer method.
Abstract: The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.
TL;DR: A new non data-aided estimator of the modulation index of continuous phase modulated (CPM) signals is proposed, based on the observation that the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a sinusoid of period 2T.
Abstract: In this paper, a new non data-aided estimator of the modulation index of continuous phase modulated (CPM) signals is proposed. It is based on the observation that the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a sinusoid of period 2T, where T is the symbol period. The asymptotic behavior of the estimator is studied. If N is the sample size, the estimation error is shown to converge to a non-Gaussian distribution at a rate of 1/N. Simulation results sustain the conclusions of the theoretical asymptotic analysis.
TL;DR: In this article, the Vlasov-Monge-Ampere system (VMA) is derived as a geometric approximation of the Euler equations of incompressible fluid mechanics in the spirit of Arnold and Ebin.
Abstract: This paper studies the Vlasov–Monge–Ampere system (VMA), a fully non-linear version of the Vlasov–Poisson system (VP) where the (real) Monge–Ampere equation det ∂2Ψ/∂x
i
∂x
j
= ρ substitutes for the usual Poisson equation. This system can be derived as a geometric approximation of the Euler equations of incompressible fluid mechanics in the spirit of Arnold and Ebin. Global existence of weak solutions and local existence of smooth solutions are obtained. Links between the VMA system, the VP system and the Euler equations are established through rigorous asymptotic analysis.
TL;DR: Tirumkudulu and Acrivos as discussed by the authors showed that the solutions of the cubic equation referred to above correctly describe the film-thickness profiles although, when shocks are involved, under exceedingly restrictive conditions, typically F~ 10−3 or less.
Abstract: It is well-known that a standard lubrication analysis of the equations of motion in thin liquid films coating the inside surface of a rotating horizontal cylinder leads, under creeping-flow conditions, to a cubic equation for the film thickness profile which, depending on the fluid properties of the liquid, the speed of rotation and the fill fraction F, has either (a) a continuous, symmetric (homogeneous) solution; (b) a solution containing a shock; or (c) no solution below a certain speed. By means of an asymptotic analysis of the recently proposed “modified lubrication equation” (MLE) [M. Tirumkudulu and A. Acrivos, Phys. Fluid 13 (2000) 14–19], it is shown that the solutions of the cubic equation referred to above correctly describe the film-thickness profiles although, when shocks are involved, under exceedingly restrictive conditions, typically F~ 10−3 or less. In addition, using the MLE, the linear stability of these film profiles is investigated and it is shown that: the “homogeneous” profiles are neutrally stable if surface-tension effects are neglected but, if the latter are retained, the films are asymptotically stable to two-dimensional disturbances and unstable to axial disturbances; on the other hand, the non-homogeneous profiles are always asymptotically stable, thus confirming results given earlier [T.B. Benjamin, W.G. Pritchard, and S.J. Tavener (preprint, 1993)] on the basis of the standard lubrication analysis.
TL;DR: In this article, the authors proved the existence and uniqueness of the weak solution to the stationary equations for non-Newtonian and incompressible fluid in a three-dimensional bounded domain with Tresca fluid-solid interface on one part of the boundary and Dirichlet one on the other part; then they studied the asymptotic analysis when one dimension of the fluid domain tend to zero.
Abstract: In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for non-Newtonian and incompressible fluid in a three-dimensional bounded domain with Tresca fluid–solid interface on one part of the boundary and Dirichlet one on the other part; then we study the asymptotic analysis when one dimension of the fluid domain tend to zero. The strong convergence of the velocity is proved, a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained. The uniqueness of the velocity limit and the pressure limit are also proved.
TL;DR: In this article, the authors construct and justify the asymptotic expansion of a solution and the corresponding energy functional of the mixed boundary-value problem for the Poisson equation in a domain with a ligament, i.e., thin curvilinear strip connecting two small parts of the boundary outside the domain.
Abstract: We construct and justify the asymptotic expansion of a solution and the corresponding energy functional of the mixed boundary-value problem for the Poisson equation in a domain with a ligament, i.e., thin curvilinear strip connecting two small parts of the boundary outside the domain. Asymptotic analysis is required in the theory of shape optimization; therefore, in contrast to other publications, we use no simplifying assumptions of the flattening of the boundary near the junction zones.
Journal Article•
TL;DR: In this article, a reduced piezoelectric plate model was proposed for a nonhomogeneous anisotropic thin plate, and the limit of the displacement vector and the electric potential was computed as the thickness of the plate approaches zero.
Abstract: We mathematically justify a reduced piezoelectric plate model. This is achieved considering the three-dimensional static equations of piezoelectricity, for a nonhomogeneous anisotropic thin plate, and using the asymptotic analysis to compute the limit of the displacement vector and electric potential, as the thickness of the plate approaches zero. We prove that the three- dimensional displacement vector converges to a Kirchhoff-Love displacement, that solves a two-dimensional piezoelectric plate model, defined on the middle surface of the plate. Moreover, the three-dimensional electric potential converges to a scalar function that is a second-order polynomial with respect to the thickness variable, with coefficients that depend on the transverse component of the Kirchhoff-Love displacement. We remark that the results of this paper generalize a previous work of A. Sene (Asymptotic Anal. 25(1) (2001), 1-20) for homogeneous and isotropic materials.
TL;DR: In this article, the authors use asymptotic analysis to study the diffusion limit of the SIMC method for the transport equation and demonstrate mathematically that the solution converges to the solution of a wrong diffusion equation.
TL;DR: New direction- and frequency-averaged approximations to the equations of radiative heat transfer in glass for optically thick, diffusive regimes are developed that represent asymptotic corrections to the familiar Rosseland, or equilibrium diffusion, approximation.
Abstract: We develop new direction- and frequency-averaged approximations to the equations of radiative heat transfer in glass for optically thick, diffusive regimes. These approximations, which are based on the $\rm SP_N$ approach given in [E. Larsen, G. Thommes, A. Klar, M. Seaid, and T. Gotz, J. Comput. Phys. 83 (2002), pp. 652--675], represent asymptotic corrections to the familiar Rosseland, or equilibrium diffusion, approximation. Numerical results for realistic problems in the simulation of radiative heat transfer in glass cooling confirm the accuracy and efficiency of the new approximations.
TL;DR: It is shown that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen.
TL;DR: This paper considers a multicarrier (MC) code-division multiple-access system where each user employs multiple signatures and an asymptotic analysis is used to derive the output signal-to-interference-plus-noise ratio (SINR) as a function of the system loading, the noise power, and the fading properties of the channel.
Abstract: This paper considers a multicarrier (MC) code-division multiple-access system where each user employs multiple signatures. The receiver is linear and minimizes the mean square error of the data estimate. Both multiple-user and single-user systems are considered, as well as single and multiple signatures per user. In each case, an asymptotic analysis is used to derive the output signal-to-interference-plus-noise ratio (SINR) as a function of the system loading, the noise power, and the fading properties of the channel. Asymptotic in this case means that the number of independent subcarriers and number of signatures per user each tends to infinity with fixed ratio. The associated bit-error rate (BER) is evaluated for binary phase-shift keying symbols. Simulations show that the asymptotic SINRs and BERs derived in each case are accurate for realistic finite systems.
TL;DR: In this article, the authors developed a new scheme for computing "Greeks" of derivatives by an asymptotic expansion approach and derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices.
Abstract: We developed a new scheme for computing “Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.
TL;DR: The analysis of the asymptotic limit for models of the mathematical kinetic theory to the nonlinearized compressible Euler equations or to the acoustic equations when the Knudsen number e tends to zero was studied in this article.
Abstract: This paper deals with the analysis of the asymptotic limit for models of the mathematical kinetic theory to the nonlinearized compressible Euler equations or to the acoustic equations when the Knudsen number e tends to zero. Existence and uniqueness theorems are proven for analytic initial fluctuations on the time interval independent of the small parameter e. As e tends to zero, the solution of kinetics models converges strongly to the Maxwellian whose fluid-dynamics parameters solve the Euler and the acoustic systems. The general results are specifically applied to the analysis of the Boltzmann and BGK equations.
TL;DR: The goal of the paper is to study asymptotic behavior of the number of lost messages with the parameters of the system typical for models of information transmission in real networks and theorems based on Tauberian theorem with remainder.
Abstract: The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message. Messages arrive to the M/GI/1 finite buffer model and can be lost in two cases as either at least one of its packets is corrupted or the buffer is overflowed. With the parameters of the system typical for models of information transmission in real networks, we obtain theorems on asymptotic behavior of the number of lost messages. We also study how the loss probability changes if redundant packets are added. Our asymptotic analysis approach is based on Tauberian theorems with remainder.
TL;DR: In this article, the authors investigated the local asymptotic behavior of the Bernstein-Durrmeyer polynomials and their derivatives with respect to Jacobi-weights.
Abstract: The purpose of this paper is the investigation of the local asymptotic behavior of the Bernstein-Durrmeyer polynomials and their derivatives with respect to Jacobi-weights. The main result is the complete asymptotic expansion for these polynomials and their derivatives. All coefficients are calculated explicitely.
TL;DR: In this article, an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue is presented, where the authors consider the behavior of solutions of critical fluid models as time approaches.
Abstract: This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches1. The main theorems of the paper provide sufficient conditions f or a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic diffusion approximation for a processor sharing queue.