Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fractals”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
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 NTRS1999

Nanoporous Silica Thermal Insulation for Space Shuttle Cryogenic Tanks: A Case Study

Nanoporous silica (with typical 10-50 nm porous radii) has been benchmarked for thermal insulators capable of maintaining a 150 K/cm temperature gradient. For cryogenic use in aerospace applications, the combined features for low-density, high thermal insulation factors, and low temperature compatibility are demonstrated in a prototype sandwich structure between two propulsion tanks. Theoretical modelling based on a nanoscale fractal structure suggest that the thermal conductivity scales proportionally (exponent, 1.7) with the material density-lower density increases the thermal insulation rating. Computer simulations, however, support the optimization tradeoff between material strength (Young moduli, proportional to density with exponent, 3.7), the characteristic (colloidal silica, less than 5 nm) particle size, and the thermal rating. The results of these simulations indicate that as nanosized particles are incorporated into the silica backbone, the resulting physical properties will be tailored by the smallest characteristic length and their fractal interconnections (dimension and fractal size). The application specifies a prototype panel which takes advantage of the processing flexibility inherent in sol-gel chemistry.

Noever, David A.↗
NASA NTRS2001

Cloud Structure and Cloud-Radiation Interaction: From Smallest Observable Scales (Less than 10 m) to GCM Grid Scales (More than 100 km)

In this presentation we review the fractal nature of internal cloud structure from cm- to km-scales as captured by in-situ probes during long horizontal penetrations by aircraft. We uncover the non-Poissonian spatial distribution of cloud droplets at submeter scales and confirm scale-invariant behavior for large scales. Based on these structural characteristics, we generate simple fractal cloud models that reproduce statistical scaling properties of real clouds. These stochastic models represent a link between nonlinear science, in general, and cloud-radiation interaction, in particular. Next we run three-dimensional radiative transfer computations on these synthetic fractal clouds and compare the structure of the resulting radiation fields with the known structure of the cloud model and with satellite images of real clouds. The different behaviors observed for small and large-scale variabilities will be discussed in detail. We find that while the large-scale fluctuations of the resulting radiation fields resemble those in the original scale-invariant cloud structure, the radiation at small scales is much smoother than its cloud liquid water counterpart. This violates scale-invariance and produces a scale-break at 0.2-0.5 km that is clearly observed in high-resolution satellite data such as from Landsat. Finally, we show how radiative transfer Green function theory in the photon diffusion limit explains (and predicts) the above phenomena of "radiative smoothing."

Marshak, Alexander↗
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 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 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 NTRS2011

Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations

In order to simulate physically plausible surfaces that represent geologically evolved surfaces, demonstrating demanding surface-relative guidance navigation and control (GN&C) actions, such surfaces must be made to mimic the geological processes themselves. A report describes how, using software and algorithms to model body surfaces as a series of digital terrain maps, a series of processes was put in place that evolve the surface from some assumed nominal starting condition. The physical processes modeled in this algorithmic technique include fractal regolith substrate texturing, fractally textured rocks (of empirically derived size and distribution power laws), cratering, and regolith migration under potential energy gradient. Starting with a global model that may be determined observationally or created ad hoc, the surface evolution is begun. First, material of some assumed strength is layered on the global model in a fractally random pattern. Then, rocks are distributed according to power laws measured on the Moon. Cratering then takes place in a temporal fashion, including modeling of ejecta blankets and taking into account the gravity of the object (which determines how much of the ejecta blanket falls back to the surface), and causing the observed phenomena of older craters being progressively buried by the ejecta of earlier impacts. Finally, regolith migration occurs which stratifies finer materials from coarser, as the fine material progressively migrates to regions of lower potential energy.

Riedel, Joseph E.↗
NASA NTRS2013

T-Matrix Modeling of Linear Depolarization by Morphologically Complex Soot and Soot-Containing Aerosols

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

atmospheric radiation↗
NASA NTRS2015

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Gnoffo, Peter A.↗
NASA NTRS2022

Optical properties of morphologically complex black carbon aerosols: Effects of coatings

Optical properties are computed for fractal-like aggregate black carbon (BC) aerosols coated with different substances. Two models are used for these aerosols: (i) the coated aggregate model (model I), where coating is added to the voids and surroundings of BC fractal-like aggregates; and (ii) the closed-cell aggregate model (model II), where coating is added concentrically to each monomer of BC fractal-like aggregates. Our results favor choosing the coated aggregate model (model I) to simulate scattering and absorption by coated BC aerosols because this model is morphologically more realistic, and because this model yields mass absorption cross section (MAC) and backscattering linear depolarization ratio (LDR) values that are consistent with field measurements. Moreover the corresponding computed degree of linear polarization (DoLP) and LDR values are very sensitive to changes in the coating volume fraction (fvol) and the coating refractive index (m). With the same absorbing BC core, the MAC value increases steadily with increasing fvol and m values. For example, using a density of 1.8 g/cm 3 and BC refractive index 1.95 + i0.79, the calculated MAC values for uncoated BC aggregates range from 6.2 to 6.8 m 2 /g at 0.55 µm. When coating material is applied to the BC aggregates, the calculated MAC values for model I particles increase to between 9.8 and 13.2 m 2 /g (depending on m) when fvol = 87.5%. The backscattering LDR values also tend to increase with the increasing m values for the shapes and sizes considered in our study. For model I particles, the backscattering LDR values span a wide range of 4.2–27.8% at a wavelength of 0.35 µm at fvol = 87.5% when m increases from 1.33 to 1.55. Our results are relevant to analyses of polarimetric and lidar observations of smoke particles, especially when these particles undergo hygroscopic growth.

Black carbon aerosols↗
DOE OSTI2026

Evaluating the role of green infrastructure features in post-disaster recovery – Case Study of Beaumont, Texas after tropical storm imelda

While green infrastructure (GI) can provide multiple environmental benefits, its role in post-disaster economic and social recovery remains relatively underexplored. This article investigates whether different characteristics of GI, such as size, shape, connectivity, and amenities, affect the resilience of local businesses following Tropical Storm Imelda in Beaumont, Texas. The study utilizes SafeGraph mobility data to analyze foot traffic patterns to local businesses before, during, and after the disaster. FRAGSTATS indices measure GI characteristics (e.g., area, shape index, fractal dimension, proximity) while park features such as sports facilities, playgrounds, water features, and accessibility are cataloged through manual observation. Ordinary Least Squares regression models assess the relationship between park characteristics and post-recovery business performance, controlling for demographic variables including income, race, and poverty levels. Results indicate that certain GI attributes significantly enhance business recovery. Points of interest within walking distance (0.5 miles) of parks demonstrated better post-recovery status compared to those beyond this range. Specifically, parks with larger areas (p < 0.01) and more complex shapes measured by fractal dimension index (p < 0.01) had the strongest positive impact on surrounding businesses' recovery. Interestingly, playgrounds showed a negative correlation with recovery (p < 0.05), likely due to flood damage rendering them unusable during the immediate recovery period. Social vulnerability factors, including higher poverty rates and minority populations, negatively affected recovery outcomes despite park proximity.

Economic resilience↗
DOE OSTI2025

Carbonation of Alkaline Earth Metal Hydroxides: Structure across Nano- to Mesoscales

The conversion of gaseous CO 2 into a solid constitution through mineralization is an active area of carbon capture, and alkaline earth metal hydroxides (M(OH) 2 , M = Ca 2+ , Mg 2+ ) are frontrunners in this area. As model systems, nanolime samples are excellent templates for the study of this reaction. Here, we have examined these under ambient pressure conditions with controlled humidity and CO 2 . Utilizing a broad range of analytical methods, we first established the purity and structures of the selected materials. We then examined the structural changes due to carbonation, using infrared spectroscopy, X-ray scattering, and neutron scattering. The resulting structural changes are resolved from nanoscale to mesoscale and from early-stage to late-stage carbonation. Ca(OH) 2 and Mg(OH) 2 are found to behave quite differently. As expected from prior work, the carbonation of Ca(OH) 2 is kinetically favored. Further, our structure studies suggest this is due to a facile reaction at the fractal interface of the particles. From early- to late-stage carbonation, there is a consistent increase in the fractal roughness. This is in contrast to Mg(OH) 2 where the same surface evolves into a smooth conformal coating. For this material the major reacting component is at the mesoscale, suggesting globular particle growth or evolving macro-porosity. Because neutron scattering is sensitive to hydrogen content, we expected a significant change as M(OH) 2 evolves to MCO 3 . Such a change is found for Ca(OH) 2 but not for Mg(OH) 2 , providing evidence for the formation of hydrated carbonates for the later material. The formation of a conformal layer along with water-rich carbonate formation is an impediment to the use of Mg(OH) 2 for carbon capture. For energy-efficient carbon capture, it would be desirable to enhance carbonation rates for Mg(OH) 2 , and one possible route would be the use of anhydrous fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Experimental Characterization of Hydrogen Diffusion in Shale Rocks for Geologic Storage Applications

As global energy systems undergo a transition to cleaner alternatives, geologic hydrogen storage has emerged as a promising solution for large-scale energy storage. A critical factor in determining the feasibility of this approach is the effectiveness of caprock formations, such as shale, in preventing hydrogen migration. This study investigates the diffusion behavior of hydrogen through shale to assess its suitability as a caprock for geologic hydrogen storage. Using a novel double-seal core holder design and a through-diffusion apparatus, hydrogen diffusion was measured through shale rock from the Eagle Ford and Wolfcamp Formations under dry conditions. These measurements were complemented by microstructural and mineralogical analyses using low-pressure nitrogen adsorption and X-ray diffraction. The effective diffusion coefficient of hydrogen in these shale caprocks ranged from 2.51 × 10 –8 to 9.85 × 10 –8 m 2 /s. Notably, we observed that the diffusion behavior was more related to the pore network structure and could not be attributed to differences in the total pore volume between shale types alone. Here, to further understand the role of pore network complexity, a fractal pore model was developed to correlate tortuosity with the fractal dimension of the pore structure (a measure of pore network complexity). The proposed model closely matched tortuosity values obtained from diffusion experiments, outperforming existing theoretical tortuosity–porosity correlations. These findings provide key quantitative parameters needed to assess the feasibility of geologic hydrogen storage as well as insights that can be applied to hydrogen storage in a range of geologic formations.

08 HYDROGEN↗
DOE OSTI2025

Effect of Sulfonation Level on the Percolated Morphology and Proton Conductivity of Hydrated Fluorine-Free Copolymers: Experiments and Simulations

Using all-atom molecular dynamics simulations and a variety of experimental methods, we previously reported on a linear polyethylene with pendant phenyl sulfonated groups precisely on every fifth carbon along the backbone. With increasing relative humidity this fluorine-free polymer self-assembled to form nanoscale water channels and exhibited exceptional proton conductivity. Expanding upon those findings, here we explore partially sulfonated random copolymers, referred to as p 5PhSH-Y. Using either acetyl sulfate or sulfuric acid, a wide range of sulfonation levels were prepared ( Y = 34−98%) corresponding to ion-exchange capacities (IEC) of 2.0−4.4 mmol/g. Combining experimental techniques and all-atom molecular dynamics simulations, we study the effect of Y on water uptake, nanoscale morphology, and the proton/water transport properties of p5PhSH- Y . The proton conductivity of p 5PhSH- Y increases with relative humidity and with Y and achieves values in excess of 0.1 S/cm. These high conductivities are attributed to high IEC and welldeveloped nanoscale percolated hydrophilic domains made possible by the flexible backbone. We quantitatively describe the nature of the water channels using the characteristic distance, channel width distribution, the area per sulfonate group at the hydrophilic/ hydrophobic interface, and the fractal dimension. Notably, the channel widths and the areas per sulfonate group are nominally independent of the level of sulfonation, while depending significantly on the level of hydration. The fractal dimension of the water channels correlates strongly with the water diffusion coefficients calculated from the molecular dynamics (MD) simulations. These findings demonstrate that the p 5PhSH- Y hydrocarbon copolymers can be modified to tune properties, particularly proton conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Magnetic devil's staircaselike behavior in quasiperiodic qubit lattices

The devil's staircase (DS) phenomenon is a fractal response of magnetization to external fields, traditionally observed in periodic ferromagnetic systems, where the commensurability between spin arrangements, lattice parameters, and external magnetic fields governs abrupt changes in magnetization. Its occurrence in aperiodic, fractal-type systems has remained largely unexplored, despite their natural compatibility with such phenomena. Using a quantum annealing device, we uncover a wealth of abrupt magnetic transitions between spin manifolds driven by increasing external magnetic fields within a simple yet effective Ising-model framework. In contrast to periodic systems, where DS arises from long-range competing interactions, our findings reveal that short-range, purely antiferromagnetic couplings in aperiodic geometries produce equally rich ground-state magnetization patterns. Here, we demonstrate that while magnetic textures are determined by the lattice size, their formation remains remarkably robust and independent of scale, with commensurability emerging locally. Our results challenge the prevailing view that DS behavior is limited to periodic systems and establish quasiperiodic geometries as a natural host for this phenomenon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν ≤ 1 , bounded below by filling factor ν = 1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν = 1 and ν = 3 . The phases near ν = 1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Ding, Jixun K.↗
NASA NTRS1987

Implications of convection in the Moon and the terrestrial planets

The early thermal and chemical evolution of the Moon is discussed. The rubidium-strontium, neodymium-samarium, and uranium-thorium-lead systems were studied. The relation of source region heterogeneity to the mixing associated with mantle convection is considered. Work on the application of fractal concepts to planetary geology and geophysics is also discussed. The fractal concept was applied to fragmentation, including the frequency-size distribution of meteorites, asteroids and particulate matter produced by impacts.

Turcotte, Donald 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.↗