Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalization”

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 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Magnetic Field-Stabilized Wigner Crystal States in a Graphene Moiré Superlattice

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here, in this work, we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott–Hofstadter transition at a high magnetic field.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Anion Association Strength as a Unifying Descriptor for the Reversibility of Divalent Metal Deposition in Nonaqueous Electrolytes

Developing next-generation battery chemistries that move beyond traditional Li-ion systems is critical to enabling transformative advances in electrified transportation and grid-level energy storage. Here, we provide the first evidence for common descriptors for improved reversibility of metal plating/stripping in nonaqueous electrolytes for multivalent ion batteries. Focusing first on the specific role of chloride (Cl – ) in promoting electrochemical reversibility in multivalent systems, rotating disk (RDE) and ring-disk electrode (RRDE) investigations were performed utilizing a variety of divalent cations (Mg 2+ , Zn 2+ , and Cu 2+ ) and the bis-(trifluoromethane sulfonyl) imide (TFSI – ) anion. By introducing varying concentrations of Cl – , a cooperative effect is observed between TFSI – and Cl – that yields the more reversible behavior of mixed electrolytes relative to electrolytes containing only TFSI – . This effect is shown to be general for Mg, Zn, and Cu electrodeposition, and mechanistic understanding of the role of Cl – in improving reversibility of TFSI-based electrolytes is obtained through the combination of R(R)DE experimental results and density functional theory (DFT) evaluation of the redox activity and thermodynamic stability of various TFSI- and Cl-based solution complexes of metal ions. The cooperative anion effect is further generalized to other mixed-anion systems, where systematic variations in anion association strength predicted from DFT (i.e., Cl – > OTf – ≈ TFSI – > BF 4 – > PF 6 – ) yield corresponding trends in redox potentials and improvements of ≥200 mV in the reversibility of metal deposition/dissolution. These results identify anion association strength as a common descriptor for the reversibility of divalent metal anodes and suggest a set of general design principles for developing new electrolytes with improved activity and stability.

25 ENERGY STORAGE↗
DOE OSTI2021

Selectivity in Yttrium Manganese Oxide Synthesis via Local Chemical Potentials in Hyperdimensional Phase Space

In sharp contrast to molecular synthesis, materials synthesis is generally presumed to lack selectivity. The few known methods of designing selectivity in solid-state reactions have limited scope, such as topotactic reactions or strain stabilization. This contribution describes a general approach for searching large chemical spaces to identify selective reactions. This novel approach explains the ability of a nominally “innocent” Na 2 CO 3 precursor to enable the metathesis synthesis of single-phase Y 2 Mn 2 O 7 : an outcome that was previously only accomplished at extreme pressures and which cannot be achieved with closely related precursors of Li 2 CO 3 and K 2 CO 3 under identical conditions. By calculating the required change in chemical potential across all possible reactant-product interfaces in an expanded chemical space including Y, Mn, O, alkali metals, and halogens, using thermodynamic parameters obtained from density functional theory calculations, we identify reactions that minimize the thermodynamic competition from intermediates. In this manner, only the Na-based intermediates minimize the distance in the hyperdimensional chemical potential space to Y 2 Mn 2 O 7 , thus providing selective access to a phase which was previously thought to be metastable. Experimental evidence validating this mechanism for pathway-dependent selectivity is provided by intermediates identified from in situ synchrotron-based crystallographic analysis. Finally, this approach of calculating chemical potential distances in hyperdimensional compositional spaces provides a general method for designing selective solid-state syntheses that will be useful for gaining access to metastable phases and for identifying reaction pathways that can reduce the synthesis temperature, and cost, of technological materials.

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

Climatology of Melting Layer Heights Estimated From Cloud Radar Observations at Various Locations

A melting layer (ML) detection algorithm for cloud radar with polarimetric capability was developed and applied to the cloud radar data collected from five different sites around the world for several years. The retrieved melting layer top height (MLH) showed a very good correspondence with the ECMWF Reanalysis 5 zero degree level data for all five sites. The ML characteristics were distinctively different for different sites, revealing climatological characteristics of ML forming clouds in different regions. Generally, ML tended to occur more frequently in summer than in winter except for a maritime site, where low stratiform clouds formed frequently in summer, the top of which might be lower than the freezing level. In contrast, at two Arctic sites, ML occurred almost exclusively in summer because it was too cold to have an ML in the other seasons. The MLH also varied significantly from site to site but generally was higher during warmer seasons. Based on MLH, two new indices, bulk temperature lapse rate (BLR) and relative depth (RD) of liquid cloud below MLH (RD) were developed, which were useful to explain the environmental characteristics of the five sites. BLR generally increased with the surface temperature at all sites except at the marine site that showed an opposite trend, where a unique synoptic pattern in winter generated high BLR in this cold season. Finally, these findings confirm that studies on thermodynamic structures using cloud radars can be broadened, taking advantage of BLR and RD information, as these indices can represent environmental thermodynamic characteristics of the clouds that have ML.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Evaluating Climate Models’ Cloud Feedbacks Against Expert Judgment

Abstract The persistent and growing spread in effective climate sensitivity (ECS) across global climate models necessitates rigorous evaluation of their cloud feedbacks. Here we evaluate several cloud feedback components simulated in 19 climate models against benchmark values determined via an expert synthesis of observational, theoretical, and high‐resolution modeling studies. We find that models with smallest feedback errors relative to these benchmark values generally have moderate total cloud feedbacks (0.4–0.6 W m −2 K −1 ) and ECS (3–4 K). Those with largest errors generally have total cloud feedback and ECS values that are too large or too small. Models tend to achieve large positive total cloud feedbacks by having several cloud feedback components that are systematically biased high rather than by having a single anomalously large component, and vice versa. In general, better simulation of mean‐state cloud properties leads to stronger but not necessarily better cloud feedbacks. The Python code base provided herein could be applied to developmental versions of models to assess cloud feedbacks and cloud errors and place them in the context of other models and of expert judgment in real‐time during model development.

58 GEOSCIENCES↗
DOE OSTI2021

Using TRMM Latent Heat as a Source to Estimate Convection Induced Gravity Wave Momentum Flux in the Lower Stratosphere

Due to a lack of observations, it is a big challenge to quantify the momentum flux transported from the troposphere into the lower stratosphere by gravity waves generated by convection. This limits our understanding of the dynamics of general circulation in the stratosphere and the realism of simulations of the Quasi Biennial Oscillation. In the past decade, some general circulation models have linked the momentum flux to the latent heating from subgrid scale convective precipitation with some success. However, there is still a large uncertainty in the sources of subgrid scale convection in these models. This study applies the links between the momentum flux and convective latent heating directly to the convective precipitation derived from 16 years of TRMM precipitation radar observations in the tropics and subtropics. The total and directional momentum flux at 100 hPa are derived at individual convective pixels by using the TRMM Spectrum Latent Heating product and large-scale wind profiles from the ERA-Interim dataset. For the first time, we are able to estimate the geographical distribution of momentum flux at 100 hPa in tropics and subtropics from the observed convective sources. The diurnal, seasonal, and interannual variations of the derived momentum flux are presented and discussed. These results could provide a reference to validate the dynamic coupling between the tropical troposphere and the stratosphere in the general circulation models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Mesoscale Convective Systems Tracking Method Intercomparison (MCSMIP): Application to DYAMOND Global km‐Scale Simulations

Abstract Global kilometer‐scale models represent the future of Earth system modeling, enabling explicit simulation of organized convective storms and their associated extreme weather. Here, we comprehensively evaluate tropical mesoscale convective system (MCS) characteristics in the DYAMOND (DYnamics of the atmospheric general circulation modeled on non‐hydrostatic domains) simulations for both summer and winter phases. Using 10 different feature trackers applied to simulations and satellite observations, we assess MCS frequency, precipitation, and other key characteristics. Substantial differences (a factor of 2–3) arise among trackers in observed MCS frequency and their precipitation contribution, but model‐observation differences in MCS statistics are more consistent across trackers. DYAMOND models are generally skillful in simulating tropical mean MCS frequency, with multi‐model mean biases ranging from −2%–8% over land and −8%–8% over ocean (summer vs. winter). However, most DYAMOND models underestimate MCS precipitation amount (23%) and their contribution to total precipitation (17%). Biases in precipitation contributions are generally smaller over land (13%) than over ocean (21%), with moderate inter‐model variability. While models better simulate MCS diurnal cycles and cloud shield characteristics, they overestimate MCS precipitation intensity and underestimate stratiform rain contributions (up to a factor of 2), particularly over land, albeit observational uncertainties exist. Additionally, models exhibit a wide range of precipitable water in the tropics compared to reanalysis and satellite observations, with many models showing exaggerated sensitivity of MCS precipitation intensity to precipitable water. The MCS metrics developed here provide process‐oriented diagnostics to guide future model development.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Microbial Ecology and Site Characteristics Underlie Differences in Salinity-Methane Relationships in Coastal Wetlands

Methane (CH 4 ) is a potent greenhouse gas emitted by archaea in anaerobic environments such as wetland soils. Tidal freshwater wetlands are predicted to become increasingly saline as sea levels rise due to climate change. Previous work has shown that increases in salinity generally decrease CH 4 emissions, but with considerable variation, including instances where salinization increased CH 4 flux. We measured microbial community composition, biogeochemistry, and CH 4 flux from field samples and lab experiments from four different sites across a wide geographic range. We sought to assess how site differences and microbial ecology affect how CH 4 emissions are influenced by salinization. CH 4 flux was generally, but not always, positively correlated with CO 2 flux, soil carbon, ammonium, phosphate, and pH. Methanogen guilds were positively correlated with CH 4 flux across all sites, while methanotroph guilds were both positively and negatively correlated with CH 4 depending on site. There was mixed support for negative relationships between CH 4 fluxes and concentrations of alternative electron acceptors and abundances of taxa that reduce them. CH 4 /salinity relationships ranged from negative, to neutral, to positive and appeared to be influenced by site characteristics such as pH and plant composition, which also likely contributed to site differences in microbial communities. The activity of site-specific microbes that may respond differently to low-level salinity increases is likely an important driver of CH 4 /salinity relationships. Our results suggest several factors that make it difficult to generalize CH 4 /salinity relationships and highlight the need for paired microbial and flux measurements across a broader range of sites.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Unraveling the convoluted and dynamic interphasial mechanisms on Li metal anode

Accurate understanding of the chemistry of solid-electrolyte interphase (SEI) is key to developing new electrolytes for high-energy batteries using lithium metal (Li-0) anodes(1). SEI is generally believed to be formed by the reactions between Li-0 and electrolyte(2,3). However, our new study shows this is not the whole story. Through synchrotron-based X-ray diffraction and pair distribution function analysis, we reveal a much more convoluted formation mechanism of SEI, which receives considerable contributions from electrolyte, cathode, moisture and native surface species on Li-0, with highly dynamic nature during cycling. Using isotope labelling, we traced the origin of LiH to electrolyte solvent, moisture and a new source: the native surface species (LiOH) on pristine Li-0. When lithium accessibility is very limited as in the case of anode-free cells, LiOH develops into plate-shaped large crystals during cycling. Alternatively, when the lithium source is abundant, as in the case of Li||NMC811 cells, LiOH reacts with Li-0 to form LiH and Li2O. While the desired anion-derived LiF-rich SEI is typically found in the concentrated electrolytes or their derivatives, we found it can also be formed in low-concentration electrolyte via the crosstalk effect, emphasizing the importance of formation cycle protocol and opening up opportunities for low-cost electrolyte development.

Polzin, Bryant J.↗
DOE OSTI2023

Observation of the effect of gravity on the motion of antimatter

Einstein’s general theory of relativity from 1915 remains the most successful description of gravitation. From the 1919 solar eclipse to the observation of gravitational waves, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac’s theory appeared in 1928; the positron was observed in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive ‘antigravity’ is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Unveiling four decades of intensifying precipitation from tropical cyclones using satellite measurements

Increases in precipitation rates and volumes from tropical cyclones (TCs) caused by anthropogenic warming are predicted by climate modeling studies and have been identified in several high intensity storms occurring over the last half decade. However, it has been difficult to detect historical trends in TC precipitation at time scales long enough to overcome natural climate variability because of limitations in existing precipitation observations. We introduce an experimental global high-resolution climate data record of precipitation produced using infrared satellite imagery and corrected at the monthly scale by a gauge-derived product that shows generally good performance during two hurricane case studies but estimates higher mean precipitation rates in the tropics than the evaluation datasets. General increases in mean and extreme rainfall rates during the study period of 1980–2019 are identified, culminating in a 12–18%/40-year increase in global rainfall rates. Overall, all basins have experienced intensification in precipitation rates. Increases in rainfall rates have boosted the mean precipitation volume of global TCs by 7–15% over 40 years, with the starkest rises seen in the North Atlantic, South Indian, and South Pacific basins (maximum 59–64% over 40 years). In terms of inland rainfall totals, year-by-year trends are generally positive due to increasing TC frequency, slower decay over land, and more intense rainfall, with an alarming increase of 81–85% seen from the strongest global TCs. As the global trend in precipitation rates follows expectations from warming sea surface temperatures (11.1%/°C), we hypothesize that the observed trends could be a result of anthropogenic warming creating greater concentrations of water vapor in the atmosphere, though retrospective studies of TC dynamics over the period are needed to confirm.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A universal variational quantum eigensolver for non-Hermitian systems

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$O(log_{2}{N})$$ O ( l o g 2 N ) quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Predicting the chemical reactivity of organic materials using a machine-learning approach

Stability and compatibility between chemical components are essential parameters that need to be considered in the selection of functional materials in configuring a system. In configuring devices such as batteries or solar cells, not only the functionality of individual constituting materials such as electrodes or electrolyte but also an appropriate combination of materials which do not undergo unwanted side reactions is critical in ensuring their reliable performance in long-term operation. While the universal theory that can predict the general chemical reactivity between materials is long awaited and has been the subject of studies with a rich history, traditional ways proposed to date have been mostly based on simple electronic properties of materials such as electronegativity, ionization energy, electron affinity and hardness/softness, and could be applied to only a small group of materials. Moreover, prediction has often been far from accurate and has failed to offer general implications; thus it was practically inadequate as a selection criterion from a large material database, i.e. data-driven material discovery. Herein, we propose a new model for predicting the general reactivity and chemical compatibility among a large number of organic materials, realized by a machine-learning approach. As a showcase, we demonstrate that our new implemented model successfully reproduces previous experimental results reported on side-reactions occurring in lithium–oxygen electrochemical cells. Furthermore, the mapping of chemical stability among more than 90 available electrolyte solvents and the representative redox mediators is realized by this approach, presenting an important guideline in the development of stable electrolyte/redox mediator couples for lithium–oxygen batteries.

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

A kinetic model of friction in strongly coupled strongly magnetized plasmas

Plasmas that are strongly magnetized in the sense that the gyrofrequency exceeds the plasma frequency exhibit novel transport properties that are not well understood. As a representative example, we compute the friction force acting on a massive test charge moving through a strongly coupled and strongly magnetized one-component plasma using a generalized Boltzmann kinetic theory. Recent works studying the weakly coupled regime have shown that strong magnetization leads to a transverse component of the friction force that is perpendicular to both the Lorentz force and velocity of the test charge, in addition to the stopping power component aligned antiparallel to the velocity. Recent molecular dynamics simulations have also shown that strong Coulomb coupling in addition to strong magnetization gives rise to a third component of the friction force in the direction of the Lorentz force. Here, we show that the generalized Boltzmann kinetic theory captures these effects and generally agrees well with the molecular dynamics simulations over a broad range of Coulomb coupling and magnetization strength regimes. The theory is also used to show that the “gyro” component of the friction in the direction of the Lorentz force arises due to asymmetries associated with gyromotion during short-range collisions. Computing the average motion of the test charge through the background plasma, the transverse force is found to strongly influence the trajectory by changing the gyroradius and the gyrofriction force is found to slightly change the gyrofrequency of the test charge resulting in a phase shift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

An E and B gyrokinetic simulation model for kinetic Alfvén waves in tokamak plasmas

The gyrokinetic particle simulation is a powerful tool for studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general form and has been implemented in simulating kinetic Alfvén waves in uniform plasma. In our work, the Chen et al. GK-E&B model has been expressed, in general, tokamak geometry using the local orthogonal coordinates and general tokamak coordinates. Its reduction for uniform plasma is verified, and the numerical results show good agreement with the original work. The theoretical dispersion relation and numerical results in the local model in screw pinch geometry are also in excellent agreement. Numerical results show excellent performance in a realistic parameter regime of burning plasmas with high values of β/(M e k$^{2}_{⊥}$ρ$^{2}_{i}$), which is a challenge for traditional methods due to the “cancellation” problem. As one application, the GK-E&B model is implemented with kinetic electrons in the local single flux surface limit. With the matched International Tokamak Physics Activity-Toroidicity-induced Alfvén Eigenmodes parameters adopted, numerical results show the capability of the GK-E&B in treating the parallel electron Landau damping for realistic tokamak plasma parameters. As another application, the global GK-E&B model has been implemented with the dominant electron contribution in the cold electron limit. Its capability in simulating the finite E || due to the finite electron mass is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

42 ENGINEERING↗
DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗