A data-fitting procedure for chaotic time series

Applied Mathematics and Computation

Volumn 95, Issue 2-3, 1998, Pages 219-243

  McDonough, J M ^a   Mukerji, S ^a,c   Chung, S ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c KOHLER CO   (United States)

Author keywords

Chaotic dynamical systems; Subgrid scale turbulence models; Time series analysis

Indexed keywords

EID: 0141466899     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)10062-5     Document Type: Article

References (15)

1. E.G. Hylin, J.M. McDonough, Theoretical development of a stochastic model for small-scale turbulence in an additive decomposition of the Navier-Stokes equations, Mechanical Engineering Report No. CFD-02-96, University of Kentucky, Lexington, KY, 1996.
2. J.M. McDonough, Parallelization of ATD/chaotic-map turbulence models, in: P. Schiano et al. (Eds.), Parallel Computational Fluid Dynamics: Algorithms and Results Using Advanced Computers, Elsevier, Amsterdam, 1997.
3. P. Collet, J.P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston, 1980.
4. K.R. Sreenivasan, R. Ramshankar, Transition intermittency in open flows, and intermittency routes to chaos, Physica D 23 (1986) 246-258.
5. T.H. Pulliam, J.A. Vastano, Transition to chaos in an open unforced 2D flow, J. Comput. Phys. 105 (1993) 133-149.
6. M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Statist. Phys. 19 (1978) 25-52.
7. U. Frisch, Turbulence, Cambridge University Press, Cambridge, 1995.
8. H. Tennekes, J.L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, MA, 1983.
9. M.P. Mengüç, J.M. McDonough, S. Manickavasagam, S. Mukerji, S. Ghosal, Fluctuations of soot in turbulent diffusion flames: Experimental data and chaotic map models, Presented at the International Mechanical Engineering Congress and Exposition (IMECE) in Atlanta, November 1996.
10. M. Casdagli, S. Eubank (Eds.), Nonlinear Modeling and Forecasting, Santa Fe Institute Studies in the Sciences of Complexity, Proceedings vol. XII, Addison-Wesley, Reading, MA, 1992.
11. N.F. Hunter, Application of nonlinear time-series models to driven systems, in: M. Casdagli, S. Eubank (Eds.), Nonlinear Modeling and Forecasting, Santa Fe Institute Studies in the Sciences of Complexity, Proceedings vol. XII, Addison-Wesley, Reading, MA, 1992.
12. J.-S. Peng, An Analysis of Reynolds Averaging via One-dimensional Burgers' Equation, M.S. Thesis, University of California, Los Angeles, CA, 1990.
13. R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, vol. 68, Springer, New York, 1988.
14. P. Constantin, C. Foias, B. Nicolaenko, R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Applied Mathematical Sciences, vol. 70, Springer, New York, 1989.
15. S. Mukerji, J.M. McDonough, M.P. Mengüç, S. Manickavasagam, S. Chung, Chaotic map models of soot fluctuations in turbulent diffusion flames, in press in Int. J. Heat Transfer.