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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Fractal dimension of optical cirrus in Stripe82

ABSTRACT The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the 2D fractal dimension D of a cloud projected on to the sky plane. In previous studies, which were mostly based on infrared (IR) data, the fractal dimension of individual clouds was found to be in a range from 1.1 to 1.7 with a preferred value of 1.2–1.4. In this work, we use data from Stripe82 of the Sloan Digital Sky Survey to measure the fractal dimension of the cirrus clouds. This is done here for the first time for optical data with significantly better resolution as compared to IR data. To determine the fractal dimension, the perimeter-area method is employed. We also consider IR (IRAS and Herschel) counterparts of the corresponding optical fields to compare the results between the optical and IR. We find that the averaged fractal dimension across all clouds in the optical is $\langle D \rangle =1.69^{+0.05}_{-0.05}$ which is significantly larger than the fractal dimension of its IR counterparts $\langle D\rangle =1.38^{+0.07}_{-0.06}$. We examine several reasons for this discrepancy (choice of masking and minimal contour level, image and angular resolution, etc.) and find that for approximately half of our fields the different angular resolution (point spread function) of the optical and IR data can explain the difference between the corresponding fractal dimensions. For the other half of the fields, the fractal dimensions of the IR and visual data remain inconsistent, which can be associated with physical properties of the clouds, but further physical simulations are required to prove it.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗
DOE OSTI2025

Characterization of the fractal dimension of helium plumes in laminar to turbulent transition

Abstract Schlieren imaging in conjunction with a high-speed camera was used to observe the behavior of metered helium plumes as they transition from laminar to turbulent flow in an air environment. The plumes were visualized at twelve jet Reynolds numbers ranging from 200 to 2980. The fractal dimension of the flows was obtained by applying a box counting algorithm to the recorded schlieren images. The results were analyzed to determine the correlation between the Reynolds number of the flow and the fractal dimension of the observed turbulence. A trend of increasing fractal dimension with increasing Reynolds number was observed for several different types of schlieren cutoffs including horizontal cutoff, vertical cutoff, circular cutoff, focused shadowgraphy and de-focused shadowgraphy. The vertical cutoff and focused shadowgraphy imaging methods showed the most consistent results for the fractal dimension characterization during the laminar to turbulent transition. For transitional plumes, it was observed that fractal dimension increased with distance from the jet outlet.

42 ENGINEERING↗
DOE OSTI2025

Linking Lattice Strain and Fractal Dimensions to Non‐monotonic Volume Changes in Irradiated Nuclear Graphite

Graphite's resilience to high temperatures and neutron damage makes it vital for nuclear reactors, yet irradiation alters its microstructure, degrading key properties. We used small- and wide-angle X-ray scattering to study neutron-irradiated fine-grain nuclear graphite (Grade G347A) across varied temperatures and fluences. Results show significant shifts in internal strain and porosity, correlating with radiation-induced volume changes. Notably, porosity volume distribution (fractal dimensions) follows non-monotonic volume changes, suggesting a link to the Weibull distribution of fracture stress.

X-ray scattering↗
DOE OSTI2023

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent -β. Here, the static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension d f . In three dimensions, d f ≈ 2.0 for 2.5≤ β ≤ 3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0≲ d f ≲1.34 for 2.1≤ β ≤ 2.9. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long-wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Machine learning-assisted upscaling analysis of reservoir rock core properties based on micro-computed tomography imagery

Optimum solutions for geologic modeling and reservoir simulation in industries such as oil and gas recovery and carbon capture and storage require accurate characterization of reservoir properties, which are often heterogeneous. In this study, high-quality micro-computed tomography (CT) images (1.475-μm/pixel resolution) of a sandstone core acquired from the Bell Creek oil field, USA, were used to provide nondestructive analysis of pore- and core-scale heterogeneity across measurement scales of 94–566 μm. In addition to characterizing the as-received sample, the core sample was flooded with brine to evaluate the capacity of the core sample to receive injected fluids. The micro-CT images were systematically segmented into pore spaces and grains via machine learning (ML) steps including image preprocessing, label creation using a traditional ML method based on limited manual image annotation, and finally U-Net segmentation. The segmented image stacks were reconstructed into digital cubes of various scales of voxel lengths. The 3D porosity values were calculated for all the digital cubes, and the fractal dimensions of the cubes were estimated using a box-counting method. The results showed that smaller cubes had greater heterogeneity and that the porosity values could be accurately estimated by fractal dimension and voxel lengths using ML models. For the core sample with brine flooding, the ratio of pores filled by brine to the total pore space was related to the porosity and could also be accurately estimated by porosity, fractal dimension, and voxel lengths using ML models. In conclusion, the results of this study demonstrate that the concept of fractal dimension can be a useful vector to perform upscaling analysis of sandstone rock heterogeneity from the pore to core scale and that fractal dimensions can be used to estimate porosity values and pore space-filling capacity across those scales.

58 GEOSCIENCES↗
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↗
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↗
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↗
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 OSTI2022

Random Knotting in Fractal Ring Polymers

Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property—the random knotting probability—for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0 (N) ∝ exp(–N/N 0 ). However, no such simple considerations can account for the dependence of the knotting length, N 0 , on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where “knotting” is defined as the intersection of any two segments.

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