Showing papers on "Asymptotic analysis published in 1985"
TL;DR: In this paper, the authors consider the problem of finding the appropriate quantum mechanical description of a given classical mechanical system, where the classical system in question is represented by a symplectic manifold, X, and a classical observable p: X + R.
334 citations
228 citations
TL;DR: A set of easily verifiable sufficient conditions for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients is given in this paper.
Abstract: A set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.
162 citations
TL;DR: In this article, a free boundary problem for semilinear parabolic equations is studied, which describes the habitat segregation phenomenon in population ecology, and the main purpose is to show the global existence, uniqueness, regularity and asymptotic behavior of solutions.
Abstract: This article is concerned with a free boundary problem for semilinear parabolic equations, which describes the habitat segregation phenomenon in population ecology. The main purpose is to show the global existence, uniqueness, regularity and asymptotic behavior of solutions for the problem. The asymptotic stability or instability of each solution is completely determined using the comparison theorem.
67 citations
TL;DR: In this paper, a general family of asymptotic solutions to Einstein's equation are presented, all of which satisfy the peeling theorem but do not satisfy the full peeling property.
Abstract: We present a general family of asymptotic solutions to Einstein's equation which are asymptotically flat but do not satisfy the peeling theorem. Near scri, the Weyl tensor obeys a logarithmic asymptotic flatness condition and has a partial peeling property. The physical significance of this asymptotic behavior arises from a quasi-Newtonian treatment of the radiation from a collapsing dust cloud. Practically all the scri formalism carries over intact to this new version of asymptotic flatness.
66 citations
TL;DR: In this article, the asymptotic behavior of a linear compartment model for the environmental movement of radionuclides is investigated and an approach to sensitivity analysis employing Latin hypercube sampling, rank transformations and stepwise regression is presented and then applied to this system.
46 citations
TL;DR: In this paper, the authors discuss computational and asymptotic aspects of the Born inversion method and show how asymPTotic analysis is exploited to reduce the number of integrations in an f-k-like solution formula for the velocity variation.
Abstract: We discuss computational and asymptotic aspects of the Born inversion method and show how asymptotic analysis is exploited to reduce the number of integrations in an f-k like solution formula for the velocity variation The output of this alternative algorithm produces the reflectivity function of the surface This is an array of singular functions—Dirac delta functions which peak on the reflecting surfaces—each scaled by the normal reflection strength at the surface Thus, imaging of a reflector is achieved by construction of its singular function and estimation of the reflection strength is deduced from the peak value of that function By asymptotic analysis of the application of the algorithm to the Kirchhoff representation of the backscattered field, we show that the peak value of the output estimates the reflection strength even when the condition of small variation in velocity (an assumption of the original derivation) is violated Furthermore, this analysis demonstrates that the method provides a m
40 citations
TL;DR: In this article, generalized asymptotic approximations to Gamma (x+1), which contain an arbitrary parameter, are derived both from the integral representation of the gamma function without assuming a knowledge of the Stirling series, and through elementary rearrangements of the stirling series.
Abstract: Generalised asymptotic approximations to Gamma (x+1), which contain an arbitrary parameter, are derived both from the integral representation of the gamma function without assuming a knowledge of the Stirling series, and through elementary rearrangements of the Stirling series. By optimising the arbitrary parameter according to appropriate criteria, several known Stirling-like approximations are recovered in a unifying way. These are as compact as but numerically superior to the standard Stirling approximation, and are meaningful on intervals that even include parts of the negative x-axis. It is pointed out that these results-arrived at by elementary but generally applicable asymptotic techniques-can be exploited in physics teaching to demonstrate the power and utility of asymptotic methods in the analysis of a variety of physics problems.
31 citations
01 Jan 1985
TL;DR: In this article, the asymptotic behavior of solutions of Volterra integrodifferential equations of the form x'(t) = A (t)x(t), + J K(t, s),x(s) ds + F(t).
Abstract: The asymptotic behavior of solutions of Volterra integrodifferential equations of the form x'(t) = A(t)x(t) + J K(t, s)x(s) ds + F(t) is discussed in which A is not necessarily a stable matrix. An equivalent equation which involves an arbitrary function is derived and a proper choice of this function would pave a way for the new coefficient matrix B (corresponding A) to be stable.
25 citations
TL;DR: In this paper, the room temperature stresses induced in a composite structure after cooling down from a high temperature were studied within the framework of linear thermoelasticiry, and the equations governing a one-dim...
Abstract: The room temperature stresses induced in a composite structure after cool-down from a high temperature are studied within the framework of linear thermoelasticiry. The equations governing a one-dim...
25 citations
TL;DR: The model penetrative-convection problem of ice-water convection is considered in this paper, where it is shown that horizontally long convection cells are preferred when the heat flux is fixed on the boundaries.
Abstract: The model penetrative-convection problem of ice–water convection is considered. Analytical progress is made through the remarkable simplification that horizontally long convection cells are preferred when the heat flux is fixed on the boundaries (Chapman & Proctor 1980). However, a linear analysis shows that long horizontal scales are preferred only when the convection is mildly penetrative (i.e. the overlying layer of stable fluid is not deep). A straightforward nonlinear asymptotic analysis of the convection only provides the relatively uninteresting information that the convection is subcritical. Using the technique of reconstitution (Roberts 1985) to provide higher-order corrections to the asymptotic theory, flow properties at larger amplitudes are calculated and predictions about the extent of the subcriticality are made.
01 Jan 1985
TL;DR: Stochastic Space-Time Models and Limit Theorems: An Introduction as discussed by the authors An introduction to stochastic space-time models and limit theorems can be found in Section 2.1.
Abstract: Stochastic Space-Time Models and Limit Theorems: An Introduction.- I: Stochastic Analysis in Infinite Dimensions.- Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfaces.- Maximal Regularity for Stochastic Convolutions and Applications to Stochastic Evolution Equations in Hilbert Spaces.- Stochastic Integration of Banach Space Valued Functions.- A Semigroup Model for Parabolic Equations with Boundary and Pointwise Noise.- On the Semigroup Approach to Stochastic Evolution Equations.- Markovianization of Random Vibrations.- Stochastic Analysis on Nuclear Spaces and its Applications.- II. Limit Theorems.- Stochastic Limit Theorems: Some Examples from Nonequilibrium Physics.- On the Functional Limit Theorems.- Tightness of Sequences of Hilbert Valued Martingales.- Asymptotic Analysis of a Semi-Linear PDE with Wide-Band Noise Disturbances.- A Central Limit Theorem for a System of Interacting Particles.- Moments of States over Nuclear LSF Spaces.
TL;DR: In this article, the asymptotic estimate for large solutions of one-dimensional generalized diffusion equations with regularly varying Green functions was given for all solutions of the semigroup T_tf(x) with speed measure functions.
Abstract: We give the asymptotic estimate for large $t$ of elementary solutions of one-dimensional generalized diffusion equations with regularly varying Green functions. As a corollary we obtain the precise asymptotic behavior of the semigroup $T_tf(x)$ for all $f \in L_1(dm)$ if the speed measure function $m(x)$ is regularly varying as $x \rightarrow \pm \infty$.
TL;DR: In this article, an asymptotic analysis based on detailed conservation and diffusion equations and on a detailed reaction scheme is presented for ozone-decomposition flame and compared with the numerical results reported by Heimerl and Coffee.
TL;DR: In this paper, it was shown that a distribution of electrons in resonance with traveling waves, but colliding with background distributions of electrons and ions, evolves to a steady state, and details of the steady state were given analytically in the asymptotic limit of high electron energy and compared with numerical solutions.
Abstract: It is shown that a distribution of electrons in resonance with traveling waves, but colliding with background distributions of electrons and ions, evolves to a steady state. Previously, the existence of such solutions had been assumed, but not proved, in numerical and other calculations. Details of the steady state are given analytically in the asymptotic limit of high electron energy and are compared with numerical solutions. The asymptotic analytic solution may be useful for quickly relating emission data to likely excitations and is more reliable than conventional numerical solutions at high energy. A method of improving numerics at high energy is suggested.
TL;DR: In this paper, the authors explored the ranges of applicability of some asymptotic theories, using the problem of radiation from a spherical elastic shell as the bench mark, and found that the added mass and plane wave approximations are quite adequate, respectively, for ka 5, where ka is the ratio of the circumference of the spherical shell to the acoustic wavelength.
Abstract: It is well known that at extremely high or low frequencies, the fluid–structure interaction effects can be represented asymptotically by simple equations. Thus, it appears that an optimum computation scheme for predicting acoustic pressure field radiated from a submerged elastic structure could be a combination of various asymptotic theories and the exact formulation. This paper explores the ranges of applicability of some asymptotic theories, using the problem of radiation from a spherical elastic shell as the bench mark. It is found that the ‘‘added mass’’ and ‘‘plane‐wave’’ approximations are quite adequate, respectively, for ka 5, where ka is the ratio of the circumference of the spherical shell to the acoustic wavelength. For the intermediate frequency range, a theory termed second‐order Doubly Asymptotic Approximation (DAA2) is suitable. At intermediate frequencies near resonances, however, the exact formulation is needed.
TL;DR: In this article, the authors investigated the asymptotic behavior of the integral if(w) = eJo (Wx)f(x2)xdx, where Jo(x) is the Bessel function of the first kind and w is a large positive parameter.
Abstract: Asymptotic behavior of the integral if(w) = eJo (Wx)f(x2)xdx is investigated, where Jo(x) is the Bessel function of the first kind and w is a large positive parameter. It is shown that 1f(w) decays exponentially like ewy2, y > 0, when f (z) is an entire function subject to a suitable growth condition. A complete asymptotic expansion is obtained when f(z) is a meromorphic function satisfying the same growth condition. Similar results are given when f(z) has some specific branch point singularities.
TL;DR: In this paper, discussion d'un modele unidimensionnel simplifie propose par Majda pour l'etude qualitative des ondes de combustion is discussed.
Abstract: Discussion d'un modele unidimensionnel simplifie propose par Majda pour l'etude qualitative des ondes de combustion
TL;DR: In this paper, the authors give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour in the shadow zone.
Abstract: In the paper we give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour γ in the shadow zone. We assume that one of the source and observation points is on the boundary γ and the other one outside γ. We consider the case of the Dirichlet problem.
TL;DR: A closed Markovian queueing network model of a multiprocessor system with a two-level memory hierarchy with a special structure of branching probabilities is considered and is reduced to a nonlinear machine interference model.
TL;DR: In this paper, an asymptotic analysis of the three-dimensional motion of a piston ring in its groove is presented, with appropriate nondimensional scaling, and it is shown that the calculations in the literature use both a regular expansion and a multiple time scale expansion.
Abstract: An asymptotic analysis of the three-dimensional motion of a piston ring in its groove is presented, with appropriate nondimensional scaling. It is shown that the calculations in the literature use both a regular expansion and a multiple time scale expansion. The analysis is used to develop three ideas. First, the nondimensional parameters on which friction, F, and oil flow under the ring, Q, are identified. The variations of F and Q with the nondimensional parameters are calculated. Second, it is shown that for normal wear on the second ring of a 2.6-L engine, there is a fivefold azimuthal variation in Q, suggesting that the azimuthal symmetry assumption must be relaxed, and that wear patterns must be taken into account in oil consumption calculations. Finally, a novel, gas-lubricated ring is described, and the variations in F and Q with nondimensional parameters calculated. Overall, it is found that the approach substantially simplifies the friction and oil consumption problem in reciprocating engines: f...
TL;DR: In this paper, conditions for almost-sure and mean-square convergence, as well as the conditions providing for asymptotic normality of normalized deviations of an algorithm path from the minimum point, are established.
Abstract: This paper is concerned with asymptotic characteristics of gradient procedures of stochastic approximation, with dependent noise distorting the observations of an optimized function gradient. Conditions for almost-sure and mean-square convergence, as well as the conditions providing for asymptotic normality of normalized deviations of an algorithm path from the minimum point, are established. Convergence rates are given. Examples are considered, involving different kinds of dependent noise.
TL;DR: In this article, an asymptotic decomposition technique for 2 by 2 first order singularly perturbed linear differential systems was developed and used for multi-turning point problems.
Abstract: An asymptotic decomposition technique is developed. It is designed and used for 2 by 2 first order singularly perturbed linear differential systems. A new set of decoupled linear integral equations is introduced in the process of the asymptotic analysis. Its usefulness is demonstrated with multi-turning point problems. An adiabatic theorem in quantum mechanics is proved in a general case of degenerate energy levels.
TL;DR: In this article, an asymptotic method for the analysis of strongly nonlinear autonomous oscillators is presented, and the amplitude and stability of the corresponding limit cycles are determined.
Abstract: In this paper, an asymptotic method is presented for the analysis of a class of strongly nonlinear autonomous oscillators. The equations governing the amplitude and phase factor are obtained, and the amplitude and stability of the corresponding limit cycles are determined.
TL;DR: Analyse des problemes de valeurs limites pour un systeme d'equations differentielles ordinaires non lineaires perturbees de maniere singuliere and modelisant de grandes deflexions de poutres minces.
Abstract: Analyse des problemes de valeurs limites pour un systeme d'equations differentielles ordinaires non lineaires perturbees de maniere singuliere et modelisant de grandes deflexions de poutres minces
01 Jan 1985
TL;DR: The approach presented here is called the symbolirr' operator method: a large set 01 combinatorial c onstructions have direct translations c.s operators on counting generating functims, so that junctional equations over generating functions can be obtained rather directly for many combinatorially structures o j interest.
Abstract: ?his paper is intended both as a. tutorial paper and a partial review of advanced mathematical methods in the average case enalysis of algorithms and d ata structures. An analysi-. usually decomposes into several c ombinatorial enumeration problems (of words, trees, permutations, distributions ...) whose outcome is then subjected to asymptotic analysis in order to obtain results in a form that is easy to interpret. 7he main technique to solve combinatorial enumeration problems is wia the use oj generating junctions. Be approach presented here is called the symbolirr' operator method: a large set 01 combinatorial c onstructions have direct translations c.s operators on counting generating functims, so that junctional equations over generating functions can be obtained rather directly for many combinatorial structures o j interest. 7PLe main technique tor asymptotic analysis in this context relies on complex analysis: analytic function theory and uses of CcLuchy's residue theorem. h most cases the asymptotic recovered directly jrom the generating function itselj with a proper choice of integration contour (singularity analysis, saddle point methods ...). These methods are briej9.W illustrated with several examples relating t o: (I) tree manipulation a.lgorithms in compiling and symbolic manipulation systems ; (2) sorting and searching techniques based on comparisons between keys ; (3) digital search alg orithms . behaviour 01 coefficients of a generating function can be z