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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Shape-persistent ladder molecules exhibit nanogap-independent conductance in single-molecule junctions

Molecular electronic devices require precise control over the flow of current in single molecules. However, the electron transport properties of single molecules critically depend on dynamic molecular conformations in nanoscale junctions. Here, in this work, we report a unique strategy for controlling molecular conductance using shape-persistent molecules. Chemically diverse, charged ladder molecules, synthesized via a one-pot multicomponent ladderization strategy, show a molecular conductance (d[log( G/G 0 )]/d x ≈ -0.1 nm -1 ) that is nearly independent of junction displacement, in stark contrast to the nanogap-dependent conductance (d[log( G/G 0 )]/d x ≈ -7 nm -1 ) observed for non-ladder analogues. Ladder molecules show an unusually narrow distribution of molecular conductance during dynamic junction displacement, which is attributed to the shape-persistent backbone and restricted rotation of terminal anchor groups. These principles are further extended to a butterfly-like molecule, thereby demonstrating the strategy's generality for achieving gap-independent conductance. Overall, our work provides important avenues for controlling molecular conductance using shape-persistent molecules. Achieving robust and controllable conductance in single-molecule junctions is challenging due to the dynamic nature of molecular conformations that fluctuate over operational timescales. A strategy using shape-persistent molecules has now been developed that demonstrates nearly junction-displacement-independent conductance, providing a stable solution for single-molecule electronic properties.

molecular electronics↗
DOE OSTI2024

Machine learning-driven descriptions of protein dynamics at solid-liquid interfaces

This chapter has described how ML has enabled quantitative analysis of HS-AFM data to discover the physical phenomena governing protein dynamics and ordering at solid-liquid interfaces. The research detailed in this chapter modeled the rotation models of protein nanorods, the discovery of which would otherwise not be possible. By tracking the trajectories of individual protein rods from frame to frame, it was possible to model Brownian type motion and behaviors and Levy-flight dynamics that had not previously been shown. We also described the application of the Python package AtomAI, which has been developed specifically to analyze and extract physical phenomena, providing exemplar code for training an ensemble of deep neural networks to produce the semantic segmentation of AFM data and functions for encoding and decoding local environments. We last described a combinatorial approach to analyze very noisy data with a densely covered substrate where the emergence of order for the protein liquid crystals could be elucidated. By combining the methods from Case 1 and 2, it was possible to obtain the center of mass and angle for each rod in the images and track the assembly of the rods over time into a 2D liquid crystal array on the surface of mica.

protein dynamics, solid-liquid interfaces, atomic ↗
DOE OSTI2024

Rotation in attosecond vibronic coherence spectroscopy for molecules

Abstract Excitation or ionization of a molecule by ultrafast laser pulses can create a superposition of electronic states, whose dynamics is influenced by the interplay of electronic coherence and nuclear motion, resulting in charge migration and possibly charge transfer. Probing the vibronic coherence is therefore vital to monitoring electronic dynamics and controlling chemical reactivity, as recently demonstrated in molecules via attosecond transient absorption spectroscopy (ATAS). However, theories supporting the interpretation of ATAS experiments neglect the effects of molecular rotation, often leading to inaccurate interpretation of experimental data. Here, we develop a comprehensive theory for ATAS of molecules encompassing the entire pump-probe process. Applying the theory to N 2 , we demonstrate that the emergence of coherent signals critically depends on the consideration of molecular rotation. This work contributes to close the gap between theory and ATAS experiments, paving the way for monitoring electronic motion and controlling chemical reactivity in diverse molecular systems.

Physics↗
DOE OSTI2021

Experimental Investigation of Fuel Staging Effect on Modal Dynamics of Thermoacoustic Azimuthal Instabilities in a Multi-Nozzle Can Combustor

Abstract This paper analyzes the dynamics of unstable azimuthal thermoacoustic modes in a lean premixed combustor. Azimuthal modes can be decomposed into two counter rotating waves where they can either compete and potentially suppress one of them (spinning) or coexist (standing), depending on the operating conditions. This paper describes experimental results of the dynamical behaviors of these two waves. The experimental data were taken at different mass flow rates as well as different azimuthal fuel staging in a multi-nozzle can combustor. It is shown that at a low flow rate with uniform fuel distribution, the two waves have similar amplitudes, giving rise to a standing wave. However, the two amplitudes are slowly oscillating out of phase to each other, and the phase difference between the two waves also shows oscillatory behavior. For an intermediate flow rate, the dynamics show intermittency between standing and spinning waves, indicating that the system is bistable. In addition, the phase difference dramatically shifts when the mode switches between standing and spinning waves. For a high flow rate, the system stabilizes at a spinning wave most of the time. These experimental observations demonstrate that not only the amplitudes of two waves but also the phase difference plays an important role in the dynamics of azimuthal mode. For non-uniform azimuthal fuel staging, the modal dynamics exhibit only an oscillatory standing wave behavior regardless of the mass flow rate. Compared to the uniform fuel staging, however, the pressure magnitude is considerably reduced, which provides a potential strategy to mitigate and/or suppress the instabilities.

Kim, J.↗
DOE OSTI2023

Layer-dependent optically induced spin polarization in InSe

Optical control of spin in semiconductors has been pioneered using nanostructures of III-V and II-VI semi-conductors, but the emergence of two-dimensional van der Waals materials offers an alternative low-dimensional platform for spintronic phenomena. Indium selenide (InSe), a group-III monochalcogenide van der Waals material, has shown promise for optoelectronics due to its high electron mobility, tunable direct band gap, and quantum transport. In addition to these confirmed properties, there are predictions of spin-dependent optical selection rules, suggesting the potential for all-optical excitation and control of spin in a two-dimensional layered material. Despite these predictions, layer-dependent optical spin phenomena in InSe have yet to be explored. Here, we present measurements of layer-dependent optical spin dynamics in few-layer and bulk InSe. Polarized photoluminescence reveals layer-dependent optical orientation of spin, thereby demonstrating the optical selection rules in few-layer InSe. Spin dynamics are also studied in many-layer InSe using time-resolved Kerr rotation spectroscopy. By applying out-of-plane and in-plane static magnetic fields for polarized emission measurements and Kerr measurements, respectively, the g factor for InSe was extracted. Further investigations are done by calculating precession values using a k · p model, which is supported by ab initio density functional theory. Comparison of predicted precession rates with experimental measurements highlights the importance of excitonic effects in InSe for understanding spin dynamics. In conclusion, optical orientation of spin is an important prerequisite for optospintronic phenomena and devices, and these first demonstrations of layer-dependent optical excitation of spins in InSe lay the foundation for combining layer-dependent spin properties with advantageous electronic properties found in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Study of a High-speed Outer Rotor Burst Containing Enclosure

The increasing demand for high-speed electric machines in many applications pushes the development of high-power density electric motors. Outer rotor motors, which can be designed with a larger airgap diameter than inner rotor motors for the same overall diameter and, therefore, provide higher torque, distinguish themselves in space-constrained but high torque applications. However, increasing the motor speed and diameter results in significant centrifugal loads for the outer rotor motor due to its higher airgap diameter. Additional attention must be paid at the design stage to consider the extreme situation of possible mechanical failure, such as the sudden burst of the high-speed rotating parts in the motor, and measures must be taken to prevent their damage to other system components in advance. Through the finite element dynamic impact analysis, we studied the damage caused by broken parts on the inner wall of the electric motor housing when the motor rotates at 20,000 RPM. The proposed method is expected to provide reasonable recommendations of the enclosure material and its thickness required to protect other components in the same powertrain system when the high-power density motor fails unexpectedly.

Lin, Lianshan↗
DOE OSTI2025

Spin Dynamics of Triple-𝐐 Magnetic Orderings in a Triangular Lattice: Implications for Multi-𝐐 Orderings in General Two-Dimensional Lattices

Multi-𝐐 magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multidomain single- or double-𝐐 magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: Triple-𝐐 orders that preserve rotational symmetry and single- or double-𝐐 orders that break it exhibit qualitatively distinct anisotropies in their Goldstone-mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular-lattice antiferromagnet Co 0.325 ⁢TaS 2 , which hosts both a stripe-type single-𝐐 state and a triple-𝐐 tetrahedral ordering at different temperatures. Using inelastic neutron-scattering and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model’s predictions: markedly anisotropic for the single-𝐐 phase and near isotropic for the triple-𝐐 phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-𝐐 phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-𝐐 phase, due to its noncollinear configuration. This work provides universal insight into the dynamical properties of topological multi-𝐐 magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-𝐐 counterparts. The unequivocal confirmation of the triple-𝐐 structure in Co 0.325 ⁢TaS 2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Park, Pyeongjae [Oak Ridge National Laboratory (OR↗
DOE OSTI2026

Chaos as the cause of randomness in tearing mode onset times in DIII-D ITER baseline scenario plasmas

The first evidence of widespread chaotic plasma dynamics relevant to the onset of disruptive tearing modes is found in DIII-D tokamak discharges. This evidence is obtained by calculating positive maximal Lyapunov exponents from Mirnov signals using the Rosenstein algorithm, implying the chaotic growth and/or rotation of magnetohydrodynamic modes in DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] plasmas. Such chaotic dynamics offer an explanation for the random tearing mode onset times previously observed in ITER baseline scenario discharges. Further, the Lyapunov timescales associated with this chaos could inhibit reliable prediction of tearing mode onset beyond the angular momentum confinement timescale; this constraint should inform the design of plasma control systems on ITER.

Chaotic dynamics↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2023

Mechanistic origins of methyl-driven Overhauser DNP

The Overhauser effect in the dynamic nuclear polarization (DNP) of non-conducting solids has drawn much attention due to the potential for efficient high-field DNP as well as a general interest in the underlying principles that enable the Overhauser effect in small molecules. We recently reported the observation of 1 H and 2 H Overhauser effects in H 3 C- or D 3 C-functionalized Blatter radical analogs, which we presumed to be caused by methyl rotation. In this work, we look at the mechanism for methyl-driven Overhauser DNP in greater detail, considering methyl librations and tunneling in addition to classical rotation. Here, we predict the temperature dependence of these mechanisms using density functional theory and spin dynamics simulations. Comparisons with results from ultralow-temperature magic angle spinning-DNP experiments revealed that cross-relaxation at temperatures above 60 K originates from both libration and rotation, while librations dominate at lower temperatures. Due to the zero-point vibrational nature of these motions, they are not quenched by very low temperatures, and methyl-driven Overhauser DNP is expected to increase in efficiency down to 0 K, predominantly due to increases in nuclear relaxation times.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

All-Atom Simulations Uncover Structural and Dynamical Properties of STING Proteins in the Membrane System

Recent studies have shown that the stimulator of interferon gene (STING) protein plays a central role in the immune system by facilitating the production of type I interferons in cells. The STING signaling pathway is also a prominent activator of cancer-killing T cells that initiate a powerful adaptive immune response. Since biomolecular signaling pathways are complicated and not easily identified through traditional experiments, molecular dynamics (MD) has often been used to study structural and dynamical responses of biological pathways. In this work, we carried out MD simulations for full-length chicken and human STING (chSTING and hSTING) proteins. Specifically, we investigated ligand-bound closed (holo) and ligand-unbound open (apo) forms of STING in the membrane system by comparing their conformational and dynamical differences. Our research provides clues for understanding the mechanism of the STING signaling pathway by uncovering detailed insights for the examined systems: the residues from each chain in the binding pocket are strongly correlated to one another in the open STING structure compared with those in the closed STING structure. Ligand-bound closed STING displays ~174° rotation of the ligand-binding domain (LBD) relative to the open STING structure. The dynamical analysis of residue Cys148 located in the linker region of hSTING does not support the earlier hypothesis that Cys148 can form disulfide bonds between adjacent STING dimers. We also demonstrate that using the full-length proteins is critical, since the MD simulations of the LBD portion alone cannot properly describe the global conformational properties of STING.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Multifunctional Chiral Chemically‐Powered Micropropellers for Cargo Transport and Manipulation

Practical applications of synthetic self-propelled nano and microparticles for microrobotics, targeted drug delivery, and manipulation at the nanoscale are rapidly expanding. However, fabrication limitations often hinder progress, resulting in relatively simple shapes and limited functionality. Here, taking advantage of 3D nanoscale printing, chiral micropropellers powered by the hydrogen peroxide reduction reaction are fabricated. Due to their chirality, the propellers exhibit multifunctional behavior controlled by an applied magnetic field: spinning in place (loitering), directed migration in the prescribed direction, capture, and transport of polymer cargo particles. Design parameters of the propellers are optimized by computation modeling based on mesoscale molecular dynamics. It is predicted by computer simulations, and confirmed experimentally, that clockwise rotating propellers attract each other and counterclockwise repel. These results shed light on how chirality and shape optimization enhance the functionality of synthetic autonomous micromachines.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Virtual texture analysis to investigate the deformation mechanisms in metal microstructures at the atomic scale

Understanding the deformation behavior of metallic materials at high strain rates requires the characterization of plasticity contributors such as twins, phase transformed regions, and dislocations. However, predicting the contributions from phase transformation and twinning relies on a complete understanding of the selection of variants for various loading orientations and the evolution of their volume fractions. This manuscript presents a new virtual texture (VirTex) analysis approach to characterize phase transformation and twinning variants in deformed microstructures generated using molecular dynamics (MD) simulations. Furthermore, the VirTex method involves the construction of a rotation matrix to calculate the angle/axis pairs and misorientation angles for each atom in the microstructure. Any changes in the orientation angle from angle/axis pairs and/or structure types are analyzed to determine the nucleation and evolution of variants in the microstructure. The study uses shock deformed single-crystal Fe, Ta, and Cu to analyze the variant selections for phase transformation or twinning or both in BCC and FCC systems. In addition, the VirTex analysis is able to characterize the phase transformation and twinning variants in nanocrystalline Fe and Ta microstructures. Besides characterizing variants, orientation mapping also provides an accelerated and on-the-fly approach for quantifying twin fractions in MD microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Elucidating the chemical dynamics of the elementary reactions of the 1-propynyl radical (CH 3 CC; X 2 A 1 ) with 2-methylpropene ((CH 3 ) 2 CCH 2 ; X 1 A 1 )

Exploiting the crossed molecular beam technique, we studied the reaction of the 1-propynyl radical (CH 3 CC; X 2 A 1 ) with 2-methylpropene (isobutylene; (CH 3 ) 2 CCH 2 ; X 1 A 1 ) at a collision energy of 38 ± 3 kJ mol –1 . The experimental results along with ab initio and statistical calculations revealed that the reaction has no entrance barrier and proceeds via indirect scattering dynamics involving C 7 H 11 intermediates with lifetimes longer than their rotation period(s). The reaction is initiated by the addition of the 1-propynyl radical with its radical center to the π-electron density at the C1 and/or C2 position in 2-methylpropene. Further, the C 7 H 11 intermediate formed from the C1 addition either emits atomic hydrogen or undergoes isomerization via [1,2-H] shift from the CH 3 or CH 2 group prior to atomic hydrogen loss preferentially leading to 1,2,4-trimethylvinylacetylene (2-methylhex-2-en-4-yne) as the dominant product. The molecular structures of the collisional complexes promote hydrogen atom loss channels. RRKM results show that hydrogen elimination channels dominate in this reaction, with a branching ratio exceeding 70%. Since the reaction of the 1-propynyl radical with 2-methylpropene has no entrance barrier, is exoergic, and all transition states involved are located below the energy of the separated reactants, bimolecular collisions are feasible to form trimethylsubstituted 1,3-enyne (p1) via a single collision event even at temperatures as low as 10 K prevailing in cold molecular clouds such as G+0.693. As a result, the formation of trimethylsubstituted vinylacetylene could serve as the starting point of fundamental molecular mass growth processes leading to di- and trimethylsubstituted naphthalenes via the HAVA mechanism.

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

Experimental and theoretical evidence for hydrogen doping in polymer solution-processed indium gallium oxide

The field-effect electron mobility of aqueous solution-processed indium gallium oxide (IGO) thin-film transistors (TFTs) is significantly enhanced by polyvinyl alcohol (PVA) addition to the precursor solution, a >70-fold increase to 7.9 cm 2 /Vs. To understand the origin of this remarkable phenomenon, microstructure, electronic structure, and charge transport of IGO:PVA film are investigated by a battery of experimental and theoretical techniques, including In K-edge and Ga K-edge extended X-ray absorption fine structure (EXAFS); resonant soft X-ray scattering (R-SoXS); ultraviolet photoelectron spectroscopy (UPS); Fourier transform-infrared (FT-IR) spectroscopy; time-of-flight secondary-ion mass spectrometry (ToF-SIMS); composition-/processing-dependent TFT properties; high-resolution solid-state 1 H, 71 Ga, and 115 In NMR spectroscopy; and discrete Fourier transform (DFT) analysis with ab initio molecular dynamics (MD) liquid-quench simulations. The 71 Ga{ 1 H} rotational-echo double-resonance (REDOR) NMR and other data indicate that PVA achieves optimal H doping with a Ga···H distance of ~3.4 Å and conversion from six- to four-coordinate Ga, which together suppress deep trap defect localization. This reduces metal-oxide polyhedral distortion, thereby increasing the electron mobility. Finally, hydroxyl polymer doping thus offers a pathway for efficient H doping in green solvent-processed metal oxide films and the promise of high-performance, ultra-stable metal oxide semiconductor electronics with simple binary compositions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Novel Grid-forming Voltage Control Strategy for Supplying Unbalanced Microgrid Loads Using Inverter-based Resources

This paper presents a novel grid-forming voltage control strategy for a battery energy storage system to maintain balanced three-phase output voltages when serving unbalanced loads. A stationary reference frame (αβ) based control scheme is proposed to regulate positive-sequence and negative-sequence voltages. Compared with the conventional rotating reference frame (dq) based control scheme, the proposed scheme shows better dynamic performance. Then, we analyze the system zero-sequence network and propose adding a grounding transformer to the Y/Yg connected output transformer to further reduce the voltage unbalance at the point of common coupling. The simulation results demonstrate the effective performance of the proposed voltage control scheme. Based on the results, the power-voltage unbalance curve is derived for different output transformer configurations to establish the relationship between the power unbalance limit and the voltage unbalance limit for microgrid power scheduling.

Xu, Bei↗
DOE OSTI2022

Effects of a CFD-improved dimple stepped-lip piston on thermal efficiency and emissions in a medium-duty diesel engine

Diesel piston-bowl shape is a key design parameter that affects spray-wall interactions and turbulent flow development, and in turn affects the engine’s thermal efficiency and emissions. It is hypothesized that thermal efficiency can be improved by enhancing squish-region vortices as they are hypothesized to promote fuel-air mixing, leading to faster heat-release rates. However, the strength and longevity of these vortices decrease with advanced injection timings for typical stepped-lip (SL) piston geometries. Dimple stepped-lip (DSL) pistons enhance vortex formation at early injection timings. Previous engine experiments with such a bowl show 1.4% thermal efficiency gains over an SL piston. However, soot was increased dramatically [SAE 2022-01-0400]. In a previous study, a new DSL bowl was designed using non-combusting computational fluid dynamic simulations. This improved DSL bowl is predicted to promote stronger, more rotationally energetic vortices than the baseline DSL piston: it employs shallower, narrower, and steeper-curved dimples that are placed further out into the squish region. In the current experimental study, this improved bowl is tested in a medium-duty diesel engine and compared against the SL piston over an injection timing sweep at low-load and part-load operating conditions. No substantial thermal efficiency gains are achieved at the early injection timing with the improved DSL design, but soot emissions are lowered by 45% relative to the production SL piston, likely due to improved air utilization and soot oxidation. However, these benefits are lost at late injection timings, where the DSL piston renders a lower thermal efficiency than that of the SL piston. Energy balance analyses show higher wall heat transfer with the DSL piston than with the SL piston despite a 1.3% reduction in the piston surface area. Vortex enhancement may not necessarily lead to improved efficiency as more energetic squish-region vortices can lead to higher convective heat transfer losses.

42 ENGINEERING↗
DOE OSTI2020

Potential Vorticity Mixing in a Tangled Magnetic Field

A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is introduced. The analysis is in the context of β -plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfvénizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field–resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfvénization—i.e., before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose here a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.

79 ASTRONOMY AND ASTROPHYSICS↗