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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z -graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z -graded graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Areal coverage of storm precipitation

The probability distributions of the spatial distribution of precipitation from storms of different types were studied. The occurrence of wetted rainstorm area within a catchment was modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed as through fractals. The portion of a catchment covered by a stationary rainstorm was modeled by the common area of two overlapping circles. The first two moments of the distribution of the common area were derived from purely geometrical considerations. The spatial structure of the depth of rainfall from a stationary rainstorm was investigated using point process techniques. Total storm rainfall at the center of each cell is a random variable, and rainfall is distributed around the center specified by a spread function that may incorporate random parameters.

Eagleson, P. S.↗
NASA NTRS1987

Lunar and Planetary Science Conference, 17th, Houston, TX, Mar. 17-21, 1986, Proceedings. Part 2

The topics discussed in this volume include lunar endogenic rocks and processes; lunar regoliths and breccias; the terrestrial planets; shergottites; primitive materials, exposure, and atmospheres; and impacts and crater tectonics. Papers are presented on the petrology and geochemistry of alkali gabbronorites from lunar breccia 67975; the formation of Apollo 17 orange and black glass beads; mixing levels, the Apennine Front soil component, and compositional trends in the Apollo 15 soils; the meteorite component of Apollo 16 noritic impact melt breccias; and constraints on the lithospheric structure of Venus from mechanical models and tectonic surface features. Consideration is also given to a fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars; rare earth patterns in shergottite phosphates and residues; nuclide production by primary cosmic-ray protons; gas chromatographic instrumentation for the analysis of aerosols and gases in Titan's atmosphere; and finite-element models of non-Newtonian crater relaxation.

Ryder, Graham↗
NASA NTRS1991

Electron distribution functions in electric field environments

The amount of current carried by an electric discharge in its early stages of growth is strongly dependent on its geometrical shape. Discharges with a large number of branches, each funnelling current to a common stem, tend to carry more current than those with fewer branches. The fractal character of typical discharges was simulated using stochastic models based on solutions of the Laplace equation. Extension of these models requires the use of electron distribution functions to describe the behavior of electrons in the undisturbed medium ahead of the discharge. These electrons, interacting with the electric field, determine the propagation of branches in the discharge and the way in which further branching occurs. The first phase in the extension of the referenced models , the calculation of simple electron distribution functions in an air/electric field medium, is discussed. Two techniques are investigated: (1) the solution of the Boltzmann equation in homogeneous, steady state environments, and (2) the use of Monte Carlo simulations. Distribution functions calculated from both techniques are illustrated. Advantages and disadvantages of each technique are discussed.

Rudolph, Terence H.↗
DOE OSTI2022

Can fractal dimensions objectivize gastropod shell morphometrics? A case study from Lake Lugu (SW China)

1. Morphometrics are fundamental for the analysis of size and shape in fossils, particularly because soft parts or DNA are rarely preserved and hard parts such as shells are commonly the only source of information. Geometric morphometrics, that is, landmark analysis, is well established for the description of shape but it exhibits a couple of shortcomings resulting from subjective choices during landmarking (number and position of landmarks) and from difficulties in resolving shape at the level of micro-sculpture. 2. With the aid of high-resolution 3D scanning technology and analyses of fractal dimensions, we test whether such shortcomings of linear and landmark morphometrics can be overcome. As a model group, we selected a clade of modern viviparid gastropods from Lake Lugu, with shells that show a high degree of sculptural variation. Linear and landmark analyses were applied to the same shells in order to establish the fractal dimensions. 3. The genetic diversity of the gastropod clade was assessed. The genetic results suggest that the gastropod clade represents a single species. The results of all morphometric methods applied are in line with the genetic results, which is that no specific morphotype could be delimited. Apart from this overall agreement, landmark and fractal dimension analyses do not correspond to each other but represent data sets with different information. Generally, the fractal dimension values quantify the roughness of the shell surface, the resolution of the 3D scans determining the level. In our approach, we captured the micro-sculpture but not the first-order sculptural elements, which explains that fractal dimension and landmark data are not in phase. 4. We can show that analyzing fractal dimensions of gastropod shells opens a window to more detailed information that can be considered in evolutionary and ecological contexts. We propose that using low-resolution 3D scans may successfully substitute landmark analyses because it overcomes the subjective landmarking. Analyses of 3D scans with higher resolution than used in this study will provide surface roughness information at the mineralogical level. We suggest that fractal dimension analyses of a combination of differently resolved 3D models will significantly improve the quality of shell morphometrics.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2007

A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields

A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.

Prigarin, Sergei M.↗
DOE OSTI2021

Multifractal Characterization of Distribution Synchrophasors for Cybersecurity Defense of Smart Grids

“Source ID Mix” spoofing emerged as a new type of cyber-attack on Distribution Synchrophasors (DS) where adversaries have the capability to swap the source information of DS without changing the measurement values. Accurate detection of such a highly-deceptive attack is a challenging task especially when the spoofing attack happens on short fragments of DS recorded within a relatively small geographical scale. Herein this letter proposes an effective approach to detect this cyber-attack by realizing the multifractal characteristics of DS measurements. First, the multifractal cross-correlation of DS measured at multiple intra-state locations is revealed. Then the derived correlation is integrated with weighted two-dimensional multifractal surface interpolation to reconstruct quasi high-resolution signals. Finally, informative location-specific signatures are extracted from the high-resolution DS and they are integrated with advanced machine learning techniques for source authentication. Experiments using the real-life DS are performed to verify the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

NLR CSP Optical Facilities: Illuminating the Path Forward Through Innovation and Impact: Agreement 38490

This initiative is a multi-faceted project at the National Laboratory of the Rockies (NLR) aimed at strengthening its Concentrating Solar Power (CSP) Optical Facilities to advance the development of low-cost, high-performance materials for solar and other applications. The project's strategy is built on three pillars: strategic stakeholder engagement, diligent facility maintenance and utilization, and the development of new research capabilities. The overarching goal is to ensure the facilities remain state-of-the-art resources for industry and academia, thereby accelerating the conversion of concentrated sunlight into energy. A key driver of the project is an international Advisory Board, which provides critical guidance on research priorities and industry needs, leading to new collaborations and secured funding. This external engagement, combined with proactive outreach to industry partners, ensures the lab's work remains aligned with real-world challenges, including materials durability and performance certification. Significant efforts in facility maintenance have addressed challenges with aging infrastructure. Notable achievements include the complete refurbishment of the hail-damaged Ultra-Accelerated Weathering System (UAWS) and the successful replacement of a failing 15-year-old Lambda 1050 spectrophotometer with a new-generation model, substantially upgrading material characterization capabilities. These maintenance activities were complemented by achieving a prestigious ISO 9001:2015 certification for the Advanced Optical Materials Labs, formally recognizing the quality and reliability of NLR's measurement capabilities. Despite these successes, challenges remain, including high demand for the High Flux Solar Furnace (HFSF) and intermittent failures of other key instruments. The project has delivered major advancements in research techniques and capabilities. At the Flatirons campus, a new indoor laboratory, was established to house advanced deflectometry and photogrammetry systems for heliostat characterization. For on-sun testing, a novel, actively cooled turning mirror was developed for the HFSF, enabling more realistic testing of particle receivers and components. A collaboration with Virginia Tech successfully demonstrated the high-temperature durability of a new solar absorber coating through extensive cyclic testing. Concurrently, new modeling took place to better predict material degradation on rough, fractal surfaces. In summary, this project has systematically enhanced NLR's CSP Optical Facilities through strategic upgrades, rigorous maintenance, and stakeholder-guided research. By overcoming equipment failures, budgetary constraints, and logistical hurdles, the project has reinforced NLR's role as a central hub for CSP innovation and materials testing. Future work will focus on securing diverse funding, expanding collaborations, and continuing to provide the critical infrastructure needed to accelerate the development and deployment of next-generation technologies.

14 SOLAR ENERGY↗
NASA NTRS1991

Target Detection Using Fractal Geometry

The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.

Fuller, J. Joseph↗
NASA NTRS1992

Quantitative analysis of surface characteristics and morphology in Death Valley, California using AIRSAR data

The Jet Propulsion Laboratory Airborne Synthetic Aperture Radar (JPL-AIRSAR) is used to collect full polarimetric measurements at P-, L-, and C-bands. These data are analyzed using the radar analysis and visualization environment (RAVEN). The AIRSAR data are calibrated using in-scene corner reflectors to allow for quantitative analysis of the radar backscatter. RAVEN is used to extract surface characteristics. Inversion models are used to calculate quantitative surface roughness values and fractal dimensions. These values are used to generate synthetic surface plots that represent the small-scale surface structure of areas in Death Valley. These procedures are applied to a playa, smooth salt-pan, and alluvial fan surfaces in Death Valley. Field measurements of surface roughness are used to verify the accuracy.

Kierein-Young, K. S.↗
NASA NTRS1988

Generating fractal-like surfaces on general purpose mesh-connected computers

Realistic images of natural surfaces are often generated using computationally expensive stochastic modeling techniques. Here a parallel procedure to generate such models is presented. The target machines are general-purpose mesh-connected computers. The complexity of the procedure is similar to that of a proposed special-purpose parallel fractal generator.

Wainer, Michael↗
DOE OSTI2022

Novel fractal-textured solar absorber surfaces for concentrated solar power

The solar absorptance of a thermal receiver surface significantly affects the photothermal conversion efficiency of concentrated solar power (CSP) plants. The development of low-cost Gen3 CSP systems calls for increasing the solar absorptance of the thermal receivers at operating temperatures above 750 °C. This study presents an innovative approach to the fractal, multiscale texturing of absorber surfaces to significantly enhance solar energy absorption for Gen3 CSP applications. The absorber surface is described in terms of its fractal parameters that are uniquely determined from surface profile measurements. The interaction of solar radiation with the fractal surface is numerically simulated by solving the governing Maxwell’s equations for electromagnetic wave propagation to investigate the effect of texturing on the absorptance of the surfaces. It is shown that absorption of the solar spectrum increases with an increase in the fractal dimension and the multiscale asperity height of the surface texturing. Here, the theoretical model is demonstrated to be in close agreement with experimental measurements of spectral absorptance of electrodeposited copper (Cu), copper mono-oxide (CuO), and copper-manganese oxide (CuMnO) surfaces that are textured to produce a range of fractal parameters by tailoring the deposition parameters. Fractal surface texturing is shown to reduce reflectance by over one order of magnitude, yielding an absorptance of greater than 0.985 for CuMnO. For the first time, the study presents a significant effective means of increasing solar absorptance and a fundamental theoretical description of the underlying physics.

14 SOLAR ENERGY↗
DOE OSTI2021

Thermal Experiments for Fractured Rock Characterization: Theoretical Analysis and Inverse Modeling

Abstract Field‐scale properties of fractured rocks play a crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross‐borehole thermal experiments data. It is based on a particle‐based heat‐transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of the heat‐transfer model runs and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to be estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding nonuniform prior information related to the DFN connectivity improves the inference of this parameter.

Zhou, Zitong↗
NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗
DOE OSTI2021

Interpretable Deep Learning for the Earth System with Fractal Nets

Focal Area 3: Explainable AI Our confidence in the projections made by Earth System Models (ESMs) depends on understanding them to be, in some important respects, faithful representations of the Earth system. Here we present an “explainable Artificial Intelligence (AI)” method that allows us to uncover the dynamical structure of the observed and modeled Earth system, discover hidden links across wide spatiotemporal scales, target model development efforts at poorly-represented dynamics, and optimize observed or modeled data collection to maximize predictive information. Science Challenge: Dynamical system science for the Earth system poses unique challenges given the large degree of internal climate variability. Thus, tools that help us understand how ESMs succeed and fail at representing these dynamics are crucial, particularly in relation to the observed system. Furthermore, the computational and memory constraints on ESM data output motivate in situ analysis of ESM dynamics, including automatic detection of dynamical shifts. Also, of key importance are procedures that leverage ESMs to optimize observational campaigns for improving process representation, reducing structural uncertainty and improving model skill.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Multivariate degradation modeling using generalized cauchy process and application in life prediction of dye-sensitized solar cells

Recently, the Generalized Cauchy (GC) process has been applied to capture a Long Memory (LM) phenomenon in product degradation modeling and life prediction. Compared with the traditional fractional Brownian motion that captures the LM using a single Hurst parameter, the GC process has two free parameters (Hurst and fractal dimension parameters) that flexibly capture both global LM and local irregularity. However, all existing GC-based degradation models are for a single Degradation Characteristic (DC). In this article, motivated by a real degradation problem of dye-sensitized solar cells that jointly exhibits multiple DCs, global LM, local irregularity and DC-wise cross-correlation, we propose a novel GC-based Multivariate Degradation Model (GC-MDM) to simultaneously capture the aforementioned effects. A maximum likelihood estimation approach is developed to estimate parameters of the GC-MDM. Subsequently, product life prediction based on the GC-MDM is developed. The proposed GC-MDM is validated through a simulation study and a physical experiment of dye-sensitized solar cells. Furthermore, results show that the proposed GC-MDM fundamentally improves the life prediction accuracy in comparison with conventional degradation models which significantly misestimate the uncertainty of product life.

14 SOLAR ENERGY↗
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 OSTI2025

Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe 2 bilayers

Twisted bilayer transition metal dichalcogenides, such as MoTe 2 , provide a versatile platform for exploring correlated topological phases. This work investigates the interplay between perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer MoTe 2 (t-MoTe 2 ) across two distinct regimes: a low-twist-angle phase (θ ≈ 2.1°) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase (θ ≈ 3.89°) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain fractal FCIs with higher Chern numbers. As a result, the electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.

Anyons↗