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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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Journal ArticleDOI
TL;DR: It is shown that this asymptotic behavior of a class of functional differential equations with state-dependent delays can be numerically observed by computing corresponding solutions of approximating equations with piecewise constant arguments.

7 citations

Journal ArticleDOI
TL;DR: A differential calculus for the non-operator norms of m-times continuously differentiable matrix function χ(t), t ≥ t 0 is presented and combined with the study of the asymptotic behavior of the evolution Φ(t, t 0) for periodic linear dynamical systems.
Abstract: In this paper, a differential calculus for the non-operator norms |·|1 and |·|∞ of m-times continuously differentiable matrix function χ(t), t ≥ t 0, is presented and combined with the study of the asymptotic behavior of the evolution Φ(t, t 0) for periodic linear dynamical systems. The upper bound describing the asymptotic behavior (for short, asymptotic bound or asymptotic estimate) is based on Floquet's theory and on a bound containing the spectral abscissa of a constant matrix; it compares favorably with other asymptotic bounds. The minimal constant in the asymptotic estimate is computed by the differential calculus of norms. As far as we are aware, the achieved result cannot be obtained by other methods.

7 citations

Journal ArticleDOI
TL;DR: The main thrust of this work will be to obtain conditions which ensure that to each bounded solution v of (1) there corresponds a (not necessarily unique) bounded solution u of (2) such that limt~®]u(t)-v(t) I = 0.
Abstract: are asymptotically equivalent, where each F and G is a continuous function from Ro × Y to Y. The major advantage of the present study is that not only is equation (I) not assumed to linear, but no differentiability hypotheses are placed on F. Our hypotheses on F will be such that solutions of (I) are unique and can be continued indefinitely rightward. The main thrust of our work will be to obtain conditions which ensure that to each bounded solution v of (1) there corresponds a (not necessarily unique) bounded solution u of (2) such that limt~®]u(t)-v(t) I = 0. Our results will be such that, if F is linear, they are implied by recent work of P. Talpalaru [15, Th6or6mes 2.1 and 3.1]. The primary tools used here will be the circle of ideas involving the H61der inequality developed by R. Conti [1], V. A. Staikos [14], and Talpalaru [15], and the notion of logarithmic derivative developed by T. Wa~,ewski [16] and S. M. Lozinskii [10], and most recently employed by R. H. Martin, Jr. and the present author [11], [6], [9], [7], and [8]. The reader familiar with [1 I], [6], [9], [7], and [8] will note that in none of those articles was a restriction placed on the dimension of Y. The restriction is necessary here so that we may apply the fixed-point theorem of J. Schauder [13] to Banach spaces of Y-valued functions. The type of Schauder argument we use is similar to that developed by C. Corduneanu [3].

7 citations

Dissertation
01 Jan 2005
TL;DR: In this article, the effect of a uniformly pulsating free-s tream with the leading edge of a body is considered, and the effect on transition is investigated by using the Parabolized Stability Equation (PSE).
Abstract: We consider the interaction of a uniformly pulsating free-s tream with the leading edge of a body, and consider its effect on transition. The free-st r am is assumed to be incompressible, high Reynolds number flow parallel to the chord of t he body, with a small, unsteady, perturbation of a single harmonic frequency. We p resent a method which calculates Tollmien-Schlichting (T-S) wave amplitudes downs tream of the leading edge, by a combination of an asymptotic receptivity approach in the l eading edge region and a numerical method which marches through the Orr-Sommerfeld egion. The asymptotic receptivity analysis produces a three deck eigenmode which , in its far downstream limiting form, produces an upstream initial condition for our num erical Parabolized Stability Equation (PSE). Downstream T-S wave amplitudes are calculated for the flat pl ate, and good comparisons are found with the Orr-Sommerfeld asymptotics ava ilable in this region. The importance of theO(Re− 1 2 ) term of the asymptotics is discussed, and, due to the complexity in calculating this term, we show the importance of n umerical methods in the Orr-Sommerfeld region to give accurate results. We also discuss the initial transients present for certain p rameter ranges, and show that their presence appears to be due to the existence of high er T-S modes in the initial upstream boundary condition. Extensions of the receptivity/PSE method to the parabola an d the Rankine body are considered, and a drop in T-S wave amplitudes at lower branch is observed for both bodies, as the nose radius increases. The only exception to this trend occurs for the Rankine body at very large Reynolds numbers, which are not accessible in experiments, where a double maximum of the T-S wave amplitude at lower branch is ob served. The extension of the receptivity/PSE method to experimenta lly realistic bodies is also considered, by using slender body theory to model the invisc id flow around a modified super ellipse to compare with numerical studies.

7 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526