Sharp Transition Research Articles

Imitation versus serendipity in ranking dynamics.

Participants in socio-economic systems are often ranked based on their performance. Rankings conveniently reduce the complexity of such systems to ordered lists. Yet, it has been shown in many contexts that those who reach the top are not necessarily the most talented, as chance plays a role in shaping rankings. Nevertheless, the role played by chance in determining success, i.e. serendipity, is underestimated, and top performers are often imitated by others under the assumption that adopting their strategies will lead to equivalent results. We investigate the tradeoff between imitation and serendipity in an agent-based model. Agents in the model receive payoffs based on their actions and may switch to different actions by either imitating others or through random selection. When imitation prevails, most agents coordinate on a single action, leading to non-meritocratic outcomes, as a minority of them accumulate the majority of payoffs. Yet, such agents are not necessarily the most skilled ones. When serendipity dominates, instead, we observe more egalitarian outcomes. The two regimes are separated by a sharp transition, which we characterize analytically in a simplified setting. We discuss the implications of our findings in a variety of contexts, ranging from academic research to business.

Rarefied cylindrical Couette problem: Effect of a very sharp transition from weakly rarefied flow near the inner cylinder to free molecular flow at very low average Knudsen numbers

We consider the rarefied cylindrical Couette flow. The outer cylinder rotates at a constant angular velocity, and the inner one is at rest. The Knudsen number, calculated from the average gas density, is much less than one. To find the fluid dynamic variables and fluxes, the direct simulation Monte Carlo method (DSMC) is used. We find the effect of a very sharp decrease in shear stress and energy fluxes transferred to the cylinders if the Knudsen number is sufficiently low and the rotation speed of the outer cylinder is sufficiently high. We show that when the average Knudsen number is sufficiently low, if the velocity is initially high and increases slightly further, the weakly rarefied flow regime near the inner cylinder transitions abruptly to a free molecular flow regime. Thus, the flow abruptly separates from the inner cylinder. We compare the fluxes obtained by solving the Navier–Stokes equations and by the DSMC method. It turns out that the solutions of the Navier–Stokes equations with slip boundary conditions also change abruptly at certain critical values, and these critical values are close to the appropriate DSMC values.

Three‐Dimensional Probabilistic Hydrofacies Modeling Using Machine Learning

AbstractCharacterizing the 3D distribution of hydraulic properties in glacial sediments is challenging due to fine‐scale heterogeneity and complexity. Borehole lithological data provide high vertical resolution but low horizontal resolution. Geophysical methods can fill gaps between boreholes, providing improved horizontal resolution but low vertical resolution. Machine learning can combine borehole and geophysical data to overcome these challenges. However, few studies have compared multiple machine learning methods for predicting hydrofacies in glacial aquifer systems. This study uses colocated airborne electromagnetic resistivity and borehole lithology data to train multiple machine learning models and predict the 3D distribution of hydrofacies in glacial deposits of eastern Nebraska, USA. Random Forest, Gradient Boosting Classifier, Extreme Gradient Boosting, Multilayer Perceptron, and Stacking Classifier were used to model 3D probabilistic distributions of hydrofacies (sand and clay) at a grid size of 200 m × 200 m × 3 m. Comparison of the predicted 3D hydrofacies models shows that the probability distributions and the contrasts between hydrofacies vary. The classification metrics show that the Stacking Classifier model performed better than other machine learning models in predicting hydrofacies. Multi‐Layer Perceptron and Stacking Classifier models show sharp vertical transitions between the low and high sand probability while other machine learning models show gradual transitions. K‐means clustering was used to translate the Stacking Classifier model into a 4‐class hydraulic conductivity model. This study shows that machine learning methods advance our understanding of glacial hydrogeology by improving the vertical and horizontal resolution of hydrofacies distribution and resolving aquifer‐aquifer and stream‐aquifer connections.

Detecting planted partition in sparse multilayer networks

Abstract Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multilayer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023, IEEE Trans. Inf. Theory, 69, 3203–3239) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network are greater than $1$. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provides a quasi-polynomial time algorithm to estimate it.

GaN-based E-mode p-FETs with polarization-doped p-type graded AlGaN channels

Herein, a novel enhancement-mode (E-mode) GaN-based p-channel FETs (p-FETs) with a linearly graded AlGaN (LGA) p-channel is proposed and numerically studied by Silvaco TCAD. Thanks to strong polarization-induced doping, three-dimensional hole gas (3DHG) can be uniformly generated in LGA to form a continuous p-channel with a hole concentration over 1018 cm–3. Combined with an optimized recessed gate structure, the LGA p-FET can simultaneously achieve a large threshold voltage (|V TH|) > 2 V and a high current density (|J DS|) of ∼10 mA mm−1 at V DS = −10 V. Additionally, two critical parameters of the LGA p-FETs, i.e. the depth of recessed gate and initial Al composition of LGA, are specifically studied to reveal the unique carrier behavior of 3DHG in the devices. Importantly, the LGA structure is further optimized and implemented as the p-type cap layer to construct an E-mode GaN n-FET. Thereby, based on the same LGA configuration, a GaN-based inverter with the matched complementary n- and p-FETs is monolithically constructed, showing sharp voltage transition. The reported novel LGA structure and its availability in both GaN-based E-mode n- and p-FETs provides valuable insights and guidance to construct highly efficient GaN p-type devices and All-GaN-based integrated circuits for compact power electronic systems.

AMICO galaxy clusters in KiDS-DR3: Measuring the splashback radius from weak gravitational lensing

Context. Weak gravitational lensing offers a powerful method to investigate the projected matter density distribution within galaxy clusters, granting crucial insights into the broader landscape of dark matter on cluster scales. Aims. In this study, we make use of the large photometric galaxy cluster data set derived from the publicly available Third Data Release of the Kilo-Degree Survey, along with the associated shear signal. Our primary objective is to model the peculiar sharp transition in the cluster profile slope, that is what is commonly referred to as the splashback radius. The data set under scrutiny includes 6962 galaxy clusters, selected by AMICO (an optimised detection algorithm of galaxy clusters) on the KiDS-DR3 data, in the redshift range of 0.1 ≤ z ≤ 0.6, all observed at a signal-to-noise ratio greater than 3.5. Methods. Employing a comprehensive Bayesian analysis, we model the stacked excess surface mass density distribution of the clusters. We adopt a model from recent results on numerical simulations that capture the dynamics of both orbiting and infalling materials, separated by the region where the density profile slope undergoes a pronounced deepening. Results. We find that the adopted profile successfully characterizes the cluster masses, consistent with previous works, and models the deepening of the slope of the density profiles measured with weak-lensing data up to the outskirts. Moreover, we measure the splashback radius of galaxy clusters and show that its value is close to the radius within which the enclosed overdensity is 200 times the mean matter density of the Universe, while theoretical models predict a larger value consistent with a low accretion rate. This points to a potential bias of optically selected clusters preferentially characterized by a high density at small scales compared to a pure mass-selected cluster sample.

Progressive Induction Hardening: Measurement and Alteration of Residual Stresses

Progressive induction hardening is an in-line steel heat treatment method commonly used to surface harden powertrain components. It produces a martensitic case layer with a sharp transition zone to the base material. This rapid process will induce large residual stresses, where a compressive state in the case layer will shift to a tensile state in the transition zone. For fatigue performance, it is important to quantify the magnitude and distribution of these stresses, and moreover how they depend on material and processing parameters. In this work, x-ray diffraction in combination with a layer removal method is used for efficient and robust quantification of the subsurface stress state, which combines electropolishing with either turning or milling. Characterization is done on C45E steel samples that were progressively induction hardened using either a fast or slow (27.5 or 5 mm/s, respectively) scanning speed. The results show that although the hardening procedures will meet arbitrary requirements on surface hardness, case depth and microstructure, the subsurface tensile stress peak magnitude is doubled when using a fast scanning speed. However, the near-surface compressive residual stresses are comparable. In addition, the subsurface tensile residual stress peak is compared with the on-surface tensile stresses in the fade-out zone.

Optimizing anaerobic digestion: Benefits of mild temperature transition from thermophilic to mesophilic conditions

Anaerobic digestion (AD) plays a significant role in renewable energy recovery. Upgrading AD from thermophilic (50–57 °C) to mesophilic (30–38 °C) conditions to enhance process stability and reduce energy input remains challenging due to the high sensitivity of thermophilic microbiomes to temperature fluctuations. Here we compare the effects of two decreasing-temperature modes from 55 to 35 °C on cell viability, microbial dynamics, and interspecies interactions. A sharp transition (ST) is a one-step transition by 20 °C d−1, while a mild transition (MT) is a stepwise transition by 1 °C d−1. We find a greater decrease in methane production with ST (88.8%) compared to MT (38.9%) during the transition period. ST mode overproduced reactive oxygen species by 1.6-fold, increased membrane permeability by 2.2-fold, and downregulated microbial energy metabolism by 25.1%, leading to increased apoptosis of anaerobes by 1.9-fold and release of intracellular substances by 2.9-fold, further constraining methanogenesis. The higher (1.6 vs. 1.1 copies per gyrA) metabolic activity of acetate-dependent methanogenesis implied more efficient methane production in a steady mesophilic, MT-mediated system. Metagenomic binning and network analyses indicated that ST induced dysbiosis in keystone species and greatly enhanced microbial functional redundancy, causing loss of microbial syntrophic interactions and redundant metabolic pathways. In contrast, the greater microbial interconnections (average degrees 44.9 vs. 22.1) in MT at a steady mesophilic state suggested that MT could better maintain necessary system functionality and stability through microbial syntrophy or specialized pathways. Adopting MT to transform thermophilic digesters into mesophilic digesters is feasible and could potentially enhance the further optimization and broader application of practical anaerobic engineering.

Stability and chaos in dynamical last passage percolation

Many complex disordered systems in statistical mechanics are characterized by intricate energy landscapes. The ground state, the configuration with lowest energy, lies at the base of the deepest valley. In important examples, such as Gaussian polymers and spin glass models, the landscape has many valleys and the abundance of near-ground states (at the base of valleys) indicates the phenomenon of chaos, under which the ground state alters profoundly when the disorder of the model is slightly perturbed. In this article, we compute the critical exponent that governs the onset of chaos in a dynamic manifestation of a canonical model in the Kardar-Parisi-Zhang [KPZ] universality class, Brownian last passage percolation [LPP]. In this model in its static form, semidiscrete polymers advance through Brownian noise, their energy given by the integral of the white noise encountered along their journey. A ground state is a geodesic, of extremal energy given its endpoints. We perturb Brownian LPP by evolving the disorder under an Ornstein-Uhlenbeck flow. We prove that, for polymers of length n n , a sharp phase transition marking the onset of chaos is witnessed at the critical time n − 1 / 3 n^{-1/3} . Indeed, the overlap between the geodesics at times zero and t > 0 t > 0 that travel a given distance of order n n will be shown to be of order n n when t ≪ n − 1 / 3 t\ll n^{-1/3} ; and to be of smaller order when t ≫ n − 1 / 3 t\gg n^{-1/3} . We expect this exponent to be universal across a wide range of interface models. The present work thus sheds light on the dynamical aspect of the KPZ class; it builds on several recent advances. These include Chatterjee’s harmonic analytic theory [Superconcentration and related topics, Springer, Cham, 2014] of equivalence of superconcentration and chaos in Gaussian spaces; a refined understanding of the static landscape geometry of Brownian LPP developed in the companion paper (see S. Ganguly and A. Hammond [Electron. J. Probab. 28 (2023), 80 pp.]); and, underlying the latter, strong comparison estimates of the geodesic energy profile to Brownian motion (see J. Calvert, A. Hammond, and M. Hegde [Astérisque 441 (2023), pp. v+119]).

Data-driven distortion compensation for laser powder bed fusion process using Gaussian process regression and inherent strain method

The repeated melting and solidification cycles in the laser powder bed fusion (L-PBF) process lead to significant thermal gradients, resulting in notable distortion in the as-built part. Distortion compensation methods, which pre-deform the part design so the as-built shape aligns with the target, have been widely adopted to mitigate this issue. This research introduces a data-driven distortion compensation framework for the L-PBF process. It employs an experimentally-calibrated inherent strain method to generate a dataset and utilizes Gaussian process regression to create the compensated geometry. Experimental validation shows that the proposed method can reduce the maximum distortion by up to 82.5% for a lattice structure and 77.8% for a canonical part. Furthermore, the compensation results reveal that (1) the lumped layer thickness in finite element models has little impact on simulated distortion reduction but can notably affect the experimental reduction; (2) discrepancies between simulated and experimental compensation performance are largely attributed to the curvy surfaces with sharp transitions in trial and compensated shapes, a result of pre-deforming the design; (3) the number of trial geometries considerably affects the effectiveness of compensation, while the number of deformation states does not have a statistically significant impact.

Evolutionary rescue in resistance to pesticides.

Evolutionary rescue occurs when the genetic evolution of adaptation saves a population from decline or extinction after environmental change. The evolution of resistance to pesticides is a special scenario of abrupt environmental change, where rescue occurs under (very) strong selection for one or a few de novo resistance mutations of large effect. Here, a population genetic model of evolutionary rescue with density-dependent population change is developed, with a focus on deriving results that are important to resistance management. Massive stochastic simulations are used to generate observations, which are accurately predicted using analytical approximations. Key results include the probability density function for the time to resistance and the probability of population extinction. The distribution of resistance times shows a lag period, a narrow peak and a long tail. Surprisingly, the mean time to resistance can increase with the strength of selection because, if a mutation does not occur early on, then its emergence is delayed by the pesticide reducing the population size. The probability of population extinction shows a sharp transition, in that when extinction is possible, it is also highly likely. Consequently, population suppression and (local) eradication can be theoretically achievable goals, as novel strategies to delay resistance evolution.

Spin flop transitions and complex magnetic behaviour in CoMoO4 powders and [formula omitted]-CoMoO4 thin films

Magnetic measurements were made on α-CoMoO4 powder and β-CoMoO4 thin film samples. α-CoMoO4 powder showed antiferromagnetic ordering below 13 K and two sharp spin flop transitions with complete magnetic saturation after the second transition (>5 T). A magnetic phase diagram for α-CoMoO4 was constructed, revealing three low-temperature magnetic phases: an antiferromagnetic phase at low field, an intermediate spin-flop phase, and a paramagnetic phase at high field. Two well-defined magnetisation plateaus were observed either side of the spin-flop phase: the first occurred with a moment per Co ion of 1/3 of spin saturation (where Co moments are completely aligned to the applied magnetic field), whereas the second occurred at a moment per Co ion matching calculations for spin saturation (3 μB per Co). No geometric origin for this factor of 1/3 could be found. Hysteresis was observed around the first spin-flop transition, indicating the presence of spin canting or magnetic domains under an applied field. The first successful fabrication of CoMoO4 thin films was achieved via RF magnetron sputtering, yielding β phase films which remain in the β phase upon cooling. The β-CoMoO4 thin films demonstrated antiferromagnetic ordering below 10 K. While two spin-flop transitions are seen in the β phase films (with a hysteresis around the first), spin saturation is not reached in fields up to 6 T, suggesting the existence of a third spin reorientation at higher field. A magnetic phase diagram was also constructed for the β-CoMoO4 film, which demonstrated the same three low-temperature magnetic phases, though with lower critical fields and transition temperatures. Comparisons with isostructural Ni and Mn molybdates showed that the key differences in the α and β phases arise from the different coordination of the Mo tetramers, indicating differences in magnetic properties in both phases arise from variations in the inter-tetramer exchange coupling.

Beyond the First Tipping Points of Southern Hemisphere Climate

Analysis of observations, reanalysis, and model simulations, including those using machine learning methods specifically designed for regime identification, has revealed changes in aspects of the Southern Hemisphere (SH) circulation and Australian climate and extremes over the last half-century that indicate transitions to new states. In particular, our analysis shows a dramatic shift in the metastability of the SH climate that occurred in the late 1970s, associated with a large-scale regime transition in the SH atmospheric circulation, with systematic changes in the subtropical jet, blocking, zonal winds, and storm tracks. Analysis via nonstationary clustering reveals a regime shift coincident with a sharp transition to warmer oceanic sea surface temperatures and increased baroclinicity in the large scales of the Antarctic Circumpolar Circulation (ACC), extending across the whole hemisphere. At the same time, the background state of the tropical Pacific thermocline shoaled, leading to an increased likelihood of El Niño events. The SH climate shift in the late 1970s is the first hemispheric regime shift that can be directly attributed to anthropogenic climate change. These changes in dynamics are associated with additional regional tipping points, including reductions in mean and extreme rainfall in south-west Western Australia (SWWA) and streamflow into Perth dams, and also with increases in mean and extreme rainfall over northern Australia since the late 1970s. The drying of south-eastern Australia (SEA) occurred against a background of accelerating increases in average and extreme temperatures across the whole continent since the 1990s, implying further inflection points may have occurred. Analysis of climate model simulations capturing the essence of these observed shifts indicates that these systematic changes will continue into the late 21st century under high greenhouse gas emission scenarios. Here, we review two decades of work, revealing for the first time that tipping points characteristic of regime transitions are inferred to have already occurred in the SH climate system.

Constraining Primordial Black Hole Formation from Single-Field Inflation.

The most widely studied formation mechanism of a primordial black hole is collapse of large-amplitude perturbation on small scales generated in single-field inflation. In this Letter, we calculate one-loop correction to the large-scale power spectrum in a model with sharp transition of the second slow-roll parameter. We find that models producing an appreciable amount of primordial black holes induce nonperturbative coupling on a large scale probed by cosmic microwave background radiation. Our result implies that a small-scale power spectrum can be constrained by large-scale cosmological observations.

Unexpectedly High Magma Productivity Inferred From Crustal Roughness and Residual Bathymetry on the Eastern Part of the Ultra‐Slow Spreading Gakkel Ridge Since ∼45 Ma, Eurasian Basin, Arctic Ocean

AbstractThe Gakkel Ridge in the Eurasian Basin has the slowest seafloor spreading worldwide. The western Gakkel Ridge (3°W–85°E; 14–11 mm/a) alternate between magmatic and sparsely magmatic zones, while the eastern Gakkel Ridge (85–126°E; 11–6 mm/a) appears to be dominated by magmatic zones despite ultraslow spreading. Little is known about the seafloor spreading conditions in the past along the entire ridge. Here, we exploit the residual bathymetry and basement roughness to assess the crustal accretion process of the Gakkel Ridge over time using 23 published regional multichannel seismic reflection profiles. Full seafloor spreading rates were faster (20–24 mm/a) up to ∼45 Ma, and residual bathymetry for the older crust is deeper than the world average in the entire Eurasian Basin. There is a sharp transition to 300–400 m shallower residual bathymetry for seafloor <45 Ma in the eastern Eurasian Basin. The crustal roughness versus spreading rate of the western Eurasian Basin is on the global trend, while that of the eastern is significantly below. Both low roughness and shallow residual bathymetry of the eastern Eurasian Basin is close to that of oceanic crust for spreading rates above 30 mm/a, demonstrating increased magmatic production of the eastern Gakkel Ridge since ∼45 Ma. A recent mantle tomography model predicts partial melting in the upper mantle based on the low Vs anomaly underneath. The sedimentary pattern toward the Lomonosov Ridge indicates that this hot mantle anomaly started to cause dynamic uplift of the area at ∼45 Ma.

Robustness of the random language model.

The random language model [Phys. Rev. Lett. 122, 128301 (2019)0031-900710.1103/PhysRevLett.122.128301] is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first-language learning as a type of annealing in the vast space of potential languages. In its simplest formulation, it implies a single continuous transition to grammatical syntax, at which the symmetry among potential words and categories is spontaneously broken. Here this picture is scrutinized by considering its robustness against extensions of the original model, and trajectories through parameter space different from those originally considered. It is shown here that (i) the scenario is robust to explicit symmetry breaking, an inevitable component of learning in the real world, and (ii) the transition to grammatical syntax can be encountered by fixing the deep (hidden) structure while varying the surface (observable) properties. It is also argued that the transition becomes a sharp thermodynamic transition in an idealized limit. Moreover, comparison with human data on the clustering coefficient of syntax networks suggests that the observed transition is equivalent to that normally experienced by children at age 24 months. The results are discussed in light of the theory of first-language acquisition in linguistics, and recent successes in machine learning.

Symmetry breaking in optimal transport networks

Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers. Here, we show that optimal networks undergo sharp transitions from symmetric to asymmetric shapes, indicating that it is sometimes better to avoid serving a whole area to save on switching costs. Also, we analyze the real transportation networks of the cities of Atlanta, Boston, and Toronto using our theoretical framework and find that they are farther away from their optimal shapes as traffic congestion increases.

Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation.

Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy conservation. A fundamental question in this setting is how well one can prepare good coherent states from low coherent states and whether a given coherent state is convertible to another one. Here, we show that any low coherent state is convertible to any high coherent state arbitrarily well in two operational settings: asymptotic and catalytic transformations. For a variant of asymptotic coherence manipulation where one aims to prepare desired states in local subsystems, the rate of transformation becomes unbounded regardless of how weak the initial coherence is. In a non-asymptotic transformation with a catalyst, a helper state that locally remains in the original form after the transformation, we show that an arbitrary state can be obtained from any low coherent state. Applying this to the standard asymptotic setting, we find that a catalyst can increase the coherence distillation rate significantly-from zero to infinite rate. We also prove that such anomalous transformation requires small but nonzero coherence in relevant modes, establishing the condition under which a sharp transition of the operational capability occurs. Our results provide a general characterization of the coherence transformability in these operational settings and showcase their peculiar properties compared to other common resource theories such as entanglement and quantum thermodynamics.

Fourth-order phase-field simulation of cracks using strong form meshless method

The prediction of crack propagation in fracture mechanics is still a fundamental challenge. In recent decades, phase-field formulation emerged as a powerful tool for the simulation of crack evolution, which offers a continuous representation of cracks from intact to broken material. For the first time, the present study combines a fourth-order phase field and a strong-form meshless method to investigate crack propagation in brittle elastic material. The local radial basis function collocation method, structured with the augmented polyharmonic splines, is used to solve the coupled mechanical and phase-field models. Due to the smooth nature of the fourth-order phase-field model, the sharp transition at the crack surface can be avoided. It is found that the presented method successfully predicts the crack propagation for a material subjected to tensile loading. The obtained results agree well with the benchmark case. Further study will include elastoplastic material behaviour and applications to crack formation in different steel processing steps.

Emergent two-band conduction at Ti delta-doped LaAlO3/KTaO3 (111) heterointerface

Recently, several intriguing interfacial phenomena have been discovered at the KTaO3 (111)-based heterointerfaces, such as the two-dimensional electron gas, superconductivity, anisotropic conductivity, etc. However, the available techniques to systematically manipulate such interfacial states are quite limited. Here, we devise a delta-doping strategy by inserting a sub-nanometer Ti layer with distinct reducibilities to the LaAlO3/KTaO3 (111) interface. In the delta-doped samples, we observe an unforeseen two-band conduction, evidenced by the emergence of a new type of electron carrier with an order-of-magnitude enhancement of mobility (∼1800 cm2V−1s−1) than the original carriers. Moreover, the appearance of the high-mobility carriers causes a sharp transition between the non-Fermi-liquid superconducting state and the Fermi-liquid state with reduced spin–orbit scattering. Further evidence shows that the new type of carriers stems from another in-gap state with a shallower energy level compared to the original carriers. Our study broadens the spectrum of interfacial carrier manipulation by introducing an extra band/channel for carrier conduction, which not only opens up new possibilities in device applications but also shines a light on the underlying physics of interfacial superconductivity.