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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

Lam, Nina Siu-Ngan↗
DOE OSTI2023

Assessing pore network heterogeneity across multiple scales to inform CO2 injection models

Geologic heterogeneity is a key feature that must be considered when translations of scaled data are performed. This paper presents the assessment of geologic heterogeneity using a multiscale workflow that includes image analysis-based methods coupled with well log analysis to provide data in which fractals and machine learning methods estimate the carbon dioxide (CO 2 ) storage resource potential of a reservoir. The heterogeneity of rock properties of the complex Bell Creek reservoir in Montana, USA, was explored at the pore scale (~nm to mm), core scale (~mm to m), and well scale (~cm to m). The data used in this study included advanced image analysis of micro-CT (computed tomography) images (pore scale), thin sections (pore scale), plugs and core images (core scale) and well logs (well scale). The micro-CT images were segmented using a U-net segmentation approach into objects of pores and grains. Further, the segmented images were reconstructed into subvolumes of different sizes. Physical properties (porosity and permeability) and fractal dimensions were calculated for the various subvolumes, and Lorenz coefficient (Lc) values, a single parameter to describe the degree of heterogeneity within a pay zone section, were calculated from thin-section images and well logs. Porosity and fractal dimension values were used to estimate the 188-µm threshold of representative elementary volume (REV) in this study. Both the Lc and fractal dimension values were found to be negatively correlated. When these two parameters are combined, it is possible to discern differences in the complex porous networks of the samples analyzed in this study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1992

Fractal analysis: A new remote sensing tool for lava flows

Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.

Bruno, B. C.↗
NASA NTRS1989

Fractal mapping of digitized images - Application to the topography of Arizona and comparisons with synthetic images

The concept of fractal mapping is introduced and applied to digitized topography of Arizona. It is shown that the fractal statistics satisfy the topography of the state to a good approximation. The fractal dimensions and roughness amplitudes from subregions are used to construct maps of these quantities. It is found that the fractal dimension of actual two-dimensional topography is not affected by the adding unity to the fractal dimension of one-dimensional topographic tracks. In addition, consideration is given to the production of fractal maps from synthetically derived topography.

Huang, J.↗
NASA NTRS1999

Fractal Characterization of Hyperspectral Imagery

Two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral images selected from the Los Angeles area, one representing urban and the other, rural, were used to examine their spatial complexity across their entire spectrum of the remote sensing data. Using the ICAMS (Image Characterization And Modeling System) software, we computed the fractal dimension values via the isarithm and triangular prism methods for all 224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect changes in image complexity across the spectral range of the hyperspectral images. Both the isarithm and triangular prism methods detect unusually high D values on the spectral bands that fall within the atmospheric absorption and scattering zones where signature to noise ratios are low. Fractal dimensions for the urban area resulted in higher values than for the rural landscape, and the differences between the resulting D values are more distinct in the visible bands. The triangular prism method is sensitive to a few random speckles in the images, leading to a lower dimensionality. On the contrary, the isarithm method will ignore the speckles and focus on the major variation dominating the surface, thus resulting in a higher dimension. It is seen where the fractal curves plotted for the entire bandwidth range of the hyperspectral images could be used to distinguish landscape types as well as for screening noisy bands.

Qiu, Hon-Iie↗
DOE OSTI2021

Self-Similarity, Fractality and Entropy Principle in Collisions of Hadrons and Nuclei at Tevatron, RHIC and LHC

$z$-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated.The scaling for negative particle production in $Au+Au$ collisionsfrom BES-I program at RHIC is demonstrated. The scaling variable $z$ depends on the momentum fractions of the colliding objects carried by the interacting constituents, and momentum fractions of the produced objects in the scattered and recoil directions, which carries the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final stateare expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function $\psi(z)$ reveals energy, angular, multiplicity, and flavor independence.It has a power behavior at high $z$ (high $p_T$). Based on entropy principle and $z$-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated.New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
NASA NTRS1996

Self-Consistent Simulation of the Brownian Stage of Dust Growth

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to undergo a collision, we use a particle-in-cell (PIC) method for the early stages of the simulation where the system is still very homogeneous and a tree method later when the particles are more clustered.

Kempf, S.↗
NASA NTRS2003

Classifying Urban Land Covers Using Local Indices of Spatial Complexity

The skewed statistical distributions of land cover types in complex, heterogeneous urban areas limits the effectiveness of traditional spectrally based maximum-likelihood classifiers. This work examines the utility of fractal dimension and Moran's I index of spatial autocorrelation in segmenting high-resolution panchromatic and lower-resolution multispectral imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze multi-temporal and multi-platform imagery of Atlanta, Georgia. In this example, land cover change trajectories from forest or grassland to built up land covers lead to decreased spatial autocorrelation. In lower resolution imagery such as Landsat MSS, the complex details of forested land covers and urbanized areas are smoothed, and texture-based change detection is less effective. Although segmentation of panchromatic images is possible using fractal dimension or Moran's I, widely differing 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.

Arumugam, Mahesh↗
NASA NTRS1994

Rarefied solids

One important limit to creating low density materials is the objects' own weight. As a solid or colloidal matrix becomes more rarefied, gravity acts destructively to compress its suporting skeleton. We describe experimental results and propose a model which matches the low gravity behavior of rarefied or fractal solids. On parabolic airplane flights, we sought to demonstrate a key component of producing higher surface area fractals. Flight paths were selected to give a range of gravity levels: 0.01 g/g(sub 0) (low), 0.16 g(sub 0) (Lunar), 0.33 g/g(sub 0) (Martian), 1 g/g(sub 0) (Earth) and 1.8 g/g(sub 0) (high) (where g(sub 0) = 980 cm/sq s). Results using the model material of hydrophobic silica indicated that stable agglomeration of such tenuous objects can increase markedly in reduced gravity. Optical characterization revealed that fractal dimension changed directly with varying gravity. As measured by fractal dimension, effective surface area and roughness increased by 40% in low gravity. This finding supports the conclusion that relieving internal weight stresses on delicate aggregates can enhance their overall size (by two orders of magnitude) and internal surface area. We conclude that gravitational restructuring limits the overall size and void content of low-density solids. These sparse colloidal regimes may present new and technologically attractive physics, ranging from improved insulators, liquid-like tension in a 'solid' matrix, and characteristically low conductivities for sound and (8 to 14 micrometers wavelength) infrared radiation.

Noever, D. A.↗
DOE OSTI2024

Fractal analysis on Ag 2 O thin film using a data-driven approach

The synthesis of fractal Ag oxide (Ag 2 O) on the surface of Ag thin film has been achieved at room temperature by using Synchrotron X-ray irradiation. We have performed an automated quantitative analysis of a batch of 1879 fractal Ag 2 O patterns in a scanning electron microscopy (SEM) image within a radius of 2000 mm outward from the center of the X-ray beam. The morphology is similar to that of the diffusion-limited cluster aggregation (DLCA) model. The fractal dimension (D) of Ag 2 O is between 1.7 and 1.5 from the center to the edge. The area distribution density of fractal Ag 2 O follows a quadratic function with radius R. It is found that the branches’ number of fractal Ag 2 O is a key factor affecting the fractal dimension. The more branches the fractal has, the greater the D is. This is the first time that Ag fractal has been investigated by combining automated data analysis methods with batch experimental data. This data-driven approach provides a new research perspective for rationally regulating materials’ fractal morphology and performance.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Diffraction by fractally serrated apertures

An investigation of light diffracted by irregularly serrated apertures yields a closed-form analytical solution that confirms experimental recording of the diffracted patterns. These serrated apertures are modeled by a fractal function. Examples are given for both sinusoidal and fractal aperture perimeters with varying fractal dimension. Relations between the far-zone diffracted fields and the fractal dimension are examined.

Kim, Y.↗
NASA NTRS1997

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.

Emerson, Charles W.↗
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 reaction is verified using product generation measurements and fractal dimensions derived from the 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 of the flow field during the first pairing interaction. It is suggested that the structures reponsible for this transition are nondeterministic, nonrandom, inhomogeneous fractals. In the range of Schmidt numbers investigated (0.25-4), 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 NTRS1992

Multiresolution processing for fractal analysis of airborne remotely sensed data

Images acquired by NASA's Calibrated Airborne Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension: Shelberg's (1982, 1983) line-divider method, the variogram method, and the triangular prism method. A description of these methods and the result of applying these methods to a remotely-sensed image is also presented. The scanner data was acquired over western Puerto Rico in January, 1990 over land and water. The aim is to study impacts of man-induced changes on land that affect sedimentation into the near-shore environment. The data were obtained over the same area at three different pixel sizes: 10 m, 20 m, and 30 m.

Jaggi, S.↗
NASA NTRS1992

Multi-resolution processing for fractal analysis of airborne remotely sensed data

Fractal geometry is increasingly becoming a useful tool for modeling natural phenomenon. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Since they are characterized by self-similarity, an ideal fractal surface is scale-independent; i.e. at different scales a fractal surface looks the same. This is not exactly true for natural surfaces. When viewed at different spatial resolutions parts of natural surfaces look alike in a statistical manner and only for a limited range of scales. Images acquired by NASA's Thermal Infrared Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension - Schelberg's line-divider method, the variogram method, and the triangular prism method. A description of these methods and the results of applying these methods to a remotely-sensed image is also presented. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected was the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. This corresponds to 3 different pixel sizes - 5m, 15m, and 30m. After, simulating different spatial sampling intervals within the same image for each of the 3 image sets, the results are cross-correlated to compare the extent of detail and complexity that is obtained when data is taken at lower spatial intervals.

Jaggi, S.↗
NASA NTRS1986

Fractals and fragmentation

The use of renormalization group techniques on fragmentation problems is examined. The equations which represent fractals and the size-frequency distributions of fragments are presented. Method for calculating the size distributions of asteriods and meteorites are described; the frequency-mass distribution for these interplanetary objects are due to fragmentation. The application of two renormalization group models to fragmentation is analyzed. It is observed that the models yield a fractal behavior for fragmentation; however, different values for the fractal dimension are produced . It is concluded that fragmentation is a scale invariant process and that the fractal dimension is a measure of the fragility of the fragmented material.

Turcotte, D. L.↗