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DOE OSTI2026

Toward memory-efficient melt pool monitoring: a classification framework using event-based imaging and sparse sensing technique

Vision sensors like CMOS and CCD cameras are often used for in-process monitoring of melt pools in laser-based additive and welding processes, but they require transferring large amounts of data and computational processing resources. Event-based neuromorphic imagery, on the other hand, detects only the change in pixel intensity, thus potentially reducing the data amount and latency. With an event imager, this study develops a framework for melt pool condition classification, including image construction, time scale selection, optimal pixel selection, and sparse classification, to achieve a highly memory-efficient scheme. These are based on sparse sensing techniques with singular value decomposition (SVD) and QR pivoting, the two fundamental matrix transformations for linear dimensionality reduction. The framework is then validated by classifying a controlled experiment by exciting various mode shapes of liquid gallium pools of varying depths (3, 6, and 8 mm). At 200 pixels, the classifier can reach overall accuracy of 75%, while at 2000 pixels (0.013% of the total possible pixels), the accuracy is nearly 90% (89.86%). At the same number of pixels, random selection can only achieve 46% and 67%, respectively. The memory savings of the sparsely sampled event data compared to a conventional imager is about 500 times. In addition to performance, implementation and limitations of the framework are also discussed.

42 ENGINEERING↗

NASA NTRS1994

Process modelling for materials preparation experiments

The main goals of the research under this grant consist of the development of mathematical tools and measurement techniques for transport properties necessary for high fidelity modelling of crystal growth from the melt and solution. Of the tasks described in detail in the original proposal, two remain to be worked on: development of a spectral code for moving boundary problems, and development of an expedient diffusivity measurement technique for concentrated and supersaturated solutions. We have focused on developing a code to solve for interface shape, heat and species transport during directional solidification. The work involved the computation of heat, mass and momentum transfer during Bridgman-Stockbarger solidification of compound semiconductors. Domain decomposition techniques and preconditioning methods were used in conjunction with Chebyshev spectral methods to accelerate convergence while retaining the high-order spectral accuracy. During the report period we have further improved our experimental setup. These improvements include: temperature control of the measurement cell to 0.1 C between 10 and 60 C; enclosure of the optical measurement path outside the ZYGO interferometer in a metal housing that is temperature controlled to the same temperature setting as the measurement cell; simultaneous dispensing and partial removal of the lower concentration (lighter) solution above the higher concentration (heavier) solution through independently motor-driven syringes; three-fold increase in data resolution by orientation of the interferometer with respect to diffusion direction; and increase of the optical path length in the solution cell to 12 mm.

Rosenberger, Franz↗

DOE OSTI2023

Implementation of a High-Fidelity Interface Resolving Method in Nek5000

The development and utilization of computational fluid dynamics (CFD) models for large, high-temperature electric melters in the Waste Treatment and Immobilization Plant (WTP) in eastern Washington State have proven to be valuable for various purposes. These models allow for a better understanding of the physio-chemical processes occurring within the melter vessels and can contribute to improving operational efficiency, throughput, and addressing operational issues related to vitrification. The CFD models employed for these melter vessels incorporate multiphase fluid flow and heat transfer simulations in different regions, including the plenum, cold cap, and molten glass regions. As the tank waste and glass formers are introduced into the melter, a reacting batch layer known as the cold cap forms on top of the molten glass. To enhance the melt rate, forced convection bubblers located at the bottom of the melters generate convection currents that help homogenize the molten glass and provide heat to the cold cap. As the bubbles rise through the highly viscous glass, they adopt a spherical-cap shape [1]. Meanwhile, the conversion of the batch to glass generates significant amounts of gases (such as water vapor, carbon dioxide, sulfur dioxide, and NOx) due to thermal decomposition [2]. These gases become trapped between the cold cap and molten glass, forming a foam layer [3]. For modeling multiphase flow in CFD and heat transfer simulations of waste glass melters at different scales, efforts are underway to augment the capabilities of the Nek5000 [4] and NekRS [5] open-source codes [6]. Nek5000/NekRS is a scalable and efficient spectral element code that has been successfully applied to a wide range of fluid dynamics problems. By leveraging the Nek5000/NekRS software, it becomes possible to model the melter systems more affordably and with lower computational requirements compared to currently utilized commercial CFD software. The specific objectives of this ongoing effort include: 1. Implementation of a level set method in Nek5000/NekRS: The level set method is a numerical technique commonly employed in CFD simulations to track and represent the interface between different phases or materials accurately. By incorporating this method into Nek5000/NekRS, the ability to simulate multiphase flows in waste glass melters at a high level of fidelity can be achieved. 2. Demonstration of capability for air bubbling through molten glass: As part of the development process, a specific case of air bubbling through molten glass will be simulated using the augmented Nek5000/NekRS code. This demonstration aims to showcase the ability of the software to accurately capture and analyze the complex phenomena involved in the multiphase flow within waste glass melters. By achieving these objectives, the improved Nek5000/NekRS code will offer a powerful computational tool for simulating and analyzing waste glass melter systems, enabling better understanding, optimization, and troubleshooting of these vitrification processes. The ability to accurately model and simulate multiphase flows has broad relevance across many industries and scientific domains, and the improved functionality can contribute to advancements in various fields beyond waste glass melter simulations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1994

Influence of flow on interface shape stability in low gravity

The objectives are to: (1) Understand the influence in low gravity of flow on interface shape. For example, document and control the influence of axial flow on the Plateau-Rayleigh instability of a liquid bridge; and (2) Extend the ground-based density-matching technique of low gravity simulation to situations with flow; that is, develop Plateau chamber experiments for which flow can be controlled. Containerless containment of liquid by surface tension has broad importance in low gravity. For space vehicles, the behavior of liquid/gas interfaces is crucial to successful liquid management systems. In microgravity science, free interfaces are exploited in various applications. Examples include float-zone crystal growth, phase separation near the critical point of liquid mixtures (spinoidal decomposition) and quenching of miscibility gap molten metal alloys. In some cases, it is desired to stabilize the capillary instability while in others it is desired to induce capillary breakup. In all cases, understanding the stability of interface shape in the presence of liquid motion is central.

Steen, Paul H.↗

DOE OSTI2022

ARPA-E PNDIODES "PN Junctions by Ion Implantation" Project (Final Report)

Electricity accounts for nearly 40% of the energy generated in the United States, of which 65% is lost to electrical system inefficiency before reaching end-use sectors. Power electronics will play a growing role in this distribution and end-use, with up to 80% of electricity estimated to pass through power electronics from generation to consumption by 2030. This gives technical improvements in power electronics enormous potential to drive efficiency gains throughout the U.S. economy. Current Si-based power architectures including MOSFETs and IGBTs are limited by high losses, low switching frequency, and poor high-temperature performance. Given the material properties of GaN, devices can exhibit a given turn-on resistance and breakdown voltage with a minute fraction of the area of a Si device—all with higher switching speeds. While n-type doping of III-nitrides has reached a high level of maturity and integration into commercialized products, p-type doping presents distinct challenges that requires continued research. The success of the next generation of GaN-based power devices depends in large part on the ability to form selective-area p-type regions, which can be accomplished by ion implantation of the prevailing acceptor dopant, Mg. This approach is relatively inexpensive and is a fab-ready processing step for creation of current-generation power electronic devices including BJTs, IGBTs, and diode rectifiers. However, ion implantation induces lattice damage and creates point defects within the material, which negatively impacts dopant activation annealing. These forms of damage may be removed by high-temperature annealing, however short annealing time and higher pressures are required to prevent decomposition of the material. We approach this challenge through an innovative combination of approaches toward obtaining high-conductivity p-type GaN. By the novel employment of a gyrotron, a microwave source that can be shaped into a highly localized beam to dissipate very high power in a semiconductor target, a wafer of GaN can be annealed in short (<2 s) ‘pulses’ at temperatures of 1450 °C (2640 °F) to achieve p-type activation without appreciable surface degradation. The p-type activation of Mg-implanted GaN can be further aided by co-implantation with N, believed to enhance the removal of point defects that compensate the acceptors dopant. Elevation to such high temperatures for even a short time induces degradation of GaN-to overcome, we have implemented additional measures to retain high-quality crystalline GaN while removing implant damage and activating Mg dopant. A bilayer cap of AlN is deposited by a combination of chemical and physical vapor deposition to protect the GaN surface. To prevent decomposition of GaN loss of N during annealing, a custom vessel—to contain pressurized N while allowing injection of microwave energy—is employed. By detailed study of the interaction of various measures that are implemented to protect the sample surface (GaN), activate the implanted dopants, and mitigate damage of the lattice heating damage during annealing, we are able to achieve p-type GaN and observe recovery of the crystal and removal of substantial density of defects created during the implantation process.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1994

Subband And Transform Compression Of Video Signals

Class of hierarchical subband coders developed primarily for compression of image data at video rates. Offers good performance with limited computational complexity and with flexibility inherent in subband decomposition. Particular subband decomposition chosen for coders appears to hide large quantitative errors effectively, largely because decomposition occurs along two-dimensional spatial-frequency-domain boundaries resembling spatial-frequency-domain curves of constant sensitivity of human visual system. Curves found approximately diamond-shaped: thus, low-pass filtering for reduction of data ideally involves nonrectangular passbands.

Sauer, Ken↗

NASA NTRS2019

High-Speed Schlieren Analysis of Retropropulsion Jet in Mach 10 Flow

High-speed schlieren imaging of a 5-in.-diam, 70° sphere-cone model with a single centerline 15° half-angle nozzle was performed in a Mach 10 flow. Image sequences captured at 100 kHz were obtained with the nozzle plugged (fully blunted model), no nozzle flow, and with nozzle flow over a range of supply pressures. The freestream unit Reynolds number was kept constant for all runs at3.38×106m−1. Time-average information pertaining to the location, width, and stand-off distance of the bow shock, interface, terminal shock, and triple point as a function of jet pressure ratio are presented based on analysis of covariance images from each run. Measurement of jet plume boundary shape as a function of jet pressure ratio is also presented. Analyses of frequency content associated with the jet structure are shown, as are results of the proper orthogonal decomposition of these data. For all runs with nozzle flow, a dominant fundamental frequency of 2 kHz was observed. Finally, a discussion of bow shock unsteadiness resulting from interaction with freestream disturbances for the blunted and no nozzle flow is provided, as is a discussion on the formation of weak waves emanating from the bow shock resulting from this interaction.

Brett F Bathel↗

NASA NTRS1992

An efficient solution procedure for the thermoelastic analysis of truss space structures

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

Givoli, D.↗

DOE OSTI2023

Reversibly growing crosslinked polymers with programmable sizes and properties

Growth constitutes a powerful method to post-modulate materials’ structures and functions without compromising their mechanical performance for sustainable use, but the process is irreversible. To address this issue, we here report a growing-degrowing strategy that enables thermosetting materials to either absorb or release components for continuously changing their sizes, shapes, compositions, and a set of properties simultaneously. The strategy is based on the monomer-polymer equilibrium of networks in which supplying or removing small polymerizable components would drive the networks toward expansion or contraction. Using acid-catalyzed equilibration of siloxane as an example, we demonstrate that the size and mechanical properties of the resulting silicone materials can be significantly or finely tuned in both directions of growth and decomposition. The equilibration can be turned off to yield stable products or reactivated again. During the degrowing-growing circle, material structures are selectively varied either uniformly or heterogeneously, by the availability of fillers. Our strategy endows the materials with many appealing capabilities including environment adaptivity, self-healing, and switchability of surface morphologies, shapes, and optical properties. Since monomer-polymer equilibration exists in many polymers, we envision the expansion of the presented strategy to various systems for many applications.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Strength characterization of solar-synthesized cylindrical graphite carbon–carbon composites

The present work describes a new morphology of cylindrical graphite synthesized in a unique manner by direct solar decomposition of methane and reports the mechanical properties of its manifestation in woven carbon–carbon composites. Whereas traditional carbon–carbon composites are formed via epoxy impregnation, the deposited material in the process presented here conformally follows the existing shape and orientation of individual carbon fibers. Through this process, cylindrical graphite fibers are synthesized that possess superior strength due to their graphitic layers that amalgamate into interlocked pathways between disparate fibers. Here, strength measurements, taken in tandem with Raman, XRD, and SEM, paint a picture of the shift from cloth to composite behavior via graphitization of the original substrate combined with sheets of graphene coalescing into a unified composite, with a notable improvement in elastic modulus from 0.19 to 2.66 GPa.

Carbon–carbon composite↗

NASA NTRS2021

Moisture and Temperature Influences on Nonlinear Vegetation Trends in Serengeti National Park

While long-term vegetation greening trends have appeared across large land areas over the late 20th century, uncertainty remains in identifying and attributing finer-scale vegetation changes and trends, particularly across protected areas. Serengeti National Park (SNP) is a critical East African protected area, where seasonal vegetation cycles support vast populations of grazing herbivores and a host of ecosystem dynamics. Previous work has shown how non-climate drivers (e.g. land use) shape the SNP ecosystem, but it is still unclear to what extent changing climate conditions influence SNP vegetation, particularly at finer spatial and temporal scales. We fill this research gap by evaluating long-term (1982–2016) changes in SNP leaf area index (LAI) in relation to both temperature and moisture availability using Ensemble Empirical Mode Decomposition and Principal Component Analysis with regression techniques. We find that SNP LAI trends are nonlinear, display high sub-seasonal variation, and are influenced by lagged changes in both moisture and temperature variables and their interactions. LAI during the long rains (e.g. March) exhibits a greening-to-browning trend reversal starting in the early 2000s, partly due to antecedent precipitation declines. In contrast, LAI during the short rains (e.g. November, December) displays browning-to-greening alongside increasing moisture availability. Rising temperature trends also have important, secondary interactions with moisture variables to shape these SNP vegetation trends. Our findings show complex vegetation-climate interactions occurring at important temporal and spatial scales of the SNP, and our rigorous statistical approaches detect these complex climate-vegetation trends and interactions, while guarding against spurious vegetation signals.

Moisture↗

DOE OSTI2022

Measuring the thermal and ionization state of the low- z IGM using likelihood free inference

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2005

Carbon Nanotubes/Nanofibers by Plasma Enhanced Chemical Vapour Deposition

Plasma enhanced chemical vapour deposition (PECVD) has been recently used for the production of vertically aligned carbon nanotubedfibers (CN) directly on substrates. These structures are potentially important technologically as electron field emitters (e.g. microguns, microwave amplifiers, displays), nanoelectrodes for sensors, filter media, superhydrophobic surfaces and thermal interface materials for microelectronics. A parametric study on the growth of CN grown by glow discharge dc-PECVD is presented. In this technique, a substrate containing thin film Ni catalyst is exposed to C2H2 and NH3 gases at 700 C. Without plasma, this process is essentially thermal CVD which produces curly spaghetti-like CN as seen in Fig. 1 (a). With the plasma generated by biasing the substrate at -6OOV, we observed that the CN align vertically during growth as shown in Fig. l(b), and that the magnitude of the applied substrate bias affects the degree of alignment. The thickness of the thin film Ni catalyst was found to determine the average diameter and inversely the length of the CN. The yield and density of the CN were controlled by the use of different diffusion barrier materials under the Ni catalyst. Patterned CN growth [Fig. l(c)], with la variation in CN diameter of 4.1% and 6.3% respectively, is achieved by lithographically defining the Ni thin film prior to growth. The shape of the structures could be varied from very straight nanotube-like to conical tip-like nanofibers by increasing the ratio of C2H2 in the gas flow. Due to the plasma decomposition of C2H2, amorphous carbon (a-C) is an undesirable byproduct which could coat the substrate during CN growth. Using a combination of depth profiled Auger electron spectroscopy to study the substrate and in-situ mass spectroscopy to examine gas phase neutrals and ions, the optimal conditions for a-C free growth of CN is determined.

Teo, K. B. K.↗

DOE OSTI2025

Revisiting the Role of Ocean Circulation Changes in Polar Ocean Heat Transport Anomalies under Global Warming

In response to greenhouse gas forcing, climate models predict that poleward ocean heat transport (OHT) weakens in the Southern Ocean but increases in the Arctic. The role of ocean circulation changes in this OHT response has been evaluated by decomposing OHT anomalies into a dynamic component (holding ocean temperature fixed while circulation evolves) and a thermodynamic component (holding ocean circulation fixed while temperature evolves). However, ocean temperature changes are themselves shaped by circulation changes through redistribution of the existing heat reservoir and subsequent effects on air–sea heat fluxes. The thermodynamic component can therefore be influenced by circulation changes, making the standard thermodynamic–dynamic decomposition incomplete for isolating the role of circulation changes in OHT anomalies. To address this issue, we use a passive–active decomposition to assess the relative contributions of ocean circulation and passive ocean temperature changes to polar OHT anomalies in a fully coupled climate model. Passive temperature changes are defined as those thermally forced by the atmosphere in the absence of circulation changes. In this passive–active decomposition, an advective term involving both circulation and passive temperature changes remains ambiguous—classifying it as active implies circulation changes dominate Southern Ocean OHT anomalies, whereas classifying it as passive implies temperature changes dominate. However, both interpretations imply that ocean circulation changes have a much weaker effect on polar OHT anomalies than inferred from the standard decomposition. In conclusion, these results help reconcile conclusions from studies using the standard decomposition with those using passive tracer methods to assess the role of circulation changes in polar OHT anomalies.

Arctic↗

NASA NTRS1990

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Geer, James F.↗

DOE OSTI2022

The effect of Ti content on age hardening and mechanical properties of uranium-titanium alloys

Here, the effect of Ti content on age hardening and the resulting mechanical properties are described for -quenched U-Ti alloys containing 0.3 wt.% to 2.0 wt.%Ti. Age hardening occurs between ~250°C and ~450°C. Overaging occurs at higher temperatures by cellular decomposition. Age hardening kinetics suggest that different mechanisms occur depending on Ti content and initial microstructure. Strengthening in 'a acicular martensites begins by the formation of Ti clusters which evolve into thin U 2 Ti disc shaped precipitates and later mature into continuous U 2 Ti rods beginning at peak hardness. The mechanism of hardening in 'b banded martensite is more elusive, as significant hardening occurs where atomic mobility is lower than that required for precipitate formation, similar to that reported for age hardening in ''b banded martensite in U-6%Nb. The activation energy for aging varies with Ti content and microstructure. In fully martensitic alloys containing 0.75% to 2.0%Ti it is in the vicinity of ~44 kcal/mole (184 kJ/mole). But it is lower in alloys containing less than 0.6%Ti where quenched microstructures are less than fully martensitic. Tensile ductility is high prior to aging, decreases with age hardening, is effectively zero at peak hardness, and remains low in overaged conditions. Attractive combinations of strength and ductility are best obtained in alloys containing 0.6% to 1.0%Ti which have been partially aged to fractional hardening levels no greater than ~0.6. This corresponds to the very early stages of aging, associated with clustering and the earliest stages of U 2 Ti disc formation. Alloys containing 0.45%Ti or less are not as responsive to age hardening. Alloys containing 1.5% and 2.0%Ti can be aged to higher strengths, but extreme quench rate sensitivity prevents them from being effectively heat treated in realistic section thicknesses.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field (B 0 ) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0 ) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

97 MATHEMATICS AND COMPUTING↗