Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fractal dimension”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

A Hierarchical Approach to Fracture Mechanics

Recent research conducted under NASA LaRC's Creativity and Innovation Program has led to the development of an initial approach for a hierarchical fracture mechanics. This methodology unites failure mechanisms occurring at different length scales and provides a framework for a physics-based theory of fracture. At the nanoscale, parametric molecular dynamic simulations are used to compute the energy associated with atomic level failure mechanisms. This information is used in a mesoscale percolation model of defect coalescence to obtain statistics of fracture paths and energies through Monte Carlo simulations. The mathematical structure of predicted crack paths is described using concepts of fractal geometry. The non-integer fractal dimension relates geometric and energy measures between meso- and macroscales. For illustration, a fractal-based continuum strain energy release rate is derived for inter- and transgranular fracture in polycrystalline metals.

Saether, Erik↗
NASA NTRS1993

Size distributions in two porous chondritic micrometeorites

Quantitative size measurements of granular units (GUs), and nm-sized minerals in these units, in two porous chondritic micrometeorites are investigated. The matrix of these micrometeorites consist of loosely packed, 0.1 micron-sized, GUs. These objects were a major component of the solar nebula dust that accreted into protoplanets. The matrix in micrometeorite W7010*A2 has a fractal dimension with a small coefficient that supports efficient sticking of carbon-rich GUs during accretion. The fractal nature of the matrix provides a way to calculate the density using the aggregate size. The resulting very low density for porous chondritic micrometeorites is 0.08-0.14 g/cu cm, which supports the view that they are the solid debris from unconsolidated solar system bodies. Chondritic GUs contain ultrafine olivines, pyroxenes, and sulfides, embedded in hydrocarbons and amorphous carbons. Nanocrystals in the micrometeorites W7010*A2 and U2015*B show log normal size distributions. The high incidence of disk-shaped grains, a changeover from disk-shaped to euhedral grains, the unevolved nature of the size distributions, and multiple populations for grains less than 127 nm in size, are consistent with continuous postaccretion nucleation and growth in amorphous GUs, including coarsening via Ostwald ripening.

Rietmeijer, Frans J. M.↗
NASA NTRS1993

Fractal geometry of some Martian lava flow margins: Alba Patera

Fractal dimension for a few lava flow margins on the gently sloping flanks of Alba Patera were measured using the structured walk method. Fractal behavior was observed at scales ranging from 20 to 100 pixels. The upper limit of the linear part of log(margin length) vs. log(scale) profile correlated well to the margin length. The lower limit depended on resolution and flow properties.

Kauhanen, K.↗
NASA NTRS2012

VESGEN Software for Mapping and Quantification of Vascular Regulators

VESsel GENeration (VESGEN) Analysis is an automated software that maps and quantifies effects of vascular regulators on vascular morphology by analyzing important vessel parameters. Quantification parameters include vessel diameter, length, branch points, density, and fractal dimension. For vascular trees, measurements are reported as dependent functions of vessel branching generation. VESGEN maps and quantifies vascular morphological events according to fractal-based vascular branching generation. It also relies on careful imaging of branching and networked vascular form. It was developed as a plug-in for ImageJ (National Institutes of Health, USA). VESGEN uses image-processing concepts of 8-neighbor pixel connectivity, skeleton, and distance map to analyze 2D, black-and-white (binary) images of vascular trees, networks, and tree-network composites. VESGEN maps typically 5 to 12 (or more) generations of vascular branching, starting from a single parent vessel. These generations are tracked and measured for critical vascular parameters that include vessel diameter, length, density and number, and tortuosity per branching generation. The effects of vascular therapeutics and regulators on vascular morphology and branching tested in human clinical or laboratory animal experimental studies are quantified by comparing vascular parameters with control groups. VESGEN provides a user interface to both guide and allow control over the users vascular analysis process. An option is provided to select a morphological tissue type of vascular trees, network or tree-network composites, which determines the general collections of algorithms, intermediate images, and output images and measurements that will be produced.

Parsons-Wingerter, Patricia A.↗
NASA NTRS1990

Analysis of stratocumulus cloud fields using LANDSAT imagery: Size distributions and spatial separations

Stratocumulus cloud fields in the FIRE IFO region are analyzed using LANDSAT Thematic Mapper imagery. Structural properties such as cloud cell size distribution, cell horizontal aspect ratio, fractional coverage and fractal dimension are determined. It is found that stratocumulus cloud number densities are represented by a power law. Cell horizontal aspect ratio has a tendency to increase at large cell sizes, and cells are bi-fractal in nature. Using LANDSAT Multispectral Scanner imagery for twelve selected stratocumulus scenes acquired during previous years, similar structural characteristics are obtained. Cloud field spatial organization also is analyzed. Nearest-neighbor spacings are fit with a number of functions, with Weibull and Gamma distributions providing the best fits. Poisson tests show that the spatial separations are not random. Second order statistics are used to examine clustering.

Welch, R. M.↗
NASA NTRS1996

Lava Flow Dynamics

This grant originally had four major tasks, all of which were addressed to varying extents during the course of the research: (1) Measure the fractal dimensions of lava flows as a function of topography, substrate, and rheology; (2) The nature of lava tube systems and their relation to flow fields; (3) A quantitative assessment of lava flow dynamics in light of the fractal nature of lava flow margins; and (4) Development and application of a new remote sensing tool based on fractal properties. During the course of the research, the project expanded to include the following projects: (1) A comparison of what we can-learn from remote sensing studies of lava flow morphology and from studies of samples of lava flows; (2) Study of a terrestrial analog of the nakhlites, one of the groups of meteorites from Mars; and (3) Study of the textures of Hawaiian basalts as an aid in understanding the dynamics (flow rates, inflation rates, thermal history) of flow interiors. In addition, during the first year an educational task (development and writing of a teacher's guide and activity set to accompany the lunar sample disk when it is sent to schools) was included.

Taylor, G. Jeffrey↗
NASA NTRS1991

Fractal interfaces and product generation in the two dimensional mixing layer

The dependence of product generation on Peclet and Reynolds numbers in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is related theoretically to the fractal dimension of the passive scalar interfaces. This relation is verified using product generation measurements and dimensions derived from a standard box counting technique. A transition from a low initial dimension to a higher one of approximately 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transitions, either in the spectra of the vorticity field or in the mixing behavior, are found for Reynolds numbers up to 90,000.

Jimenez, Javier↗
NASA NTRS1990

A fractal transition in the two dimensional shear layer

The dependence of product generation with the Peclet and Reynolds number in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is used to compute the fractal dimension of passive scalar interfaces. A transition from a low dimension of 4/3 to a higher one of 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transition is found for Reynolds numbers up to 20,000.

Jimenez, Javier↗
NASA NTRS1992

Lava flows are fractals

Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.

Bruno, B. C.↗
NASA NTRS2007

A Small Angle Scattering Sensor System for the Characterization of Combustion Generated Particulate

One of the critical issues for the US space program is fire safety of the space station and future launch vehicles. A detailed understanding of the scattering signatures of particulate is essential for the development of a false alarm free fire detection system. This paper describes advanced optical instrumentation developed and applied for fire detection. The system is being designed to determine four important physical properties of disperse fractal aggregates and particulates including size distribution, number density, refractive indices, and fractal dimension. Combustion generated particulate are the primary detection target; however, in order to discriminate from other particulate, non-combustion generated particles should also be characterized. The angular scattering signature is measured and analyzed using two photon optical laser scattering. The Rayleigh-Debye-Gans (R-D-G) scattering theory for disperse fractal aggregates is utilized. The system consists of a pulsed laser module, detection module and data acquisition system and software to analyze the signals. The theory and applications are described.

Feikema, Douglas A.↗
NASA NTRS1990

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗
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 NTRS2016

Analysis of Retinal Vascular Branching in Human Subjects Undergoing 70-Day Head-Down Tilt by NASAs VESGEN Software

Significant risks for visual impairment were discovered recently in astronauts following spaceflight, especially after long-duration missions. We hypothesize that microgravity-induced fluid shifts result in pathological changes within the retinal vasculature that precede visual and other ocular impairments. We therefore are analyzing retinal vessels in healthy subjects before and after head-down tilt (HDT), a ground-based microgravity analog with NASA's VESsel GENeration Analysis (VESGEN) software. Methods. Spectralis® infrared (IR) fundus images were collected from both eyes of 6 subjects before and after 70 days of bed rest at 6 degree HDT (NASA Campaign 11). For our retrospective study, branching patterns in arterial and venous trees are mapped by VESGEN into vessel branching generations (Gx) that are quantified by parameters such as densities of vessel length (Lv), area (Av), number (Nv) and fractal dimension (Df) as described previously for diabetic retinopathy (IOVS 51(1):498). Results are further assigned by VESGEN into groups of large (G1-3), medium (G4-6) and small (G≥7) vessels. Results. All subjects remained asymptomatic throughout duration of HDT. To date, we have analyzed one IR image from each of the 12 eyes. Interestingly, two groups of the masked study population identified by VESGEN are distinguished by the presence or absence of small veins (G≥7). For example, L≥7 and Av≥7 are 2.7+/-1.3 E-4 px/px2 and 7.2+/-3.6 E-4 px2/px2 in 6 retinas, but 0 in the other 6 retinas. Nonetheless, the space-filling properties of the entire venous trees were remarkably uniform by all parameters, such as Df = 1.56+/-0.02 for 6 retinas with G≥7 and 1.55+/-0.02 for retinas without G≥7. No small arteries (G≥7) were detected. Conclusions. For our preliminary masked analysis, two groups of venous trees with and without small veins (G≥7) were clearly revealed by VESGEN. Upon completing all images and unmasking the subject status of before and after HDT, we will determine whether differences in the presence or absence of small veins are important correlates, and perhaps reliable predictors, of other ocular and physiological adaptations to prolonged head-down tilt and microgravity. Clinical methods for examining adaptive microvascular remodeling in the retina to microgravity space flight are not currently established.

Fractal↗
NASA NTRS1987

Chaotic nature of the spin-glass phase

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

Bray, A. J.↗
NASA NTRS1987

Stochastic and fractal analysis of fracture trajectories

Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.

Bessendorf, Michael H.↗
NASA NTRS1987

Long-wavelength absorption by fractal dust grains

The far-infrared and submillimeter absorption properties of random aggregates of conducting spheres have been studied as a possible source for the long-wavelength absorption of interstellar dust grains. The complex shapes of random aggregates have various fractal dimensions, depending on the process that forms them. The long wavelength absorption versus frequency is affected more by the shape of a conducting grain than by its composition.

Wright, Edward L.↗
NASA NTRS1988

Marine stratocumulus cloud fields off the coast of southern California observed using Landsat imagery. I - Structural characteristics

The structural characteristics of stratocumulus cloud fields off the coast of southern California are investigated using Landsat Multispectral Scanner imagery. Twelve scenes in this area are examined along with three other stratocumulus scenes near San Francisco, over central Oregon, and in the Gulf of Mexico. Results from this initial study of stratocumulus clouds indicate that cloud-background threshold selection techniques based upon edge detection gradient assumptions are not appropriate for cloud segmentation and classification algorithms, cloud size distributions obey a power law, and cell horizontal aspect ratio increases with cell diameter. It was also found that stratocumulus clouds are bifractal in nature with fractal dimension of d of about 1.2 for cells with diameter D smaller than 0.5 km and d of about 1.5 for cells with D greater than 0.5 km; stratocumulus cloud fields appear to be homogeneous over regions of about 100 km x 100 km, a much smaller region than the 2.5-deg x 2.5-deg boxes to be used in the ISCCP regional averaging algorithms; and that structural properties of stratocumulus clouds observed off the coast of southern California are similar to those observed for stratocumulus clouds at three other locations.

Welch, R. M.↗
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.↗