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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

General trends of dihedral conformational transitions in a globular protein

In this paper, dihedral conformational transitions are analyzed systematically in a model globular protein, cytochrome P450cam, to examine their structural and chemical dependences through combined conventional molecular dynamics (cMD), accelerated molecular dynamics (aMD) and adaptive biasing force (ABF) simulations. The aMD simulations are performed at two acceleration levels, using dihedral and dual boost, respectively. In comparison with cMD, aMD samples protein dihedral transitions approximately two times faster on average using dihedral boost, and ~3.5 times faster using dual boost. In the protein backbone, significantly higher dihedral transition rates are observed in the bend, coil, and turn flexible regions, followed by the β bridge and β sheet, and then the helices. Moreover, protein side chains of greater length exhibit higher transition rates on average in the aMD-enhanced sampling. Side chains of the same length (particularly Nχ = 2) exhibit decreasing transition rates with residues when going from hydrophobic to polar, then charged and aromatic chemical types. The reduction of dihedral transition rates is found to be correlated with increasing energy barriers as identified through ABF free energy calculations. In conclusion, these general trends of dihedral conformational transitions provide important insights into the hierarchical dynamics and complex free energy landscapes of functional proteins.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Magnetostructural phase transitions and magnetocaloric effect in (Gd 5-x Sc x )Si 1.8 Ge 2.2

Future advancements in magnetocaloric refrigeration/heat pumping technologies depend on the discovery of new materials that demonstrate large, tunable magnetocaloric effects (MCEs) in the vicinity of coupled magnetic and structural phase transitions that occur reversibly with minimum hysteresis. Here, with this in mind, we investigate phase transitions, microstructure, magnetic, thermal, magnetocaloric, and transport properties of (Gd 5-x Sc x )Si 1.8 Ge 2.2 compounds. Replacement of magnetic Gd with non-magnetic Sc in Gd 5-x Sc x Si 1.8 Ge 2.2 increases the ferromagnetic to paramagnetic first order phase transition temperature, T C , with only a minor reduction in MCE when x ≤ 0.2. We also demonstrate that hydrostatic pressure further increases T C and reduces the hysteresis of the first order phase transition in Gd 4.8 Sc 0.2 Si 1.8 Ge 2.2 from 7 to 4 K. Temperature-dependent x-ray powder diffraction study of Gd 4.8 Sc 0.2 Si 1.8 Ge 2.2 confirms the monoclinic ↔ orthorhombic structural transformation at T C , in agreement with magnetic, calorimetric, and electrical transport measurements. In addition to the substantial magnetocaloric effect, a large magnetoresistance of ~20% is also observed in Gd 4.8 Sc 0.2 Si 1.8 Ge 2.2 for ΔH = 50 kOe in the vicinity of the magnetostructural transition. Finally, in a drastic reversal of the initial doping behavior further additions of Sc (x > 0.2) suppress formation of the monoclinic phase, change the nature of the transition from first-to second-order, and reduce both the transition temperature and magnetocaloric effect.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Observable measurement-induced transitions

One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across the entire system. As the measurement density is increased, a phase transition occurs that is characterized by the disentanglement of different parts of the system. Unfortunately, this transition is impossible to observe experimentally for macroscopic systems because it requires an exponentially costly full tomography of the many-body wave function or a comparison with the simulation on an oracle classical computer. In this work we report the discovery of another measurement-induced phase transition that can be observed experimentally if quantum dynamics can be reversed. On one side of this phase transition the quantum information encoded in some part of the Hilbert space is fully recovered after the time inversion. On the other side, all quantum information is corrupted. This transition also manifests itself as the change in the behavior of the probability to observe the same measurement outcome in the process that consists of identical blocks repeated many times. In each block the unitary evolution is followed by the measurement. On one side of the transition the probability decreases exponentially with the number of repetitions, on the other it tends to a constant as the number of repetitions is increased. We confirm the existence of the proposed phase transition through numerical simulations of realistic quantum circuits and analytical calculations using an effective random-matrix theory model.

Measurement-induced phase transitions↗
DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Solid-state phase transitions of two quaternary metallic fuel alloys (U-2.5Mo-2.5Ti-5.0Zr and U-1.5Mo-1.5Ti-7.0Zr in wt. %)

This study focuses on the solid-state phase transitions of two quaternary fuel alloys for fast reactors: U-1.5Mo-1.5Ti-7.0Zr (U-MT7Z) and U-2.5Mo-2.5Ti-5.0Zr (U-MT5Z). Here, the phase transitions were determined by differential scanning calorimetry (DSC), X-ray powder diffraction (XRD), and scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDS). To identify the high temperature phases, the alloys were annealed at 873K, 948K, 1023K, and 1123K (all under 72 hours). Combining those characterizations, the phase transitions are determined. In U-MT7Z, there is one phase transition observed, and it is ascribed to α + U 2 Ti → γ transition. In U-MT5Z, two transitions are found. The first transition is α → γ, while the second is U 2 Ti → γ. The γ phase onset temperature of U-MT5Z is lower than that of U-MT7Z due to the higher Mo content.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Reentrant glass transition leading to ultrastable metallic glass

Polyamorphs are often observed in amorphous matters, and a representative example is the reentrant glass transition in colloid systems. For metallic amorphous alloys, however, the cases reported so far are limited to metallic glasses (MGs) that undergo electronic transitions under gigapascal applied pressure, or the presence of two liquids at the same composition. In this paper, we report the first observation of a reentrant glass transition in MGs. This unusual reentrant glass transition transforms an MG from its as-quenched state (Glass I) to an ultrastable state (Glass II), mediated by the supercooled liquid of Glass I. Specifically, upon heating to above its glass transition temperature under ambient pressure, Glass I first transitions into its supercooled liquid, which then transforms into a new Glass II, accompanied by an exothermic peak in calorimetric scan, together with a precipitous drop in volume, electrical resistance and specific heat, as well as clear evidence of local structural ordering on the short-to-medium-range scale revealed via in-situ synchrotron X-ray scattering. Atomistic simulations indicate enhanced ordering of locally favored motifs to establish correlations in the medium range that resemble those in equilibrium crystalline compounds. The resulting lower-energy Glass II has its own glass transition temperature higher than that of Glass I by as much as 50 degrees. This route thus delivers a thermodynamically and kinetically ultrastable MG that can be easily retained to ambient conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Redesigning large-scale multimodal transit networks with shared autonomous mobility services

Here, this study addresses a large-scale multimodal transit network design problem, with Shared Autonomous Mobility Services (SAMS) as both transit feeders and an origin-to-destination mode. The framework captures spatial demand and modal characteristics, considers intermodal transfers and express services, determines transit infrastructure investment and path flows, and generates transit routes. A system-optimal multimodal transit network is designed with minimum total door-to-door generalized costs of users and operators, satisfying transit origin-destination demand within a pre-set infrastructure budget. Firstly, the geography, demand, and modes in each zone are characterized with continuous approximation. The decisions of network link investment and multimodal path flows in zonal connection optimization are formulated as a minimum-cost multi-commodity network flow (MCNF) problem and solved efficiently with a mixed-integer linear programming (MILP) solver. Subsequently, the route generation problem is solved by expanding the MCNF formulation to minimize intramodal transfers. The model is illustrated through a set of experiments with the Chicago network comprised of 50 zones and seven modes, under three scenarios. The computational results present savings in traveler journey time and operator cost demonstrating the potential benefits of collaboration between multimodal transit systems and SAMS.

Autonomous vehicles↗
DOE OSTI2018

Mechanisms of Semiconducting 2H to Metallic 1T Phase Transition in Two-dimensional MoS 2 Nanosheets

In the present work, phase transition mechanisms from semiconducting 2H phase to metallic 1T phase in MoS 2 nanosheets were studied using density functional theory (DFT) method. Various 2H→1T phase transition mechanisms that consist of nucleation and propagation steps, which simulated by collective rotational and rotational/translational movements, single atom translational movement, as well as the gliding movement of one row for sulfur (S) atoms, on both the basal plane and Mo- and S-edges with different S coverages were investigated. On the perfect basal plane, the 1T phase nucleation is unlikely due to the extremely high barrier of 2.25 eV/atom. Whereas the presence of defective S vacancies on the basal plane dramatically facilitate the 1T phase nucleation and propagation around the defective sites by the collective rotational movement of three S atoms. On the 2H phase basal plane with two S vacancies, the kinetic barriers for the 1T phase nucleation are as low as of 0.66~0.77 eV/atom. Like the promoting effect of S vacancies on the phase transition over the basal plane, DFT results suggest that the S coverage on the Mo- and S-edges will affect the 1T phase nucleation and propagation. The 1T phase nucleation starting with the translational movement of single S atom on the bare Mo-edge and the gliding movement of an entire row of S atoms on the S-edge with 50%S coverage are kinetically favorable. While the 1T phase formation at the Mo-edge with 50%S coverage and the S-edge with 100% S coverage are unlikely. The present work not only confirms the important role of S vacancies/coverages in the 2H-1T phase transition, but also provides new insight into how and where the 2H-1T phase transition occurs at the atomic level, which also sheds light on the general phase transition mechanism for two-dimensional transition metal dichalcogenide materials. The work was financially supported by the National Natural Science Foundation of China (No. 21476012, 21571012, and 91534201). Q. Jin appreciates the joint Ph.D. scholarship support from the China Scholarship Council. The computing time was granted by a scientific theme user proposal in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), which is a U.S. Department of Energy national scientific user facility located at PNNL in Richland, Washington. D. Mei is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences.

Molybdenum disulfide, phase transition, sulfur vac↗
DOE OSTI2026

An Atom-Precise Approach to Damp First-Order Phase Transitions and Its Implications for Neuromorphic Signal Processing

Neuromorphic computing inspired by mammalian intelligence aims to emulate the nonlinear dynamics of biological neurons and synapses to achieve fast, low-energy, and highly efficient information processing. Brain-inspired computing relies on the design and discovery of materials exhibiting nonlinear current–voltage profiles, frequently underpinned by electronic state transitions, to achieve spiking neurons and dynamically tunable synapses. A signature challenge in the design of artificial neurons is controlling the steepness of first-order transitions in active elements, as abrupt transitions are at risk of driving unstable voltage and temperature oscillations, which result in catastrophic device failure. A critical knowledge gap is the lack of structure–function correlations mapping the composition and atomistic structure of crystalline solids to nonlinear dynamical response characteristics. Here, we address the key question of how modification of atomistic structure correlates with alteration of neuron-like functionality. Constructing oscillator circuits from millimeter-scale single crystals enables high-resolution atomic structure solutions, which we use to demonstrate that the selective positioning of Pb cations modifies charge ordering along a one-dimensional CuxV2O5 framework even at low insertion stoichiometries, thereby providing an atom-precise design parameter for damping first-order transitions. We use temperature-variant X-ray diffraction and X-ray spectroscopy to elucidate the suppression of Cu-ion shuttling based on the precise positioning of Pb ions in seven-coordinated tunnel interstitial sites as the mechanistic basis for transition broadening, thus bridging a critical gap between statistical mechanics and quantum chemical descriptions of phase transitions. Such mechanistic understanding thus paves the way to site-selective modification strategies for modulating the sharpness of first-order transitions, with an exemplary demonstration here in tuning neuronal signal processing.

Crystal structure↗
DOE OSTI2021

Ferroelectric phase-transition frustration near a tricritical composition point

Phase transition describes a mutational behavior of matter states at a critical transition temperature or external field. Despite the phase-transition orders are well sorted by classic thermodynamic theory, ambiguous situations interposed between the first- and second-order transitions were exposed one after another. Here, we report discovery of phase-transition frustration near a tricritical composition point in ferroelectric Pb(Zr 1-x Ti x )O 3 . Our multi-scale transmission electron microscopy characterization reveals a number of geometrically frustrated microstructure features such as self-assembled hierarchical domain structure, degeneracy of mesoscale domain tetragonality and decoupled polarization-strain relationship. Associated with deviation from the classic mean-field theory, dielectric critical exponent anomalies and temperature dependent birefringence data unveil that the frustrated transition order stems from intricate competition of short-range polar orders and their decoupling to long-range lattice deformation. With supports from effective Hamiltonian Monte Carlo simulations, our findings point out a potentially universal mechanism to comprehend the abnormal critical phenomena occurring in phase-transition materials.

42 ENGINEERING↗
DOE OSTI2018

Structural, vibrational, and electronic topological transitions of Bi 1.5 Sb 0.5 Te 1.8 Se 1.2 under pressure

Topological insulators have been the subject of intense research interest due to their unique surface states that are topologically protected against scattering or defects. However, the relationship between the crystal structure and topological insulator state remains to be clarified. Here, we show the effects of hydrostatic pressure on the structural, vibrational, and topological properties of the topological insulator Bi 1.5 Sb 0.5 Te 1.8 Se 1.2 up to 45 GPa using X-ray diffraction and Raman spectroscopy in a diamond anvil cell, together with first-principles theoretical calculations. Two pressure-induced structural phase transitions were observed: from ambient rhombohedral R3¡m phase to a monoclinic C2/m phase at ~13 GPa, and to a disordered I4/mmm phase at ~22 GPa. In addition, the alloy undergoes several electronic transitions within the R3¯m phase: indirect to direct bulk band gap transition at ~5.8 GPa, bulk gap closing with an appearance of Dirac semimetal (DSM) state at ~8.2 GPa, and to a trivial semimetal state at ~12.1 GPa. Anomalies in c/a ratio and Raman full width at half maximum that coincide with the DSM phase suggest the contribution of electron-phonon coupling to the transition. Here, compared to binary end members Bi 2 Te 3 , Bi 2 Se 3 , and Sb 2 Te 3 , the structural phase transition and anomaly were observed at higher pressures in Bi 1.5 Sb 0.5 Te 1.8 Se 1.2 . These results suggest that the topological transitions are precursors to the structural phase transitions.

42 ENGINEERING↗
DOE OSTI2021

Entanglement transitions from restricted Boltzmann machines

The search for novel entangled phases of matter has lead to the recent discovery of a new class of “en- tanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Furthermore, our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Constraints on a split superconducting transition under uniaxial strain in Sr 2 RuO 4 from scanning SQUID microscopy

More than two decades after the discovery of superconductivity in Sr 2 RuO 4 , it is still unclear whether the order parameter has a single component or two degenerate components. For any two-component scenario, application of uniaxial strain is expected to lift the degeneracy, generating two distinct phase transitions. The presence of a second (lower-temperature) transition may be observable by probes that are sensitive to changes in the London penetration depth, λ, as a function of temperature, T. Furthermore, we use scanning SQUID microscopy combined with a uniaxial strain device to test for a second transition under strain. We only observe a single transition. Within the temperature range where a second transition has been suggested by μSR measurements, we further place a tight upper bound of less than 1% on the change in the zero temperature superfluid density n s ∝ λ –2 (0) due to a second transition, suggesting that such a transition does not occur. These results constrain theories of the order parameter in Sr 2 RuO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Quantum field theory for the chiral clock transition in one spatial dimension

We describe the quantum phase transition in the N-state chiral clock model in spatial dimension d = 1. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N = 3, the clock model is expected to have a direct phase transition from a gapped phase with a broken global Z N symmetry, to a gapped phase with the Z N symmetry restored. The transition has dynamical critical exponent z ≠ 1, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d = 1, involving the onset of a single-boson condensate in the background of a higher-dimensional N-boson condensate. Here, we present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2 – d, with 4 – N chosen to be of order 2 – d. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N = 3, finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e2 to h/2e 2 , concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Study of Seamless Microgrid Transition Operation Using Grid-Forming Inverters

This paper investigates operational techniques to achieve seamless (smooth) microgrid (MG) transitions by dispatching a grid-forming (GFM) inverter. In traditional approaches, the GFM inverter must switch between grid-following (GFL) and GFM control modes during MG transition operation. Today's inverter technology allows GFM inverters to always operate in GFM control mode, so it is worth exploring how to use them to achieve smooth MG transition operation. This paper proposes three operational techniques: a traditional scheme of switching between GFL and GFM control; a new scheme of consistent GFM control and shifting the droop intercept up before islanding operation; and a new scheme of consistent GFM control and shifting the droop intercept up before synchronization operation. A full hardware setup is established to compare the three techniques and showcase their implementations in real-world applications. The results show that the third technique outperforms the others and exhibits the best transition performance because the GFM inverter maintains the same operating points during the transition operation. Therefore, we conclude that ensuring smooth MG transition operation requires that the GFM inverter(s) maintain the same operating points (v, f, P, Q, and phase angle) during the transition operation in addition to minimizes the point of common coupling power flow.

grid-forming control↗
DOE OSTI2018

Design of a State Machine for Smooth Microgrid Transition Operation

A state machine is proposed in the energy management system (EMS) of a microgrid as the solution for smooth microgrid's transition operation. This state machine includes six 'states' that cover all the operating modes during the microgrid's transition operation: two basic modes (grid-connected and islanded) and four temporary modes (preparing for disconnection, transition to islanding, preparing for resynchronization, and transition to grid-connected). Temporary modes are designed to fine-tune the control references for the microgrid assets to avoid harmful transients during microgrid transitions, therefore achieving smooth transition operation. The developed state machine is validated by simulation in MATLAB with a sample microgrid, and the test results show excellent performance of the state machine and smooth microgrid transition operation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Energy Exchange Dynamics across L-H Transitions in NSTX

We studied the energy exchange dynamics across the low-to-high-confinement (L-H) in NSTX discharges using the gas-puff imaging (GPI) diagnotic. The investigation focused on the energy exchange between flows and turbulence, to help clarify the mechanism of the L-H transition. We apply this study to three type of heating schemes, including a total of 17 shots from the NSTX 2010 campaign run. Results show that the edge fluctuation characteristics (fluctuation levels, radial and poloidal correlation lengths) measured using GPI do not vary just prior to the H-mode transition, but change after the transition. Using a velocimetry approach (orthogonal-programming decomposition), velocity fields of a 24 $\times$ 30 cm GPI view during the L-H transition were obtained with good spatial ($\sim$1 cm) and temporal ($\sim$2.5 $\mu$s) resolutions. Analysis using these velocity fields shows that the production term is systematically negative just prior to the L-H transition indicating transfer from mean flows to turbulence, which is inconsistent with the predator-prey paradigm. Moreover, using the inferred absolute value of the production term, an estimate of the L-H transition duration is found to be 25 ms, which is much larger than the measured duration. These discrepancies are further reinforced by consideration of the ratio between the kinetic energy in the mean flow to the thermal free energy, which is estimated to be much less than 1, suggesting again that turbulence depletion mechanism may not be playing an important role in the transition to the H-mode. Although the Reynolds work is too small to directly deplete the turbulent free energy reservoir, order-of-magnitude analysis shows that the Reynolds stress may still make a non-negligible contribution to the observed poloidal flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗