Physical Model Research Articles

Modeling Absorption Dynamics of Differently Shaped Gold Glioblastoma and Colon Cells Based on Refractive Index Distribution in Holotomographic Imaging.

Herein, it is demonstrated that the toxic effect of gold nanoparticles (Au NPs) on three different cancer cell lines (U-118 and LN-299 glioblastoma and HCT-116 colon) depends on their absorption dynamics by cells, related to the shapes of the NPs. This hypothesis is confirmed by showing that i) based on refractive index (RI) values, typical for cell components and gold nanoparticles, it is possible to show the absorption dynamics and accumulation locations of the latter ones inside and outside of the cells. Moreover, ii) the saturation of the accumulated Au NPs volume in the cells depends on the nanoparticle shape and is reached in the shortest time for star-shaped Au NPs (AuS NPs) and in the longest time for spherical Au NPs (AuSph NPs) and on the cancer cells, where the longest and the shortest saturation are noticed for HCT-116 and LN-229 cells, respectively. A physical model of Au NPs absorption dynamics is proposed, where the diameter and shape of the Au NPs are used as parameters. The obtained theoretical data are consistent with experimental data in 85-98%.

PRODIGE - Planet-forming disks in Taurus with NOEMA. II. Modeling the CO (2-1) isotopologue emission of the Class II T Tauri disks in Taurus

To understand how planets form in protoplanetary disks, it is necessary to characterize their gas and dust distribution and masses. This requires a combination of high-resolution dust continuum and molecular line interferometric observations, coupled with advanced theoretical models of protoplanetary disk physics, chemical composition, and radiative transfer. We aim to constrain the gas density and temperature distributions as well as gas masses in several T Tauri protoplanetary disks located in Taurus. We use the 12CO, 13CO, and C18O (2-1) isotopologue emission observed at $0.9 with the IRAM NOrthern Extended Millimeter Array (NOEMA) as part of the MPG-IRAM Observatory Program PRODIGE (PROtostars and DIsks: Global Evolution \, PIs: P. Caselli Th. Henning). Our sample consists of Class II disks with no evidence of strong radial substructures. We use these data to constrain the thermal and chemical structure of these disks through theoretical models for gas emission. To fit the combined optically thick and thin CO line data in Fourier space, we developed the DiskCheF code, which includes the parameterized disk physical structure, machine-learning (ML) accelerated chemistry, and the RADMC-3D line radiative transfer module. A key novelty of DiskCheF is the fast and feasible ML-based chemistry trained on the extended grid of the disk physical-chemical models precomputed with the ANDES2 code. This ML approach allows complex chemical kinetics models to be included in a time-consuming disk fitting without the need to run a chemical code. We present a novel approach to incorporate chemistry into disk modeling without the need to explicitly calculate a chemical network every time. Using this new disk modeling tool, we successfully fit the 12CO, 13CO, and C$ $O (2-1) data from the CI, CY, DL, DM, DN, and IQ Tau disks. The combination of optically thin and optically thick CO lines allows us to simultaneously constrain the disk temperature and mass distribution, and derive the CO-based gas masses. The best-fit disk gas masses range between 0.005 and $0.04 M_ sun $. These values are in reasonable agreement with the disk dust masses rescaled by a factor of 100 as well as with other indirect gas measurements via, for example, modeling of the wavelength dependence of the dust continuum emission radii, and HD and CO isotopologue emission.

Application of Bayesian networks based on Sequential Monte Carlo simulation and physical model in fault diagnosis of horizontal three-phase separator system

In offshore production platforms, horizontal three-phase separator is common process equipment. Its main function is to complete the dehydration and degassing of crude oil. Separator system is more complex, and its failure may cause significant economic losses and disastrous consequences. Therefore, it is critical to accurately and quickly identify where and why faults occur in the separator system. In this study, separator fault diagnosis model based on Bayesian networks is developed. Moreover, Sequential Monte Carlo simulation and physical model are introduced to overcome field problems such as missing separator failure data and the inability of experts to provide accurate empirical knowledge. Using this model, 13 faults in a separator in an offshore crude oil processing system are successfully diagnosed. Meanwhile, the proposed model is compared with deep neural network, convolutional neural network, and deep residual network, with accuracy rates of 100%, 91.34%, 87.99%, and 94.62%, respectively. Then, the diagnostic accuracy of each model for different faults is also compared in this paper under various signal-to-noise ratios. The results show that the method proposed in this paper has better noise immunity compared to the other three models. Therefore, the accuracy and robustness of the proposed model is further demonstrated. Finally, to analyze the fault-tolerance of the proposed model, 2–3 error evidence is randomly entered. The results show that the proposed model has better fault tolerance compared to data-driven Bayesian networks.

Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations

In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

Discrete Boltzmann model with split collision for nonequilibrium reactive flows

Abstract A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the righ-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman-Enskog analysis, it is proved that the DBM is consistent with the reactive Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise description of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin-Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.

A novel residual hybrid dynamic model for unmanned helicopters: combining both physical and deep learning models

A novel residual hybrid dynamic model for unmanned helicopters: combining both physical and deep learning models

Constraints on dark matter and astrophysics from tomographic γ -ray cross-correlations

We study the cross-correlation between maps of the unresolved γ-ray background constructed from the 12-year data release of the Large-Area Telescope, and the overdensity of galaxies in the redshift range z≲0.4 as measured by the 2MASS photometric redshift survey and the WISE-SuperCOSMOS photometric survey. A signal is detected at the 8−10σ level, which we interpret in terms of both astrophysical γ-ray sources, and weakly interacting massive particles (WIMP) dark matter decay and annihilation. The sensitivity achieved allows us to characterise the energy and redshift dependence of the signal, and we show that the latter is incompatible with a pure dark matter origin. We thus use our measurement to place an upper bound on the WIMP decay rate and the annihilation cross section, finding constraints that are competitive with those found in other analyses. Our analysis is based on the extraction of clean model-independent observables that can then be used to constrain arbitrary astrophysical and particle physics models. In this sense we produce measurements of the γ-ray emissivity as a function of redshift and rest-frame energy ϵ, and of a quantity F(ϵ) encapsulating all WIMP parameters relevant for dark matter decay or annihilation. We make these measurements, together with a full account of their statistical uncertainties, publicly available. Published by the American Physical Society 2024

From Data to Design: Constructing Scapula and Hip Bone Through Online Datasets, Open-Source Software and 3D Printers.

Introduction Human skeletons and bones are essential for medical and allied sciences students. Nowadays, it is becoming challenging to procure bone legally, resulting in medical students' inadequacy of bone. Plaster-of-Paris or resin bone models sold on the market are less detailed than real bones. Aims and objectives This study aims to create a three-dimensional (3D)-printed human bone model with free, open-source software and fused deposition modelling (FDM) 3D printers, compare its accuracy with the original bones and validate it with a textbook description. Methods Scapula and hip bone models were produced using open-source software 3D Slicer from computed tomography (CT) data from the "New Mexico Decedent Image Database". After automated segmentation, bones were edited manually with tools in a 3D Slicer(https://www.slicer.org/) and Meshmixer software(Autodesk Inc., San Rafael, California, United States) and 3D bone models were printed using polylactic (PLA) filament. Results and discussions 3Ddigital models of both bones were successfully created with the maximum possible accuracy with an FDM 3D printer. A 3D digital replica of the scapula obtained after segmentation retained most anatomical features except for the glenoid cavity, as the head of the humerus obscured the glenoid cavity. The 3D digital skeleton of the hip bone retained all anatomical features except articulating surfaces, such as the acetabulum and auricular surface ilium, which were obscured by the head of the femur and sacrum. A few morphological features of both bones differed from the original dry bone, and a few finer details were unclear in the iliac fossa and ischium. After manual editing and post-processing, the final physical model obtained has all the features. Conclusions We conclude that it is possible to produce anatomically accurate models with the greatest possible resemblance and accuracy to the original bones using free and open-source data with an FDM 3D printer.

The combined effects of physical and virtual models in learning cellular biology

Physical models have long been used in science education for visualization of complex cellular structure and dynamics during face-to-face lecture (F2F). Recent advancement of technology has enabled us to create virtual models and to share knowledge remotely. This study aims to find out whether physical and virtual models work synergistically to enhance student engagement in learning an undergraduate Life Sciences module. Three independent experiments were conducted to assess learning effectiveness on three biology concepts through four learning approaches: video with virtual model only, video with integration of virtual and physical model demonstration, F2F lecture using virtual model only, F2F lecture using virtual and physical models. Participants were randomly assigned to different groups each with one learning approach. Data collected through pre- and post-tests revealed that significant improvement in learning scientific concepts occurred in one of three controlled experiments when the video contains both virtual and physical models, while no obvious difference found in the other two experiments. This data suggests that well-prepared digital media alone may convey scientific information well and additional physical models do not aid in information acquisition. However, feedback survey on student learning experience showed that all participants preferred to learn from physical models. In all three experiments, students consistently voted that the physical models attracted their attention and enhanced their interests. They made better mind maps and raised more questions. These hint that a combination of digital media with physical models might improve engagement and promote higher order thinking.

How do the non‐linear I–V curves of ZnO‐based adaptive composites behave with electrodes placed on the opposite sides with a series of horizontal distances?

AbstractRecently, ZnO‐based composites have been widely applied in the field of electric power. To meet the diverse application requirements, it is necessary to figure out the I–V characteristics of ZnO composites whose high‐voltage and ground‐voltage electrodes are arranged on the opposite sides with a certain horizontal distance. 30 vol%, 40 vol% and 50 vol% ZnO‐based silicone rubber composites were prepared. The horizontal distance between their electrodes was set as 50, 100, 500 μm, 1 and 2 mm, respectively. Results showed that with the increase of ZnO fillers volume fraction under a fixed horizontal distance of 100 μm, from 30 vol% to 50 vol%, the I–V curves shifted left, the leakage current increased and the switching voltage decreased. When the horizontal distance between electrodes increased from 50 μm to 1 mm under a fixed doping concentration of 40%, the I–V curves shifted to the right, the leakage current dropped and the switching voltage rose. The mathematical and physical models were established to explain the results. This work provides a referential significance for the practical application of ZnO composites, such as 5G folding mobile phones and power electronic modules.

Development and validation of a biomechanically fidelic surgical training knee model.

Knee arthroplasty technique is constantly evolving and the opportunity for surgeons to practice new techniques is currently highly dependent on the availability of cadaveric specimens requiring certified facilities. The high cost, limited supply, and heterogeneity of cadaveric specimens has increased the demand for synthetic training models, which are currently limited by a lack of biomechanical fidelity. Here, we aimed to design, manufacture, and experimentally validate a synthetic knee surgical training model which reproduces the flexion dependent varus-valgus (VV) and anterior-posterior (AP) mechanics of cadaveric knees, while maintaining anatomic accuracy. A probabilistic finite element modeling approach was employed to design physical models to exhibit passive cadaveric VV and AP mechanics. Seven synthetic models were manufactured and tested in a six-degree-of-freedom hexapod robot. Overall, the synthetic models exhibited cadaver-like VV and AP mechanics across a wide range of flexion angles with little variation between models. In the extended position, two models showed increased valgus rotation (<0.5°), and three models showed increased posterior tibial translation (<1.7 mm) when compared to the 95% confidence interval (CI) of cadaveric measurements. At full flexion, all models showed VV and AP mechanics within the 95% CI of cadaveric measurements. Given the repeatable mechanics exhibited, the knee models developed in this study can be used to reduce the current reliance on cadaveric specimens in surgical training.

BASES OF THE METHOD OF PHYSICAL MODELING OF THE PROCESS OF CRUSHING OF MUNICIPAL SOLID WASTE

A large number of studies are aimed at increasing the energy efficiency of grinding processes of various solid materials, while maintaining the values ​​of other important indicators, such as material consumption, productivity, etc. Based on this trend, a new method for physically modeling the process of grinding municipal solid waste (MSW) was proposed for the first time. Existing physical modeling techniques are designed for homogeneous and isotropic materials (for example, soil, crushed stone, snow, coal, etc.). The strength properties of solid waste vary widely due to the significant heterogeneity of their components. Consequently, when crushing solid waste, traditional crusher designs have low efficiency in terms of energy intensity, material intensity and product quality. The purpose of this work is to develop a new technique for physical modeling of the grinding process, based on the main principles of similarity theory and modeling, considering the properties of waste heterogeneity. As a result of the research, a block diagram of the physical modeling methodology for the interaction of the working bodies of impact crushing machines with solid waste was developed. A list of tasks for the modeling process and similarity criteria have been determined based on the development of rheological models of the “working body - municipal solid waste” system and the laws of mechanics that characterize the waste grinding process. Based on the developed similarity criteria, scale equations for the grinding process are substantiated and formulas are derived for determining the expected parameters of the original based on the parameters measured on the model. The developed methodology makes it possible to create a crusher design with improved energy efficiency indicators with the least material and labor costs.

HI discs of L* galaxies as probes of the baryonic physics of galaxy evolution

Abstract Understanding what shapes the cold gas component of galaxies, which both provides the fuel for star formation and is strongly affected by the subsequent stellar feedback, is a crucial step towards a better understanding of galaxy evolution. Here, we analyse the HI properties of a sample of 46 Milky Way halo-mass galaxies, drawn from cosmological simulations (EMP-Pathfinder and Firebox). This set of simulations comprises galaxies evolved self-consistently across cosmic time with different baryonic sub-grid physics: three different star formation models [constant star formation efficiency (SFE) with different star formation eligibility criteria, and an environmentally-dependent, turbulence-based SFE] and two different feedback prescriptions, where only one sub-sample includes early stellar feedback. We use these simulations to assess the impact of different baryonic physics on the HI content of galaxies. We find that the galaxy-wide HI properties agree with each other and with observations. However, differences appear for small-scale properties. The thin HI discs observed in the local Universe are only reproduced with a turbulence-dependent SFE and/or early stellar feedback. Furthermore, we find that the morphology of HI discs is particularly sensitive to the different physics models: galaxies simulated with a turbulence-based SFE have discs that are smoother and more rotationally symmetric, compared to those simulated with a constant SFE; galaxies simulated with early stellar feedback have more regular discs than supernova-feedback-only galaxies. We find that the rotational asymmetry of the HI discs depends most strongly on the underlying physics model, making this a promising observable for understanding the physics responsible for shaping the interstellar medium of galaxies.

Remote Sensing and Modeling of the Cryosphere in High Mountain Asia: A Multidisciplinary Review

Over the past decades, the cryosphere has changed significantly in High Mountain Asia (HMA), leading to multiple natural hazards such as rock–ice avalanches, glacier collapse, debris flows, landslides, and glacial lake outburst floods (GLOFs). Monitoring cryosphere change and evaluating its hydrological effects are essential for studying climate change, the hydrological cycle, water resource management, and natural disaster mitigation and prevention. However, knowledge gaps, data uncertainties, and other substantial challenges limit comprehensive research in climate–cryosphere–hydrology–hazard systems. To address this, we provide an up-to-date, comprehensive, multidisciplinary review of remote sensing techniques in cryosphere studies, demonstrating primary methodologies for delineating glaciers and measuring geodetic glacier mass balance change, glacier thickness, glacier motion or ice velocity, snow extent and water equivalent, frozen ground or frozen soil, lake ice, and glacier-related hazards. The principal results and data achievements are summarized, including URL links for available products and related data platforms. We then describe the main challenges for cryosphere monitoring using satellite-based datasets. Among these challenges, the most significant limitations in accurate data inversion from remotely sensed data are attributed to the high uncertainties and inconsistent estimations due to rough terrain, the various techniques employed, data variability across the same regions (e.g., glacier mass balance change, snow depth retrieval, and the active layer thickness of frozen ground), and poor-quality optical images due to cloudy weather. The paucity of ground observations and validations with few long-term, continuous datasets also limits the utilization of satellite-based cryosphere studies and large-scale hydrological models. Lastly, we address potential breakthroughs in future studies, i.e., (1) outlining debris-covered glacier margins explicitly involving glacier areas in rough mountain shadows, (2) developing highly accurate snow depth retrieval methods by establishing a microwave emission model of snowpack in mountainous regions, (3) advancing techniques for subsurface complex freeze–thaw process observations from space, (4) filling knowledge gaps on scattering mechanisms varying with surface features (e.g., lake ice thickness and varying snow features on lake ice), and (5) improving and cross-verifying the data retrieval accuracy by combining different remote sensing techniques and physical models using machine learning methods and assimilation of multiple high-temporal-resolution datasets from multiple platforms. This comprehensive, multidisciplinary review highlights cryospheric studies incorporating spaceborne observations and hydrological models from diversified techniques/methodologies (e.g., multi-spectral optical data with thermal bands, SAR, InSAR, passive microwave, and altimetry), providing a valuable reference for what scientists have achieved in cryosphere change research and its hydrological effects on the Third Pole.

Dynamical Modeling and Dynamic Characteristics Analysis of a Coaxial Dual-Rotor System

The dual-rotor structure is the primary excitation source of aero-engine vibration. It is essential to study the dynamical model and analyse the dynamic characteristics such as critical speed and the unbalanced response for rotor system dynamics. The coaxial dual-rotor support scheme of an aero-engine was introduced in the previous work, and the physical model with a high-speed flexible inner rotor of a sizeable length-diameter ratio has been designed. Then a finite element dynamic model based on the Timoshenko beam elements and rigid body kinematics of the dual-rotor system is modelled, with the Newmark-β method and Newton-Raphson method used for the numerical calculation to study the dynamic characteristics of the system. Three different simulation models, including beam-based FE (1D finite element) model, solid-based FE (3D finite element) model, and TM (transfer matrix) model, were designed to study the characteristics of mode and the critical speed characteristic of the dual-rotor system. The unbalanced response of the dual-rotor system was analysed to study the influence of mass unbalance on the rotor system. The effect of different disc unbalance phases and different speed ratios on the dynamic characteristics of the dual-rotor system were investigated in detail. The experimental result shows that the beam-based FE model is effective and suitable for studying the dual-rotor system. Conflict of Interest Statement The authors declare no conflicts of interest.

Revisiting the bleeding effect in historical cobalt porcelain pigments: Mechanism, influence and technical responses

The bleeding phenomenon, a persistent and widespread issue in the application of cobalt-bearing pigment during porcelain decoration, has spurred different civilisations to develop various response strategies to alleviate this problem. In this study, we challenge the prevailing hypotheses concerning the role of composition and viscosity in determining the bleeding effect on blue-and-white wares, proposing a novel physical model framing it as a diffusion process that occurs within vitreous silicate, where the severity can be qualitatively expressed using the diffusion distance. Drawing upon the phenomenological Fick's law and microscopic diffusion mechanism, we quantitatively discuss the primary physical parameters that influence the diffusion behaviour for the first time, clarifying that the diffusion of cobalt ions is not related to the medium viscosity. Moreover, compared with the microstructural features of blue decors with and without the bleeding effect, we reveal that domestic cobalt particles are all encapsulated by anorthite crystals, acting as a passivation shell to hinder the dissolution of cobalt particles. Significantly, our reinterpretation has broader archaeological implications for the bleeding effect associated with cobalt pigment in ceramics, elucidating the historical trajectories of responsive practices and the multifaceted interplay between resource form, artistic expression and technological advancement across varying environmental and cultural contexts. Overall, these responses to the bleeding effect exemplify the complexities of technological evolution, highlighting that technology is not merely an extension of technical knowledge but also functions as a form of social construction deeply intertwined with its local context. This comprehensive understanding contributes to our understanding of historical narratives in ceramics and the diversity of human ingenuity in ancient societies, with potential implications for contemporary pigment manufacture.

A multi-period topology and design optimization approach for district heating networks

The transition to modern, low-carbon district heating creates a growing need for scalable, automated design tools that accurately capture the spatial and temporal details of heating network operations. This paper presents an automated design approach for the optimal design of district heating networks that combines scalable density-based topology optimization with a multi-period approach. In this way, temporal variations in demand, supply, and heat losses can be taken into account while optimizing the network design based on a nonlinear physics model. The transition of the automated design approach from worst-case to multi-period shows a design progression from separate branched networks to a single integrated meshed network topology connecting all producers. These integrated topologies emerge without imposing such structures a priori. They increase network connectivity, and allow for more flexible shifting of heat loads between different producers and heat consumers, resulting in more cost-effective use of heat. In a case study, this integrated design resulted in an increase in waste heat share of 42.8 % and a subsequent reduction in project cost of 17.9 %. We show how producer unavailability can be accounted for in the automated design at the cost of a 3.1 % increase in the cost of backup capacity. The resulting optimized network designs of this approach connect multiple low temperature heat sources in a single integrated network achieving high waste heat utilization and redundancy, highlighting the applicability of the approach to next-generation district heating networks.

Pullout behaviour of strip plate anchors in clay overlying sand

Plate anchors are being increasingly employed to establish mooring systems for offshore floating facilities owing to their notable efficiency and cost-effectiveness. The majority of prior studies have concentrated on plate anchors, examining the vertical to horizontal orientations, particularly when embedded in single layer clay or sand. However, it is common to encounter multiple layers of soil with varying characteristics in practical engineering, leading to inaccurate estimation of pullout capacity when based solely on the properties of a single soil layer. This paper reports pullout behaviours of strip plate anchors in clay overlying sand by adopting two dimensional finite element analysis. To simulate the hardening and subsequent softening behaviour of medium to dense sand, a modified Mohr-Coulomb model is considered. The current Finite Element (FE) results are in good agreement when compared with both previous FE simulations and physical model test data. Then, the soil flow mechanisms (e.g. the accumulated plastic shear strain, the friction angle) surrounding the anchor during pullout out are revealed. Based on a series of FE results, a calculation framework considering the effect of thickness of clay layer is designed to predict the pullout behaviour of plate anchors in clay overlying sand.

Physical Model of Inclusions Removal at Static Steel–Slag Interface

Inclusions are one of the important factors affecting the cleanliness of molten steel. The current optimization of inclusion removal methods mainly focuses on promoting inclusions to float to the slag–steel interface so that the inclusions can be absorbed and removed by the refining slag. However, the research on the floating removal of inclusions cannot be carried out directly in the ladle, so methods such as mathematical models and physical models were developed. This article uses silicone oil to simulate the slag layer; polypropylene particles; and aluminum oxide particles to simulate inclusions to establish a water model experiment. By changing the viscosity of silicone oil and the diameter of particles, the factors affecting the movement of inclusions at the slag–steel interface were explored. Based on the water model, a mathematical model of the floating behavior of inclusions at the slag–steel interface was constructed, and parameters such as particle diameter and interfacial tension in the water model experiment were studied by the mathematical model for calculation. Both the mathematical model and the water model experimental results show that after the viscosity of silicone oil increases from 0.048 Pa·s to 0.096 Pa·s, the dimensionless displacement and terminal velocity of the particles decreases. When the diameter of the same particle increases, the dimensionless displacement and terminal velocity increases. The dimensionless displacement of polypropylene particles of the same diameter is larger than that of aluminum oxide particles, and the terminal velocity is smaller than that of aluminum oxide particles. This is attributed to the better overall three-phase wettability of polypropylene particle. When the liquid level increases, the dimensionless displacement and terminal velocity of particles under the same conditions show only slight differences (less than 10%).

Coexistence of superconductivity with partially filled stripes in the Hubbard model

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.