On the choice of coarse variables for dynamics

International Journal for Multiscale Computational Engineering

Volumn 5, Issue 6, 2007, Pages 483-489

  Acharya, Amit ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Autonomous dynamics; Coarse variables; Delay reconstruction

Indexed keywords

APPROXIMATION ALGORITHMS; AUTONOMOUS AGENTS; PROBLEM SOLVING;

AUTONOMOUS DYNAMICS; COARSE VARIABLES; DELAY RECONSTRUCTION;

RANDOM VARIABLES;

EID: 39049128878     PISSN: 15431649     EISSN: None     Source Type: Journal    
DOI: 10.1615/IntJMultCompEng.v5.i6.50     Document Type: Article

References (15)

1. Acharya, A., Parameterized invariant manifolds: A recipe for multiscale modeling? Comput. Methods Appl. Mech. Eng. 194:3067-3089, 2005.
2. Sawant, A., and Acharya, A., Model reduction via parameterized locally invariant manifolds: Some examples. Comput. Methods Appl. Mech. Eng. 195:6287-6311, 2005.
3. Acharya, A., and Sawant, A., On a computational approach for the approximate dynamics of averaged variables in nonlinear ODE systems: Toward the derivation of constitutive laws of the rate type. J. Mech. Phys. Solids. 54:2183-2213, 2006.
4. Gear, C. W., Kevrekidis, I. G., and Theodoropoulos, C., Coarse integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Comput. Chem. Eng. 26:941-963, 2002.
5. Kevrekidis, I. G., Gear, C. W., Hyman, J. M., Kevrekidis, P. G., Runborg, O., and Theodoropoulos, K., Equation-free coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level tasks. Commun. Math. Sci. 1:715-762, 2003.
6. Kevrekidis, I. G., Gear, C. W., and Hummer, G., Equation-free: The computer-assisted analysis of complex, multiscale systems. AIChE J. 50:1346-1354, 2004.
7. Artstein, Z., and Vigodner, A., Singularly perturbed ordinary differential equations with dynamic limits. Proc. R. Soc. Edinburgh. 126A:541-569, 1996.
8. Takens, F., Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence. Lecture Notes in Mathematics, vol. 898. Rand, D. A., and Young, L. S., Eds., Springer-Verlag, 366-381, 1980.
9. Abarbanel, H. D. I., Analysis of Observed Chaotic Data. Springer, New York, 1996.
10. Kennel, M. B., and Abarbanel, H. D. I., False neighbors and false strands: A reliable minimum embedding dimension algorithm. Phys. Rev. E. 66:026209, 2002.
11. Ding, M., Grebogi, C., Ott, E., Sauer, T., and Yorke, J. A., Estimating correlation dimension from a chaotic time series: When does plateau onset occur? Phys. D. 69:404-124, 1993.
12. Eckmann, J.-P., and Ruelle, D., Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:617-656, 1985.
13. Sauer, T., Yorke, J. A., and Casdagli, M., Embedology. J. Stat. Phys. 65:579-616, 1991.
14. Broomhead, D. S., Huke, J. P., and Muldoon, M. R., Linear filters and non-linear systems. J. R. Stat. Soc., Ser. B. 54:373-382, 1992.
15. Pecora, L. M., and Carroll, T. L., Discontinuous and non-differentiable functions and dimension increase induced by filtering chaotic data. Chaos. 6:432-439, 1996.