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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.

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At least 325 records · Page 18

Long-term Evolution of Tightly Packed Stellar Black Holes in AGN Disks: Formation of Merging Black Hole Binaries via Close Encounters

We study the long-term evolution of two or more stellar black holes (BHs) on initially separated but unstable circular orbits around a supermassive BH (SMBH). Such a close-packed orbital configuration can naturally arise from BH migrations in the AGN disk. Dynamical instability of the orbits leads to recurring close encounters between two BHs, during which the BH separation r p becomes less than the Hill radius R H . In rare very close encounters, a tight merging BH binary can form with the help of gravitational wave emission. We use N-body simulations to study the time evolution of close encounters of various degrees of closeness. For a typical "SMBH+2BH" system, the averaged cumulative number of close encounters (with r p ≲ R H ) scales approximately as ∝ t 0.5 . The minimum encounter separation r p follows a cumulative distribution P( p ) ∝ r p for r p « R H . We obtain a semi-analytical expression for the averaged rate of binary captures that lead to BH mergers. Our results suggest that close-packed BHs in AGN disks may take a long time (≳10 7 orbits around the SMBH) to experience a sufficiently close encounter and form a bound binary. This time can be shorter if the initial BH orbits are highly aligned. The BH binary mergers produced in this scenario have high eccentricities when entering the LIGO band and broad distribution of orbital inclinations relative to the original AGN disk. We explore the effects of the gas disk and find that simple gas drags on the BHs do not necessarily lead to an enhanced BH binary capture rate.

79 ASTRONOMY AND ASTROPHYSICS↗

Autonomous monitoring of algal biomass: Success stories and lessons learned from long-term field deployment

Autonomous, high-frequency monitoring of outdoor algal ponds is needed to quantify biomass productivity and detect culture decline in environments prone to contamination, grazers, and variable operating conditions. We report successes and lessons learned in translating a laboratory spectroradiometric monitoring approach to a multi-year autonomous field deployment at the Arizona Center for Algae Technology and Innovation (AzCATI). The system measures spectrally resolved pond reflectance by ratioing upwelling radiance from each raceway to simultaneous downwelling sky irradiance using fiber-coupled spectrometers. A physics-based reflectance model (ASHARP) is fit to each spectrum pair to estimate optical parameters, including a biomass-proxy coefficient (C a ) which enables near-real-time tracking of biomass accumulation and culture state at 2–5 min intervals. From May 2022 through September 2025 the platform operated continuously while scaling from two to six raceway ponds. Several strains of algae were monitored successfully, including the high productivity Tetraselmis striata and Picochlorum celeri. Transitioning data acquisition from a Windows laptop to a Raspberry Pi improved uptime from 57% (2022) to ~89% (2024–2025) and enabled routine real-time analysis. Further, we converted relative biomass estimates to absolute ash-free dry weight (AFDW) using experimentally-derived calibrations, providing field-relevant biomass predictions with conservative confidence bounds. These results demonstrate the feasibility of long-term, autonomous optical monitoring for well-mixed open-raceway algal cultivation and provide practical guidance for reliable field operation and scaling.

Katinas, Christopher Michael [Sandia National Labo↗

Oxidation Lifetime Modeling of 625 and 120 Foils After Long-term Exposure in Flowing Air + 10% ${\hbox {H}_2\hbox {O}}$ at 700 and 800 $^\circ$C

A model describing oxidation kinetics considering simultaneous oxidation and volatilization of external oxide scales was integrated with a CALPHAD-based coupled thermodynamic and kinetic approach to predict the oxidation-induced lifetime of foils of alloys 625 and 120. Long-term exposures in flowing air +10% H 2 O at 700 and 800 °C under two flow velocities were used to validate the modeling results. The time to a critical Cr concentration of 10 wt% at the oxide/alloy interface, t 10 , was shown to correlate with the breakdown of the Cr 2 O 3 scale for the studied experimental conditions. Finally, the modeling approach was extended to consider time-dependent oxidation and volatilization rate constants to develop a more appropriate lifetime criterion for microturbine recuperator foils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using Neural Network Force Fields to Ascertain the Quality of Ab Initio Simulations of Liquid Water

Accurately simulating the properties of bulk water, despite the apparent simplicity of the molecule, is still a challenge. In order to fully understand and reproduce its complex phase diagram, it is necessary to perform simulations at the ab initio level, including quantum mechanical effects both for electrons and nuclei. This comes at a high computational cost, given that the structural and dynamical properties tend to require long timescales and large simulation cells. In this work, we evaluate the errors that density functional theory (DFT)-based simulations routinely incur into due time- and size-scale limitations. These errors are evaluated using neural-network-trained force fields that are accurate at the level of DFT methods. We compare different exchange and correlation potentials for properties of bulk water that require large timescales. Here we show that structural properties are less dependent on the system size and that dynamical properties such as the diffusion coefficient have a strong dependence on the simulation size and timescale. Our results facilitate comparisons of DFT-based simulation results with experiments and offer a path to discriminate between model and convergence errors in these simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Automatic Drift Correction through Nonlinear Sensing

For successful design and operation of advanced monitoring and control systems, engineers rely on high quality sensor signals that are simultaneously accurate, representative, voluminous, and timely. Unfortunately, sensor faults are common and lead to short-lived symptoms, such as outliers and spikes as well as long-lived symptoms, such as sensor drift. Sensor drift belongs to the category of incipient faults. These are particularly challenging to detect, diagnose, and correct as the time scales of these faults are typically longer than the time scales of the system dynamics that are of interest. Moreover, if sensor drift occurs as a result of exposure to measured medium, then it is likely that multiple sensors will exhibit similar drift rates, thus challenging fault management strategies based on redundancy. In this contribution, we present a first method that can handle this unique challenge.

Chowdhury, Dhruba↗

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗

Transformers and Long Short-Term Memory Transfer Learning for GenIV Reactor Temperature Time Series Forecasting

Automated monitoring of the coolant temperature can enable autonomous operation of generation IV reactors (GenIV), thus reducing their operating and maintenance costs. Automation can be accomplished with machine learning (ML) models trained on historical sensor data. However, the performance of ML usually depends on the availability of large amount of training data, which is difficult to obtain for GenIV, as this technology is still under development. We propose the use of transfer learning (TL), which involves utilizing knowledge across different domains, to compensate for this lack of training data. TL can be used to create pre-trained ML models with data from small-scale research facilities, which can then be fine-tuned to monitor GenIV reactors. In this work, we develop pre-trained Transformer and long short-term memory (LSTM) networks by training them on temperature measurements from thermal hydraulic flow loops operating with water and Galinstan fluids at room temperature at Argonne National Laboratory. The pre-trained models are then fine-tuned and re-trained with minimal additional data to perform predictions of the time series of high temperature measurements obtained from the Engineering Test Unit (ETU) at Kairos Power. The performance of the LSTM and Transformer networks is investigated by varying the size of the lookback window and forecast horizon. The results of this study show that LSTM networks have lower prediction errors than Transformers, but LSTM errors increase more rapidly with increasing lookback window size and forecast horizon compared to the Transformer errors.

LSTM↗

The channel-source hypothesis: Empirical evidence for in-channel sourcing of dissolved organic carbon to explain hysteresis in a headwater mountain stream

Catchment hydrologists have long puzzled over the question: How can catchments rapidly generate storm flows and pulses of solutes in response to storm events? Conceptual models viewing catchments as composed of discrete source areas generating flow at unique time scales and with unique chemical characteristics have been used to explain the observed changes in flow and water chemistry. Surprisingly, those conceptual models usually do not treat the stream channel as one of the potential source areas. We propose the channel-source hypothesis in which the stream itself should be considered as a potential source with the same rigour as other contributing areas. We pose this in the spirit of the scientific use of the word: a hypothesis is not a proven idea but rather a provisional supposition serving as the basis for further study. We suggest that the channel should be considered as a potential source for dissolved organic carbon (DOC). Channels store substantial amounts of organic matter, and stream ecologists have long studied stream carbon cycling. From those studies, we know that leaching and decomposition can generate DOC from particulate organic carbon (POC). Further, POC is stored in channel ‘dead-zones’—regions of low flow velocity - that can be activated as flow velocity increases, thus releasing accumulated DOC during storms. All catchments are different; there is no reason to assume that channel sources are always important, in every catchment, in every storm. Thus, the channel-source hypothesis does not replace existing conceptual models. Instead, it adds another potential mechanism that may explain DOC dynamics observed in streams. The channel-source hypothesis has substantial implications for catchment studies examining sources of DOC in stream water or using DOC as a tracer to determine the locations of, and proportional contributions of, different source areas for streamflow generation.

54 ENVIRONMENTAL SCIENCES↗

Post-compression of long-wave infrared 2 picosecond sub-terawatt pulses in bulk materials

We have experimentally demonstrated the post-compression of a long-wave infrared (9.2 μm) 150 GW peak power pulse from 2 ps to less than 500 fs using a sequence of two bulk materials with negative group velocity dispersion (GVD). The compression resulted in up to 1.6-fold increase of the peak power and up to 2.8-fold increase of the intensity in the center of a quasi-Gaussian beam. The partial decoupling of the self-phase modulation and chirp compensation stages by using two materials with significantly different ratios of nonlinear refractive index to GVD provides accurate optimization of the compression mechanism and promises a viable path to scaling peak powers to supra-terawatt levels. During the preparatory study, we measured, for the first time to our knowledge, the nonlinear refractive indices of NaCl, KCl, and BaF 2 for picosecond pulses in the long-wave infrared region.

43 PARTICLE ACCELERATORS↗

Little prairie under the panel: testing native pollinator habitat seed mix establishment at three utility-scale solar sites in Minnesota

Abstract As more land is being utilized for large-scale solar energy projects, there are increasing discussions from stakeholders on how to utilize land under solar panels to promote biodiversity. One path is to plant habitat beneficial to pollinators and other insects, but there have been few long-term studies that examine how different vegetation and seed mixes establish underneath solar panels. This study addresses a scientific gap to determine whether native pollinator seed mixes successfully establish over time under solar arrays using a systematic assessment of eight seed mixes planted at three utility-scale solar sites in Minnesota. We assess establishment with a percent native coverage metric, which is an assessment of native species observations compared to total observations during percent cover analyses in our vegetative test plots. The percent native coverage metric allows for a measurement of how the seed mix established and how the seed mix persists over time. The percent native coverage under and in between the solar photovoltaic (PV) arrays rose from 10% after one year of planting to 58% after three years across all sites, while the native coverage of the full sun control area rose from 9.6% to 70% under the same period, showing that native prairie and pollinator plants successfully established under the array, although to a lesser extent than in full sun conditions. Percent native coverage under the PV arrays rose 5- to 8-fold for each of the three sites from over the course of the study, while the coverage of weeds decreased for all three sites over the same period. Percent native coverage varied by seed mix over the project years, but every seed mix experienced a higher percent native coverage year after year under the PV arrays. Our results did not indicate a difference in establishment across placement within the array; the center, west, and east portions of the areas in between panels had similar establishment rates at two out of three sites, indicating that the same seed mix can be applied throughout the array. Out of 101 plant species seeded, we observed the establishment of 68 species in our vegetative test plots, and we detailed the top 20 observed species to inform future seed mix development. Based on these findings, native pollinator vegetation can establish over time at solar arrays, and it can be suitable for creating habitat at utility-scale solar sites.

14 SOLAR ENERGY↗

A robust deep learning workflow to predict multiphase flow behavior during geological C O 2 sequestration injection and Post-Injection periods

Simulation of multiphase flow in porous media is essential to manage the geologic CO 2 sequestration (GCS) process, and physics-based simulation approaches usually take prohibitively high computational cost due to the nonlinearity of the coupled physics. This paper contributes to the development and evaluation of a deep learning workflow that accurately and efficiently predicts the temporal-spatial evolution of pressure and CO 2 plumes during injection and post-injection periods of GCS operations. Based on a Fourier Neural Operator, the deep learning workflow takes input variables or features including rock properties, well operational controls and time steps, and predicts the state variables of pressure and CO 2 saturation. To further improve the predictive fidelity, separate deep learning models are trained for CO 2 injection and post-injection periods due to the difference in primary driving force of fluid flow and transport during these two phases. We also explore different combinations of features to predict the state variables. We use a realistic example of CO 2 injection and storage in a 3D heterogeneous saline aquifer, and apply the deep learning workflow that is trained from physics-based simulation data and emulate the physics process. Through this numerical experiment, we demonstrate that using two separate deep learning models to distinguish post-injection from injection period generates the most accurate prediction of pressure, and a single deep learning model of the whole GCS process including the cumulative injection volume of CO 2 as a deep learning feature, leads to the most accurate prediction of CO 2 saturation. For the post-injection period, it is key to use cumulative CO 2 injection volume to inform the deep learning models about the total carbon storage when predicting either pressure or saturation. The deep learning workflow not only provides high predictive fidelity across temporal and spatial scales, but also offers a speedup of 250 times compared to full physics reservoir simulation, and thus will be a significant predictive tool for engineers to manage the long-term process of GCS.

58 GEOSCIENCES↗

Optically heralded microwave photon addition

Photons with optical frequencies of a few hundred terahertz are perhaps the only way to distribute quantum information over long distances. Superconducting qubits, which are one of the most promising approaches for realizing large-scale quantum machines, operate on microwave photons at frequencies that are ~40,000 times lower. To network these quantum machines across appreciable distances, we must bridge this frequency gap. Here we implement and demonstrate a transducer that can generate correlated optical and microwave photons. In this study, we use it to show that by detecting an optical photon we generate an added microwave photon with an efficiency of ~35%. Our device uses a gigahertz nanomechanical resonance as an intermediary, which efficiently couples to optical and microwave channels through strong optomechanical and piezoelectric interactions. We show continuous operation of the transducer with 5% frequency conversion efficiency, input-referred added noise of ~100, and pulsed microwave photon generation at a heralding rate of 15 Hz. Optical absorption in the device generates thermal noise of less than two microwave photons. Improvements of the system efficiencies and device performance are necessary to realize a high rate of entanglement generation between distant microwave-frequency quantum nodes, but these enhancements are within reach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Structural dynamics of a thermally silent triiron( II ) spin crossover defect grid complex

The structural evolution of spin crossover (SCO) complexes during their spin transition at equilibrium and out-of-equilibrium conditions needs to be understood to enable their successful utilisation in displays, actuators and memory components. In this study, diffraction techniques were employed to study the structural changes accompanying the temperature increase and the light irradiation of a defect [2 × 2] triiron(II) metallogrid of the form [Fe II 3 L H 2 (HL H ) 2 ](BF 4 ) 4 ·4MeCN (FE3), L H = 3,5-bis{6-(2,2'-bipyridyl)}pyrazole. Although a multi-temperature crystallographic investigation on single crystals evidenced that the compound does not exhibit a thermal spin transition, the structural analysis of the defect grid suggests that the flexibility of the grid, provided by a metal-devoid vertex, leads to interesting characteristics that can be used for intermolecular cooperativity in related thermally responsive systems. Time-resolved photocrystallography results reveal that upon excitation with a ps laser pulse, the defect grid shows the first two steps of the out-of-equilibrium process, namely the photoinduced and elastic steps, occurring at the ps and ns time scales, respectively. Similar to a previously reported [2 × 2] tetrairon(II) metallogrid, FE3 exhibits a local distortion of the entire grid during the photoinduced step and a long-range distortion of the lattice during the elastic step. Although the lifetime of the pure photoinduced high spin (HS) state is longer in the tetranuclear grid than in the defect grid, suggesting that the global nuclearity plays a crucial role for the lifetime of the photoinduced species, the influence of the co-crystalising solvent on the lifetime of the photoinduced HS state remains unknown. This study sheds light on the out-of-equilibrium dynamics of a thermally silent defect triiron SCO metallogrid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The use of wholesale market purchases by Western U.S. electric utilities

Load Serving Entities (LSEs) can procure electricity from their owned generation or purchase it on bilateral or centrally organized markets. Electric utility procurement decisions have important implications for resource adequacy, which is gaining attention especially in the Western U.S. However, there is little or no research on trends of utility procurement practices, and the role that wholesale market transactions can have for resource adequacy and other applications. This paper leverages information from the U.S. Department of Energy’s Energy Information Administration, Berkeley Lab’s Resource Planning Portal, and structured interviews with regulatory and utility staff. We find that use of market transactions to meet electric energy needs has been increasing across U.S. LSEs. The reasons for this trend include a general stagnation in building owned resources, a preference towards contracting renewable energy resources to meet RPS targets, and the lower relative cost of wholesale market electricity. Among market transactions across different time scales, short-term transactions were prevalent in Western U.S. LSEs until the 2008 recession, and thereafter declined to about a quarter of total purchases. In contrast, long-term market transactions have become more prevalent and resource planning reports project the share of these transactions in the procurement mix may continue to increase. Results suggest resource adequacy obligations may drive preferences for asset ownership more than a profit incentive. We also recommend improving the planning to procurement connection by reflecting in planning assumptions the operational constraints of market transactions. These results provide insights on key issues in electric utility procurement that could improve overall market efficiency, respond to rapidly changing industry conditions, and identify practices that LSEs and regulators should consider incorporating into their long-term transmission and capacity planning processes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Sentinel Devices LLC (CRADA Final Report)

Industrial equipment is a critical component of virtually all at-scale manufacturing and infrastructure. Broadly speaking, modern equipment is predominantly controlled using hardened digital controllers – computers designed to be able to operate continuously for sometimes extremely long periods of time, with little to no maintenance. Due to the nature of how these digital controllers have evolved, they are solely optimized to execute a single task, and do not have the capabilities or resources to monitor or analyze their internal state beyond simple execution of their program. As a result, for many “common sense” situations where individual data points can be easily determined to be out-of-normal, the controllers are unable to identify these incorrect operational modes unless a human has explicitly programmed in detection of this degradation. This project seeks to develop an AI/ML system which can identify incorrect or anomalous trends in industrial data streams, of exactly the kind that would be produced and seen by these digital controllers, with a minimal amount of computing resources. The benefits produced by developing this system would ultimately be self-monitoring and self-reporting infrastructure, capable of identifying and alerting humans to issues as soon as they happen, potentially long before they have the chance to impact the industrial process.

42 ENGINEERING↗

Crucible Melter Simulation in Nek5000

Nuclear tank waste at the Hanford site is slated for vitrification in large scale refractory-lined melters to transform it into a stable borosilicate waste form suitable for long-term storage or disposal. Molten glass corrodes the refractory lining over time at a rate correlated to the velocity of molten glass against the refractory-lined wall. To properly design a melter and plan for maintenance, it is necessary to accurately model the glass flow and find the correlation between flow velocity and corrosion rate. This modeling was started in STAR-CCM+ CFD software and is being continued in Nek5000 for its fast-running and quick turnaround code. This poster explains the basic process of reconstructing the geometry, fluid properties, and heating of test melters in Nek5000. The geometry is imported from a mesh file and boundary conditions assigned based on surface IDs. The fluid properties are set in the .par and .usr case files. The heating of the actual crucibles in joule heating with electrodes but simulated in Nek5000 with a volumetric heat source term. This volumetric heat source is fit to the actual heating profile with piecewise polynomials and exponentials. Basic results and verification methods are explained in the poster, as well as further work that must be done to complete modeling.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Numerical Simulations in Support of a Long-Term Test of Gas Production from Hydrate Accumulations on the Alaska North Slope: Reservoir Response to Interruptions of Production (Shut-Ins)

In this work, we investigate by means of numerical simulation a planned year-long field test of depressurization-induced production from a permafrost-associated hydrate reservoir on the Alaska North Slope at the site of the recently drilled Hydrate-01 Stratigraphic Test Well. The main objective of this study is to assess quantitatively the impact of temporary interruptions (well shut-ins) on the expected fluid production performance from the B1 Sand of the stratigraphic Unit B during controlled depressurization over different time scales, as well as on other relevant aspects of the system response that have the potential to significantly affect the design of the field test. We consider eight different cases of depressurization, including (a) rapid depressurization over a 60-day period to a terminal bottomhole pressure P W of 2.8 MPa and (b) a slower depressurization rate to a final P W of 0.6 MPa at the end of the year-long production test, in addition to (c) a multi-step depressurization regime and (d) a quasi-linear continuous depressurization strategy. The results of the study indicate that shut-ins obviously reduce gas release and production during and immediately after their occurrence, but their longer-term effects are strongly dependent on the depressurization regime and on the time of observation, covering the entire range of potential outcomes. Shut-ins (a) have a universally strong negative effect when quasi-linear depressurization is involved regardless of the length of the production period, and (b) have a strong positive effect in multi-step depressurization schemes that becomes apparent earlier for large initial pressure drops, but (c) can also appear to have practically no effect for slow stepwise depressurization at the end of the year-long production test. Shut-ins lead to a rapid reformation of hydrates, even to the point of disappearance of a free gas phase in the reservoir. Rapid depressurization regimes lead to early maximum rates of hydrate dissociation and gas production, while the maximum rates occur at the end of the production test for the cases of slower depressurization. Shut-ins do not appear to have a significant impact on water production, as the cessation of production is followed by higher rates production when depressurization resumes. Similarly, (a) the fraction of produced CH 4 originating from exsolution from the water, (b) the water-to-gas ratio, and (c) the rate of replenishment of produced water by boundary inflows do not appear significantly affected by shut-ins, the effects of which seem to be temporary in the majority of the cases. The study confirmed the superiority of multi-step depressurization methods as the most effective strategies for hydrate dissociation and gas production and showed that two observation wells (located at distances of 30 and 50 m from the production well) are appropriately positioned and both able to capture the P, T, and S G behavior during the fluid production and shut-ins in any of the eight cases we investigated.

03 NATURAL GAS↗

Directional Variations in Tidal Flow Multifractality and Intermittency

We explored distinct directional variations of multifractal and intermittent characteristics of ebb and flood flow velocities at nodule point, WA, tidal energy site, and complementary inspection on the East River, NY using scaling exponents of the structure function, distribution flatness, detrending moving average (DMA) analysis, multifractal detrended fluctuation analysis (MF-DFA), and high-order spectral moments. Our findings reveal that tidal flow presents higher long-range dependence (LRD) and intermittent levels for the ebb flow sections, whereas the flood flow sections exhibit a higher degree of multifractality and greater sensitivity to larger magnitude of turbulent fluctuations. We demonstrate that long-range dependence predominantly contributes to multifractal behavior in both ebb and flood flows, as evidenced by the significantly reduced multifractal spectrum width for temporally randomly permuted time series. Moreover, spectral kurtosis analysis uncovers a higher intermittent level across all frequency scales for ebb flow sections and reveals a distinct pattern of tidal flow intermittency differing from the monotonically increasing intermittent level observed in wall-bounded and grid turbulence. Finally, we demonstrate that DMA, MF-DFA, and high-order spectral moments provide more comprehensive insights than structure function scaling exponents and PDF flatness methods.

Cheng, Shyuan [Univ. of Illinois at Urbana-Champai↗