Search NASA⌕ Search

SEARCH · Search NASA

Results for “multifractality”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Merged interaction regions and large-scale magnetic field fluctuations during 1991: Voyager 2 observations

This paper analyzes Voyager 2 observations of the magnetic field between 33.6 AU and 36.2 AU during 1991 when extraordinary events were observed on the Sun and in the heliosphere. The magnetic field strength signal B(t) has the unusual form of two large transient merged interaction regions (MIRs) on a fluctuating background. The two MIRs moved past the spacecraft in 32 days and 18 days, respectively. The mean field strength in each transient MIR was approx. equals 2.6 times the mean field during the remaining part of the year (0.11 nT). Each of the MIRs is related to a fast stream. The magnetic field is strong throughout each stream, suggesting that the strong fields are carried by the streams as well as produced by shock and stream compression. The fluctuations in B(t) during 1991 are not multifractal, and the MIRs cannot be approximated as multifractal clusters of intense magnetic fields. The distribution of the hour-averaged magnetic field strengths is approximately lognormal over 90% of its intermediate range, and it has an exponential tail for B greater than the average magnetic field strength. The elevation angles of B have a normal distribution with a standard deviation of 16 deg +/- 4 deg. The distributions of the azimuthal angles of B in the ranges 1 deg - 180 deg and 180 deg - 360 deg are approximately normal over a more limited range, and non-Gaussian tails associated with nearly radial magnetic fields; the standard deviations are approx. equal to 40 deg. Individual sectors are present throughout most of the interval, even in the MIRs, but there is no recurrent sector pattern. A model of the large-scale fluctuations in 1991 will have to include both determinaistic and statistical factors.

Burlaga, L. F.↗
NASA NTRS2005

Plasma sheet turbulence observed by Cluster II

Cluster fluxgate magnetometer (FGM) and ion spectrometer (CIS) data are employed to analyze magnetic field fluctuations within the plasma sheet during passages through the magnetotail region in the summers of 2001 and 2002 and, in particular, to look for characteristics of magnetohydrodynamic (MHD) turbulence. Power spectral indices determined from power spectral density functions are on average larger than Kolmogorov's theoretical value for fluid turbulence as well as Kraichnan's theoretical value for MHD plasma turbulence. Probability distribution functions of the magnetic fluctuations show a scaling law over a large range of temporal scales with non-Gaussian distributions at small dissipative scales and inertial scales and more Gaussian distribution at large driving scales. Furthermore, a multifractal analysis of the magnetic field components shows scaling behavior in the inertial range of the fluctuations from about 20 s to 13 min for moments through the fifth order. Both the scaling behavior of the probability distribution functions and the multifractal structure function suggest that intermittent turbulence is present within the plasma sheet. The unique multispacecraft aspect and fortuitous spacecraft spacing allow us to examine the turbulent eddy scale sizes. Dynamic autocorrelation and cross correlation analysis of the magnetic field components allow us to determine that eddy scale sizes fit within the plasma sheet. These results suggest that magnetic field turbulence is occurring within the plasma sheet resulting in turbulent energy dissipation.

Weygand, James M.↗
NASA NTRS2009

Statistical and Scaling Properties of Remotely-Sensed Soil Moisture in Two Contrasting Domains in the North American Monsoon Region

Characterizing soil moisture (theta) variability is important for inferring high-resolution information from coarse estimates provided by remote sensors. In this study, we analyze the spatial variability and scale invariance of high-resolution theta estimates collected in two contrasting semiarid areas, Arizona (AZ) and Sonora (SON), during the Soil Moisture Experiment - North American Monsoon in 2004 (SMEX04- NAME). Results reveal that as the mean theta condition ( ) becomes drier, the spatial standard deviation becomes smaller in both domains. The coefficient of variation of theta decreases with in SON, but does not display a clear tendency with in AZ. We also found the presence of scale invariance and multifractality in the range of support scales from 51.2 km to 0.8 km for all soil moisture fields in the two regions. The multifractal properties of theta are clearly linked to in SON, while the relation is affected by more dispersion in AZ. We argue this is due to differences in the dynamic (rainfall) and static (vegetation) controls on theta in the two domains.

Mascaro, Giuseppe↗
DOE OSTI2024

Thermal shock resistance of additively manufactured alumina

The mechanical behavior and cracking patterns of thermally-shocked additively manufactured alumina were investigated. The flexural strength of test specimens that had been heated to temperatures ranging from 200°C to 1000°C and then rapidly quenched in water was determined at ambient temperature by four-point bending. Results indicated that the surface cracking patterns had a multifractal structure and that an increase in the thermal shock temperature led to an increase in the density and uniformity of the crack network. Further, the flexural strength results were analyzed with Weibull statistics, where the Weibull moduli for most of the thermal shock conditions tested were found to be statistically indistinguishable. It was also found that a significant decrease (~50%) in flexural strength occurred for heating temperatures ≥300°C. The effect of the manufacturing method on cracking patterns is discussed, as well as the implication of the material behavior for practical applications of these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Magic-angle semimetals

Abstract Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

Materials Science↗
DOE OSTI2020

Magic-angle semimetals with chiral symmetry

Here, we construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states (DOS) and subdiffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique “unfreezing” transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy DOS develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

Here, we study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a “dual” composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν = 2.56 ± 0.02 and η = 0.51 ± 0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. Finally, we argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Scaling and Complexity of Stress Fluctuations Associated with Smooth and Jerky Flow in FeCoNiTiAl High-Entropy Alloy

Recent observations of jerky flow in high-entropy alloys (HEA) revealed a high role of self-organization of dislocations in their plasticity. The present work reports the first results of the investigation of stress fluctuations during plastic deformation of an FeCoNiTiAl alloy, examined in a wide temperature range covering both smooth and jerky flow. These fluctuations, which accompany the overall deformation behavior representing an essentially slower stress evolution controlled by the work hardening, were processed using complementary approaches comprising Fourier spectral analysis, refined composite multiscale entropy, and multifractal formalisms. The joint analysis at distinct scales testified that even a macroscopically smooth plastic flow is accompanied by nonrandom fluctuations, disclosing the self-organized dynamics of dislocations. Qualitative changes in such a fine-scale “noise” were found with varying temperature. The observed diversity is significant for understanding the relationships between different scales of plasticity of HEAs and crystal materials in general.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Solar wind behavior throughout the heliosphere

Observations and interpretations of solar wind behavior in the heliosphere are reviewed. The spiral magnetic field, the heliospheric vortex street, multifractals and large-scale fluctuations, and intermittent turbulence are examined. Voyager observations of the outer heliosphere are stressed.

Burlaga, L. F.↗
NASA NTRS1991

Direct simulation of turbulent combustion

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct simulation appears to be one of the most attractive tools to use in addressing this problem. From Sep. 1989 - Sep. 1990, the following problems were studied using direct simulation but also experiments and theoretical models: (1) the influence of curvature on premixed flame fronts; (2) the construction of a model for the flame stretch based on direct simulation and multifractal analysis; and (3) the simulation of the interaction between random flow field and a flame front. The general objective was to improve knowledge of turbulent combustion but also to use this information for turbulent combustion models. The transfer of direct simulation results towards models is also in progress. A submodel to evaluate the flame stretch was derived from the present study and incorporated in the Coherent Flame model used in France for piston and aircraft engines.

Poinsot, Thierry J.↗
NASA NTRS1993

Two-dimensional radiative transfer in cloudy atmospheres - The spherical harmonic spatial grid method

A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.

Evans, K. F.↗
NASA NTRS1995

On the spatial distribution of magnetic fields on the solar surface

Recent measurements of solar surface magnetic fields suggest that the spatial distribution of these fields is fractal. In order to understand the physical basis for such geometric complexity, we study here the advection of magnetic flux tubes relatively simple random motions on the surface of a fluid and investigate the spatial statistics of the resulting surface field. While this study does not directly address the question of why solar surface fields have the observed spatial structure, it is designed to build our intuition about how surface flows lead to complex spatial structuring of magnetic fields. As part of our study, we discuss the various methods by which one can describe the spatial distribution of the surface magnetic flux and relate them mathematically; this turns out to be a crucial point of our work since, as we show, a number of previous analyses have misinterpreted the analysis procedures for determining fractal dimensions. Our principal result is the explicit demonstration that simple random flows lead to magnetic flux spatial distributions with a multifractal dimension spectrum. Furthermore, we demonstrate that this magnetic spatial structure is generic, i.e., is characteristic of a very large class of random flows.

Tao, L.↗
NASA NTRS1995

Intermittency and extended self-similarity in the solar wind turbulence

Using the satellite measurements of the velocity field in the interplanetary plasma. we present some analysis which show the presence of a self-similar intermittent state in the solar wind turbulence. We used the so called Extended Self-Similarity hypothesis, which is well visible in the solar wind turbulence, showing convincing evidences for the presence of universal anomalous scaling laws. Through the Extended Self-Similarity we are able to calculate the scaling exponents of the velocity structure functions with very small uncertainties, and we show that these scaling exponents are in very good agreement with the multifractal models describing intermittency in magnetohydrodynamic flows.

Bruno, R.↗
NASA NTRS1997

Evaluation of Two Fractal Methods for Magnetogram Image Analysis

Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Centers vector magnetograph.

Stark, B.↗
NASA NTRS2000

Size-Selective Concentration of Chondrules and Other Small Particles in Protoplanetary Nebula Turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive bodY precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region. both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (less than 10(exp 5)) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.

Cuzzi, Jeffrey N.↗