Search NASA⌕ Search

SEARCH · Search NASA

Results for “material response simulation”

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 991 records · Page 55

The impact of chromium coatings on Zircaloy cladding deformation behavior under reactivity-initiated accident-like mechanical loading conditions

A reactivity-initiated accident (RIA) occurs when a control rod ejection or control blade drop causes an increase in the fission rate. The injection of energy results in an increase in fuel temperature which in turn causes rapid thermal expansion of the fuel pellet. This thermal expansion may result in pellet-cladding mechanical interaction (PCMI) in which the fuel imparts a mechanical strain to the cladding. PCMI may cause the cladding to fail, and thus, the mechanical response of cladding due to PCMI must be investigated when characterizing new cladding materials. Chromium-coated Zircaloy-4 is a near-term accident-tolerant fuel cladding that exhibits improved high-temperature oxidation resistance. Modified burst testing was utilized to experimentally simulate the effects of PCMI on both uncoated and chromium-coated Zircaloy cladding samples at hot zero power conditions. Samples were coated using either cold spraying or physical vapor deposition to understand the differences in behavior that the coating application method may cause. Digital image correlation was used to analyze images of the deforming specimens to extract the in-situ strain behavior of the cladding. The uncoated specimens burst at hoop strains ranging from 8.8 % to 17.2 %. The cold-spray chromium-coated Zircaloy specimens burst at hoop strains of 7.0 % to 11.0 %. The physical vapor deposition coated tubes burst at hoop strains of 9.1 % to 11.5 %. These results indicate that the chromium coating causes a loss in the ductility of the cladding. Furthermore, the higher burst hoop strains of the physical vapor deposition-coated samples relative to the cold-spray samples indicate that the cold-spraying technique causes more of a loss in ductility than physical vapor deposition. All samples burst at higher hoop strains than those expected to occur in an RIA for fresh cladding.

Accident-tolerant fuel↗

Battery Safety Testing

Abuse tests are designed to determine the safe operating limits of HEV\PHEV energy storage devices. Testing is intended to achieve certain worst-case scenarios to yield quantitative data on cell\module\pack response, allowing for failure mode determination and guiding developers toward improved materials and designs. Standard abuse tests with defined start and end conditions are performed on all devices to provide comparison between technologies. New tests and protocols are developed and evaluated to more closely simulate real world failure conditions. While robust mechanical models for vehicles and vehicle components exist, there is a gap for mechanical modeling of EV batteries. The challenge with developing a mechanical model for a battery is the heterogeneous nature of the materials and components (polymers, metals, metal oxides, liquids). Our work will provide empirical data on the mechanical behavior of batteries under compressive load to understand how a battery may behave in a vehicle crash scenario. This work is performed in collaboration with the U.S. Council for Automotive Research (USCAR) and Computer Aided Engineering of Batteries (CAEBAT). These programs have supported the design and development of a drop tower testing apparatus to close the gap between cell/string level testing and full scale crash testing with true dynamic rate effects.

25 ENERGY STORAGE↗

Battery Testing FY 2017 Annual Progress Report

Abuse tests are designed to determine the safe operating limits of HEV\PHEV energy storage devices. Testing is intended to achieve certain worst-case scenarios to yield quantitative data on cell\module\pack response, allowing for failure mode determination and guiding developers toward improved materials and designs. Standard abuse tests with defined start and end conditions are performed on all devices to provide comparison between technologies. New tests and protocols are developed and evaluated to more closely simulate real-world failure conditions. When scaling from cell to the battery level, a detailed understanding of cell interactions provides insight on safety performance. Single point failures from a cell or group of cells can be initiated by a number of triggers including internal short circuit, misuse or abuse, or component failure at the battery or system level. Propagation of a single failure event (regardless of the initiation trigger) through an entire battery, system, or vehicle is an unacceptable outcome with regards to EV battery safety. In this FY, our work has focused on evaluating the propagation of a single cell thermal runaway event through a battery using a variety of design considerations with an emphasis on passive thermal management impacts. This has been coupled with thermal modeling by NREL for these testing conditions. In addition, alternative failure initiation methods have been evaluated to provide direct comparisons of possible energy injection between modes. This data was compiled to better identify what propagation test method is appropriate given certain battery designs. Expanding the analysis of short circuit current during failure propagation has been done for EV relevant chemistries. Ongoing test development and validation to obtain these values has been achieved. While robust mechanical models for vehicles and vehicle components exist, there is a gap for mechanical modeling of EV batteries. The challenge with developing a mechanical model for a battery is the heterogeneous nature of the materials and components (polymers, metals, metal oxides, liquids). Our work will provide empirical data on the mechanical behavior of batteries under compressive load to understand how a battery may behave in a vehicle crash scenario. This work is performed in collaboration with the U.S. Council for Automotive Research (USCAR) and Computer Aided Engineering of Batteries (CAEBAT). These programs have supported the design and development of a drop tower testing apparatus to close the gap between cell/string level testing and full scale crash testing with true dynamic rate effects.

25 ENERGY STORAGE↗

Battery Abuse Testing

Abuse tests are designed to determine the safe operating limits of HEV\PHEV energy storage devices. Testing is intended to achieve certain worst-case scenarios to yield quantitative data on cell\module\pack response, allowing for failure mode determination and guiding developers toward improved materials and designs. Standard abuse tests with defined start and end conditions are performed on all devices to provide comparison between technologies. New tests and protocols are developed and evaluated to more closely simulate real-world failure conditions. While robust mechanical models for vehicles and vehicle components exist, there is a gap for mechanical modeling of EV batteries. The challenge with developing a mechanical model for a battery is the heterogeneous nature of the materials and components (polymers, metals, metal oxides, liquids). This year saw the stand up of a new drop tower tester capable of providing dynamic mechanical test results.

25 ENERGY STORAGE↗

I.6.C Battery Safety Testing

Abuse tests are designed to determine the safe operating limits of HEV\PHEV energy storage devices. Testing is intended to achieve certain worst-case scenarios to yield quantitative data on cell\module\pack response, allowing for failure mode determination and guiding developers toward improved materials and designs. Standard abuse tests with defined start and end conditions are performed on all devices to provide comparison between technologies. New tests and protocols are developed and evaluated to more closely simulate real world failure conditions. While robust mechanical models for vehicles and vehicle components exist, there is a gap for mechanical modeling of EV batteries. The challenge with developing a mechanical model for a battery is the heterogeneous nature of the materials and components (polymers, metals, metal oxides, liquids).

25 ENERGY STORAGE↗

Accumulation of the planets

In modeling the accumulation of planetesimals into planets, it is appropriate to distinguish between two stages: an early stage, during which approximately 10 km diameter planetesimals accumulate locally to form bodies approximate 10 to the 25th g in mass; and a later stage in which the approximately 10 to the 25th g planetesimals accumulate into the final planets. In the terrestrial planet region, an initial planetesimal swarm corresponding to the critical mass of dust layer gravitational instabilities is considered. In order to better understand the accumulation history of Mercury-sized bodies, 19 Monte-Carlo simulations of terrestrial planet growth were calculated. A Monte Carlo technique was used to investigate the orbital evolution of asteroidal collision debris produced interior to 2.6 AU. It was found that there are two regions primarily responsible for production of Earth-crossing meteoritic material and Apollo objects. The same techniques were extended to include the origin of Earth-approaching asteroidal bodies. It is found that these same two resonant mechanisms predict a steady-state number of Apollo-Amor about 1/2 that estimated based on astronomical observations.

Wetherill, G. W.↗

Probabilistic Simulation for Combined Cycle Fatigue in Composites

A methodology to compute probabilistic fatigue life of polymer matrix laminated composites has been developed and demonstrated. Matrix degradation effects caused by long term environmental exposure and mechanical/thermal cyclic loads are accounted for in the simulation process. A unified time-temperature-stress dependent multifactor interaction relationship developed at NASA Glenn Research Center has been used to model the degradation/aging of material properties due to cyclic loads. The fast probability integration method is used to compute probabilistic distribution of response. Sensitivities of fatigue life reliability to uncertainties in the primitive random variables (e.g., constituent properties, fiber volume ratio, void volume ratio, ply thickness, etc.) computed and their significance in the reliability-based design for maximum life is discussed. The effect of variation in the thermal cyclic loads on the fatigue reliability for a (0/+/- 45/90)s graphite/epoxy laminate with a ply thickness of 0.127 mm, with respect to impending failure modes has been studied. The results show that, at low mechanical cyclic loads and low thermal cyclic amplitudes, fatigue life for 0.999 reliability is most sensitive to matrix compressive strength, matrix modulus, thermal expansion coefficient, and ply thickness. Whereas at high mechanical cyclic loads and high thermal cyclic amplitudes, fatigue life at 0.999 reliability is more sensitive to the shear strength of matrix, longitudinal fiber modulus, matrix modulus, and ply thickness.

Chamis, Christos C.↗

Overview of an Indoor Sonic Boom Simulator at NASA Langley Research Center

A facility has been constructed at NASA Langley Research Center to simulate the soundscape inside residential houses that are exposed to environmental noise from aircraft. This controllable indoor listening environment, the Interior Effects Room, enables systematic study of parameters that affect psychoacoustic response. The single-room facility, built using typical residential construction methods and materials, is surrounded on adjacent sides by two arrays of loudspeakers in close proximity to the exterior walls. The arrays, containing 52 subwoofers and 52 mid-range speakers, have a usable bandwidth of 3 Hz to 5 kHz and sufficient output to allow study of sonic boom noise. In addition to these exterior arrays, satellite speakers placed inside the room are used to augment the transmitted sound with rattle and other audible contact ]induced noise that can result from low frequency excitation of a residential house. The layout of the facility, operational characteristics, acoustic characteristics and equalization approaches are summarized.

Klos, Jacob↗

Influence of Coupled Radiation and Ablation on the Aerothermodynamic Environment of Planetary Entry Vehicles

A review of recently published coupled radiation and ablation capabilities involving the simulation of hypersonic flowfields relevant to Earth, Mars, or Venus entry is presented. The three fundamental mechanisms of radiation coupling are identified as radiative cooling, precursor photochemistry, and ablation-radiation interaction. The impact of these mechanisms are shown to be significant for a 3 m radius sphere entering Earth at hypothetical Mars return conditions (approximately 15 km/s). To estimate the influence precursor absorption on the radiative flux for a wide range of conditions, a simplified approach is developed that requires only the non-precursor solution. Details of a developed coupled ablation approach, which is capable of treating both massively ablating flowfields in the sublimation regime and weakly ablating diffusion Climited oxidation cases, are presented. A review of the two primary uncoupled ablation approximations, identified as the blowing correction and film coefficient approximations, is made and their impact for Earth and Mars entries is shown to be significant for recession and convective heating predictions. Fully coupled ablation and radiation simulations are presented for the Mars return sphere throughout its entire trajectory. Applying to the Mars return sphere the Pioneer- Venus heritage carbon phenolic heatshield, which has properties available in the open literature, the differences between steady state ablation and coupling to a material response code are shown to be significant.

Johnston, Christopher O.↗

Dynamic induced softening in frictional granular materials investigated by discrete-element-method simulation

A granular system composed of frictional glass beads is simulated here using the discrete element method. The intergrain forces are based on the Hertz contact law in the normal direction with frictional tangential force. The damping due to collision is also accounted for. Systems are loaded at various stresses and their quasistatic elastic moduli are characterized. Each system is subjected to an extensive dynamic testing protocol by measuring the resonant response to a broad range of ac drive amplitudes and frequencies via a set of diagnostic strains. The system, linear at small ac drive amplitudes, has resonance frequencies that shift downward (i.e., modulus softening) with increased ac drive amplitude. Detailed testing shows that the slipping contact ratio does not contribute significantly to this dynamic modulus softening, but the coordination number is strongly correlated to this reduction. This suggests that the softening arises from the extended structural change via break and remake of contacts during the rearrangement of bead positions driven by the ac amplitude.

58 GEOSCIENCES↗

Modeling-Based Design and Optimization of a Gradient Composite Transition Joint

An innovative additively manufactured gradient composite transition joint (AM-GCTJ) has been designed to join dissimilar metals, to address the pressing issue of premature failure observed in conventional dissimilar metal welds (DMWs) when subjected to increased cyclic operating conditions of fossil fuel power plants. The transition design, guided by computational modeling, developed a gradient composite material distribution, facilitating a smooth transition in material volume fraction and physical properties between different alloys. This innovative design seeks to alleviate structural challenges arising from distinct material properties, including high thermal stress and potential cracking issues resulting from the thermal expansion mismatch typically observed in conventional DMWs. In this study, we investigated the creep properties of transition joints comprising Grade 91 steel and 304 stainless steel through a combination of simulations and creep testing experiments. The implementation of a gradient composite design in the plate transition joint resulted in a significant enhancement of creep resistance when compared to the baseline conventional DMW. For instance, the creep rupture life of the transition joint was improved by > 400% in a wide range of temperature and stress testing conditions. Meanwhile, the failure location shifted to the base material of Grade 91 steel. Such enhancement can be primarily attributed to the strong mechanical constraint facilitated by the gradient composite design, which effectively reduced the stresses on the less creep-resistant alloy in the transition zone. Beyond examining plate joints, it is crucial to assess the deformation response of tubular transition joints under pressure loading and transient temperature conditions to substantiate and demonstrate the effectiveness of the design. The simulation results affirm that the tubular transition joint demonstrates superior resistance compared to its counterpart DMW when subjected to multiaxial stresses in tubular structures. In addition, optimization of the transition joint’s geometry dimensions has been conducted to diminish the accumulated deformation and enhance the service life. Lastly, the scalability and potential of the innovative transition joints for large-diameter pipe applications are addressed.

Zhang, Wei↗

The Influence of Clocking Angle of the Projectile on the Simulated Impact Response of a Shuttle Leading Edge Wing Panel

An analytical study was conducted to determine the influence of clocking angle of a foam projectile impacting a space shuttle leading edge wing panel. Four simulations were performed using LS-DYNA. The leading edge panels are fabricated of multiple layers of reinforced carbon-carbon (RCC) material. The RCC material was represented using Mat 58, which is a material property that can be used for laminated composite fabrics. Simulations were performed of a rectangular-shaped foam block, weighing 0.23-lb., impacting RCC Panel 9 on the top surface. The material properties of the foam were input using Mat 83. The impact velocity was 1,000 ft/s along the Orbiter X-axis. In two models, the foam impacted on a corner, in one model the foam impacted the panel initially on the 2-in.-long edge, and in the last model the foam impacted the panel on the 7-in.- long edge. The simulation results are presented as contour plots of first principal infinitesimal strain and time history plots of contact force and internal and kinetic energy of the foam and RCC panel.

Jackson, Karen E.↗

Development of GENOA Progressive Failure Parallel Processing Software Systems

A capability consisting of software development and experimental techniques has been developed and is described. The capability is integrated into GENOA-PFA to model polymer matrix composite (PMC) structures. The capability considers the physics and mechanics of composite materials and structure by integration of a hierarchical multilevel macro-scale (lamina, laminate, and structure) and micro scale (fiber, matrix, and interface) simulation analyses. The modeling involves (1) ply layering methodology utilizing FEM elements with through-the-thickness representation, (2) simulation of effects of material defects and conditions (e.g., voids, fiber waviness, and residual stress) on global static and cyclic fatigue strengths, (3) including material nonlinearities (by updating properties periodically) and geometrical nonlinearities (by Lagrangian updating), (4) simulating crack initiation. and growth to failure under static, cyclic, creep, and impact loads. (5) progressive fracture analysis to determine durability and damage tolerance. (6) identifying the percent contribution of various possible composite failure modes involved in critical damage events. and (7) determining sensitivities of failure modes to design parameters (e.g., fiber volume fraction, ply thickness, fiber orientation. and adhesive-bond thickness). GENOA-PFA progressive failure analysis is now ready for use to investigate the effects on structural responses to PMC material degradation from damage induced by static, cyclic (fatigue). creep, and impact loading in 2D/3D PMC structures subjected to hygrothermal environments. Its use will significantly facilitate targeting design parameter changes that will be most effective in reducing the probability of a given failure mode occurring.

Abdi, Frank↗

SURROGATE MODEL DEVELOPMENT AND VALIDATION FOR RELIABILITY ANALYSIS OF REACTOR PRESSURE VESSELS

In nuclear light water reactors (LWRs), the reactor coolant, core and shroud are contained within a massive, thick walled steel vessel known as a reactor pressure vessel (RPV). Given the tremendous size of these structures, RPVs typically contain a large population of pre-existing flaws introduced in the manufacturing process. After many years of operation, irradiation-induced embrittlement makes these vessels increasingly susceptible to fracture initiation at the locations of the pre-existing flaws. Because of the uncertainty in the loading conditions, flaw characteristics and material properties, probabilistic methods are widely accepted and used in assessing RPV integrity. The Fracture Analysis of Vessels – Oak Ridge (FAVOR) computer program developed by researchers at Oak Ridge National Laboratory is widely used for this purpose. This program can be used in order to perform deterministic and probabilistic risk-informed analyses of the structural integrity of an RPV subjected to a range of thermal-hydraulic events. FAVOR uses a one-dimensional representation of the global response of the RPV, which is appropriate for the beltline region, which experiences the most embrittlement, and employs an influence coefficient technique to rapidly compute stress intensity factors for axis-aligned surface-breaking flaws. The Grizzly code is currently under development at Idaho National Laboratory (INL) to be used as a general multiphysics simulation tool to study a variety of degradation mechanisms in nuclear power plant components. The first application of Grizzly has been to study fracture in embrittled RPVs. Grizzly can be used to model the thermo-mechanical response of an RPV under transient conditions observed in a pressurized thermal shock (PTS) scenario. The global response of the vessel provides boundary conditions for local 3D models of the material in the vicinity of a flaw. Fracture domain integrals are computed to obtain stress intensity factors, which can in turn be used to assess whether a fracture would initiate at a pre-existing flaw. To use Grizzly for probabilistic analysis, it is necessary to have a way to rapidly evaluate stress intensity factors. To accomplish this goal, a reduced order model (ROM) has been developed to efficiently represent the behavior of a detailed 3D Grizzly model used to calculate fracture parameters. This approach uses the stress intensity factor influence coefficient method that has been used with great success in FAVOR. Instead of interpolating between tabulated solutions, as FAVOR does, the ROM approach uses a response surface methodology to compute fracture solutions based on a sampled set of results used to train the ROM. The main advantages of this approach are that the process of generating the training data can be fully automated, and the procedure can be readily used to consider more general flaw configurations. This paper demonstrates the procedure used to generate a ROM to rapidly compute stress intensity factors for axis-aligned flaws. The results from this procedure are in good agreement with those produced using the traditional influence coefficient interpolation procedure, which gives confidence in this method. This paves the way for applying this procedure for more general flaw configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

In-Situ SEM High Strain Rate Testing of Large Diameter Micropillars Followed by TEM and EBSD Postmortem Analysis

Background Dislocation dynamic simulations are intended as a tool to understand and predict the mechanical behavior of metallic materials, but its prediction has never been directly verified by experiments due to differences in specimen strain rate and size. Objective In this work, a comprehensive experimental framework is proposed to attempt direct comparison between experiments and discrete dislocation dynamics (DDD) modelling. Methods By integrating high-throughput sample fabrication and a customized testing apparatus, the sample size and strain rate typically employed in DDD simulations are explored experimentally. Constitutive properties such as stress-strain response are measured, and microstructural information is obtained from transmission electron microscopy (TEM) imaging, electron backscatter diffraction (EBSD), and TEM-based orientation mapping. Results Magnesium and copper were selected, as case studies, to demonstrate the newly developed experimental procedure. Measured stress-strain responses for Mg are consistent with those obtained with a miniaturized Hopkison bar experiments. Furthermore, by exploiting the validated workflow, the effect of strain rate on micropillar heterogeneous deformation and associated dislocation plasticity were revealed. Conclusion The work establishes a methodology for the systematic study of not only metals but also other materials and structures at the microscale and high strain rates.

42 ENGINEERING↗

Modelling pulsed field magnetization of iron-based bulk superconductors

Abstract Bulk superconductors can be used as super-strength quasi-permanent magnets capable of providing magnetic flux densities considerably superior to conventional permanent magnets. This makes them attractive for several engineering applications that rely on strong magnetic fields like rotating machines, NMR/MRI and magnetic drug delivery systems. Recently, the authors reported a record trapped magnetic field in an iron-based bulk superconductor: 2.83 T was trapped in potassium-doped barium iron arsenide (Ba, K)Fe 2 As 2 (or Ba122) at 5 K. Of particular significance is that the strength and temporal stability of this magnetic field exceeds the requirements of MRI machines, indicating iron-based bulks can now perform at levels demanded by engineering applications. One crucial challenge for their practical use, however, is the need to apply and remove an external magnetic field to magnetize them. Pulsed field magnetization (PFM) shows great promise as a practical method of magnetizing bulks, but the process generates heat in the bulk that is detrimental to its superconducting performance and ability to act as a super-strength magnet. In this paper, coupled electromagnetic–thermal numerical models are used to simulate the PFM of iron-based bulk superconductors. Here we focus on the recent-record-breaking, fine-grain polycrystalline K-doped Ba122 bulks. The impact that the specific J c ( B ) characteristics and thermal properties of the Ba122 material—all of which have been experimentally measured from state-of-the-art samples—have on the magnetic flux dynamics and thermal behaviour during PFM, including the final trapped field, is investigated. We show that because the thermal properties are similar to those of REBa 2 Cu 3 O 7 −δ bulks, a similar response to pulsed fields is obtained. A maximum trapped field of ∼0.81 T (∼43.3% of the maximum trapped field capability under ideal, field-cooling conditions) was simulated at 5 K, with a magnetization efficiency of ∼54%. The modelling framework provides a fast and flexible tool for optimising the practical PFM process at different operating temperatures to maximise the trapped field in state-of-the-art Ba122 bulks and to guide the design of future experiments.

bulk superconductors↗

BISON capability and validation for U3Si2, Cr2O3-doped UO2, FeCrAl, and Cr-coated Zircaloy ATF concepts

Development, implementation, and validation of material and behavior models for accident tolerant fuel (ATF) concepts in the BISON fuel performance code began in 2014 in response to the events that occurred at the Fukushima Daichii nuclear power plant in March 2011. Early on, the focus was on U3Si2 fuel and FeCrAl cladding as part of a high-impact problem through the Nuclear Energy and Advanced Model- ing Simulation program [1]. Then, developments for Cr2O3- doped UO2 fuel, as well as SiC-SiC and Cr-coated Zircaloy cladding began based upon industry interests. Near the end of fiscal year 2018 the Consortium for Advanced Simulation of Light Water Reactors took over further Accident Tolerant Fuel (ATF) work in BISON in support of Nuclear Regulatory Commission (NRC) engagement. Discussions with the NRC clarified their list of priority fuel and cladding concepts, which included Cr2O3-doped UO2 and U3Si2 fuels, as well as Cr-coated Zircaloy and FeCrAl claddings. Further, reports similar in form to NUREG/CR-7024 [2] that was developed for traditional light water reactor (LWR) materials, UO2 fuel with Zircaloy claddings were created for the priority fuel and cladding concepts. In this paper select details from the reports entitled "ATF material model development and validation for priority fuel concepts" [3] and "ATF material model development and validation for priority cladding concepts" [4] are presented. First, a brief overview of the available models and their associated uncertainty are provided for the priority fuel and cladding concepts. Then, for the concepts with experimental data, comparisons between simulation and experiment are shown taking into account forward uncertainty quantification (UQ) techniques. For the concepts without publicly available experimental data, parametric studies incorporating forward UQ are completed to verify claims made about the materials’ behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Nonlinear Dynamic Characteristics and Control of Giant Magnetostrictive Ultrasonic Transducer

The nonlinear dynamic characteristics of giant magnetostrictive ultrasonic transducer (GMUT) are researched in this paper, and the optimal control strategy is proposed. New nonlinear differential terms are introduced to explain the hysteretic phenomena of giant magnetostrictive materials (GMM), and the nonlinear dynamic model of a giant magnetostrictive ultrasonic transducer subjected to harmonic magnetic field and stochastic disturbance is developed. The system’s nonlinear dynamic responses are discussed, and the optimal control strategy is proposed to improve the system’s accuracy. Numerical simulation and experiment results show that there are abundant nonlinear dynamic behaviors in the system; the stability of the system varies with the parameters, which causes stochastic bifurcation; the system’s accuracy is improved through stochastic optimal control. The results of this study are helpful for the application of giant magnetostrictive ultrasonic transducer in engineering fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗