Results for “Fractal modelling” — Page 8

NASA NTRS2004

Lunar and Planetary Science XXXV: Mars Volcanology and Tectonics

Reports from the session, "Mars Volcanology and Tectonics" include:Martian Shield Volcanoes; Estimating the Rheology of Basaltic Lava Flows; A Model for Variable Levee Formation Rates in an Active Lava Flow; Deflections in Lava Flow Directions Relative to Topography in the Tharsis Region: Indicators of Post-Flow Tectonic Motion; Fractal Variation with Changing Line Length: A Potential Problem for Planetary Lava Flow Identification; Burfellshraun:A Terrestrial Analogue to Recent Volcanism on Mars; Lava Domes of the Arcadia Region of Mars; Comparison of Plains Volcanism in the Tempe Terra Region of Mars to the Eastern Snake River Plains, Idaho with Implications for Geochemical Constraints; Vent Geology of Low-Shield Volcanoes from the Central Snake River Plain, Idaho: Lessons for Mars and the Moon; Field and Geochemical Study of Table Legs Butte and Quaking Aspen Butte, Eastern Snake River Plain, Idaho: An Analog to the Morphology of Small Shield Volcanoes on Mars; Variability in Morphology and Thermophysical Properties of Pitted Cones in Acidalia Planitia and Cydonia Mensae; A Volcano Composed of Light-colored Layered Deposits on the Floor of Valles Marineris; Analysis of Alba Patera Flows: A Comparison of Similarities and Differences Geomorphologic Studies of a Very Long Lava Flow in Tharsis, Mars; Radar Backscatter Characteristics of Basaltic Flow Fields: Results for Mauna Ulu, Kilauea Volcano, Hawaii;and Preliminary Lava Tube-fed Flow Abundance Mapping on Olympus Mons.

Source record↗

NASA NTRS1999

Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction. TRACE Investigators. TRAndolapril Cardiac Evaluation

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.

Non-NASA Center↗

NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM (atmospheric radiation measurement) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth observing system) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of 'radiative smoothing' of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. 'Offbeam' Lidar returns are now being used to estimate the cloud 'radiative Green's function' (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the 'Independent Pixel Approximation' or IPA. This and other measurements of 3D (three dimensional) transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international 'Intercomparison of 3D Radiation Codes' (I3RC) program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗

NASA NTRSDate not supplied

The Tables of Aerosol Optics (TAO) Project

The Table of Aerosol Optics (TAO) project is a community repository of optics computations (extinction, absorption, single-scatter albedo, lidar ratio, etc) that are useful for global models and remote sensing applications. TAO expands upon historical efforts (e.g., Hess et al., 1998) by building an open database that uses recent measurements and new computational techniques for non-spherical particles. The ‘open’ aspect of TAO is important, since the size distributions, hygroscopicities, refractive indices, and morphological recommendations of today will undoubtedly yield to different values in the future; the open framework of TAO allows scientists to keep adding new computations to the database as the science evolves. TAO is meant to be a community repository where specialists can put their computations for other scientists to use. So for instance, some groups are advancing new techniques that can accommodate complex fractal aggregates of black carbon, other groups are working on realistic irregular shapes for mineral dust, and different groups are updating the hygroscopicity of various aerosol types using new techniques. The TAO database gives these scientists a place to distribute their products. As TAO grows, modelers and remote sensing specialists will look to TAO as a place to find a wide variety of choices for testing. Meanwhile, global modelers can also use TAO to lobby for new tables that accommodate their needs. Eventually, TAO will provide mass extinction coefficients, mass absorption coefficients, lidar ratios, etc., at popular remote sensing and global modeling wavelengths (0.25-40 µm) for all pertinent species (sulfate, sea salt, BC, OC, BrC, dust, etc.). TAO will also accept computations for aerosol ‘type’ (e.g., biomass burning, urban, background, etc.) that may include regional and seasonal variability. Multiple tables may be created for each species or type to account for the multiple valid size distributions, hygroscopicities, complex refractive indices, and shapes that can be found in the literature.

Greg Schuster↗

NASA NTRSDate not supplied

The Tables of Aerosol Optics (TAO) Project

The Table of Aerosol Optics (TAO) project is a community repository of optics computations (extinction, absorption, single-scatter albedo, lidar ratio, etc) that are useful for global models and remote sensing applications. TAO expands upon historical efforts (e.g., Hess et al., 1998) by building an open database that uses recent measurements and new computational techniques for non-spherical particles. The ‘open’ aspect of TAO is important, since the size distributions, hygroscopicities, refractive indices, and morphological recommendations of today will undoubtedly yield to different values in the future; the open framework of TAO allows scientists to keep adding new computations to the database as the science evolves. TAO is meant to be a community repository where specialists can put their computations for other scientists to use. So for instance, some groups are advancing new techniques that can accommodate complex fractal aggregates of black carbon, other groups are working on realistic irregular shapes for mineral dust, and different groups are updating the hygroscopicity of various aerosol types using new techniques. The TAO database gives these scientists a place to distribute their products. As TAO grows, modelers and remote sensing specialists will look to TAO as a place to find a wide variety of choices for testing. Meanwhile, global modelers can also use TAO to lobby for new tables that accommodate their needs. Eventually, TAO will provide mass extinction coefficients, mass absorption coefficients, lidar ratios, etc., at popular remote sensing and global modeling wavelengths (0.25-40 µm) for all pertinent species (sulfate, sea salt, BC, OC, BrC, dust, etc.). TAO will also accept computations for aerosol ‘type’ (e.g., biomass burning, urban, background, etc.) that may include regional and seasonal variability. Multiple tables may be created for each species or type to account for the multiple valid size distributions, hygroscopicities, complex refractive indices, and shapes that can be found in the literature.

Elisabeth Andrews↗

NASA NTRSDate not supplied

The Tables of Aerosol Optics (TAO) Project

The Table of Aerosol Optics (TAO) project is a community repository of optics computations (extinction, absorption, single-scatter albedo, lidar ratio, etc) that are useful for global models and remote sensing applications. TAO expands upon historical efforts (e.g., Hess et al., 1998) by building an open database that uses recent measurements and new computational techniques for non-spherical particles. The ‘open’ aspect of TAO is important, since the size distributions, hygroscopicities, refractive indices, and morphological recommendations of today will undoubtedly yield to different values in the future; the open framework of TAO allows scientists to keep adding new computations to the database as the science evolves. TAO is meant to be a community repository where specialists can put their computations for other scientists to use. So for instance, some groups are advancing new techniques that can accommodate complex fractal aggregates of black carbon, other groups are working on realistic irregular shapes for mineral dust, and different groups are updating the hygroscopicity of various aerosol types using new techniques. The TAO database gives these scientists a place to distribute their products. As TAO grows, modelers and remote sensing specialists will look to TAO as a place to find a wide variety of choices for testing. Meanwhile, global modelers can also use TAO to lobby for new tables that accommodate their needs. Eventually, TAO will provide mass extinction coefficients, mass absorption coefficients, lidar ratios, etc., at popular remote sensing and global modeling wavelengths (0.25-40 µm) for all pertinent species (sulfate, sea salt, BC, OC, BrC, dust, etc.). TAO will also accept computations for aerosol ‘type’ (e.g., biomass burning, urban, background, etc.) that may include regional and seasonal variability. Multiple tables may be created for each species or type to account for the multiple valid size distributions, hygroscopicities, complex refractive indices, and shapes that can be found in the literature.

Greg Schuster↗

NASA NTRS1999

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape,spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars. Ongoing field programs such as Department of Energy's Atmospheric Radiation Measurement (DoE/ARM) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS-AM1 instruments which will provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", G,which depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple IPA estimates of cloud radiative properties. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of adiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international "Intercomparison of 3D Radiation Codes" or I3RC, program is beginning to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.qsfc.nasa.crov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large- scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate.

Cahalan, Robert F.↗

NASA NTRS1988

SiS in Orion-KL - Evidence for 'outflow' chemistry

The J = 6-5 and J = 5-4 rotational transitions at 91 and 109 GHz toward Orion-KL provide evidence for the presence of SiS at an LSR velocity of 7.5 km/sec and with a half-width at zero power of 36 km/sec. The estimated current density corresponds to a fractal abundance of about 4 x 10 to the -9th. The implied SiO/SiS ratio of about 60 is close to the cosmic O/S ratio of about 40 and is much less than that predicted by ion-molecule models. Other unidentified lines near 91 and 109 have been identified.

Ziurys, L. M.↗

NASA NTRS1991

Three-dimensional kinematic reconnection of plasmoids

The kinematic reconnection model of Lau and Finn (1990) is applied in a theoretical investigation of three-dimensional plasmoid morphology, as seen in the solar corona and earth magnetotail. The derivation of the governing equations is outlined; long, short, and periodic plasmoid models are developed; and the evolution of the stable and unstable manifolds in these models is presented graphically. It is inferred that sheet currents and tangential discontinuities can form on surfaces topologically identical to those where Delta(phi) about equal to Delta(z) singularities occur in the kinematic reconnection model, and can be broadened in a similar way by nonideal effects. Two such surfaces exist in long plasmoids, and also in short plasmoids in the presence of finite resistivity; the intertwined surfaces characteristic of the periodic plasmoid form a fractal set but merge in the presence of finite resistivity, producing structures similar to those proposed by the sheet-current theory of Parker (1983).

Lau, Yun-Tung↗

NASA NTRS1991

The accumulation and structure of comets

The paper reviews evidence for the accumulation of the terrestrial planets and comets from solid grains, with emphasis on the various proposals for the formation of cometary nuclei. With three exceptions, all hypotheses conclude or imply that a single compact object forms. Several hypotheses start with Goldreich-Ward-type gravitational instabilities. The collapse for this case also occurs at low velocities in the cm/s to m/s range. Experiment and theory show that under these conditions, low-density, filamentary clusters form that are fractal aggregates with a fractal dimension approximately equal to 2. In order to form cometary nuclei, the initial temperature must be about 50 K and not undergo a significant temperature rise during the accumulation process. The calculations show that accumulation will occur at low temperatures. Models of cometary nuclei are reviewed, and a simple model of the structure that results fom the accumulation of fluffy aggregates is described.

Donn, Bertram↗

NASA NTRS2008

Field Observations of Soil Moisture Variability across Scales

In this study, over 36,000 ground-based soil moisture measurements collected during the SGP97, SGP99, SMEX02, and SMEX03 field campaigns were analyzed to characterize the behavior of soil moisture variability across scales. The field campaigns were conducted in Oklahoma and Iowa in the central USA. The Oklahoma study region is sub-humid with moderately rolling topography, while the Iowa study region is humid with low-relief topography. The relationship of soil moisture standard deviation, skewness and the coefficient of variation versus mean moisture content was explored at six distinct extent scales, ranging from 2.5 m to 50 km. Results showed that variability generally increases with extent scale. The standard deviation increased from 0.036 cm3/cm3 at the 2.5-m scale to 0.071 cm3/cm3 at the 50-km scale. The log standard deviation of soil moisture increased linearly with the log extent scale, from 16 m to 1.6 km, indicative of fractal scaling. The soil moisture standard deviation versus mean moisture content exhibited a convex upward relationship at the 800-m and 50-km scales, with maximum values at mean moisture contents of roughly 0.17 cm3/cm3 and 0.19 cm3/cm3, respectively. An empirical model derived from the observed behavior of soil moisture variability was used to estimate uncertainty in the mean moisture content for a fixed number of samples at the 800-m and 50-km scales, as well as the number of ground-truth samples needed to achieve 0.05 cm3/cm3 and 0.03 cm3/cm3 accuracies. The empirical relationships can also be used to parameterize surface soil moisture variations in land surface and hydrological models across a range of scales. To our knowledge, this is the first study to document the behavior of soil moisture variability over this range of extent scales using ground-based measurements. Our results will contribute not only to efficient and reliable satellite validation, but also to better utilization of remotely sensed soil moisture products for enhanced modeling and prediction.

Famiglietti, James S.↗

NASA NTRS2020

Improved LOLA Elevation Maps for South Pole Landing Sites: Error Estimates and Their Impact on Illumination Conditions

We present new high-resolution topographic models of 4 high-priority lunar south pole landing sites based exclusively on the laser altimetry data acquired by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter. By iteratively adjusting the LOLA tracks to the LOLA-based digital elevation model (LDEM) in a self-consistent fashion, we reduce the orbital geolocation errors by over a factor of 10 such that the new ground track geolocation uncertainty is ~10–20 cm horizontally and ~2–4 cm vertically over each 16 × 16 km region. These new and improved 5 m/pix LDEMs will be useful to constrain higher-resolution topographic models derived from imagery, which are not as well controlled geodetically and which can be hindered by shadows. We developed a method to estimate surface height uncertainty in the new LDEMs, which accounts for the reduced orbital errors and interpolation errors by assuming a fractal behavior for the short-scale topography. The LDEM surface height and slope uncertainties have typical RMS values of ~0.30–0.50 m and ~1.5–2.5°, respectively. Finally, we examine how height uncertainties propagate to variations in horizon elevation and thus the predicted illumination conditions at these polar latitudes, and we show how this error characterization can inform landing site studies.

Michael K Barker↗

NASA NTRS1987

Nonlinear dynamics, fractals, cardiac physiology and sudden death

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.↗

NASA NTRS1988

Characterizing forest ecosystem dynamics through modelling and remote sensing observations

To gain a better understanding of northern/boreal forest dynamics over a range of spatial and temporal scales, an approach to integrate models of forest growth, soil processes and radiative transfer with remote sensing observations was developed. The integrated model and remote sensing can be used to examine descriptors of ecosystem dynamics. To examine the scaling of vegetation pattern from the local to the regional domain, distributions of area and perimeters of vegetation community associations were determined from satellite and aircraft images. Relationships between computed fractal dimensions (1.5 to 1.8) and succession history for managed and unmanaged areas are being explored.

Ranson, K. J.↗

NASA NTRS1999

Effective Forces Between Colloidal Particles

Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.

Tehver, Riina↗

NASA NTRS1990

Low-dimensional chaos in magnetospheric activity from AE time series

The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.

Vassiliadis, D. V.↗

NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗

NASA NTRS1994

Beyond maximum entropy: Fractal pixon-based image reconstruction

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.

Puetter, R. C.↗