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NASA NTRS1994

Gamma-ray burst spectral breaks and source beaming

The principal discovery of the Compton Gamma-Ray Observatory (GRO) concerning gamma-ray bursts is that these sources are isotropic but with a comparative deficiency of fainter sources, suggesting that they are probably cosmological in origin. If they are at such large distances from Earth then they are extremely luminous and compact. A consequence of this is that two-photon pair production attenuation of the gamma-ray continuum cannot be avoided unless the source radiation is substantially beamed. Most sources do not display gamma-ray turnovers although a few gamma-ray bursts (GRB) detected by GRO exhibit distinct spectral breaks in the MeV range. A derivation of the relationship defining of the degree of beaming in burst sources with spectral breaks due to gamma-gamma attenuation, as a function of source spectral index and break energy, is presented. It is found that sources at distances of approximately 1 Gpc must typically be beamed with bulk Lorentz factors of around 10(exp 3)-10(exp 4), indicating powerful bulk acceleration in bursts, although these Lorentz factors are reduced markedly for steep source spectra. Since the source spectra are not strongly Comptonized, such beaming will blueshift the gamma-gamma attenuation breaks to energies much higher than 1 MeV; an absolute lower bound to the source bulk Lorentz factor is determined from this additional constraint. This blueshifting suggests that those sources with MeV breaks may not be cosmological, or that their breaks are produced by a mechanism that dominates gamma-gamma attenuation at these energies.

Baring, Matthew G.↗

DOE OSTI2025

The three-point form factor of Tr ϕ 3 to six loops

We study the three-point form factor of the length-three half-BPS operator (Tr ϕ 3 ) in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ 2 ). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1994

Multiple outflows in the bipolar planetary nebula M1-16: A molecular line study

Extensive observations of the molecular gas in the young, compact planetary nebula M1-16 have been made, using the Swedish-ESO-Submillimeter Telescope. A map of the CO J = 2-1 emission shows that the molecular envelope contains both a slow and a fast outflow with expansion velocities of 19 km/s and greater than 34 km/s, respectively. The slow outflow is mildly elliptical, while the fast molecular outflow is bipolar. This fast outflow is roughly aligned with the very fast outflows recently found in the optical, while the long axis of the slow elliptical outflow is roughly orthogonal to the optical outflow axis. The kinematic timescales for the CO fast outflow and the optical very fast outflow agree closely, supporting the view that the former represents material in the slow outflow accelerated by the very fast outflow. The kinematic signature of a disk expanding with about 15.5 km/s can also be seen in the CO J = 2-1 data. The mass-loss rate (a) for the slow outflow is greater than or equal to 2.8 x 10(exp -5) solar mass/yr and possibly as large as 9 x 10(exp -5) solar mass/yr, (b) for the fast outflow is greater than or equal to 5 x 10(exp -6) solar mass/yr, and (c) for the very fast optically visible outflow is approximately equal 5 x 10(exp -7) solar mass/yr. The disk mass is approximately equal 6 x 10(exp -3) solar mass. Grain photoelectric heating results in temperatures of 20-70 K in molecular gas of the slow outflow. The (13)C/(12)C abundance ratio in M1-16 is found to be 0.33, quite possibly the highest found for any evolved object. Upper limits for the (18)O/(16)O and (17)O/(16)O ratios were found to be consistent with the values found in AGB stars. A search for other molecular species in M1-16 resulted in the detection of the high-excitation species HCN, CN, (13)CN, HCO(+), and H(13)CO(+) and possibly N2H(+). Both the HCO(+)/HCN and CN/HCN line-intensity ratios are enhanced, the former by a very large factor, over the values found in the envelopes of AGB stars, probably as a result of enhancement of the CN and HCO(+) abundances due to photochemistry induced by the stellar UV. The CS J = 2-1, SiO J = 2-1 (v = 0), and SiS J = 6-5 lines were not detected to low levels. For the high-excitation molecules, adequate collisional excitation of rotational levels and survival against photodissociation by the UV radiation requires significant clumping of the molecular gas into clumps with H2 densities approximately 10(exp 5)/cu cm. The IRAS fluxes of M1-16, assuming negligible contribution from line emission, imply the presence of about (1.7-0.4) x 10(exp -3) solar mass of cool dust (temperature around 50 K) and a smaller quantity, (2.7-3.1) x 10(exp -6) solar mass, of warmer dust (temperature around 125 K) for a power-law emissivity index p = 1-2. The evolutionary nature of M1-16 cannot be explained by existing single-star models of post-AGB evolution. The very high (13)C/(12)C abundance ratio in M1-16 suggests a possible evolutionary connection between M1-16 and the rare class of J-type silicate-carbon stars which also have high (13)C/(12)C ratios and are thought to be binary systems with accretion disks.

Sahai, Raghvendra↗

DOE OSTI2026

Analog-to-digital converter based on voltage-controlled superconducting devices

The increasing demand for cryogenic electronics in superconducting and quantum computing systems calls for ultra-energy-efficient data conversion architectures that remain functional at deep cryogenic temperatures. Here, in this work, we present the first design of a voltage-controlled superconducting flash analog-to-digital converter (ADC) based on a voltage-controlled quantum-enhanced Josephson junction field-effect transistor (JJFET). Exploiting its strong gate tunability and transistor-like behavior, the JJFET offers a scalable alternative to conventional current-controlled superconducting devices while aligning naturally with CMOS-style design methodologies. Building on our previously developed Verilog-A compact model calibrated to experimental data, we design and simulate a three-bit JJFET-based flash ADC targeted for integration within cryogenic control and readout circuitry in quantum computing. The core comparator block is realized through careful bias current selection and augmented with a three-terminal nanocryotron to precisely define reference voltages. Cascaded JJFET comparators ensure robust voltage gain, cascadability, and logic-level restoration across stages. Simulation results demonstrate accurate quantization behavior with ultra-low power dissipation, underscoring the feasibility of voltage-driven superconducting mixed-signal circuits. This work establishes a critical step toward unifying superconducting logic and data conversion, paving the way for scalable cryogenic architectures in quantum–classical co-processors, low-power artificial intelligence accelerators, and next-generation energy-constrained computing platforms.

Analog-to-digital converter↗

NASA NTRS1999

A Compact Dual-Crystal Modulated Birefringence-Measurement System for Microgravity Applications

A compact modulated birefringence-measurement system has been developed for use in microgravity fluid physics applications with non-Newtonian fluids such as polymer solutions. This instrument uses a dual-crystal transverse electro-optical modulator capable of modulation frequencies in excess of 100 MHz. The two crystals are modulated 180 deg. out of phase from each other, The theoretical framework governing the development of this instrument using the Mueller-Stokes polarization matrices is discussed. Several ground-based experiments are performed to compare this system with the theoretical results. Results from this transverse electro-optical modulator-based birefringence-measurement system agree well with the theory. The instrument is also very stable and robust, making it suitable for the extreme acceleration environment to be encountered in a NASA Black Brandt sounding rocket.

Mackey, Jeffrey R.↗

DOE OSTI2025

Towards a general subtraction formula for NNLO QCD corrections to processes at hadron colliders: final states with quarks and gluons

We describe the calculation of integrated subtraction terms in the nested soft-collinear subtraction scheme for hadron collider processes with quarks and gluons, thereby extending the results presented in ref. [1]. Although this extension eventually proves to be straightforward, it requires a more careful treatment of certain collinear limits to achieve a compact and physically-transparent final result. We also show that the cancellation of infrared divergences can be organized in such a way that, once soft contributions are removed, it occurs independently for each of the external partons. We consider these results to be important stepping stones on the way to deriving finite remainders of the integrated subtraction terms for fully-general hadron collider processes in the context of the nested soft-collinear subtraction scheme.

NNLO calculations↗

NASA NTRS2008

LISA Pathfinder

USA Pathfinder is a space mission dedicated to demonstrating technology for the Laser Interferometer Space Antenna (LISA). LISA is a joint ESA/NASA mission to detect low-frequency gravitational waves on the 0.0001 to 0.1 Hz frequency band. LISA is expected to observe 100's of merging massive black hole binaries out z-15, tens of thousands of close compact binary systems in the Milky Way, merging intermediate-mass black hole binaries, tens of stellar-mass black holes falling into supermassive black holes in galactic centers, and possibly other exotic sources. Several critical LISA technologies have not been demonstrated at the requisite level of performance. In spaceflight, and some fight hardware cannot be tested in a 1-g environment. Hence, the LISA Pathfinder mission is being implemented to demonstrate these critical LISA technologies in a relevant flight environment. LISA Pathfinder mimics one arm of the LISA constellation by shrinking the 5-million-kilometer armlength down to a few tens of centimeters. The experimental concept is to measure the relative separation between two test masses nominally following their own geodesics, and thereby determine the relative residual acceleration between them near 1 mHz, about a decade above the lowest frequency required by LISA. To implement such a concept, disturbances on the test masses must be kept very small by many design features, but chiefly by "drag-free" flight. A drag-free spacecraft follows a free-falling test mass which it encloses, but has no mechanical connection to. The spacecraft senses it's orientation and separation with respect to the proof mass, and its propulsion system is commanded to keep the spacecraft centered about the test mass. Thus, the spacecraft shields the test mass from most external influences, and minimizes the effect of force gradients arising from the spacecraft, and acting on the test mass. LISA Pathfinder will compare the geodesic of one test mass against that of the other. Only a metrology system based on interferometry can achieve the displacement sensitivity. Interferometers monitor the separation of both test masses with a sensitivity comparable to that required by LISA, and using the same technologies. LISA Pathfinder is scheduled to be launched in the first half of 1020 to a Lissajous orbit around the first Sun-Earth Lagrange point, L1. In addition to a complete European technology package (the LISA Technology Package, or LTP), LISA Pathfinder will also carry thrusters and software, known as ST-7, a part of NASA's New Millennium Program.

Stebbins, Robin↗

NASA NTRS2006

Miniature Ion-Mobility Spectrometer

The figure depicts a proposed miniature ion-mobility spectrometer that would be fabricated by micromachining. Unlike prior ion-mobility spectrometers, the proposed instrument would not be based on a time-of-flight principle and, consequently, would not have some of the disadvantageous characteristics of prior time-of-flight ion-mobility spectrometers. For example, one of these characteristics is the need for a bulky carrier-gas-feeding subsystem that includes a shutter gate to provide short pulses of gas in order to generate short pulses of ions. For another example, there is need for a complex device to generate pulses of ions from the pulses of gas and the device is capable of ionizing only a fraction of the incoming gas molecules; these characteristics preclude miniaturization. In contrast, the proposed instrument would not require a carrier-gas-feeding subsystem and would include a simple, highly compact device that would ionize all the molecules passing through it. The ionization device in the proposed instrument would be a 0.1-micron-thick dielectric membrane with metal electrodes on both sides. Small conical holes would be micromachined through the membrane and electrodes. An electric potential of the order of a volt applied between the membrane electrodes would give rise to an electric field of the order of several megavolts per meter in the submicron gap between the electrodes. An electric field of this magnitude would be sufficient to ionize all the molecules that enter the holes. Ionization (but not avalanche arcing) would occur because the distance between the ionizing electrodes would be less than the mean free path of gas molecules at the operating pressure of instrument. An accelerating grid would be located inside the instrument, downstream from the ionizing membrane. The electric potential applied to this grid would be negative relative to the potential on the inside electrode of the ionizing membrane and would be of a magnitude sufficient to generate a moderate electric field. Positive ions leaving the membrane holes would be accelerated in this electric field. The resulting flux of ions away from the ionization membrane would create a partial vacuum that would draw more of the gas medium through the membrane. The figure depicts a filter electrode and detector electrodes located along the sides of a drift tube downstream from the accelerator electrode. These electrodes would apply a transverse AC electric field superimposed on a ramped DC electric field. The AC field would effect differential transverse dispersal of ions. At a given instant of time, the trajectories of most of the ions would be bent toward the electrodes, causing most of the ions to collide with the electrodes and thereby become neutralized. The DC field would partly counteract the dispersive effect of the AC field, straightening the trajectories of a selected species of ions; the selection would vary with the magnitude of the applied DC field. The straightening of the trajectories of the selected ions would enable them to pass into the region between the detector electrodes. Depending on the polarity of the voltage applied to the detector electrodes, the electric field between the detector electrodes would draw the selected ions to one of these electrodes. Hence, the current collected by one of the detector electrodes would be a measure of the abundance of ions of the selected species. The ramping of the filter- electrode DC voltage would sweep the selection of ions through the spectrum of ionic species.

Hartley, Frank T.↗

DOE OSTI2024

Novel, Middle and Long Wave Infrared Laser Sources For Accelerator Applications

The main accomplishment during Years 2020-2024 of the DOE Accelerator Stewardship Program is proof-of-principle demonstration of amplification of an ultrashort 10 µm seed pulse in a multiatmosphere CO 2 laser optically pumped by nanosecond pulses of either a ~4.3 µm Fe:ZnSe laser or a 2.8 µm electro-optically (EO) Q-switched Er: Laser. This has been accomplished at the UCLA Neptune Laboratory by using about 100 mJ, ~100 ns long pulses generated by the pump laser built for this purpose by the UAB team. Implementation of EO Q-switching regime in the solid-state Er:laser system made possible nanosecond synchronization between the pump pulse and the 0.5 ps seed pulse produced by a commercial Ti:sapphire laser based mid-IR OPA/DFG. The injection mode-locking regime realized in a compact Mult atmosphere 3 Hz CO 2 -He regenerative amplifier enabled generation of a train of ultrashort pulses separated by the cavity round-trip time of ~3.2 ns. The measured gain lifetime of ~1 µs at a total pressure of ~12-15 atm indicates that lifetime of the upper laser level is a critical limiting factor in designing high-pressure CO 2 amplifiers. A single picosecond 10 mm pulse with an energy 0.1-0.2 mJ was extracted from the amplifier’s cavity using an ultrafast Ge semiconductor switch whose reflectivity was photo-induced by a femtosecond 800 nm pulse. For direct amplification regime, nonlinear absorption in Ge at 10 mm at GW/cm 2 intensities limited the extracted energy. Therefore, the generated energy could be further increased by minimizing losses in the switch and optimizing the cavity mode size. Based on the obtained data in collaboration with BNL colleagues, we have designed a high-pressure CO 2 amplifier to be used as a preamplifier for the future experiments at the ATF BNL. The latter work is the subject of funding availability.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1982

Stellar winds in binary X-ray systems

It is thought that accretion from a strong stellar wind by a compact object may be responsible for the X-ray emission from binary systems containing a massive early-type primary. To investigate the effect of X-ray heating and ionization on the mass transfer process in systems of this type, an idealized model is constructed for the flow of a radiation-driven wind in the presence of an X-ray source of specified luminosity, L sub x. It is noted that for low values of L sub x, X-ray photoionization gives rise to additional ions having spectral lines with wavelengths situated near the peak of the primary continuum flux distribution. As a consequence, the radiation force acting on the gas increases in relation to its value in the absence of X-rays, and the wind is accelerated to higher velocities. As L sub x is increased, the degree of ionization of the wind increases, and the magnitude of the radiation force is diminished in comparison with the case in which L sub x = 0. This reduction leads at first to a decrease in the wind velocity and ultimately (for L sub x sufficiently large) to the termination of radiatively driven mass loss.

Macgregor, K. B.↗

NASA NTRS1982

Variability of compact radio sources at a wavelength of 1 millimeter

Broad-band 1 mm continuum observations of 3C 273, 3C 279, BL Lac, 3C 84, OJ 287, and 3C 345 made between 1977 March and 1981 January are reported. With the possible exception of 3C 279, all of the objects exhibited evidence for variability in the 1 mm flux density on the time scale of a few months. Flux variations at wavelengths of 1 mm and 2 cm are well correlated for the 'blazars' (BL Lac objects and optically violent variable quasars) observed; emission outbursts occur simultaneously and have similar amplitude at the two wavelengths. In contrast, an outburst in the flux from the Seyfert galaxy 3C 84 was observed at a wavelength of 1 mm in early 1980 but has not appeared at 2 cm as of 1 yr later. The observed relationship between 'blazar' emission variability at 1 mm and 2 cm is inconsistent with the canonical expanding-source model of radio variability or any of its modifications. Instead, models in which the number of synchrotron-radiating electrons is time variable (due to particle injection or acceleration behind a relativistic shock) are required.

Ennis, D. J.↗

DOE OSTI2024

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗

DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper I: Foundations and Replication Dynamics

We develop a pre-geometric cosmological framework in which existence is identified with a finite amount of unstructured energy possessing vibration as its only intrinsic property. This vibrational substrate occupies an open, bounded spectral interval $(\omega_{\min},\omega_{\max})$, ensuring finiteness of total energy and excluding infinitely stable configurations. The substrate evolves under two fundamental and competing tendencies---excitation, which amplifies coherence, and randomization, which scrambles it. Their balance produces a metastable unstructured regime in which rare fluctuations may form long-lived self-consistent spectral configurations. Because the substrate is finite and subject to competing order--disorder dynamics, no coherent configuration can be perpetually stable. We show that the only mechanism capable of sustaining long-lived organization is a replication instability: a coherent unit may reproduce into multiple offspring according to a general $1\!\to n$ rule. Replication consumes energy from the finite substrate, breaks the metastable symmetry, and induces a discrete notion of event time through the replication tick $\Delta\tau$. Temporal succession is defined through correlation ordering of spectral microstates, producing an intrinsic pre-causal structure. The compactness of the spectral domain imposes minimal and maximal timescales, bounds the internal coherence of emergent units, and limits their proliferation. These spectral constraints serve as precursors for the emergence of geometry, adjacency, and a limiting propagation speed, developed in subsequent papers of this series. Paper I provides the foundational axioms (PG1--PG9) governing the spectral substrate, its metastable dynamics, the formation of coherent units, and the necessity of replication, establishing a fully pre-geometric stage from which causal and geometric structure naturally emerge.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Progress Towards RF Conditioning of Low-Loss Couplers for a Conduction-Cooled Cryomodule

This work presents current progress on the conditioning of two new 25 kW couplers optimized for use in a compact, conduction-cooled SRF cryomodule. A connecting waveguide, previously used for conditioning the 805 MHz SNS couplers, was altered for use at 915 MHz. The necessary modifications were determined via RF modeling, while thermal analysis results identified additional cooling requirements during RF conditioning and provided insight about potential higher-power operation. Initial low-power conditioning will be performed with a 2.5 kW solid-state amplifier, with plans to use an industrial magnetron for RF conditioning at 25 kW in the near future.

Stilin, N. [Thomas Jefferson National Accelerator ↗

DOE OSTI2026

PROGRESS TOWARDS RF CONDITIONING OF LOW-LOSS COUPLERS FOR A CONDUCTION-COOLED CRYOMODULE

Wilson, Christiana [Thomas Jefferson National Acce↗

NASA NTRS1993

A Microseismometer for Terrestrial and Extraterrestrial Applications

The scientific and technical requirements of extraterrestrial seismology place severe demands on instrumentation. Performance in terms of sensitivity, stability, and frequency band must match that of the best terrestrial instruments, at a fraction of the size, mass, and power. In addition, this performance must be realized without operator intervention in harsh temperature, shock, and radiation environments. These constraints have forced us to examine some fundamental limits of accelerometer design in order to produce a small, rugged, sensitive seismometer. Silicon micromachined sensor technology offers techniques for the fabrication of monolithic, robust, compact, low-power and -mass accelerometers. However, currently available sensors offer inadequate sensitivity and bandwidth. Our implementation of an advanced silicon micro machined seismometer is based on principles developed at JPL for high-sensitivity position sensor technology. The use of silicon micro machining technology with these new principles should enable the fabrication of a 10(exp -11) g sensitivity seismometer with a bandwidth of at least 0.01 to 20 Hz. The low Q properties of pure single-crystal silicon are essential in order to minimize the Brownian thermal noise limitations generally characteristic of seismometers with small proof masses. A seismometer consists of a spring-supported proof mass and a transducer for measuring its motion. For long period motion a position sensor is generally used, for which the displacement is proportional to the ground acceleration. The mechanical sensitivity can be increased either by increasing the proof mass or decreasing the spring stiffness, neither of which is desirable for planetary applications. Our approach has been to use an ultra sensitive capacitive position sensor with a sensitivity of better than 10(exp -13) m/Hz(exp 1/2). This allows the use of a stiffer suspension and a smaller proof mass. We have built several prototypes using these principles, and tests show that these devices can exhibit performance comparable to state-of-the-art instruments.

Banerdt, W.↗

NASA NTRS1986

Classification of solar flares and the relationship between the first and second phases

A large data base on solar flares obtained during the last solar maximum years makes it necessary to revise the views on the relationship between the impulsive phase and the second phase of flares. Contrary to the view most popular before the launch of the Solar Maximum Mission, it is now known that relativistic electrons and gamma-ray-producing protons and ions are accelerated during the impulsive phase. Because flares producing nuclear gamma-rays are different from ordinary flares, it is concluded that additional processes take place in gamma-ray-line flares. Recent studies have shown that flares with gradual hard X-ray time profiles not only produce nuclear gamma-rays during the impulsive phase but also develop full-fledged second-phase phenomena. It is proposed that filament eruption plays a key role in gamma-ray-line flares. When an erupting filament interacts with an overlaying flare loop, relativistic electrons and energetic protons are produced during the impulsive phase. When the erupting filament fully distends the overlying flare loop, full-fledged second-phase phenomena, such as shocks, interplanetary energetic particles, mass ejections and etc. are observed. When the overlying flare loop is compact and strong enough to suppress the activated filament, gamma-rays are emitted during the first phase but no second-phase phenomena occur.

Bai, T.↗

DOE OSTI2024

High-Field Magnets for Future Hadron Colliders

Recent strategy updates by the international particle physics community have confirmed strong interest in a next-generation energy frontier collider after completion of the High-Luminosity LHC program and construction of a e + e - Higgs factory. Both hadron and muon colliders provide a path toward the highest energies, and both require significant and sustained development to achieve technical readiness and optimize the design. For hadron colliders, the energy reach is determined by machine circumference and the strength of the guiding magnetic field. To achieve a collision energy of 100 TeV while limiting the circumference to 100 km, a dipole field of 16 T is required and is within the reach of niobium–tin magnets operating at 1.9 K. Magnets based on high-temperature superconductors may enable a range of alternatives, including a more compact footprint, a reduction of the cooling power, or a further increase of the collision energy to 150 TeV. The feasibility and cost of the magnet system will determine the possible options and optimal configurations. In this article, I review the historical milestones and recent progress in superconducting materials, design concepts, magnet fabrication, and test results and emphasize current developments that have the potential to address the most significant challenges and shape future directions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗