Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “density matrix”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 685 records · Page 38

A novel assay to measure low-density lipoproteins binding to proteoglycans

Background: The binding of low-density lipoprotein (LDL) to proteoglycans (PGs) in the extracellular matrix (ECM) of the arterial intima is a key initial step in the development of atherosclerosis. Although many techniques have been developed to assess this binding, most of the methods are labor-intensive and technically challenging to standardize across research laboratories. Thus, sensitive, and reproducible assay to detect LDL binding to PGs is needed to screen clinical populations for atherosclerosis risk. Objectives: The aim of this study was to develop a quantitative, and reproducible assay to evaluate the affinity of LDL towards PGs and to replicate previously published results on LDL-PG binding. Methods: Immunofluorescence microscopy was performed to visualize the binding of LDL to PGs using mouse vascular smooth muscle (MOVAS) cells. An in-cell ELISA (ICE) was also developed and optimized to quantitatively measure LDL-PG binding using fixed MOVAS cells cultured in a 96-well format. Results: We used the ICE assay to show that, despite equal APOB concentrations, LDL isolated from adults with cardiovascular disease bound to PG to a greater extent than LDL isolated from adults without cardiovascular disease (p<0.05). Conclusion: We have developed an LDL-PG binding assay that is capable of detecting differences in PG binding affinities despite equal APOB concentrations. Future work will focus on candidate apolipoproteins that enhance or diminish this interaction.

59 BASIC BIOLOGICAL SCIENCES↗

Formation of Stable Interphase of Polymer-in-Salt Electrolyte in All-Solid-State Lithium Batteries

The integration of solid-polymer electrolytes into all-solid-state lithium batteries is highly desirable to overcome the limitations of current battery configurations that have a low energy density and severe safety concerns. Polyacrylonitrile is an appealing matrix for solid-polymer electrolytes; however, the practical utilization of such polymer electrolytes in all-solid-state cells is impeded by inferior ionic conductivity and instability against a lithium-metal anode. In this work, we show that a polymer-in-salt electrolyte based on polyacrylonitrile with a lithium salt as the major component exhibits a wide electrochemically stable window, a high ionic conductivity, and an increased lithium-ion transference number. The growth of dendrites from the lithium-metal anode was suppressed effectively by the polymer-in-salt electrolyte to increase the safety features of the batteries. In addition, we found that a stable interphase was formed between the lithium-metal anode and the polymer-in-salt electrolyte to restrain the uncontrolled parasitic reactions, and we demonstrated an all-solid-state battery configuration with a LiFePO 4 cathode and the polymer-in-salt electrolyte, which exhibited a superior cycling stability and rate capability.

Gao, Hongcai↗

Simple and Robust Carrier-Based PWM Technique for Single-Stage Three-phase Rectifier Indirect Matrix Converter

Indirect matrix converters (IMC) can offer high efficiency, high power density, and bidirectional power flow capability with a single-stage three-to single-phase AC-AC power conversion integrating a conventional three-phase active rectifier with a primary side full-bridge inverter of a dual active bridge converter. However, the IMCs generally require space vector modulation techniques, leading to complex sectors and dwell times calculations. A practical implementation of the modulation methods with a commonly used digital signal processor becomes even more challenging when considering power factor correction, harmonics reduction, and deadtime between sector transitions. This paper proposes a simple and robust carrier-based pulse width modulation (PWM) technique determined through a voltage-source inverter (VSI) to current-source inverter (CSI) to IMC conversion. This translation enables the adoption of all conventional VSI control methods with active and reactive power control in the IMCs through simple carrier and reference waveform comparison. The VSI vectors are first one-on-one matched with CSI vectors and translated to IMC modulation signals without calculating sectors and dwell times. Nine different carrier waveforms are proposed, and the converter performance is analyzed. Grid current THD and efficiency are estimated for each modulation method. The symmetric A and B methods had the lowest THD of the grid current, 2.80%, and the efficiency remained at approximately 98.3%, making it the most suitable carrier-based method proposed in this paper. The space vector PWM (SVPWM) modulation method was implemented to the DSP and generated the expected twelve gate signals.

Benson, Mikayla↗

Solidification of SRPPF Aqueous Recovery Liquid: Process Disruptions

Savannah River National Laboratory has identified a magnesium oxysulfate grout formulation to solidify the liquid effluent from the Savannah River Plutonium Processing Facility (SRPPF) Aqueous Recovery System (ARS). The formulation uses reactive, light burnt MgO, anhydrous MgSO 4 , and dead burnt MgO and provides good mixability, similar density to the original Portland Cement-based mix, and a leachate pH of 9.39, within the assumed Waste Isolation Pilot Plant (WIPP) brine pH range. The formulation will solidify the effluent using a solid first, lost paddle design, within a 55-gallon drum. A series of seven different process disruptions, or irregular processing during the expected ARS liquid effluent solidification process, were completed to assess the severity of the impact of the process disruption and how the formulation behaves under these conditions. Seven process disruptions were investigated including: No Mixing, Partial Mixing, Compacted/Stratified, Sealed, Overfilled, Underfilled, and Undermixed. The impact on solidification, leachate pH, Er (a Pu/Am surrogate) distribution, and density of the resulting grout were established. Overall, four of the process disruptions, No Mixing, Partial Mixing, Compacted/Stratified, and Overfilled, resulted in basic, unabsorbed liquid that would require additional solidification to be acceptable for WIPP. Most solids generated in this testing met the expected WIPP leachate pH requirements. Solids from the Compacted/Stratified process disruption test, however, produced a leachate pH slightly above the assumed range in the WIPP performance assessment. The distribution of Er for most of the tests was relatively consistent. The No Mixing process disruption test, however, resulted in non-homogeneous Er distribution, indicating that radioactive material would not be evenly distributed throughout this solid’s matrix. The Overfilled test is the only mix with a density slightly below the acceptable value. The Sealed and Overmixed tests produced a solid closest to the standard mix with no unabsorbed liquid, expected leachate pH levels, consistent Er concentrations, and expected density, indicating these process disruptions do not have a negative impact on the final grout form. Based on the other process disruptions, it is critical to have premixed dry materials and a well-defined mixing process to produce a solid, homogeneous magnesium oxysulfate cement, with no unabsorbed liquid. These process disruption tests show that the lack of adequate mixing is fundamental to creating an improperly solidified material that may require remediation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Microscopic optical potentials for medium-mass isotopes derived at the first order of Watson multiple-scattering theory

We perform a first-principles calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with self-consistent Green's function theory with a nucleon-nucleon t matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off calcium and nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65–200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the calcium and nickel isotopic chains. Published by the American Physical Society 2024

Physics↗

Helium causing disappearance of a/2<111> dislocation loops in binary Fe-Cr ferritic alloys

In this work, single and dual-beam self-ion irradiations were performed at 500°C on ultra-high purity Fe14%Cr alloy to ~0.33 displacements-per-atom (dpa), and 0 or 3030 atomic-parts-per-million (appm) helium/dpa, respectively. Using transmission electron microscopy, we reveal that helium can drastically modify the dislocation loop Burgers vector in Fe-Cr alloys. Helium co-implantation caused complete disappearance of a/2<111> type dislocation loops, and the microstructure consisted of only a<100> loops. Conversely, a/2<111> type loops were predominant without He co-implantation. The total loop density remained largely unaffected. The results strikingly contrast literature asserting that helium stabilizes a/2<111> type loops in bcc Fe alloys, based on low temperature irradiations. Collectively analyzing the results with literature suggest that the small positive interaction between helium and self-interstitial atoms (SIA) in Fe predicted by atomistic simulations maybe insufficient to holistically explain the dislocation loop microstructure development in presence of helium. Helium-SIA positive binding inadvertently implies elevated a/2<111> loop fraction and higher loop densities that the present results contradict. Helium induced high cavity density causing a preferential loss of highly glissile <111> clusters, leaving the matrix saturated with <100> type clusters is proposed as a potential mechanism. Further, the in-situ irradiations combined with Burgers vector analysis strengthened the evidence of Cr-induced dislocation loop mobility reduction that appears to stabilize the a/2<111> type loops and causes higher loop densities in Fe-Cr alloys.

36 MATERIALS SCIENCE↗

Quadrupolar interactions between acceptor pairs in $\mathcal{p}$-doped semiconductors

Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$\mathcal{j}$ symbol, $^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$^\}$ = 0. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $\mathcal{p}$-type semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Single Atomic Iron Site Catalysts via Benign Aqueous Synthesis for Durability Improvement in Proton Exchange Membrane Fuel Cells

Atomically-dispersed iron-nitrogen-carbon (Fe–N–C) catalysts have arisen as promising candidates for replacing the costly precious metal catalysts in fuel cells but still face some grand challenges, such as insufficient site density and durability. Herein, we report a self-assembly method in an aqueous solution to develop an atomically-dispersed iron catalyst with high oxygen reduction reaction (ORR) activity and stability in acidic electrolytes. As determined by high-resolution transmission electron microscopy (HR-TEM), X-ray absorption spectroscopy (XAS), and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), this benign aqueous synthesis strategy facilitates the formation of homogeneous atomic nitrogen-coordinated iron sites embedded in a popcorn-like porous graphitic carbon matrix. These catalyst properties contribute to the improved ORR kinetic current density and mass transport. By controlling synthesis chemistry, the correlation between structure and property is systematically investigated. In this work, the iron content is the most critical material property and can regulate site density and graphitic carbon structures in the catalyst, impacting catalytic activity and stability. The enhanced performance and durability were examined in both acidic aqueous electrolytes and membrane electrode assemblies.

25 ENERGY STORAGE↗

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

Ab initio calculations of electron-phonon interactions including the polar Fröhlich coupling have advanced considerably in recent years. The Fröhlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fröhlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fröhlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. In this work, we generalize previous work on the ab initio Fröhlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for three-dimensional and 2D systems when the interlayer separation tends to zero or infinity, respectively. This expression enables an accurate description of the Fröhlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct ab initio density-functional perturbation theory calculations for monolayer BN and MoS 2 , and we provide a simple expression for the 2D Fröhlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-fidelity micromechanical modeling of the effects of defects on damage and creep behavior in single tow ceramic matrix composite

Despite the superior properties of ceramic matrix composites (CMCs), their fabrication process generates inevitable defects with high density that significantly influence material integrity and residual useful life. Recent efforts have focused on CMC property prediction and investigation of their different inelastic mechanisms, but very limited work exists on understanding the influence of defects on inelastic responses of CMCs. Here, we introduce a three-dimensional micromechanics computational framework that includes experimentally informed material microstructure and architectural variabilities to investigate CMC response in the presence of manufacturing-induced defects. A developed microstructure generation algorithm is used to generate the representative volume elements in the micromechanics models from complex material morphology information obtained from extensive characterization studies of C/SiNC and SiC/SiNC CMCs. A fracture mechanics-informed matrix damage model is reformulated, in which the model considers the growth of porosity and microcracks in the as-received material. A progressive fiber damage model as well as Orthotropic viscoplasticity creep formulation are also utilized for the study. This methodology is implemented within the micromechanics framework to investigate the complex temperature- and time-dependent load transfer and damage mechanisms of CMCs under operation loading conditions. The developed framework explores the influence of as-received defects on the damage and creep behavior in service conditions. It also provides new insights into the effect of size, shape, distribution, and location of these defects on material response. The framework is then calibrated with unidirectional CMC minicomposite results available in the literature.

36 MATERIALS SCIENCE↗

MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials

We report the MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ( C ij ) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structure's crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pugh's ratio, Cauchy's pressure, Kleinman's parameter, and Lame's coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package (2016) [29] and plot the spatial variation of several elastic properties such as Poisson's ratio, linear compressibility, shear modulus, and Young's modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.

2D materials↗

Correlating microstructure and mechanical properties of harvested high dose Zorita light water reactor internals

Here, in this study, microstructural studies and micro-mechanical testing of an ex-plant material harvested from the decommissioned pressurized water reactor (PWR) is carried out. Irradiated 304 stainless steel (SS) components were harvested by the Electric Power Research Institute, U.S. Nuclear Regulatory Commission, and members of the José Cabrera Nuclear Power Station (Zorita) in Spain. The bi-crystalline micro-tensile specimens, atom probe tomography (APT) tips, and transmission electron microscopy (TEM) lamellae were fabricated from the baffle plate materials irradiated to 0.05, 15 and 50 dpa to elucidate microstructural, microchemical, and local mechanical properties changes as a function of dose. TEM and APT studies reveal radiation induced Ni, Cr, and Si rich precipitates in the 15 dpa sample that become smaller and partially redissolve into the matrix of the 50 dpa sample (decreasing size and number density). Dislocation loop and cavity number density and size were quantified as a function of dose as well as swelling. Intergranular Ni and Si enrichments with concomitant Fe and Cr depletion were observed in the 15 dpa sample and were more pronounced in the 50 dpa sample. Micro-tensile testing performed in the scanning electron microscope (SEM) at room temperature and 300 °C shows that the material's local yield strength and ultimate tensile strength decreases with increased dose and elevated test temperature and provides further insights via localized strain mapping. Current and previous mechanical data was compared with calculated values using the dispersed barrier hardening model with inputs of dislocation loops, precipitates, and cavities from microstructural characterization.

36 MATERIALS SCIENCE↗

Integrating fiber optic sensors into metallic components for sensing in harsh environments

The integration of fiber optic sensors into high-temperature materials is critical for real-time monitoring and autonomous operation of engineering systems. This study demonstrated a spark plasma sintering (SPS)-assisted embedding process for integrating sapphire fiber optic sensors into stainless steel components during part fabrication. Optical fibers were encapsulated in stainless steel 316L powders which were sintered at different fabrication conditions using SPS to investigate the effects of sintering parameters on the embedment. Measurements of optical transmittance, combined with microstructural analysis (X-ray computed tomography and scanning electron microscopy) and mechanical testing (tensile and microhardness), were conducted to examine the fiber functionality, fiber–matrix bonding quality, and properties of the sintered materials. Here, the results show that under suitable fabrication conditions, intact optical fibers can be encapsulated in highly-densified (>98 % relative density) stainless steel components. These conditions also led to a good bond at the fiber–matrix interface with micron-sized material interdiffusion across the interface. The sintering parameters were observed to affect fiber optical attenuation, where high temperature, pressure, and hold time during SPS enhanced fiber–matrix bonding and adversely affected optical transmission. Tensile testing confirmed the superior tensile strength and ductility of the matrix fabricated by SPS. Furthermore, the materials exhibited limited strength reduction (~70 MPa) upon the integration of fibers. This study demonstrates the effectiveness of SPS for fiber-material integration for high-temperature applications.

36 MATERIALS SCIENCE↗

Measurements of jet multiplicity and jet transverse momentum in multijet events in proton–proton collisions at ${\sqrt{s}=13\, \text {TeV}}$

Multijet events at large transverse momentum ($p$ T ) are measured at $\sqrt{s}$ = 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb -1 . The multiplicity of jets with $p$ T > 50 GeV that are produced in association with a high-$p$ T dijet system is measured in various ranges of the $p$ T of the jet with the highest transverse momentum and as a function of the azimuthal angle difference Δ$\phi$ 1,2 between the two highest $p$ T jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $p$ T jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simula tions of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal History of Matrix Forsterite Grains from Murchison Based on High-resolution Tomography

Protoplanetary disks are dust- and gas-rich structures surrounding protostars. Depending on the distance from the protostar, this dust is thermally processed to different degrees and accreted to form bodies of varying chemical compositions. The primordial accretion processes occurring in the early protoplanetary disk such as chondrule formation and metal segregation are not well understood. One way to constrain them is to study the morphology and composition of forsteritic grains from the matrix of carbonaceous chondrites. Here, we present high-resolution ptychographic X-ray nanotomography and multimodal chemical microtomography (X-ray diffraction and X-ray fluorescence) to reveal the early history of forsteritic grains extracted from the matrix of the Murchison CM2.5 chondrite. Here,. the 3D electron density maps revealed, at unprecedented resolution (64 nm), spherical inclusions containing Fe–Ni, very little silica-rich glass and void caps (i.e., volumes where the electron density is consistent with conditions close to vacuum) trapped in forsterite. The presence of the voids along with the overall composition, petrological textures, and shrinkage calculations is consistent with the grains experiencing one or more heating events with peak temperatures close to the melting point of forsterite (~2100 K), and subsequently cooled and contracted, in agreement with chondrule-forming conditions.

58 GEOSCIENCES↗

Slides for MS&T2022: Carbon-Carbon Composites from 3D Printed Preforms Graphitized by Electric Field Assisted Sintering

Formation of Carbon-Carbon (C-C) composite materials requires putting a carbon fiber preform through a cycle of densification, carbonization, and graphitization. This cycle is then repeated until the desired properties are achieved. The graphitization phase is particularly energy demanding as it involves heating the components to in excess of 2000°C. In traditional furnaces this is also quite time consuming as typical heating rates are low, and the actual heat treatment may be limited by component dimensions, as heat is conducted throughout the part primarily by thermal diffusion. Joule heating by means of Electric Field Assisted Sintering (EFAS) systems enables high heating rates and causes the part to be heated from the inside, which eliminates the thermal diffusion time constraint. In our process, C-C composites are formed by pyrolyzation of 3D-printed carbon fiber preforms, vacuum infiltration of naphthalene based mesophase pitch, and carbonization. The part is then graphitized in the EFAS system. By this method graphitization of the composite matrix was achieved in less than an hour. A part density of greater than 1.6g/cc (up to 1.9g/cc demonstrated) was achieved after only two rounds of infiltration and a single graphitization. Overall the process took less than a week which is significantly faster than traditional methods. Optical microscopy and XRD results are discussed to elucidate the internal porosity and characterize the degree of graphitization. Testing was performed showing the impact on fiber direction to electrical and thermal properties of the final part.

36 MATERIALS SCIENCE↗

Estimation of the Kelvin–Helmholtz Unstable Boundary

The Kelvin–Helmholtz (KH) instability is one of the most important mechanisms of the viscous-like interaction between the solar wind and the magnetosphere (MSP), which transport the mass, energy, momentum, and magnetic flux. Thus, it is important to examine whether the magnetopause boundary is KH unstable or not. Based on the KH onset conditions, this report proposes to use a matrix to identify the most KH unstable direction based on the in situ measurements of the density, velocity, and magnetic field in the MSP and magnetosheath. The range of the KH unstable direction can be easily estimated based on the eigenvalues of the matrix. The eigenvectors of the matrix provide a new boundary normal coordinate system, which could be useful for 2-D KH instability simulation.

79 ASTRONOMY AND ASTROPHYSICS↗

Long-range quadrupole electron-phonon interaction from first principles

Lattice vibrations in materials induce perturbations on the electron dynamics in the form of long-range (dipole and quadrupole) and short-range (octopole and higher) potentials. The dipole Fröhlich term can be included in current first-principles electron-phonon (e-ph) calculations and is present only in polar materials. The quadrupole e-ph interaction is present in both polar and nonpolar materials, but currently it cannot be computed from first principles. In this work, we show an approach to compute the quadrupole e-ph interaction and include it in ab initio calculations of e-ph matrix elements. The accuracy of the approach is demonstrated by comparing with direct density functional perturbation theory calculations. We apply our method to silicon as a case of a nonpolar semiconductor and tetragonal PbTiO 3 as a case of a polar piezoelectric material. In both materials we find that the quadrupole term strongly impacts the e-ph matrix elements. Analysis of e-ph interactions for different phonon modes reveals that the quadrupole term mainly affects optical modes in silicon and acoustic modes in PbTiO 3 , although the quadrupole term is needed for all modes to achieve quantitative accuracy. The effect of the quadrupole e-ph interaction on electron scattering processes and transport is shown to be important. Our approach enables accurate studies of e-ph interactions in broad classes of nonpolar, polar, and piezoelectric materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗