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NASA NTRS1999

Statistical physics and physiology: monofractal and multifractal approaches

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

NASA Discipline Cardiopulmonary↗

NASA NTRS1992

Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow

For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor's hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor's hypothesis, space-time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space-time correlation of dilatation fluctuations is explained via a wave propagation model.

Lee, Sangsan↗

NASA NTRS1971

Some heuristic procedures for analyzing random vibration of nonlinear oscillators.

The stationary response of a lightly damped nonlinear oscillator subjected to wideband random excitation can be examined as an example of thermal equilibrium. It may be assumed that the response consists of a series of free-vibration cycles with small random fluctuations in phase and amplitude. Certain statistical properties of the response can be estimated by averaging corresponding properties of the free vibration with respect to cycle amplitude distributions. Such heuristic procedures for determining the expected frequency and the autocorrelation function of the stationary response are outlined. Some additional results concerning first-passage problems for nonlinear oscillators are included.

Crandall, S. H.↗

NASA NTRS1976

Measured response of a complex structure to supersonic turbulent boundary layers

Measurements of the response of a large frame-stringer panel excited by supersonic turbulent boundary layer are reported. The statistical description of the wall pressure fluctuations in terms of the mean flow parameters governing the turbulent boundary layer is given. These results can be used in the development of design criteria on the response of sidewall structure of a large airplane in supersonic flight, since both forcing field and structure are realistic. Results indicate the significant importance of the modal coupling and the acoustic damping. The acoustic damping plays a major role in the response of the structure.

Maestrello, L.↗

NASA NTRS1980

Improved definition of crustal anomalies for Magsat data

Ongoing efforts to define and model external magnetic field activities are summarized. Data were obtained and plotted for the five international quiet days of each month Magsat was in orbit. The values of the magnetic field at midnight were also plotted for each of the quiet days. Results show that the zero level of the field fluctuates over the time interval considered. Statistical studies were made for the Kp and Ap indices and more sunspot numbers were obtained for the Magsat period. Satellite data are being thinned and reformatted to make them more amenable to testing the Dst and Sq corrections. The software for processing Magsat tapes is being tested with intermediate attitude data.

Source record↗

NASA NTRS1985

The C-12/C-13 isotope ratio toward Zeta Ophiuchi

Observations of interstellar CH(+) toward Zeta Oph were performed to determine the C-12/C-13 isotope ratio in this diffuse cloud. The very high signal-to-noise ratio spectra yield 6 sigma detections of the (C-13)H(+) features at 4232 A and 3957 A; a weighted mean C-12/C-13 ratio of 43 + or - 6 (1 sigma) is obtained. The uncertainty includes the contribution of continuum placement errors, statistical channel-to-channel signal fluctuations, and the error introduced in deconvolving the blended isotopic lines at 4232 A. This result indicates a decrease in the local galactic C-12/C-13 ratio by a factor of 2 during the 4.6 billion yr since the formation of the sun.

Hawkins, I.↗

NASA NTRS1986

Voyager 2 photopolarimeter experiment - Evidence for tenuous outer ring material at Saturn

Voyager 2 photopolarimeter data are employed to characterize two regions of optically thin material outside the Saturn F ring. The study consists of a statistical analysis of optical depth value fluctuations caused by occultations of starlight from Delta Sco as viewed through the material. One the optically thin regions surrounds the orbital semimajor axis of the outer F ring shepherd satellite Pandora and the other thin region lies 144,090 km farther outward. The first region, with an optical depth of 0.008-0.016, is about 200 km in radius and the second, with an optical depth of 0.005-0.013, is about 1000 km in radial width. The data had a resolution of 0.5 km.

Graps, A. L.↗

NASA NTRS1994

The measurement of disturbance levels in the Langley Research Center 20-inch Mach 6 tunnel

Constant-temperature anemometry was used to measure the disturbance levels in the Langley Research Center 20-inch Mach 6 Tunnel over a limited range of total pressures. The measurements were made using a dual wire probe where each wire was operated at a high but different overheat. The fluctuating voltages were digitized and a system of two equations was solved to obtain the instantaneous mass flow and total temperature fluctuations as a function of time. Statistical techniques were used to obtain statistical quantities of interest.

Stainback, P. C.↗

NASA NTRS1995

Comparison of 2- and 10-micron coherent Doppler lidar performance

The performance of 2- and 10-micron coherent Doppler lidar is presented in terms of the statistical distribution of the maximum-likelihood velocity estimator from simulations for fixed range resolution and fixed velocity search space as a function of the number of coherent photoelectrons per estimate. The wavelength dependence of the aerosol backscatter coefficient, the detector quantum efficiency, and the atmospheric extinction produce a simple shift of the performance curves. Results are presented for a typical boundary layer measurement and a space-based measurement for two regimes: the pulse-dominated regime where the signal statistics are determined by the transmitted pulse, and the atmospheric-dominated regime where the signal statistics are determined by the velocity fluctuations over the range gate. The optimal choice of wavelength depends on the problem under consideration.

Frehlich, Rod↗

NASA NTRS2011

Kinetic-Scale Magnetic Turbulence and Finite Larmor Radius Effects at Mercury

We use a nonstationary generalization of the higher-order structure function technique to investigate statistical properties of the magnetic field fluctuations recorded by MESSENGER spacecraft during its first flyby (01/14/2008) through the near-Mercury space environment, with the emphasis on key boundary regions participating in the solar wind - magnetosphere interaction. Our analysis shows, for the first time, that kinetic-scale fluctuations play a significant role in the Mercury's magnetosphere up to the largest resolvable timescale (approx.20 s) imposed by the signal nonstationariry, suggesting that turbulence at this plane I is largely controlled by finite Larmor radius effects. In particular, we report the presence of a highly turbulent and extended foreshock system filled with packets of ULF oscillations, broad-band intermittent fluctuations in the magnetosheath, ion-kinetic turbulence in the central plasma sheet of Mercury's magnetotail, and kinetic-scale fluctuations in the inner current sheet encountered at the outbound (dawn-side) magnetopause. Overall, our measurements indicate that the Hermean magnetosphere, as well as the surrounding region, are strongly affected by non-MHD effects introduced by finite sizes of cyclotron orbits of the constituting ion species. Physical mechanisms of these effects and their potentially critical impact on the structure and dynamics of Mercury's magnetic field remain to be understood.

Uritsky, V. M.↗

NASA NTRS1998

Some Results Relevant to Statistical Closures for Compressible Turbulence

For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.

Ristorcelli, J. R.↗

NASA NTRS2001

Effective Gravitational Temperature in Sedimentation

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.05 less than phi less than 0.50. During sedimentation, velocity fluctuations are found to be organized into regions of characteristic size L approximately 11 a phi(exp-1/3) and buoyant mass DELTA m given by the rms density fluctuations in a region of size L(sup 3) assuming random statistics with excluded volume effects. A simple model accurately predicts the magnitudes of the velocity fluctuations DELTA V. Finally, we find a new universal relation for particle diffusion during sedimentation that can be written in a Stokes-Einstein type form as D approximately (DELTA mg L)/(6 pi eta L), where the effective temperature DELTA mg L is the gravitational potential energy of density fluctuations.

Segre, Philip N.↗

NASA NTRS1991

A measurement of the mass fluctuation spectrum from the cluster X-ray temperature function

A statistically complete sample of galaxy clusters is presented which also has complete X-ray temperature information. Using this sample, the cluster bolometric luminosity and temperature functions are derived. The temperature function constrains the shape and amplitude of the mass fluctuation power spectrum. For a power law, i.e., with the fluctuation power spectrum proportional to k exp n, n = -(1.7 + 0.65, - 0.35), and an amplitude is obtained which implies that the rms value of delta-M/M is 0.59 + or - 0.02 on a scale of 8/h Mpc at the present epoch.

Henry, J. Patrick↗

NASA NTRS2006

Solar Wind Excitation of Pc5 Fluctuations in the Magnetosphere and on the Ground

The primary purpose of this paper is to show the strong link between solar wind compressional fluctuations in the 1-8 mHz frequency range and Pc5 fluctuations in the magnetosphere near the magnetopause, at geosynchronous orbit, over the poles, and on the ground. We focus on a time interval in March and April 2002 when there was a favorable alignment of satellites combined with ten high speed solar wind streams. We used the S3C Great Observatory: specifically, ACE and Wind in the solar wind, Geotail near the magnetopause, GOES 8 and 10 at geosynchronous orbit, Cluster over the poles, and CANOPUS/CARISMA ground stations near the footpoints of magnetic field lines connected to either the magnetopause or the GOES satellites. Using four examples and a statistical survey we show that magnetospheric Pc5 fluctuations exist regardless of IMF orientation and for a wide range of speeds and dynamic pressures; the amplitude and power of magnetospheric fluctuations depends primarily on the amplitude and power of solar wind dynamic pressure fluctuations. The driving and response frequency of these geoeffective fluctuations is in the range 0.5 - 4 mHz. The most striking magnetospheric response occurs when the solar wind speed, dynamic pressure, and dynamic pressure fluctuations all increase at approximately the same time, as frequently occurs near the leading edge of high speed streams. We show evidence of oscillating Poynting Flux at the magnetopause determined using Geotail data that both excites a FLR and propagates evanescently inward. These observations suggest that, at least for this time interval at spring equinox, the entry path is from the dayside equatorial magnetopause inward; multiple field line resonances may be excited from the magnetopause to geosynchronous orbit by propagating compressional waves, with the power decreasing inward away from the magnetopause.

Kessel, Ramona L.↗

NASA NTRS2000

Statistically Reliable 'Atomistic' Simulation of Sub 100 nm MOSFETs

A 3D 'atomistic' simulation technique to study random impurity induced threshold voltage lowering and fluctuations in sub 0. 1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level-Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

Asenov, Asen↗

NASA NTRS1972

Root mean square fluctuation of a weak magnetic field in an infinite medium of homogeneous stationary turbulence.

The generation of a magnetic field by statistically homogeneous, stationary velocity turbulence is considered. The generation of rms magnetic fluctuation is explicitly demonstrated in the limit of short turbulence correlation time. It is shown that the fluctuation associated with a growing or stationary mean field grows with time such that the ratio of the fluctuation and the square of the mean field tends to a steady value, which is a monotonically decreasing function of the growth rate of the mean field.

Low, B.-C.↗

NASA NTRS1953

On the Development of Turbulent Wakes from Vortex Streets

Wake development behind circular cylinders at Reynolds numbers from 40 to 10,000 was investigated in a low-speed wind tunnel. Standard hotwire techniques were used to study the velocity fluctuations. The Reynolds number range of periodic vortex shedding is divided into two distinct subranges. At R = 40 to 150, called the stable range, regular vortex streets are formed and no turbulent motion is developed. The range R = 150 to 300 is a transition range to a regime called the irregular range, in which turbulent velocity fluctuations accompany the periodic formation of vortices. The turbulence is initiated by laminar-turbulent transition in the free layers which spring from the separation points on the cylinder. This transition first occurs in the range R = 150 to 300. Spectrum and statistical measurements were made to study the velocity fluctuations. In the stable range the vortices decay by viscous diffusion. In the irregular range the diffusion is turbulent and the wake becomes fully turbulent in 40 to 50 diameters downstream. It was found that in the stable range the vortex street has a periodic spanwise structure. The dependence of shedding frequency on velocity was successfully used to measure flow velocity. Measurements in the wake of a ring showed that an annular vortex street is developed.

FLOW, SUBSONIC↗

NASA NTRS1954

On the Development of Turbulent Wakes from Vortex Streets

Wake development behind circular cylinders at Reynolds numbers from 40 to 10,000 was investigated in a low-speed wind tunnel. Standard hot-wire techniques were used to study the velocity fluctuations. The Reynolds number range of periodic vortex shedding is divided into two distinct subranges. At r=40 to 150, called the stable range, regular vortex streets are formed and no turbulent velocity fluctuations accompany the periodic formation of vortices. The range r=150 to 300 is a transition range to a regime called the irregular range, in which turbulent velocity fluctuations accompany the periodic formation of vortices. The turbulence is initiated by laminar-turbulent transition in the free layers which spring from the separation points on the cylinder. The transition first occurs in the range r=150 to 300. Spectrum and statistical measurements were made to study the velocity fluctuations.

Roshko, Anatol↗