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Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.

NASA Discipline Number 14-10↗

Oceanic eddy variability measured by GEOS 3 altimeter crossover differences

Eddy statistics of sea height variations associated with dynamic ocean currents, gathered by GEOS 3 altimetry (25 cm), are discussed. Time variable flow is noted to be measureable using altimeter height and orbit information by means of three techniques: collinear tracks, where rms variability can be determined for mesoscale phenomena measured along parallel tracks; mean surfaces, using a 3-dimensional mapping of the sea surface for an accurate representation of the surface undulations; and crossover differences, such as between data tracks from GEOS and Seasat which have reduced ephemeris error over scales of a few thousand km. Mesoscale energetics have been found suitable for tracing meandering ocean currents by the crossover method. Possible sources of error are considered, including altimeter noise, orbit error, short wavelength continental shelf tides, etc., and it is determined that observations of mesoscale sea height appear to be limited only by uncertainties in the altimetry, which for Seasat was 5 cm over 60% of the world's oceans.

Cheney, R. E.↗

Electric Field Induced Interfacial Instabilities

The study of the interface in a charge-free, nonpolar, critical and near-critical binary fluid in the presence of an externally applied electric field is presented. At sufficiently large fields, the interface between the two phases of the binary fluid should become unstable and exhibit an undulation with a predefined wavelength on the order of the capillary length. As the critical point is approached, this wavelength is reduced, potentially approaching length-scales such as the correlation length or critical nucleation radius. At this point the critical properties of the system may be affected. In zero gravity, the interface is unstable at all long wavelengths in the presence of a field applied across it. It is conjectured that this will cause the binary fluid to break up into domains small enough to be outside the instability condition. The resulting pattern formation, and the effects on the critical properties as the domains approach the correlation length are of acute interest. With direct observation, laser light scattering, and interferometry, the phenomena can be probed to gain further understanding of interfacial instabilities and the pattern formation which results, and dimensional crossover in critical systems as the critical fluctuations in a particular direction are suppressed by external forces.

Kusner, Robert E.↗

Evaluation of seals for high-performance cryogenic turbomachines

An approach to computing flow and dynamic characteristics for seals or bearings is discussed. The local average velocity was strongly influenced by inlet and exit effects and fluid injection, which in turn drove zones of secondary flow. For the restricted three-dimensional model considered, the integral averaged results were in reasonable agreement with selected data. Unidirectional pressure measurements alone were insufficient to define such flow variations. However, for seal and bearing leakage correlations the principles of corresponding states were found to be useful. Also discussed are three phenomena encountered during testing of three eccentric nonrotating seal configurations for the Space Shuttle Main Engine (SSME) Program. Fluid injection, choking within a seal, and pressure profile crossover are related to postulated zones of secondary flow or separation and to direct stiffness.

Hendricks, R. C.↗

Test of a new field-theoretical crossover equation-of-state

A new field-theoretical crossover equation-of-state model provides a bridge between the asymptotic behavior close to a liquid-gas critical point and the expected mean field behavior farther away.

equation-of-state critical phenomena liquid-gas cr↗

Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology

We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.

Gandhi, Amar↗

MISTE flight experiment status

The MISTE flight experiment has made significant scientific and technical progress in preparing for a future microgravity flight. We are collaborating with several theoretical modeling groups that have developed crossover (equation-of-state) models for predicting thermodynamic behavior near the liquid-gas critical point. Several of these models have already been used to test experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve in the crossover region near the 3He liquid-gas critical point. A brief description of these models and a representative fit to experimental data will be presented. In collaboration with Mission Research Corporation, MISTE has been testing a new small pneumatic valve for use at low temperatures. The results of recent successful low temperature actuation tests will also be discussed.

critical phenomena liquid-gas critical point↗

Effects of uncertainty on manual tracking performance

Transient phenomena and target acquisition modes associated with interrupted observations during ground-to-air AA tracking were investigated. Using a two-axes control stick, the subjects tracked a computer-generated airplane image on a CRT display. The airplane image excuted a low-level straight pass. At certain pseudo-random times during each 25-second run, the screen was blanked for a period of one second. When the target image reappeared, the subjects reacquired it and continued tracking, attempting to minimize vector RMS error for the entire run (including the blanked period). The results reveal an increase both in tracking error and in error variance during the blanked period, only when the target disappears while in the crossover region. Blanking at other times effected increased variance but had no effect on the mean error. A blanking period just before crossover produced an increase lag while a blanking just after crossover resulted in a lead and thus made the error curve more symmetric.

Ephrath, A. R.↗