Symbolic analysis of spatio-temporal systems: The measurement problem
- Univ. of California at San Diego, La Jolla, CA (United States)
- College of William and Mary, Williamburg, VA (United States)
We consider the problem of measuring physical quantities using time-series observations. The approach taken is to validate theoretical models which are derived heuristically or from first principles. The fitting of parameters in such models constitutes the measurement. This is a basic problem in measurement science and a wide array of tools are available. However, an important gap in the present toolkit exists when the system of interest, and hence the models used, exhibit chaotic or turbulent behavior. The development of reliable schemes for analyzing such signals is necessary before one can claim to have a quantitative understanding of the underlying physics. In experimental situations, the number of independently measured time-series is limited, but the number of dynamical degrees of freedom can be large. In addition, the signals of interest will typically be embedded in a noisy background. In the symbol statistics approach, the time-series is coarse-grained and converted into a long, symbol stream. The probability of occurrence of various symbol sequences of fixed length constitutes the symbol statistics. These statistics contain a wealth of information about the underlying dynamics and, as we shall discuss, can be used to validate models. Previously, we have applied this symbolic approach to low dimensional systems with great success. The symbol statistics are robust up to noise/signal {approx}20%. At higher noise levels the symbol statistics are biased, but in a relatively simple manner. By including the noise characteristics into the model, we were able to use the symbol statistics to measure parameters even when signal/noise is {approx} O(1). More recently, we have extended the symbolic approach to spatio-temporal systems. We have considered both coupled-map lattices and the complex Ginzburg-Landau equation. This equation arises generically near the onset of instabilities.
- OSTI ID:
- 489436
- Report Number(s):
- CONF-960354-; TRN: 97:011581
- Resource Relation:
- Conference: International Sherwood fusion theory conference, Philadelphia, PA (United States), 18-20 Mar 1996; Other Information: PBD: 1996; Related Information: Is Part Of 1996 international Sherwood fusion theory conference; PB: 244 p.
- Country of Publication:
- United States
- Language:
- English
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