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Results for “multifractality”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. By present experimental technology in solar wind measurements, we cannot directly measure the real volumetric dissipation rate, epsilon(t), but are constrained to represent it by surrogating the energy flux near the dissipation range at the proton gyro scales. There is evidence for the multifractal nature of the so defined dissipation field epsilon(t), a result derived from the scaling exponents of its statistical q-th order moments. The related generalized dimension D(q) has been determined and reveals that the dissipation field has a multifractal structure. which is not compatible with a scale-invariant cascade. The associated multifractal spectrum f(alpha) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D(q) can, for turbulence in high-speed streams, be fitted well by the functional dependence of the p-model with a comparatively large parameter, p = 0.87. indicating a strongly intermittent multifractal energy cascade. The experimental value for D(p)/3, if used in the scaling exponent s(p) of the velocity structure function, gives an exponent that can describe some of the observations. The scaling exponent mu of the auto correlation function of epsilon(t) has also been directly evaluated. It has the value of 0.37. Finally. the mean dissipation rate was determined, which could be used in solar wind heating models.

Marsch, E.↗
NASA NTRS1992

Multifractal structure of the magnetic field and plasma in recurrent streams at 1 AU

The existence of multifractal structure in the fluctuations of the magnetic field strength, temperature, and density in the recurrent flows at 1 AU is demonstrated. The multifractal scaling is observed over the range of periods from 2 to 32 hr for the magnetic field and density and from 2 to 16 hr for the temperature. The lower cutoff of 2 hr is related to the use of hour averages; it does not have physical significance. The upper cutoff of 32 hr (16 hr) represents the transition to the mesoscale regime in which the fluctuations are determined by the stream structure. Thus the multifractal structure represents fluctuations superimposed on the corotating stream profile and the heliospheric plasma sheet profile. The multifractal structure is interpreted as a texture superimposed on the mesoscale profiles, the structure of the texture being related to the mesoscale structure itself.

Burlaga, L. F.↗
NASA NTRS1992

Multifractals in the solar wind

Multifractals have been observed in the solar wind in several contexts. The velocity fluctuations observed by Voyager 2 near 8 AU have the structure of intermittent turbulence which has multifractal scaling symmetry. The velocity fluctuations in corotating streams at 1 AU and near 6 AU also have multifractal structure, and the structure evolves significantly between 1 AU and 6 AU. Multifractal scaling has also been observed in the magnetic field strength, density and temperature in recurrent streams at 1 AN and in large-scale fluctuations the magnetic field strength at 25 AU.

Burlaga, L. F.↗
NASA NTRS1993

Cosmic-ray modulation, merged interaction regions, and multifractals

The large-scale heliospheric magnetic field fluctuations and their effects on cosmic rays are discussed. Voyager 2 observations from 1983.0 to 1989.6 are used as input to the model of Perko and Burlaga (1992) to show that the few largest merged interaction regions (MIRs) provide essential details in the cosmic-ray intensity (CRI) profile. It is demonstrated that the largest MIRs determine the basic structure of the radial gradients of the CRI. It is shown that the magnetic field strength during the period 1983.0-1989.6 does have a multifractal structure, but that there are different multifractal structures in the three intervals 1983.0-1985.0, 1985.0-1987.5, and 1987.5-1989.6. The multifractal structure can be described by simple functions, the multifractal spectra. These analytical descriptions can be used to generate realizations of the heliospheric magnetic field with the same statistical properties as those observed by Voyager 2. Thus, the starting point is provided for realistic global statistical models of the 11-yr variation of the Galactic CRI.

Burlaga, L. F.↗
NASA NTRS1999

Multifractality in human heartbeat dynamics

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

Non-NASA Center↗
NASA NTRS1987

Spatial correlations in multifractals

Spatial correlations within multifractals or fractal measures are considered. It is shown how scaling dimensions can be used to predict scaling laws for spatial correlation functions. It is concluded that the overlaid singularity picture does not provide an adequate description of the spatial properties of multifractals, and that blob concepts seem to provide a much more suitable description of multifractal correlations.

Cates, M. E.↗
NASA NTRS1991

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Ukeiley, L.↗
NASA NTRS1991

Multifractal structure of speed fluctuations in recurrent streams at 1 AU and near 6 AU

This paper demonstrates the existence of multifractal structure in the velocity fluctuations associated with recurrent streams at 1 AU and near 6 AU. There is a significant evolution of the multifractal spectrum from 1 AU to 6 AU. At 1 AU the fluctuations on all scales in the indicated range are related to the local speed gradients associated with the stream structure. Near 6 AU the multifractal structure of the speed fluctuations approaches the universal form for intermittent turbulence for moments when q is greater than 5, and it has approximately the value expected for a set of discontinuities for q = 2.

Burlaga, L. F.↗
NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗
NASA NTRS1999

Concept of Fractal Dimension use of Multifractal Cloud Liquid Models Based on Real Data as Input to Monte Carlo Radiation Models

The purpose of this paper is discuss the concept of fractal dimension; multifractal statistics as an extension of this; the use of simple multifractal statistics (power spectrum, structure function) to characterize cloud liquid water data; and to understand the use of multifractal cloud liquid water models based on real data as input to Monte Carlo radiation models of shortwave radiation transfer in 3D clouds, and the consequences of this in two areas: the design of aircraft field programs to measure cloud absorptance; and the explanation of the famous "Landsat scale break" in measured radiance.

Wiscombe, W.↗
NASA NTRS2010

Downscaling Soil Moisture in the Southern Great Plains Through a Calibrated Multifractal Model for Land Surface Modeling Applications

Accounting for small-scale spatial heterogeneity of soil moisture (theta) is required to enhance the predictive skill of land surface models. In this paper, we present the results of the development, calibration, and performance evaluation of a downscaling model based on multifractal theory using aircraft!based (800 m) theta estimates collected during the southern Great Plains experiment in 1997 (SGP97).We first demonstrate the presence of scale invariance and multifractality in theta fields of nine square domains of size 25.6 x 25.6 sq km, approximately a satellite footprint. Then, we estimate the downscaling model parameters and evaluate the model performance using a set of different calibration approaches. Results reveal that small-scale theta distributions are adequately reproduced across the entire region when coarse predictors include a dynamic component (i.e., the spatial mean soil moisture ) and a stationary contribution accounting for static features (i.e., topography, soil texture, vegetation). For wet conditions, we found similar multifractal properties of soil moisture across all domains, which we ascribe to the signature of rainfall spatial variability. For drier states, the theta fields in the northern domains are more intermittent than in southern domains, likely because of differences in the distribution of vegetation coverage. Through our analyses, we propose a regional downscaling relation for coarse, satellite-based soil moisture estimates, based on ancillary information (static and dynamic landscape features), which can be used in the study area to characterize statistical properties of small-scale theta distribution required by land surface models and data assimilation systems.

Mascaro, Giuseppe↗
NASA NTRS1989

Multifractal spectra in shear flows

Numerical simulations of three-dimensional homogeneous shear flow and fully developed channel flow, are used to calculate the associated multifractal spectra of the energy dissipation field. Only weak parameterization of the results with the nondimensional shear is found, and this only if the flow has reached its asymptotic development state. Multifractal spectra of these flows coincide with those from experiments only at the range alpha less than 1.

Keefe, L. R.↗
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 NTRS1988

Multifractal spectra in homogeneous shear flow

Employing numerical simulations of 3-D homogeneous shear flow, the associated multifractal spectra of the energy dissipation, scalar dissipation and vorticity fields were calculated. The results for (128) cubed simulations of this flow, and those obtained in recent experiments that analyzed 1- and 2-D intersections of atmospheric and laboratory flows, are in some agreement. A two-scale Cantor set model of the energy cascade process which describes the experimental results from 1-D intersections quite well, describes the 3-D results only marginally.

Deane, A. E.↗
NASA NTRS1999

Turbulent Concentration of Chondrules: Size Distribution and Multifractal Scaling

Size-selective concentration of particles in 3D turbulence may be related to collection of chondrules and other constituents into primitive bodies in a weakly turbulent protoplanetary nebula. In the terrestrial planet region, both the characteristic size and narrow size distribution of chondrules are explained, whereas "fluffier" particles would be concentrated in lower density, or more intensely turbulent, regions of the nebula. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a dose tie to the turbulent cascade process. This scaling behavior allows predictions of the concentration probabilities to be made in the protoplanetary nebula, which are so large (> 10(exp 3) - 10(exp 4)) that further studies must be made of the role of mass loading.

Cuzzi, Jeffrey N.↗
NASA NTRS2004

Self-Organized Criticality, Multifractals, and Intermittent Turbulence in Earth's Magnetotail

We have achieved all the goals stated in our grant proposal in collaboration with Dr. C.C. Wu of the University of California at Los Angeles. Specifically, these include: The understanding of the complexity induced nonlinear spatiotemporal structures and the coexisting propagating modes. The development of plasma resonances and coherent structures in space plasmas. The study of fluctuation-induced nonlinear instabilities and their role in the reconfiguration of magnetic topologies in the magnetotail. The development of "anisotropic three-dimensional complexity" in the plasma sheet due to localized merging and interactions of the magnetic coherent structures and associated topological phase transitions. The understanding of the intermittent turbulence and energization process of the observed Bursty Bulk Flows (BBF's) in the Earth s magnetotail. The acceleration of ions due to the intermittent turbulence of propagating arid nonpropagating fluctuations In the following, we include lists of our published papers, invited talks, and professional activities. A detailed description of our accomplished research results is given in Section IV.

Chang, Tom↗