SEARCH · Engineering Papers

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.

SourceResearch connectionFrom yearThrough year

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

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Fractal coatings of Ni and NiYSZ for high-temperature corrosion mitigation in solar salt

This paper introduces a novel approach to corrosion mitigation using electrodeposited, fractal Ni and NiYSZ coatings. Highly adherent, durable multiscale coatings with fractal dimensions above 1.80 were fabricated. Corrosion characteristics of coated plain and etched surfaces of In800H, SS310, SS316 and SS347, in comparison to Ha230, were studied in molten 60% NaNO 3 + 40% KNO 3 at 600 °C. The corrosion rate of coated Fe-based alloys reduced by up to 68% compared to uncoated alloys and was on par with or lower than the corrosion rate of Ha230. Furthermore, the corrosion-resistant coatings provide for use of low-cost alloys in high temperature corrosive environments.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Fractal mechanisms in the electrophysiology of the heart

The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

NASA Discipline Cardiopulmonary↗

NASA NTRS1992

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.

Non-NASA Center↗

NASA NTRS1995

Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

NASA Discipline Cardiopulmonary↗

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 OSTI2025

Spectroscopy of the fractal Hofstadter energy spectrum

Hofstadter’s butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux quanta per lattice unit cell, this spectrum shows self-similar distributions of energy levels that reflect its recursive construction. For most materials, Hofstadter’s butterfly is predicted under experimental conditions that are unachievable using laboratory-scale magnetic fields. More recently, electrical transport studies have provided evidence for Hofstadter’s butterfly in materials engineered to have artificially large lattice constants, such as those with moiré superlattices. Yet, so far, direct spectroscopy of the fractal energy spectrum predicted by Hofstadter nearly 50 years ago has remained out of reach. Here, in this work, we use high-resolution scanning tunnelling microscopy/spectroscopy (STM/STS) to investigate the flat electronic bands in twisted bilayer graphene (TBG) near the predicted second magic angle, an ideal setting for spectroscopic studies of Hofstadter’s spectrum. Our study shows the fractionalization of flat moiré bands into discrete Hofstadter subbands and discerns experimental signatures of self-similarity of this spectrum. Moreover, our measurements uncover a spectrum that evolves dynamically with electron density, showing phenomena beyond that of Hofstadter’s original model owing to the combined effects of strong correlations, Coulomb interactions and the quantum degeneracy of electrons in TBG.

electronic properties and materials↗

DOE OSTI2021

Lattice thermal transport in two-dimensional alloys and fractal heterostructures

Abstract Engineering thermal transport in two dimensional materials, alloys and heterostructures is critical for the design of next-generation flexible optoelectronic and energy harvesting devices. Direct experimental characterization of lattice thermal conductivity in these ultra-thin systems is challenging and the impact of dopant atoms and hetero-phase interfaces, introduced unintentionally during synthesis or as part of deliberate material design, on thermal transport properties is not understood. Here, we use non-equilibrium molecular dynamics simulations to calculate lattice thermal conductivity of $${\mathrm {(Mo|W)Se_2}}$$ ( Mo | W ) Se 2 monolayer crystals including $${\mathrm {Mo}}_{1-x}{\mathrm {W}}_x{\mathrm {Se_2}}$$ Mo 1 - x W x Se 2 alloys with substitutional point defects, periodic $${\mathrm {MoSe_2}|\mathrm {WSe_2}}$$ MoSe 2 | WSe 2 heterostructures with characteristic length scales and scale-free fractal $${\mathrm {MoSe_2}}|{\mathrm {WSe_2}}$$ MoSe 2 | WSe 2 heterostructures. Each of these features has a distinct effect on phonon propagation in the crystal, which can be used to design fractal and periodic alloy structures with highly tunable thermal conductivities. This control over lattice thermal conductivity will enable applications ranging from thermal barriers to thermoelectrics.

42 ENGINEERING↗

DOE OSTI2021

Spectra of perfect state transfer Hamiltonians on fractal-like graphs

Abstract In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer (PQST): the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between PQST, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.

Physics↗

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 OSTI2025

Mesoscale fractal whey protein particles derived from microscale linear-shaped protein assemblies (Part 1): Manufacturing method and particle characteristics

Whey protein isolates (WPI) are widely used in processed foods for their versatile functional properties. Modifying the structural properties of proteins by assembling them into mesoscale or microscale particles may improve their functionality and broaden their applications. This study aims to manufacture and characterize mesoscale whey protein particles (WPP) derived from WPI. Two types of WPP, WPP1 (0.05 mL/min) and WPP2 (0.25 mL/min), were prepared through a multistep approach involving liquid antisolvent (LAS) precipitation, heat treatment, and microfluidization. Liquid antisolvent precipitation was performed by injecting a 20% (wt/vol) WPI dispersion (pH 7) into an ethanol-glycerol mixture (75:25, vol/vol) under laminar flow, followed by heat treatment at 80°C for 20 min as a particle hardening step. This process produced stable fiber- and ribbon-shaped whey protein assemblies (WPA), which served as precursors to WPP. Subsequent microfluidization (150 MPa, 6 passages) reduced the size of WPA, yielding mesoscale WPP with irregular morphologies and a more uniform size distribution, as revealed by microscopy and dynamic light scattering. ζ-Potential and fluorescence labeling indicated higher surface charge and surface hydrophobicity of WPP compared with untreated WPI. The WPP showed internal mass fractal and surface fractal structures at larger length scales, analyzed using small-angle X-ray scattering. Fourier transform infrared spectroscopy demonstrated an increased fraction of intermolecular β-sheets in WPP, suggesting that hydrogen bonding contributed to their formation. Gel electrophoresis confirmed that disulfide bonds served as the primary cross-links stabilizing the WPP structure. Furthermore, turbidity measurements showed that WPP exhibited superior colloidal phase stability compared with untreated WPI and maintained high colloidal stability under both acidic and neutral pH conditions.

Antisolvent precipitation↗

NASA NTRS1987

A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars

Global spectra are available for topography and geoid on the earth, Venus, Mars, and the moon. If the spectral energy density has a power law dependence on wave number, a fractal is defined. The topography spectrum for the earth is a well-defined fractal with D = 1.5; this corresponds to Brown noise with the amplitude proportional to the wavelength. Although there is more scatter for the other planetary bodies, the data for Mars and the moon correlate well with the data for the earth. Venus topography also exhibits a Brown noise behavior but with a smaller amplitude. The power law dependence of the earth's geoid is known as Kaula's law. It is shown that uncompensated Brown topography gives a geoid with a power law dependence that is in quite good agreement with Kaula's law. However, the required amplitude is only 8 percent of the observed topography. A similar result is found for the other bodies, with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72 percent for the moon.

Turcotte, Donald L.↗

NASA NTRS1988

Aerodynamic properties of fractal grains - Implications for the primordial solar nebula

Gas-grain and grain-grain interactions have a significant role in the evolution of the primordial solar nebula. There is also compelling evidence for larger grains in dense interstellar clouds than in the diffuse interstellar medium. In the usual treatments of grain collisions, where it is assumed that collisions produce compact bodies with a constant density, the gas drag decreases rapidly with size. The first step toward a quantitative analysis of the aerodynamic behavior of fractal aggregates is reported here, and it is shown that for fractals drag decreases very slowly.

Meakin, P.↗

NASA NTRS1988

Fractal structure of interstellar cirrus

The paper investigates the fractal structure of some of the infrared cirrus discovered by IRAS. The clouds studied are characterized by a perimeter with fractal dimension 1.26 + or - 0.04 using the method of Lovejoy. This dimension was found to be essentially constant from region to region. Methods of calculating this dimension are compared and the relation of this quantity to some other observable cloud properties is discussed.

Bazell, D.↗

NASA NTRS1988

The topology of fractal universes

It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.

Hamilton, A. J. S.↗

NASA NTRS1987

Nonlinear dynamics, fractals, cardiac physiology and sudden death

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.↗

NASA NTRS1989

Fractal dust grains around R Coronae Borealis stars

Discrete dipole approximation calculations of the optical properties of random fractal aggregates of graphite spheroids show a UV absorption feature that is too wide and centered at too long a wavelength to fit the observed interstellar 2200-A feature, but which is a good match to the 2400-A feature seen in the hydrogen-deficient R CrB stars reported by Hecht et al. (1984). Graphite fractal grains also match the UV bump and large long-wavelenvth extinction seen in laboratory studies of carbon smoke published by Bussoletti et al. (1987), which are usually attributed to amorphous carbon.

Wright, Edward L.↗

NASA NTRS1990

Fractal boundaries in magnetotail particle dynamics

It has been recently established that particle dynamics in the magnetotail geometry can be described as a nonintegrable Hamiltonian system with well-defined entry and exit regions through which stochastic orbits can enter and exit the system after repeatedly crossing the equatorial plane. It is shown that the phase space regions occupied by orbits of different numbers of equatorial crossings or different exit modes are separated by fractal boundaries. The fractal boundaries in an entry region for stochastic orbits are examined and the capacity dimension is determined.

Chen, J.↗

NASA NTRS1990

The effects of compositional inhomogeneities and fractal dimension on the optical properties of astrophysical dust

Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects.

Bazell, David↗