A data-fitting procedure for chaotic time series

Abstract

DECLAIMER DISCLAIMERPortions of this document may be illegible in electronic image products. Images are produced from the best available original document. AbstractIn this paper we introduce data characterizations for fitting chaotic data to linear combinations of one-dimensional maps (say, of the unit interval) for use in subgrid-scale turbulence models. We test the efficacy of these characterizations on data generated by a chaotically-forced Burgers' equation and demonstrate, very satisfactory results in terms of modeIed time series, power spectra and delay maps.

Chaotic map models of soot fluctuations in turbulent diffusion flames

“…We will briefly discuss the procedures successfully used for model problem data in [12] now applied to the experimental data sets shown in Fig. 2(a-c).…”

“…We discuss each of these briefly in what follows and provide specific formulas used in our analyses. More details can be found in [12].…”

“…Even though the results presented in [l] are quite promising, the need for more thorough analysis is obvious. A detailed description of the map construction procedure, per se, in the context of a model problem is presented by McDonough et al [12].…”

“…Thus the modeling effort must employ more sophisticated analyses and quantification of the time series behavior itself, e. g., use of total variation per unit time, frequency of zero crossings, etc., in order to more precisely model complex, aperiodic deterministic phenomena. These latter techniques have recently been employed in [12] in the context of fitting data obtained from a model problem. We will utilize several of the most effective techniques identified in that study below.…”

A ‘poor man's Navier–Stokes equation’: derivation and numerical experiments—the 2‐D case

“…Gollub and Benson [9]), and in many cases the corresponding time series are physically realistic. In fact, McDonough et al [10] and Mukerji et al [11] have demonstrated the ability to model both numerical simulations and experimental data with linear combinations of a slight modiÿcation of (1). This raises the question of whether algebraic expressions such as Equations (3) might be of value for producing practical, computational models of turbulence, e.g.…”