Showing papers on "Asymptotic analysis published in 1988"

Asymptotic Distribution Theory and Efficiency Results for Case-Cohort Studies

Abstract: A case-cohort design was recently proposed [Prentice (1986)] as a means of reducing cost in large epidemiologic cohort studies. A "pseudolikelihood" procedure was described for relative risk regression parameter estimation. This procedure involves covariate data only on subjects who develop disease and on a random subset of the entire cohort. In contrast, the usual partial likelihood estimation procedure requires covariate histories on the entire cohort. Accordingly, a case-cohort design may affect cost saving, particularly with large cohorts and infrequent disease occurrence. Asymptotic distribution theory for such pseudolikelihood estimators, along with that for corresponding cumulative failure rate estimators, are presented here. Certain asymptotic efficiency expressions relative to full-cohort estimators are developed and tabulated in situations of relevance to the design of large-scale disease prevention trials. The theoretical developments make use of martingale convergence results and finite population convergence results.

Asymptotic normality of r-estimates in the linear model

Abstract: It is shown that the R-estimators of the parameters in a linear model are asymptotically normally distributed under the same conditions on the regressors that are necessary and sufficient for the asymptotic normality of ordinary least squares estimators. The assumptions in JURECKOVA (1971) are essentially weakened, This is done by exploiting and further developping some results of convex analysis

Asymptotic behavior of solutions of semilinear heat equations on S1

Abstract: We study the dynamical behavior of the initial value problem for the equation u t = u xx + f(u, u x ), x ∈ S 1 =R/Z, t > 0. One of our main results states that any C 1-bounded solution approaches either a single periodic solution or a set of equilibria as t → ∞. We also consider the case where the solution blows up in a finite time and prove that under certain conditions on f the blow-up set of any solution with nonconstant initial data is a finite set.

Natural convection in a long vertical cylinder under gravity modulation

Abstract: This study is devoted to the onset of convection in differentially heated cylinders under gravity modulation. It specifically concerns the case of a vertical cylinder of infinite length, when a negative temperature gradient is maintained in the upward direction. The effect of modulation on the stability limits given by linear theory in the standard steady case is analysed. A method based on Floquet theory is proposed in the case of small values of the modulation amplitude e, for a fixed value of the frequency ω. A general technique, called matrix method, which can easily be adapted to various kinds of geometries and boundary conditions, has been developed. Analytical approaches have been derived in some cases. Finally, an asymptotic analysis is presented for large ω, under very general boundary conditions and periodic constraints, for finite e. An asymptotic relation is established for the onset of convection under periodic gravity modulation for large ω values, when e [Lt ] ω; the mathematical and physical foundations of this inequality are discussed.

An asymptotic analysis of supersonic reacting mixing layers

Abstract: The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter.

New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces

Abstract: Recent advances in mathematical analysis of problems described by several small parameters equations are used to revisit the general roughness problem. In this paper, we put forward a new qualitative study of a thin film flow with a rapidly varying gap. Using an asymptotic analysis of the three-dimensional Stokes system we obtain a family of new generalized Reynolds equations. We are led to distinguish three different cases in which the periodic roughness wavelength is on the order of, greater or shorter than the mean thickness of the gap.

An ODE-solver based on the method of averaging

Abstract: In this paper we describe an efficient code for the long-term integration of systems of the type $$\dot x = f^0 (x) + \varepsilon f^1 (x)$$ where ? is a small parameter and (1)0 is assumed to have periodic solutions only. This situation frequently occurs in celestial mechanics, in nonlinear oscillations and various other situations. We give a thorough asymptotic analysis of the method.

Inclined entry of a blunt profile into an ideal fluid

Abstract: A study is made of the two-dimensional unsteady motion of an ideal incompressible fluid due to the entry into it of a blunt profile at a given angle of attack. In the initial stage of the process, when the penetration depth is relatively small, the problem can be investigated by the methods of asymptotic analysis. The dimensionless time t plays the part of the small parameter. It is shown that to 0(t2) as t → 0 the displacement field of the fluid particles does not depend on the angle of attack and is determined by the solution to the problem of vertical entry. The asymptotic behaviors of the principal vector and principal moment of the forces exerted on the profile by the fluid at short times are found. The asymptotic behavior of the principal moment of the forces is proportional to the distance traversed by the body along the surface of the fluid.

A transient analysis of a data network with a processor-sharing switch

Abstract: This paper gives a simple, accurate, first-order asymptotic analysis of the transient behavior of a data network. The network is based on a switch, such as the Datakit® virtual circuit switch, which receives packetized traffic from many message sources of diverse classes and multiplexes the traffic over a trunk line. The network has a regulatory mechanism based on acknowledgments that produces a closed model. Assuming that the switch has a processor-sharing discipline, and assuming an asymptotic regime of high loading of the switch and high-capacity trunks, we derive the explicit, first-order transient behavior of the means of queue lengths — and hence response times. We then give a simple procedure for finding the time constants (eigenvalues) that govern the approach to steady state. Our numerical experiments show that the analysis is quite accurate.

An asymptotic analysis of the Sal’nikov thermokinetic oscillator

Abstract: The Sal'nikov thermokinetic oscillator is studied in the limiting case where the dimensionless heat capacity tends to zero. This is equivalent to the \`no fuel consumption' approximation in classical thermal explosion theory and is equally revealing in that many exact results can be obtained by simple algebraic methods. Regions in parameter space are found where, although the system is asymptotically stable, a large single excursion occurs before the steady state is approached. These regions border the region of oscillations which in the limiting case are of the relaxation type. All the interesting behaviour requires $RT/E < \frac{1}{4}$, an obvious parallel with thermal explosion theory. The unstable limit cycles that occur in the Sal'nikov oscillator disappear in this limiting case. However, the requirements for an unstable limit cycle to exist in the \`relaxation' limit are discussed. The homoclinic bifurcation in the limiting case is also examined and it is shown that this bifurcation can (in theory) be calculated exactly. In addition, an extension to the Sal'nikov oscillator scheme in a closed system to include fuel consumption is studied both numerically and in a limiting case. It is shown that the full scheme exhibits finite trains of almost periodic behaviour before monotonically approaching equilibrium.

The Concept of Asymptotic Efficiency

Abstract: Partly of an expository nature this note brings out the fact that an estimator, though asymptotically much less efficient (in the classical sense) than another, may yet have much greater probability concentration (as defined in this article) than the latter.

An asymptotic analysis of hierarchical control of manufacturing systems

Abstract: An asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair is presented. The machine fluctuations are much faster than the accumulation and discounting of costs, and this gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. The limiting problem is computationally tractable and sometimes has a closed-form solution. >

A uniform asymptotic analysis of the diffraction by an edge in a curved screen

Abstract: An approximate asymptotic high-frequency solution is obtained for the electromagnetic wave diffraction by an edge in a curved conducting screen. The solution is uniform across the various ray shadow boundaries and is expressed in the simple format of the geometrical theory of diffraction. The transition functions associated with this uniform solution involve previously published special functions and can be calculated efficiently. Since the effect of the whispering gallery modes associated with the concave side of the curved screen is not included in this study, the present asymptotic solution is valid when neither the source nor the field points are close to the concave side of the screen.

Correlations at a liquid-gas interface: asymptotic analysis for weak gravity

Abstract: Density-density correlation functions at the phase-separating layer in a two-dimensional solid-on-solid lattice model are studied. The authors perform for weak gravitational fields an exact asymptotic analysis and obtain explicit expressions. A recent numerical analysis by Stecki and Dudowicz (1986) is shown to be in good agreement with their exact expansion.

Asymptotic analysis of G/G/K queueing-loss system with retrials and heterogeneous servers

Abstract: The asymptotic performance of a G/G/K queueing-loss system with a stationary-counting arrival process, generally-distributed service times, K parallel heterogeneous servers, no waiting room, and retrials, is analysed by a recursive technique. In queueing-loss systems with retrials, the units which find all processors busy are not lost: these units try again to be processed by merging with the incoming arrival units at the system. Furthermore, numerical results are provided and the approximation outcomes are compared against those from a simulation study.

S-asymptotic expansion of distributions

Abstract: This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging to G′Rn, named S-asymptotic expansion, as also its properties and application to partial differential equations.

Circuit-dependent adiabatic phase factors from phase integral theory

Abstract: The authors show that circuit-dependent adiabatic phase factors occur naturally in the phase integral theory of atomic collisions, being a physical manifestation of the Stokes phenomenon familiar in asymptotic analysis. This implies a generalisation of Berry's work (1984) on geometric phase factors for situations involving adiabatic parallel transport around closed circuits in the complex plane.

Antialiasing methods for two-dimensional spatial wavelets in seismic modeling

Abstract: Two methods of circumventing spatial aliasing in seismic reflection modeling of zero‐offset data were examined. The first approach used asymptotic approximations of the near‐ and far‐field variants of the space‐frequency domain wave‐field continuation operator. This technique controls spatial aliasing but puts a lower limit on the extrapolation step size and an upper limit on frequencies that can be used in the modeling. The second method used Fourier (wavenumber) analysis of the same operator to identify the aliased components and wavenumber windowing to remove the unwanted portions of the wavenumber spectrum. In contrast to the asymptotic analysis, the Fourier analysis approach was simple and flexible to use and did not restrict other variables.

Accurate one‐dimensional fixed‐bed reactor model based on asymptotic analysis

Abstract: Mise en place d'un modele unidimensionnel par approximation asymptotique des modeles bidimensionnels existant pour le calcul des profils de temperatures et de concentration radiaux et axiaux dans le reacteur

Beam propagation method and geometrical optics

Abstract: An asymptotic analysis is made of the BPM algorithm, leading to the derivation of ray and transport equations. A second-order equation is derived the properties of which are compared with those of the true wave-equation. The implications of the results for the interpretation of BPM computations are discussed.