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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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Perspectives on the integration between first-principles and data-driven modeling

Efficiently embedding and/or integrating mechanistic information with data-driven models is essential if it is desired to simultaneously take advantage of both engineering principles and data-science. Further the opportunity for hybridization occurs in many scenarios, such as the development of a faster model of an accurate high-fidelity computer model; the correction of a mechanistic model that does not fully-capture the physical phenomena of the system; or the integration of a data-driven component approximating an unknown correlation within a mechanistic model. At the same time, different techniques have been proposed and applied in different literatures to achieve this hybridization, such as hybrid modeling, physics-informed Machine Learning (ML) and model calibration. In this paper we review the methods, challenges, applications and algorithms of these three research areas and discuss them in the context of the different hybridization scenarios. Moreover, we provide a comprehensive comparison of the hybridization techniques with respect to their differences and similarities, as well as advantages and limitations and future perspectives. Finally, we apply and illustrate hybrid modeling, physics-informed ML and model calibration via a chemical reactor case study.

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

Modular machine learning-based elastoplasticity: Generalization in the context of limited data

The development of highly accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. This ability to extrapolate from limited data was the main reason for the early and continued success of phenomenological models and the main shortcoming in machine learning-enabled constitutive modeling approaches. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

42 ENGINEERING↗
DOE OSTI2020

Revealing High Na-Content P2-Type Layered Oxides as Advanced Sodium-Ion Cathodes

Layered Na-based oxides with the general composition of Na x TMO 2 (TM: transition metal) have attracted significant attention for their high compositional diversity that provides tunable electrochemical performance for electrodes in sodium-ion batteries. The various compositions bring forward complex structural chemistry that is decisive for the layered stacking structure, Na-ion conductivity, and the redox activity, potentially promising new avenues in functional material properties. In this work, we have explored the maximum Na content in P2-type layered oxides and discovered that the high-content Na in the host enhances the structural stability; moreover, it promotes the oxidation of low-valent cations to their high oxidation states (in this case Ni 2+ ). This can be rationalized by the increased hybridization of the O(2p)-TM(3d-e g *) states, affecting both the local TM environment as well as the interactions between the NaO 2 and TMO 2 layers. These properties are highly beneficial for the Na storage capabilities as required for cathode materials in sodium-ion batteries. It leads to excellent Na-ion mobility, a large storage capacity (>100 mAh g –1 between 2.0-4.0 V), yet preventing the detrimental sliding of the TMO 2 layers (P2–O2 structural transition), as reflected by the ultralong cycle life (3000 (dis)charge cycles demonstrated). These findings expand the horizons of high Na-content P2-type materials, providing new insights of the electronic and structural chemistry for advanced cathode materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Extending quantum probabilistic error cancellation by noise scaling

Here, we propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device’s noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Analysis of picosecond coherent anti-Stokes Raman spectra for gas-phase diagnostics

We present a hybrid frequency- and time-domain solution, applicable to the case of picosecond coherent anti-Stokes Raman scattering (CARS), for gas-phase diagnostics. A solution has been derived based on both physical arguments and four-wave mixing equations for picosecond CARS, with pulse durations that are comparable to the dephasing time scale for gas-phase Raman coherence—a regime where commonly employed solutions for impulsive (femtosecond) or cw (nanosecond) pump/Stokes forcing are not strictly valid. We present the ps-CARS spectrum in the form of incoherent sums of CARS intensity spectra, calculated from the fundamental solution for impulsive pump/Stokes Raman preparation. The solution was examined for temperatures from 1000–3000 K, for four plausible experimental configurations, with laser pulse durations of 50–150 ps, and probe pulse delays from −20 to 240 ps. Approximations based on cw and impulsive pump/Stokes preparation to fit picosecond CARS spectra at atmospheric pressure were examined and the relative thermometric accuracy and computational cost of these approximations were quantified for the case of a zero nonresonant CARS contribution, and a nonresonant susceptibility equal to 10% of the Raman-resonant value at the N 2 bandhead. The nanosecond CARS approximation can result in large fitting errors when the probe pulse time delay is less than the probe pulse duration. Errors as large as 10–20% are observed in the fit temperatures for a zero picosecond probe pulse delay, when the nonresonant background is neglected, largely due to an inability of the time-independent cw model to capture transient frequency spread dephasing effects at the Q -branch bandhead. The inclusion of a nonresonant background results in 40–60% thermometry errors with a nanosecond model at a zero-probe delay. Time-dependent impulsive calculations used for femtosecond CARS better approximate the structure of the N 2 bandhead, reducing temperature fitting errors to 5–10% at a short probe pulse delay. The impulsive approximation results in errors up to 10% at intermediate probe pulse delays, where the coherence of the pump and probe pulses leads to multiple terms in the picosecond CARS solution. Both approximations improve as the probe pulse delay exceeds the probe duration. The nanosecond approximation results in a 2–3% error, while the impulsive model results in differences of less than 1% in some cases. Fits to experimental data obtained using short, ∼60ps pulses at a zero probe time delay and longer 100 ps pulses at a substantial 200 ps delay are presented with accuracies of 1–3% in the fit temperature.

Kearney, Sean P.↗
DOE OSTI2020

Fleet-wide Electrification Impacts Assessment for the Valley Transportation Authority

This report explores the long-term electrification opportunities for the Valley Transit Authority’s (VTA) transit bus fleet. The potential for transit bus electrification at VTA as well as the economic impacts of partial and complete electrification are explored. We use the Revenue Operation and Device Optimization model to determine the optimal charging, operation and lowest capital and operating cost solution to achieve different levels of electrification to meet their existing routes. This study finds that, relying on only depot charging, around 70% of the daily trips by VTA’s transit bus fleet can be replaced with battery electric buses (BEBs) today. The benefits and drawbacks of five methods for improving the electrification potential beyond that achievable with only depot charging are discussed including (1) increase charger power, (2) purchase of larger vehicle batteries, (3) en-route charging, (4) purchasing additional buses and swapping them to enable the existing routes/blocks1 to be met, and (5) route/block redesign. A strategy is developed to enable full fleet electrification by increasing charger power or allowing intraday charging as a proxy for the options mentioned above. This method allows us to develop an understanding of the impacts and trade-offs of full fleet electrification. Two charging strategies are examined. Immediate charging, when the bus is charged as soon as it arrives at a depot or en-route charging station, and smart charging, which uses a controller to determine the best times to charge to achieve the lowest charging cost, while maintaining the same trip schedules. Smart charging is effective at reducing the peak power consumption, which can be reduced by between 31% and 65% compared to immediate charging. This translates directly to lower electricity demand charges and lower costs for possible distribution system upgrades. The total lifetime net present value (NPV) costs for different scenarios are presented in Figure ES-1. Scenarios are separated into three sections. The first stacked bar on the left is the base case (business-as-usual) where all buses are diesel hybrids, the next four bars include partial and full fleet electrification utilizing only immediate charging, and the last four bars include partial and full fleet electrification utilizing smart charging. The results show that smart charging scenarios are within ±4% of the lifetime NPV cost of the diesel-hybrid only (business-as-usual) scenario. The scenarios with full fleet electrification (i.e., including intraday charging) are 4% lower cost and those with partial fleet electrification (i.e., without intraday charging) are 2%–3% higher. However, it is important to note that the intraday charging scenarios do not include any additional costs for the equipment necessary to achieve intraday charging (e.g., additional chargers, larger batteries, new route design). Additionally, it is worth noting that the Low Carbon Fuel Standard (LCFS) credit received for implementing electric buses is essential to achieving these results.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Relativistic Hybrid Stars with Sequential First-order Phase Transitions in Light of Multimessenger Constraints

In this work, we consider the properties of compact stars in which quark matter has low- and high-density phases that are separated by a first-order phase transition. Thus, unlike the commonly considered case of a single phase transition from hadronic to quark matter, our models of hybrid stars contain sequential phase transitions from hadronic matter to low- and then to high-density quark matter phases. We extend our previous study of the parameter space of hybrid stars with a single phase transition to those with sequential phase transitions, taking into account the constraints on the mass and radius of neutron stars from the NICER experiment, the experimental inferences of the neutron skin thickness of the lead nucleus by the PREX-II experiment, and constraints on the tidal deformability from the gravitational-wave event GW170817. We determine the range of the masses for which both twin and triplet configurations, i.e., identical-mass stars with two and three different values of radii, arise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1987

An unconditionally-stable central differencing scheme for high Reynolds number flows

The central difference scheme (CDS) is a second order accurate scheme which is free of numerical diffusion (in the second order sense) and is simple to implement: However, for grid Peclet numbers larger than 2, the CDS leads to over- and undershoots and is unstable. The present paper describes a method, called CONDIF, which retains the essential nature of the CDS but eliminates the over- and under-shoots. It leads to unconditionally positive coefficients and, in the limit, approaches the CDS for all values of grid Peclet numbers. The CONDIF modifies the CDS by introducing a controlled amount of numerical diffusion based on the local gradients. In the worst case the scheme yields results similar to those of the hybrid scheme. This paper reports the results obtained from CONDIF for a number of test problems which have been widely used for comparative study of numerical schemes in the published literature. For most of these problems, the CONDIF results are significantly more accurate than the hybrid scheme at high Peclet numbers. In particular, the CONDIF scheme depicts much lower level of numerical diffusion than the hybrid scheme even when the Peclet number is very high and the flow is at large angles to the grid.

Runchal, Akshai K.↗
NASA NTRS2018

A 6U Hybrid Propulsion Module for CUBESATS

A 6U hybrid propulsion module is presented. It is designed to be used as a stage for a 6U CubeSat with a combined wet mass up to 25 kg. Hybrid rocket propulsion is utilized because it is responsive, high performance, capable of multiple burns and safe/non-toxic. Hybrid rockets employ a solid fuel and liquid or gaseous oxidizer. In this case, the fuel is PolyMethyl MethAcrylate and the oxidizer is gaseous oxygen. This propellant combination produces an Isp of greater than 300 seconds. The gaseous oxidizer simplifies the design and is used in dual mode with cold gas thrusters for attitude control. In general, hybrid propulsion is higher performance and higher thrust than conventional options considered for CubeSats (e.g. monopropellants), making it ideal for larger manuevers such as plane changes. The Attitude Control System has been sized to ensure that the CubeSat can be controlled under the thrust loads of the propulsion system. A hybrid rocket motor of this size is currently being tested at the Jet Propulsion Laboratory. Thirty-four successful tests have been completed at JPL with this propellant combination during the last 2.5 years. Current tests include long duration tests (> 95 seconds) and multiple starts (five). These tests and applicability to potential mission requirements will be discussed. Future test plans to move the motor into a vacuum facility to achieve a Technology Readiness Level of 5 by the end of September 2018 will be discussed, and an overview of the proposed TRL 5 to 6 maturity plan will also be presented.

Nakazono, B.↗
NASA NTRS2016

A Hybrid Mars Ascent Vehicle Concept for Low Temperature Storage and Operation

A hybrid propulsion system presents many advantages for a potential Mars Ascent Vehicle including high specific impulse, restartability and predicted excellent low temperature survivability. This additional benefit of low temperature storage and operation could substantially reduce the power required to maintain the system while on Mars and therefore decrease the total landed system mass required for the system. A new wax-based hybrid fuel has been formulated to realize these low temperature benefits, while still preserving high performance (Isp). The freezing point of the oxidizer can be selected to match the capabilities of the fuel, in this case Mixed Oxides of Nitrogen has been selected. The main disadvantages of this system are associated with the relatively low technology readiness level of the selected hybrid propulsion system for operation on Mars. However, technology development efforts are currently underway to advance the hybrid propulsion system to a level where it could potentially compete with heritage propulsion systems. An internal study completed at JPL in 2015 identified the single stage to orbit hybrid MAV as the lowest gross liftoff mass case from a large range of potential propulsion systems. Updates to this design are presented here.

Karp, Ashley Chandler↗
DOE OSTI2023

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Kaltsas, Dimitrios A. (ORCID:0000000300769015)↗
NASA NTRS2013

Qualification of UHF Antenna for Extreme Martian Thermal Environments

The purpose of this development was to validate the use of the external Rover Ultra High Frequency (RUHF) antenna for space under extreme thermal environments to be encountered during the surface operations of the Mars Science Laboratory (MSL) mission. The antenna must survive all ground operations plus the nominal 670 Martian sol mission that includes summer and winter seasons of the Mars thermal environment.The qualification effort was to verify that the RUHF antenna design and its bonding and packaging processes are adequate to survive the harsh environmental conditions. The RUHF is a quadrifilar helix antenna mounted on the MSL Curiosity rover deck. The main components of the RUHF antenna are the helix structure, feed cables, and hybrid coupler, and the high-power termination load. In the case of MSL rover externally mounted hardware, not only are the expected thermal cycle depths severe, but there are temperature offsets between the Mars summer and winter seasons. The total number of temperature cycles needed to be split into two regimes of summer cycles and winter cycles. The qualification test was designed to demonstrate a survival life of three times more than all expected ground testing, plus a nominal 670 Martian sol missions. Baseline RF tests and a visual inspection were performed prior to the start of the qualification test. Functional RF tests were performed intermittently during chamber breaks over the course of the qualification test. For the RF return loss measurements, the antenna was tested in a controlled environment outside the thermal chamber with a vector network analyzer that was calibrated over the antenna s operational frequency range. A total of 2,010 thermal cycles were performed. Visual inspection showed a dulling of the solder material. This change will not affect the performance of the antenna. No other changes were observed. RF tests were performed on the RUHF helix antenna, hybrid, and load after the 2,010 qualification cycles test. The RF performance of the RUHF antenna, hybrid, and load were almost identical before and after the complete test. Therefore, the developed design of RUHF is qualified for a long-duration MSL mission. The RUHF antenna has not been used for long-duration missions such as MSL in the past. The state-of-the-art technology of the RUHF antenna is used to develop the antennas for MSL mission survivability. This developmental test data provides the confidence in using this RUHF antenna for future NASA missions to Mars.

Ramesham, Rajeshuni↗
DOE OSTI2024

Optimal hybrid power plants for electric vehicle charging demand

Transmission constraints, increasing motivations to decarbonize, and concerns over peak electric vehicle (EV) load impacts on local grids have driven electric customers to consider behind-the-meter, hybrid power plant generation and storage at the distributed-grid level for EV charging. In this study, we develop capabilities to optimize hybrid power plant component capacities for EV charging. We then demonstrate these capabilities in a case study for Boulder, Colorado, using public EV charging data as well as wind and solar resource data. Our results show system designs that balance the cost of energy with load-meeting and peak shaving performance. Within the case study, systems designed for wind, solar photovoltaic (PV), and storage resulted in lower cost of energy than those optimized for PV and storage only. This indicates that in areas where wind resource exists, hybrid power plants that include wind, PV, and battery assets can better meet EV charging loads (including peak loads that are prone to overloading local grids) than PV and battery assets alone. Future work to address limitations in this paper include extending cost modeling to include performance losses (e.g., based on operations or weather) and charging station costs to estimate levelized cost of charging, and quantifying uncertainty and error in our aggregation methods for estimating EV charging loads at the hourly timescale.

14 SOLAR ENERGY↗
DOE OSTI2023

Fidelity Analysis of Complex Large-Scale Simulation Models of PEs (MARS) in Future Power Grids

With the proliferation of power electronic (PE)-based resources in the electric grid, there have been numerous different kinds of simulation models developed and studied to understand their dynamic behavior. Study of PE-based resources using each simulation model has its own distinct advantages and disadvantages. Therefore it is very important to carefully select the appropriate model for the evaluation of the PE-based resources. In this paper, one such effort is made to analyze the different types of models in the case of a multi-port autonomous reconfigurable solar power plant (MARS). The MARS integrates a hybrid photovoltaic (PV)-energy storage system (ESS) plant to high-voltage direct current (HVdc) system and transmission alternating current (ac) grid. The dynamic models are evaluated under different test cases varying the short-circuit ratio (SCR) and control algorithms. Recommendations are provided on the equipment study needs based on the analysis completed.

Marthi, Phani Ratna Vanamali↗
NASA NTRS2021

Potential origin of the state-dependent high-energy tail in the black hole microquasar Cygnus X-1 as seen with INTEGRAL

Context. 0.1–10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body (0.1–10 keV) and Comptonization (10–200 keV) components observed by INTEGRAL in several black-hole X-ray binaries. This so-called “high-energy tail” was recently shown to be strong in the hard spectral state of Cygnus X-1, and, in this system, has been interpreted as the high-energy part of the emission from a compact jet. Aims. This result was nevertheless obtained from a data set largely dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a high-energy tail could be derived. Using an extended data set, we aim to obtain better constraints on the properties of this spectral component in both states. Methods. We make use of data obtained from about 15 years of observations with the INTEGRAL satellite. The data set is separated into the different states and we analyze stacked state-resolved spectra obtained from the X-ray monitors, the gamma-ray imager, and the gamma-ray spectrometer (SPI) onboard. Results. A high-energy component is detected in both states, confirming its earlier detection in the hard state and its suspected presence in the soft state with INTEGRAL, as seen in a much smaller SPI data set. We first characterize the high-energy tail components in the two states through a model-independent, phenomenological analysis. We then apply physical models based on hybrid Comptonization (eqpair and belm). The spectra are well modeled in all cases, with a similar goodness of the fits. While in the semi-phenomenological approach the high-energy tail has similar indices in both states, the fits with the physical models seem to indicate slightly different properties. Based on this approach, we discuss the potential origins of the high-energy components in both the soft and hard states, and favor an interpretation where the high-energy component is due to a compact jet in the hard state and hybrid Comptonization in either a magnetized or nonmagnetized corona in the soft state.

accretion↗
NASA NTRS2017

Large-Eddy Simulation (LES) of a Compressible Mixing Layer and the Significance of Inflow Turbulence

In the context of Large Eddy Simulations (LES), the effects of inflow turbulence are investigated through the Synthetic Eddy Method (SEM). The growth rate of a turbulent compressible mixing layer corresponding to operating conditions of GeobelDutton Case 2 is investigated herein. The effects of spanwise width on the growth rate of the mixing layer is investigated such that spanwise width independence is reached. The error in neglecting inflow turbulence effects is quantified by comparing two methodologies: (1) Hybrid-RANS-LES methodology and (2) SEM-LES methodology. Best practices learned from Case 2 are developed herein and then applied to a higher convective mach number corresponding to Case 4 experiments of GeobelDutton.

les↗
DOE OSTI2024

Resilient and Cost-Effective Hybrid Li-Ion Battery Energy Storage System for Sites with Solar Generation and Electric Vehicle (EV) Charging (CRADA Final Report, CRD-19-00799)

The batteries of an energy storage system designed for multiple use-cases are traditionally selected to withstand the highest rate at which a battery is discharged relative to its maximum capacity (C-rate) and cycling requirements of the most intense use-case. However, this is not cost-effective given that the price of the batteries is strongly correlated to C-rate and cyclability. We propose to establish design guidelines for a hybrid energy storage system and test an edge controller that uses high-power and high-energy batteries for high- cyclability use cases such as frequency regulation and electric vehicle (EV) charging and low-cost batteries for low-power and low-cyclability use cases such as summer peak loads. The three main objectives of this proposal are (i) establishing sizing guidelines for such a hybrid storage system, (ii) installing a hybrid storage system in the Energy Systems Integration Facility (ESIF) sized based on those guidelines, and (iii) testing an edge controller specific for the system through hardware tests.

14 SOLAR ENERGY↗
DOE OSTI2021

Superconductinglike response in a driven gapped bosonic system

In this study, we propose a mechanism for the photoinduced superconductinglike response recently reported in cuprates and other strongly correlated materials. This mechanism relies on quantum-fluctuating bosons consisting of electron pairs. With periodic drive, the electron pairs and vacancies of pairs form a coherent nonequilibrium condensate, different from conventional superconductors, yet showing a superconductinglike response in some regime even with dissipation. Unlike the case of driven fermionic bands, which results in the familiar Floquet bands with hybridization gaps, for driven bosons the “gap” opens up in the momentum direction, resulting in a resonant region in momentum space where the eigenvalues are complex. We give a simple physical argument for why this picture leads to a “perfect conductor” which exhibits superconductinglike frequency-dependent conductivity but no Meissner response. While our model is quite general, in the case of cuprates, a quantum-fluctuating pair density wave in the pseudogap region may serve as the origin of the quantum-fluctuating electron pairs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗