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All sourcesNASA NTRSDOE OSTI
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 NTRS2015

Empirical Relationships Between Optical Properties and Equivalent Diameters of Fractal Soot Aggregates at 550 Nm Wavelength.

Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.

deuterium fluorides↗
NASA NTRS1997

Statistical Modeling of Landscape Pattern and the Effects of Coarse Spatial Resolution

Analysis of classified satellite imagery was conducted to characterize errors in estimates of area based on coarse resolution satellite imagery which are due to distortions in sizes of small fragments, and to explore the feasibility of correcting for these errors using a statistical modeling approach. Sizes of bodies of open water on European Remote-Sensing (ERS-1) synthetic aperture radar (SAR) and fire scars on Landsat Multispectral Scanner (MSS) imagery were measured using geographic information system (GIS) software. Statistical analysis of the smaller scars and ponds as observed with this imagery of relatively fine resolution demonstrated that the distribution of the sizes could be modeled by either of two types of statistical distributions-a power distribution related to fractal processes or a simple exponential distribution. A comparison of the size distribution of small burn scars as observed with Landsat with the distribution observed with the much coarser Advanced Very High Resolution Radiometer (AVHRR) imagery revealed effects of coarse resolution, each of which were associated with a particular size range, and whose net effect accounted for the bias in total burn area due to coarse spatial resolution. Size dependent area correction procedures are therefore feasible. A statistical modeling approach to area estimation, based models of the underlying and observed size distributions of fragments in the scene, may lead to a procedure which requires little or no ancillary data.

Hlavka, C. A.↗
NASA NTRS1986

Lacunarity and intermittency in fluid turbulence

It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).

Smith, L. A.↗
NASA NTRS2003

Stochastic Models of Tropical Rain-Rate Fields

Because of the extreme variability of rain rate in space and time and the difficulties with remote sensing methods of measuring rain rates, accurate determination of rainfall over large areas and time periods has long been a problem for hydrologists, meteorogists, and climatologists. A number of statistical models of rain have been developed in order to investigate the impact of rain variability on satellite remote sensing methods, validation of satellite rain products, and generation of rain maps with accompanying error estimates. These models may be useful in examining 'sub-grid scale' issues in representing precipitation in numerical mdoels. A stochastic model will first be described which can generate time-dependent high-resolution spatial rain fields with space and time correlations similar to those seen in rain data, as well as representing the presence of areas with zero rain rate and log-normally distributed rain rates where there is rain. A simpler model derived from this, formulated in the spectral domain, seems to imply fractal-like rain statistics at small scales when fit to rain data.

Bell, Thomas L.↗
NASA NTRS1988

Cluster-cluster correlations and constraints on the correlation hierarchy

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes in hierachical clustering models. The distributions which saturate these constraints are the Rayleigh-Levy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.

Hamilton, A. J. S.↗
NASA NTRS1996

Statistical Models of Landscape Pattern and the Effects of Coarse Resolution of Satellite Imagery on Estimation of Area

Analysis of classified satellite imagery was conducted to characterize errors in estimates of area based on coarse resolution satellite imagery which are due to distortions in sizes of small fragments, and to explore the feasibility of correcting for these errors using a statistical modeling approach. Sizes of bodies of open water on ERS-1 SAR and fire scars on Landsat MSS imagery were measured. Statistical analysis of the smaller scars and ponds as observed with this imagery of relatively fine resolution demonstrated that the distribution of the sizes could be modeled by either of two types of statistical distributions - a power distribution related to fractal processes or a simple exponential distribution. Comparison of the distribution of small bum scars as observed with Landsat to the distribution observed with AVHRR showed distortions due to the coarse spatial resolution of AVHRR caused a net overestimation of bum area. This bias was primarily caused by detection in 2 or 3 AVHRR pixels of bums whose true size was on the order of an AVHRR pixel.

Hlavka, Christine A.↗
NASA NTRS1999

Fractal fluctuations in cardiac time series

Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.

NASA Discipline Cardiopulmonary↗
NASA NTRS2009

Multiscale Computer Simulation of Tensile and Compressive Strain in Polymer- Coated Silica Aerogels

While the low thermal conductivities of silica aerogels have made them of interest to the aerospace community as lightweight thermal insulation, the application of conformal polymer coatings to these gels increases their strength significantly, making them potentially useful as structural materials as well. In this work we perform multiscale computer simulations to investigate the tensile and compressive strain behavior of silica and polymer-coated silica aerogels. Aerogels are made up of clusters of interconnected particles of amorphous silica of less than bulk density. We simulate gel nanostructure using a Diffusion Limited Cluster Aggregation (DLCA) procedure, which produces aggregates that exhibit fractal dimensions similar to those observed in real aerogels. We have previously found that model gels obtained via DLCA exhibited stress-strain curves characteristic of the experimentally observed brittle failure. However, the strain energetics near the expected point of failure were not consistent with such failure. This shortcoming may be due to the fact that the DLCA process produces model gels that are lacking in closed-loop substructures, compared with real gels. Our model gels therefore contain an excess of dangling strands, which tend to unravel under tensile strain, producing non-brittle failure. To address this problem, we have incorporated a modification to the DLCA algorithm that specifically produces closed loops in the model gels. We obtain the strain energetics of interparticle connections via atomistic molecular statics, and abstract the collective energy of the atomic bonds into a Morse potential scaled to describe gel particle interactions. Polymer coatings are similarly described. We apply repeated small uniaxial strains to DLCA clusters, and allow relaxation of the center eighty percent of the cluster between strains. The simulations produce energetics and stress-strain curves for looped and nonlooped clusters, for a variety of densities and interaction parameters.

Good, Brian↗
NASA NTRS2019

Planetary Rover Simulation for Lunar Exploration Missions

When planning planetary rover missions it is useful to develop intuition and skills driving in, quite literally, alien environments before incurring the cost of reaching said locales. Simulators make it possible to operate in environments that have the physical characteristics of target locations without the expense and overhead of extensive physical tests. To that end, NASA Ames and Open Robotics collaborated on a Lunar rover driving simulator based on the open source Gazebo simulation platform and leveraging ROS (Robotic Operating System) components. The simulator was integrated with research and mission software for rover driving, system monitoring, and science instrument simulation to constitute an end-to-end Lunar mission simulation capability. Although we expect our simulator to be applicable to arbitrary Lunar regions, we designed to a reference mission of prospecting in polar regions. The harsh lighting and low illumination angles at the Lunar poles combine with the unique reflectance properties of Lunar regolith to present a challenging visual environment for both human and computer perception. Our simulator placed an emphasis on high fidelity visual simulation in order to produce synthetic imagery suitable for evaluating human rover drivers with navigation tasks, as well as providing test data for computer vision software development.In this paper, we describe the software used to construct the simulated Lunar environment and the components of the driving simulation. Our synthetic terrain generation software artificially increases the resolution of Lunar digital elevation maps by fractal synthesis and inserts craters and rocks based on Lunar size-frequency distribution models. We describe the necessary enhancements to import large scale, high resolution terrains into Gazebo, as well as our approach to modeling the visual environment of the Lunar surface. An overview of the mission software system is provided, along with how ROS was used to emulate flight software components that had not been developed yet. Finally, we discuss the effect of using the high-fidelity synthetic Lunar images for visual odometry. We also characterize the wheel slip model, and find some inconsistencies in the produced wheel slip behaviour.

Allan, Mark↗
NASA NTRS1985

Post-instability behavior of solids

The necessity of model reformulation in elasticity results from the failure of hyperbolicity of the governing equations of motion for classical models. The reformulation is based upon the introduction of additional kinematical microstructures in the form of multivalued displacement and velocity field (or fractal functions) which are generated by the mechanism of the instability. The small scale motions describing this microstructure interact with the original large scale motion and restore the hyperbolicity of new governing equations of motion. The applications of the reformulated models to the problem of vibrational control and impact energy absorption are discussed.

Zak, M.↗
NASA NTRS2004

A Comparison of Local Variance, Fractal Dimension, and Moran's I as Aids to Multispectral Image Classification

The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.

Emerson, Charles W.↗
NASA NTRS1990

Fractal dimension of bioconvection patterns

Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.

Noever, David A.↗
NASA NTRS1984

The distribution of catchment coverage by stationary rainstorms

The occurrence of wetted rainstorm area within a catchment is modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed in space and whose areas are fractals. The two Poisson parameters and hence the first two moments of the wetted fraction are derived in terms of catchment average characteristics of the (observable) station precipitation. The model is used to estimate spatial properties of tropical air mass thunderstorms on six tropical catchments in the Sudan.

Eagleson, P. S.↗
NASA NTRS1989

Predictability of weather and climate in a coupled ocean-atmosphere model: A dynamical systems approach

A dynamical systems approach is used to quantify the instantaneous and time-averaged predictability of a low-order moist general circulation model. Specifically, the effects on predictability of incorporating an active ocean circulation, implementing annual solar forcing, and asynchronously coupling the ocean and atmosphere are evaluated. The predictability and structure of the model attractors is compared using the Lyapunov exponents, the local divergence rates, and the correlation, fractal, and Lyapunov dimensions. The Lyapunov exponents measure the average rate of growth of small perturbations on an attractor, while the local divergence rates quantify phase-spatial variations of predictability. These local rates are exploited to efficiently identify and distinguish subtle differences in predictability among attractors. In addition, the predictability of monthly averaged and yearly averaged states is investigated by using attractor reconstruction techniques.

Nese, Jon M.↗
NASA NTRS1999

MOLA-derived Roughness Data Used to Predict Surface Scattering for Mars Subsurface Radar Sounding

The Mars Express orbiter, to be launched by the European Space Agency in 2003, will carry a low-frequency radar sounding instrument, MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding). The primary goal of MARSIS is to map the distribution of water, both solid and (if present) liquid, in the upper several km of the martian crust. Detecting discontinuities in the crust, such as an ice-water transition, presents many challenges for a Mars orbital radar sounder. One challenge that must be overcome is the presence of radar scattering (echoes) from the surface of Mars, expected to be detected by the sounder antennas at the same time as any echoes aris-ing from subsurface interfaces. As the transmitted spherical wavefront spreads within the crust of Mars,. it also interacts with surface topography at off-nadir positions, creating a "clutter" signal that can mask the subsurface echoes. The MARSIS instrument will utilize Doppler filtering to limit the off-nadir clutter in the along-track direction, and a nadir-null secondary antenna to identify strong off-nadir clutter from the cross-track direction. To evaluate the effects of off-nadir surface clutter and the capability of these schemes to reduce the clutter, it is necessary to predict the range of scattering behavior that may be expected from martian surface topography. In this paper, we utilize Mars Orbital Laser Altimeter (MOLA) data from the current Mars Global Surveyor mission to characterize the topographic roughness of a variety of martian terrain types, at scales relevant to the MARSIS clutter problem. Segments of MOLA altimetry profiles are reduced to the topographic parameters rms slope and fractal dimension, which then are used as inputs to a near-nadir radar scattering model to predict the strength of the clutter signal. Additional information is contained in the original extended abstract.

Plaut, J. J.↗
DOE OSTI2020

The Sensitivity of Hyporheic Exchange to Fractal Properties of Riverbeds

Hyporheic exchange in riverbeds is driven by current-bed topography interactions. Because riverbeds exhibit topographic roughness across scales, from individual grains to bedforms and bars, they can exhibit fractal patterns. This study analyzed the influence of fractal properties of riverbed topography on hyporheic exchange. A set of synthetic fractal riverbeds with different scaling statistics was used as inputs to sequentially coupled numerical simulations of turbulent channel flow and hyporheic flow. In the analysis, the maximum power spectrum (dune size) and the fractal dimension (topographic complexity) were considered as independent variables and we then investigated how interfacial fluxes and hyporheic travel times are functionally related to these variables. As the maximum power spectrum increases (i.e., dune height to flow depth ratio), the average interfacial flux increases logarithmically whereas it increases exponentially with an increase in fractal dimension. Hyporheic exchange is more sensitive to additional roughness (larger fractal dimensions) than to bedform size (larger maximum power). Our results imply that fractal properties of riverbeds are crucial to predicting hyporheic exchange. The predictive relationships we propose could be integrated with reduced complexity, large-scale models. Further, they can also be used to design artificial topographies that target hyporheic ecosystem services.

54 ENVIRONMENTAL SCIENCES↗