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At least 217 records · Page 12

Comparison of URANS and LES predictions for the open phase of the OECD NEA CSNI fluid structure interaction CFD benchmark

The OECD NEA CSNI WGAMA CFD Task Group ran a benchmark in 2020 and 2021 to assess the predictive capabilities of coupled fluid structure interaction (FSI) CFD analysis methods. This paper presents the predictions made for the open phase of the benchmark using URANS and LES turbulence modelling approaches, and a comparison of the results to the experimental data. The benchmark comprised a channel containing two inline cylinders in cross-flow. The cylinders were fixed at one end, free at the other, and had measured resonant frequencies and damping properties. The URANS modelling used ANSYS Fluent 2-way coupled to ANSYS Mechanical. The LES modelling used Nek5000, 1-way coupled to Diablo. Comparisons with cross-channel velocity profiles are presented, both for the mean flow and its RMS. Comparisons are also made to the frequency spectra for point measurements of fluid velocity and pressure, and for the accelerations of the free end of each cylinder. URANS predicts the average velocity profiles relatively well, and is able to predict the velocity and acceleration spectra at the shedding frequency. However, the frequency content at the 4th harmonic of the shedding frequency is low in the URANS flow fields, and so does not excite accelerations at the resonant frequency of the cylinders. LES makes better predictions of the average profiles, and the velocity spectra agree well at both the shedding frequency and at higher frequencies. In conclusion, the 1-way coupled LES results show good agreement for acceleration spectra.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Magnus force induced magnetic diode effect in skyrmion systems

We show that skyrmions can exhibit a “magnetic diode effect,” where there is a nonreciprocal response in the transport when the magnetic field is reversed. This effect can be achieved for skyrmions moving in channels with a sawtooth potential on one side and a reversed sawtooth potential on the other side. We consider the cases of both spin-transfer torque (STT) and spin–orbit torque (SOT). When the magnetic field is held fixed, the velocity response of the skyrmion is the same for current applied in either direction for both torques, so there is no current diode effect. When the magnetic field is reversed, under STT driving the velocity of the skyrmion reverses and its absolute value changes. Under SOT driving, the velocity remains in the same direction but drops to a much lower value, resulting in negative differential conductivity. For a fixed current, we find a nonreciprocal skyrmion velocity as a function of the applied field’s sign, in analogy to the velocity–current curves observed in the usual diode effect. The nonreciprocity is generated by the Magnus force, which causes skyrmions to interact preferentially with one side of the channel. Since the channel sides have opposite asymmetry, a positive magnetic field can cause the skyrmion to interact with the “hard” asymmetry side of the channel, while a negative magnetic field causes the skyrmion to interact with the “easy” asymmetry side. This geometry could be used to create new kinds of magnetic-field-induced diode effects that can be harnessed in new types of skyrmion-based devices.

36 MATERIALS SCIENCE↗

Precision ultranarrow-linewidth resonance excitation (PURE) preparation of a molecular beam of nitric oxide molecules for inelastic scattering with argon

We recently reported a novel technique that utilizes narrow-linewidth lasers to selectively excite molecules into a pure quantum state with a well-resolved, tunable distribution of velocities [O. A. Krohn and D. W. Chandler, J. Phys. Chem. Lett. 15(50), 12455–12463 (2024)]. We refer to the preparation of molecules by this technique as precision ultranarrow-linewidth resonant excitation (PURE) preparation. Here, in this study, we pair this PURE preparation methodology with active frequency stabilization of the quantum cascade laser that drives the excitation. In doing so, highly velocity-resolved packets of molecules are possible, with the limitations of this velocity resolution set by the stability of the laser locking and the spectral linewidth of the transition. We show that side-of-fringe locking to a Doppler-broadened absorption spectrum of our target molecule is sufficiently stable for PURE preparation of molecules for long timescales (several hours) with highly resolved velocity spreads (σ < 3 m/s). To demonstrate the scientific utility of this new capability, we present differential cross sections from scattering between a neat molecular beam of argon and a velocity-selected beam of nitric oxide (NO) in a pure quantum state. We observe well-resolved quantum diffraction oscillations in the forward-scattered collisions as well as general trends consistent with prior characterized collisions of NO + Ar.

Krohn, Olivia A. [Sandia National Laboratories (SN↗

Unravelling the orbits of cluster galaxy populations according to their dominant gas ionization source

ABSTRACT We investigate the kinematical and dynamical properties of cluster galaxy populations classified according to their dominant source of gas ionization, namely: star-forming (SF) galaxies, optical active galactic nuclei (AGNs), mixed SF plus AGN ionization (transition objects, T), and quiescent (Q) galaxies. We stack 8892 member galaxies from 336 relaxed galaxy clusters to build an ensemble cluster and estimate the observed projected profiles of numerical density and velocity dispersion, $\sigma _P(R)$, of each galaxy population. The MAMPOSSt code and the Jeans equations inversion technique are used to constrain the velocity anisotropy profiles of the galaxy populations in both parametric and non-parametric ways. We find that Q (SF) galaxies display the lowest (highest) typical cluster-centric distances and velocity dispersion values. Transition galaxies are more concentrated and tend to exhibit lower velocity dispersion values than SF galaxies. Galaxies that host an optical AGN are as concentrated as Q galaxies but display velocity dispersion values similar to those of the SF population. MAMPOSSt is able to find equilibrium solutions that successfully recover the observed $\sigma _P(R)$ profile only for the Q, T, and AGN populations. We find that the orbits of all populations are consistent with isotropy in the inner regions, becoming increasingly radial with the distance from the cluster centre. These results suggest that Q galaxies are in equilibrium within their clusters, while SF galaxies have more recently arrived in the cluster environment. Finally, the T and AGN populations appear to be in an intermediate dynamical state between those of the SF and Q populations.

Valk, Greique A. (ORCID:0009000827731299)↗

XRISM/Resolve view of Abell 2319: Turbulence, sloshing, and ICM dynamics

Here, we present results from XRISM/Resolve observations of the core of the galaxy cluster Abell 2319, focusing on its kinematic properties. The intracluster medium (ICM) exhibits temperatures of approximately 8 keV across the core, with a prominent cold front and a high-temperature region (⁠~11 keV) in the north-west. The average gas velocity in the 3' x 4' region around the brightest cluster galaxy (BCG) covered by two Resolve pointings is consistent with that of the BCG to within 40 km s -1 ⁠ and we found modest average velocity dispersion of 230–250 km s -1 ⁠. On the other hand, spatially resolved spectroscopy reveals interesting variations. A blueshift of up to ~230 km s -1 ⁠ is observed around the east edge of the cold front, where the gas with the lowest specific entropy is found. The region further south inside the cold front shows only a small velocity difference from the BCG; however, its velocity dispersion is enhanced to ~400 km s -1 ⁠, implying the development of turbulence. These characteristics indicate that we are observing sloshing motion with some inclination angle following BCG and that gas phases with different specific entropy participate in sloshing with their own velocities, as expected from simulations. No significant evidence for a high-redshift ICM component associated with the subcluster Abell 2319B was found in the region covered by the current Resolve pointings. These results highlight the importance of sloshing and turbulence in shaping the internal structure of Abell 2319. Further deep observations are necessary to better understand the mixing and turbulent processes within the cluster.

Astronomy and AstroPhysics↗

Microstructure development during rapid alloy solidification

Abstract Solidification processing of structural alloys can take place over an extremely wide range of solid–liquid interface velocities spanning six orders of magnitude, from the low-velocity constitutional supercooling limit of microns/s to the high-velocity absolute stability limit of m/s. In between these two limits, the solid–liquid interface is morphologically unstable and typically forms cellular-dendritic microstructures, but also other microstructures that remain elusive. Rapid developments in additive manufacturing have renewed the interest in modeling the high-velocity range, where approximate analytical theories provide limited predictions. In this article, we discuss recent advances in phase-field modeling of rapid solidification of metallic alloys, including a brief description of state-of-the-art experiments used for model validation. We describe how phase-field models can cope with the dual challenge of carrying out simulations on experimentally relevant length- and time scales and incorporating nonequilibrium effects at the solid–liquid interface that become dominant at rapid rates. We present selected results, illustrating how phase-field simulations have yielded unprecedented insights into high-velocity interface dynamics, shedding new light on both the absolute stability limit and the formation of banded microstructures that are a hallmark of rapid alloy solidification near this limit. We also discuss state-of-the-art experiments used to validate those insights. Graphical abstract

36 MATERIALS SCIENCE↗

A New Vehicle-to-Vehicle Communication System: Visual-Enhanced Cooperative Traffic Operations

The advent of Connected and Autonomous Vehicles (CAVs) has highlighted the necessity for robust communication systems between vehicles and their environment. This study introduces a novel vehicle-to-vehicle (V2V) communication system, termed the Visual-Enhanced Cooperative Traffic Operations (VECTOR) system. The VECTOR system addresses the need for robust communication by converting dynamic data (including velocity and yaw angle data) into binary code, which is displayed on an LED panel mounted on the top of the vehicle. Following vehicles detect this panel and decode the information using a camera, implementing a visual-based communication method. VECTOR system employs a comprehensive five-module process. Initially, polynomial fitting techniques are applied to velocity data over fixed time intervals using third-degree polynomials, with validation via R² and MSE metrics. The second module converts velocity and yaw angle data into binary form, thereby enhancing detection and processing efficiency. The third module focuses on improving detection stability across various environmental conditions to enhance traffic safety. The fourth module decodes the binary data back into trajectory information, ensuring the fidelity of velocity and yaw angles. The final module integrates eco-control through the VECTOR system, employing advanced control algorithms to minimize energy consumption in CAVs. Experimental evaluations conducted using a modified CAV test platform based on the Lincoln MKZ demonstrate the feasibility and efficiency of the VECTOR system, achieving a 75% R-squared accuracy rate in replicating original velocity data. This methodology not only highlights potential applications but also underscores significant implications for advancing CAV technology.

Ma, Ke↗

Sub-Alfvénic Turbulence: Magnetic-to-kinetic Energy Ratio, Modification of Weak Cascade, and Implications for Magnetic Field Strength Measurements

Abstract We study the properties of sub-Alfvénic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfvén mach number M A = V L / V A < 1, where V L is the velocity at the injection scale and V A is the Alfvén velocity. We demonstrate that MHD turbulence can have different properties, depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces acting upon the fluid, i.e., is velocity driven, in an incompressible conducting fluid we predict that the kinetic energy is M A − 2 times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes with k ∥ / k ⊥ < M A . We also predict that as the MHD turbulent cascade reaches the strong regime, the energy of slow modes exceeds the energy of Alfvén modes by a factor M A − 1 . These effects are absent if the turbulence is driven through magnetic fluctuations at the injection scale. We confirm our predictions with numerical simulations. Since the assumption of magnetic and kinetic energy equipartition is at the core of the Davis–Chandrasekhar–Fermi (DCF) approach to measuring magnetic field strength in sub-Alfvénic turbulence, we conclude that the DCF technique is not universally applicable. In particular, we suggest that the dynamical excitation of long azimuthal wavelength modes in the galactic disk may compromise the use of the DCF technique. We discuss alternative expressions that can be used to obtain magnetic field strength from observations and consider ways of distinguishing the cases of velocity and magnetically driven turbulence using observational data.

79 ASTRONOMY AND ASTROPHYSICS↗

Kinematic Evidence for Bipolar Ejecta Flows in the Galactic Supernova Remnant W49B

W49B is a unique Galactic supernova remnant with centrally peaked, “bar”-like ejecta distribution, which was once considered evidence for a hypernova origin that resulted in a bipolar ejection of the stellar core. However, chemical abundance measurements contradict this interpretation. Closely connected to the morphology of the ejecta is its velocity distribution, which provides critical details for understanding the explosion mechanism. We report the first ever observational constraint on the kinematics of the ejecta in W49B using the Resolve microcalorimeter spectrometer on the X-ray Imaging and Spectroscopy Mission (XRISM). Using XRISM/Resolve, we measured the line-of-sight velocity traced by the Fe Heα emission, which is the brightest feature in the Resolve spectrum, to vary by ±300 km s −1 with a smooth east-to-west gradient of a few tens of kilometers per second per parsec along the major axis. Similar trends in the line-of-sight velocity structure were found for other Fe-group elements Cr and Mn, traced by the Heα emission, and also for intermediate-mass elements Si, S, Ar, and Ca, traced by the Lyα emission. The discovery of the east–west gradient in the line-of-sight velocity, together with the absence of a twin-peaked line profile or enhanced broadening in the central region, clearly rejects the equatorially expanding disk model. In contrast, the observed velocity structure suggests bipolar flows reminiscent of a bipolar explosion scenario. An alternative scenario would be a collimation of the ejecta by an elongated cavity sculpted by bipolar stellar winds.

High resolution spectroscopy↗

An efficient hybrid downscaling framework to estimate high-resolution river hydrodynamics

Flow depth and velocity are the most important hydrodynamic variables that govern various river functions, including water resources, navigation, sediment transport, and biogeochemical cycling. Existing high-resolution flow depth simulations rely on either computationally expensive river hydrodynamic models (RHMs) or data-driven models with formidable training costs, whereas data-driven modeling of flow velocity has rarely been explored. Here, using the hybrid Low-fidelity, Spatial analysis, and Gaussian process learning (LSG) model, we developed a downscaling approach to construct high-resolution flow depth and velocity from a two-dimensional (2-D) RHM simulation at coarse resolution. The LSG models were trained and tested in an urban watershed in Houston using two different hurricane-driven flood events. The high-resolution (as fine as 30 m resolution) and low-resolution (mostly 1000 m resolution) meshes include 664 724 and 14 536 grid cells, respectively. The results showed that through downscaling, the simulation errors were reduced to less than one-fourth and one-third of the errors of the low-resolution 2-D RHM for flow depth and velocity, respectively. Our analysis further revealed that the dominant uncertainty sources of the downscaled hydrodynamics are different, with flow velocity dominated by the dimensionality reduction error, which we reduced by using a regionalized training procedure. The downscaling approach achieves an 84-fold acceleration in computational time compared to the high-resolution 2-D RHM, making high-fidelity ensemble flood modeling feasible. More importantly, the developed method provides an opportunity to couple large-scale hydrodynamical processes with local physical, chemical, and biological processes in river models.

Tan, Zeli [Pacific Northwest National Laboratory (↗

Single particle impact explorations on the role of powder heat treatments in cold spray: Effects of strength and oxide structure

In cold spray, the optimization of the powder feedstock for improving the final properties of the coating and for improving the process itself are two different objectives. This paper explores the latter, studying the relationship between powder pre-heat treatment and the kinetic bonding between the individual particles and the substrate. Using a laser-induced particle impact test (LIPIT), we investigate the effect of different heat treatments on the critical adhesion velocity of Al 6061. Although heat treatments change the strength of the powders as well as the thickness of the native oxide layer each by as much as ∼50 %, the critical adhesion velocity remains constant to within only ∼10 %. A deeper analysis reveals that these two factors change in somewhat complementary ways for the heat treatments explored here, leading to counteracting effects. By quantitatively evaluating these two microstructural factors in tandem, we find that they are roughly equally important in determining the critical adhesion velocity. These observations thus provide insight for the development of new heat treatment regimens that might lower the adhesion velocity.

Al 6061↗

CROCUS Urban Canyons - Space Science and Engineering Center (SPARC) Doppler lidar data

This is the netCDF format output from the Halo Photonics Streamline XR Doppler lidar that was deployed next to the Space Science and Engineering Center (SPARC) trailer at the University of Illnois-Chicago greenhouse parking lot during CROCUS Urban Canyons. The purpose of collecting this dataset is to provide vertical and horizontal wind profiles for studying the characteristics of turbulence over the urban canyon of Chicago. This data contains the radial velocity, intensity, and backscatter from the vertical profile, range height indicator, and sector scans that were performed over both Intensive Operating Period 1 and 2 of CROCUS Urban Canyons. There are four different types of files: * The Range Height Indicator (RHI) files contain scans that are along a constant azimuth, spanning the entire hemisphere of elevation values above the surface. * The Velocity Azimuth Display (VAD) files contain the raw radial velocity data from the 6-beam, 60 degree scans. * The User1 files contain stacked Plan Position Indicator scans over a 45 degree quadrant over downtown Chicago. * The Stare files contain vertically pointing scans. These are standard netCDF files that can be opened using xarray. The VAD scans can be processed from their raw radial velocities to horizontal wind speeds with the Atmospheric data Community Toolkit (https://arm-doe.github.io/ACT/).

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC WINDS↗

Dynamics of Intra-Cell Thermal Front Propagation in Lithium-Ion Battery Safety Issues

Thermal runaway (TR), a critical failure mode in lithium-ion batteries (LIBs), poses significant safety risks and hinders wider application of LIBs. TR typically begins at a localized heat source and spreads across the cell. Understanding thermal front propagation (TFP) characteristics, such as front and velocity, is crucial for assessing energy release and temperature distribution for battery hazardous estimation. Recent studies assume that TR within cells propagates at a near-constant velocity, based on the reaction kinetics and thermal properties. Here, in this study, an intra-battery TR model is further proposed and it indicates that TFP velocity stabilizes when the front is distanced from the heat source. Theoretical estimates for propagation velocity and front are developed and validated through numerical simulations and experimental tests from the NREL Battery Failure Databank. The energy release rate during TFP and the impact of preheating based on a point heat source are explored. This work clarifies the long-standing clouds of the thermal font propagation behaviors within the single cell, highlights the power and beauty of mathematics modeling to describe the complicated thermal behaviors, and provides important guidelines for thermal hazardous understanding for next-generation batteries.

25 ENERGY STORAGE↗

The role of thermal stratification on the co‐spectral properties of momentum transport above an Amazonian forest

The influence of thermal stratification on the turbulent kinetic energy balance has been widely studied; however, its influence on the turbulent stress remains less explored in the presence of tall vegetated canopies and less ideal micrometeorological conditions. Here, the impact of thermal stratification on turbulent momentum flux is considered in the roughness sublayer (RSL) and the atmospheric surface layer (ASL) using the Amazon Tall Tower Observatory (ATTO) in Brazil. A scalewise co‐spectral budget (CSB) model is developed using standard closure schemes for the pressure–velocity decorrelation. The CSB revealed that the co‐spectrum ${F}_{wu}\left({k}_x\right)$ between longitudinal (u') and vertical (w') velocity fluctuations is impacted by the energy spectrum of the vertical velocity ${E}_{ww}\left({k}_x\right)$ and the much less studied longitudinal heat‐flux co‐spectrum ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$, where ${\theta}_{\mathrm{v}}^{\prime }$ are temperature fluctuations and ${k}_x$ is the longitudinal wavenumber. Under stable, very stable, and dynamic–convective conditions, the scaling exponent ${F}_{wu}\left({k}_x\right)$ in for the inertial subrange (ISR) scales is dominated by ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ instead of ${E}_{ww}\left({k}_x\right)$. A near ${k}_x^{-7/3}$scaling in ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ robust to large variations in thermal stratification is found, whereas the Kolmogorov ISR scaling for ${E}_{ww}\left({k}_x\right)\sim {k}_x^{-5/3}$ is not found. The scale‐dependent decorrelation time between u' and w' is dominated by ${\epsilon}^{-1/3}{k}_x^{-2/3}$ in the ISR, but is nearly constant for eddies larger than the vertical velocity integral scale, regardless of stability. Implications of these findings for generalized stability correction functions that are based on the turbulent stress budget instead of the turbulent kinetic energy budget are discussed.

canopy turbulence↗

Dark kinetic heating of exoplanets and brown dwarfs

Dark kinetic heating of neutron stars has been previously studied as a promising dark matter detection avenue. Kinetic heating occurs when dark matter is sped up to relativistic speeds in the gravitational well of high-escape velocity objects, and deposits kinetic energy after becoming captured by the object, thereby increasing its temperature. We show that dark kinetic heating can be significant even in objects with low-escape velocities, such as exoplanets and brown dwarfs, increasing the discovery potential of such searches. This can occur if there is a long-range dark force, creating a “dark escape velocity”, leading to heating rates substantially larger than those expected from neutron stars. We consequently set constraints on dark sector parameters using Wide-field Infrared Survey Explorer and JWST data on Super-Jupiter WISE 0855-0714, and map out future sensitivity to the dark matter scattering cross section below 10 −40 cm 2 . We compare dark kinetic heating rates of other lower escape velocity objects such as the Earth, Sun, and white dwarfs, finding complementary kinetic heating signals are possible depending on particle physics parameters.

Astrophysics↗

Review: Pre-Darcy flows in low-permeability porous media

The widely used Darcy’s law specifies a linear relation between the Darcy velocity of fluid flow and the pressure gradient that drives the flow. However, studies have shown that Darcy velocity can exhibit a nonlinear dependence on the pressure gradient in low-permeability porous media such as clay and shale when the pressure gradient is adequately low. This phenomenon is referred to as low-velocity non-Darcian flow or pre-Darcy flow. This paper provides a comprehensive review of the theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media. The review begins by outlining the fundamental mechanisms underlying pre-Darcy flow that regulate the unique characteristics such as nonlinear dependence of the Darcy velocity on the pressure gradient and its relevance to fluid–rock interactions. The review then proceeds to present a thorough compilation of experimental investigations performed in various low-permeability geomaterials including tight sandstones, shales, and clays. Next, empirical and theoretical models and simulation methods that have been developed to fit and interpret experimental data are reviewed. Finally, the review underscores the challenges encountered in conducting and interpreting pre-Darcy flow experiments and suggests future research directions. By analyzing previous experimental investigations, this review aims to offer a valuable resource for researchers and practitioners seeking to enhance their understanding of fluid dynamics in low-permeability geomaterials. This provides insights into the application of pre-Darcy flow in numerous natural and engineered processes such as shale oil and gas recovery, contaminant transport in low-permeability aquifers, and geological disposal of nuclear waste.

58 GEOSCIENCES↗

Topography-Induced TKE Budget Behavior Over an Amazon Forest

Data from three different heights (35, 50 and 81 m) of one of the ATTO Project towers in the Amazon forest were used to calculate the TKE (turbulence kinetic energy) budget and some other statistics within the RSL (roughness sublayer). The statistical analyses were carried out for unstable and stable cases. The vertical transport and the vertical advection terms do not explain the imbalances found in the TKE budget, highlighting the impor- tance of horizontal terms in complex terrain. Indeed, patterns independent of the time of day were found for vertical transport, horizontal and vertical velocity skewness, the mean vertical component velocity, and momentum and vertical TKE flux. Here, the highest values of mean vertical velocity were observed from the direction where there is a valley near the tower, which may indicate a topographical effect. Monin-Obukhov Similarity Theory (MOST) predictions for the mean velocity gradient, strictly applicable only in the inertial sublayer (ISL), gave reasonable predictions at 35 and 50 m, but dimensionless dissipation rates displayed large scatter. At 81 m, there were clear deviations from MOST for the two functions, disclosing the effect of topography. In addition, a neutral LES (large-eddy simu- lation) study showed good agreement with tower data for the same general wind direction.

ATTO project↗

Design of a Three-Layer Impactor for Material Strength Measurements at Multi-Megabar Pressures

Off-Hugoniot loading methods for dynamic compression have been a topic of interest for many years as a means of accessing high pressures without melting a material. Simulations and an initial test experiment of a three-layer gas-gun impactor suitable for use in measuring dynamic material strength at multi-megabar pressures are described. As shown through ARES hydrocode simulations, an impactor consisting of a low-, medium-, and high-impedance material, such as TPX, Al, and Ta or Pt, can produce a quasi-isentropic loading path up to 4.6 Mbar pressure with a low homologous temperature (T/T melt = 0.1–0.25). These impactors can also be tailored to create a pressure drive suitable for a Lagrangian sound speed experiment. Simulated in-situ velocities were analyzed to determine the change in calculated strength due to non-uniformity in the impactor, which provides a measure of error sensitivity. An initial test of a three-layer projectile onto a flat target at 4.4 km/s impact velocity is reported. Finally, while the impactor incurred some delamination during firing, the measured sample/window interface velocity generally agrees with the simulated peak velocity and subsequent release, indicating the feasibility of this approach for measuring material strength.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗