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Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗

Impingement of water droplets on wedges and double-wedge airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees r, free stream Mach numbers from 1.1 to 2.0, semiapex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

Serafini, John S↗

Dynamics of the Molten Contact Line

The purpose of this program is to develop a basic understanding of how a molten material front spreads over a solid that is below its melting point, arrests, and freezes. Our hope is that the work will contribute toward a scientific knowledge base for certain new applications involving molten droplet deposition, including the "printing" of arbitrary three-dimensional objects by precise deposition of individual molten microdrops that solidify after impact. Little information is available at this time on the capillarity-driven motion and arrest of molten contact line regions. Schiaffino and Sonin investigated the arrest of the contact line of a molten microcrystalline wax spreading over a subcooled solid "target" of the same material. They found that contact line arrest takes place at an apparent liquid contact angle that depends primarily on the Stefan number S=c(T(sub f) -T(sub t)/L based on the temperature difference between the fusion point and the target temperature, and proposed that contact line arrest occurs when the liquid's dynamic contact angle approaches the angle of attack of the solidification front just behind the contact line. They also showed, however, that the conventional continuum equations and boundary conditions have no meaningful solution for this angle. The solidification front angle is determined by the heat flux just behind the contact line, and the heat flux is singular at that point. By comparing experiments with numerical computations, Schiaffino and Sonin estimated that the conventional solidification model must break down within a distance of order 0.1 - 1 microns of the contact line. The physical mechanism for this breakdown is as yet undetermined, and no first-principles theory exists for the contact angle at arrest. Schiaffino and Sonin also presented a framework for understanding how to moderate Weber number molten droplet deposition in terms of similarity laws and experimentation. The study is based on experiments with three molten materials- molten wax on solid wax, water on ice, and mercury on frozen mercury- which between them span a considerable range of the deposition/solidification similarity parameters. Correlations are obtained for the spreading velocity, spreading time scales, the spreading factor (i.e. ratio of deposited drop's final footprint radius and the drop's initial radius), post-spreading liquid oscillation amplitudes and time scales, and bulk solidification time scales. Duthaler carried out an experimental and theoretical investigation of the relationship between the liquid's apparent contact angle and the Capillary number Ca=mu U/sigma based on contact line speed, for molten materials spreading over subcooled solids. This relationship is required for modeling of melt spreading. We have adapted Voinov's methodology to the molten contact line and formulated a theoretical model for the Ca vs. contact angle relationship, based Schiaffino and Sonin#s (1997a,b) wedge-like solidification front model. With the solidification front angle taken from Schiaffino and Sonin, the model is in good agreement with the experimental results for Ca vs. contact angle. Duthaler also extended the experimental investigation of droplet deposition and contact line freezing to more materials, including solder on glass, solder on solder, water on ice, and molten microcrystalline wax on wax. The latter also included tests on inclined targets. Deposition tests have also been done with molten octacosane (C28H58) on various targets. An important objective of our program has been the development of micron-scale sensors for measuring the transient temperature at a point on the substrate surface as a molten contact line moves over it. The expectation is that this temperature history will yield a better understanding of the thermal process in the contact line region. The sensors are of the thermistor type, either 2.5 microns or 1.5 microns square, microfabricated with silicon-based technology on either pure silicon or amorphous silicon dioxide chips. Each chip has 32 sensors distributed on its surface in arrays. The time response is better than 10 ms. At the time of writing, sensor calibration is in progress. Results on thermal transients during contact line passage will be discussed at the conference. While we expect that the data will provide information on the near-contact-line heat transfer process, we also foresee possible problems. First, the spatial resolution of the sensors may be insufficient to resolve the near-contact-line region. Second, the sensors protrude about 0.5 microns above the substrate surface, and may affect the contact line motion. Third, a sensor's temperature history depends on both the heat flux distribution into it from the fusion front and the thermal properties of the substrate below it and the solidified melt between it and the fusion front. The heat flux distribution in the contact line region must therefore be unfolded from computations of the overall system's transient thermal response.

Sonin, Ain A.↗

Chandra HRC Observations of X-Rays from the Jupiter System

In support of the Cassini fly-by of Jupiter, the Chandra X-Ray Observatory's High Resolution Camera (HRC) was used to observe the Jovian system for a complete rotation of Jupiter on December 18, 2000, from 10-20 UT (Universal Time). The HRC is most sensitive to x-rays in the 0.1-10 keV range, with a peak sensitivity in the 1-1.5 keV range, and is a direct descendant of the imagers on the Einstein and ROSAT (Roentgen Satellite) satellites. Chandra differs from other x-ray observatories primarily by virtue of its remarkable 0.5 inch half-power PSF (Point Spread Function), which provides ten times the acuity of its nearest rival. Preliminary analysis of the December 18 data has yielded the following results: 1) a strong, high-latitude northern auroral 'hot spot,' which is relatively fixed near 60-70 degrees north latitude and 160-180 degrees system III longitude, and which pulsates with a period of about 40 minutes and has an average emitted power of about 1 GW; 2) relatively uniform low-latitude emissions, with a total power output of about 2 GW; 3) the first detection of x-ray emissions from the Io Plasma Torus, with a dusk/dawn brightness ratio of about 2.2 and a total emitted power of about 0.7 GW; and 4) the first detection of x-ray emissions from Io itself, with an emitted power of about 0.06 GW. These power estimates are based on an assumed emission wavelength of 653 eV (corresponding to the Lyman alpha line of OVIII ions), and is subject to revision as Chandra spectra of Jupiter are analyzed further. We will present these and other results from this unique data set.

Gladstone, G. R.↗

Carbon balance in bioregenerative life support systems: some effects of system closure, waste management, and crop harvest index

In Advanced Life Support (ALS) systems with bioregenerative components, plant photosynthesis would be used to produce O2 and food, while removing CO2. Much of the plant biomass would be inedible and hence must be considered in waste management. This waste could be oxidized (e.g., incinerated or aerobically digested) to resupply CO2 to the plants, but this would not be needed unless the system were highly closed with regard to food. For example, in a partially closed system where some of the food is grown and some is imported, CO2 from oxidized waste when combined with crew and microbial respiration could exceed the CO2 removal capability of the plants. Moreover, it would consume some O2 produced from photosynthesis that could have been used by the crew. For partially closed systems it would be more appropriate to store or find other uses for the inedible biomass and excess carbon, such as generating soils or growing woody plants (e.g., dwarf fruit trees). Regardless of system closure, high harvest crops (i.e., crops with a high edible to total biomass ratio) would increase food production per unit area and O2 yields for systems where waste biomass is oxidized to recycle CO2. Such interlinking effects between the plants and waste treatment strategies point out the importance of oxidizing only that amount of waste needed to optimize system performance. Published by Elsevier Science Ltd on behalf of COSPAR.

NASA Discipline Life Support Systems↗

Stress Analysis of B-52B and B-52H Air-Launching Systems Failure-Critical Structural Components

The operational life analysis of any airborne failure-critical structural component requires the stress-load equation, which relates the applied load to the maximum tangential tensile stress at the critical stress point. The failure-critical structural components identified are the B-52B Pegasus pylon adapter shackles, B-52B Pegasus pylon hooks, B-52H airplane pylon hooks, B-52H airplane front fittings, B-52H airplane rear pylon fitting, and the B-52H airplane pylon lower sway brace. Finite-element stress analysis was performed on the said structural components, and the critical stress point was located and the stress-load equation was established for each failure-critical structural component. The ultimate load, yield load, and proof load needed for operational life analysis were established for each failure-critical structural component.

Ko, William L.↗

Benchmark Data Set for Wheat Growth Models: Field Experiments and AgMIP Multi-Model Simulations.

The data set includes a current representative management treatment from detailed, quality-tested sentinel field experiments with wheat from four contrasting environments including Australia, The Netherlands, India and Argentina. Measurements include local daily climate data (solar radiation, maximum and minimum temperature, precipitation, surface wind, dew point temperature, relative humidity, and vapor pressure), soil characteristics, frequent growth, nitrogen in crop and soil, crop and soil water and yield components. Simulations include results from 27 wheat models and a sensitivity analysis with 26 models and 30 years (1981-2010) for each location, for elevated atmospheric CO2 and temperature changes, a heat stress sensitivity analysis at anthesis, and a sensitivity analysis with soil and crop management variations and a Global Climate Model end-century scenario.

climate change impact↗

Method Development for In-situ Detection of Latent Herpesvirus DNA from Saliva using Nanopore Sequencing

Research toward latent herpesvirus reactivation has been intensively addressed through Space Shuttle and International Space Station (ISS) investigations. This work has provided the understanding that persistent reactivation of herpesviruses from asymptomatic crew can be detected through viral shedding in saliva, urine, and blood. Occasionally, viral reactivation from the latency stage can pose a threat to crew health (clinical manifestation) before, during, and after flight missions. Furthermore, previous work detailing correlations with immunity indicate that monitoring viral reactivation could be implemented to assess potential immune dysfunction. While in-flight monitoring is desirable, there is no well-established procedure or method for real-time evaluations, and research to date has relied on postflight, ground-based analysis. The development of portable molecular technologies like the miniPCR™ (miniPCR Bio) thermal cycler and the MinION™ sequencer (Oxford Nanopore Technologies) have confirmed that real-time monitoring is possible in extreme and low resource environments. These devices, combined with simple sample preparation methods, have been used to demonstrate bacterial identification onboard the ISS, as well as rapid viral detection in remote locations on Earth. The work here builds upon previous molecular advancements onboard the ISS toward the development and validation of a spaceflight-compatible method for viral detection from crew samples. Several herpesviruses can be detected in saliva, which provides a non-invasive means to collect samples for monitoring. While the basis for this method lies in previous spaceflight investigations, key points for method optimization include DNA extraction from saliva, viral primer selection, and bioinformatic processes for data analysis. To increase viral yield, numerous DNA extraction methods have been evaluated and will be discussed in detail. For initial development and testing, varicella-zoster virus (VZV) is being targeted though open reading frame 51 and 63 (ORF51, ORF63), as the replication origin-binding protein is highly expressed during latency. Optimization of the thermal cycling parameters has resulted in the ability to test the entire process. The full method has been tested with both viral VZV DNA standards and saliva spiked with varying concentrations of VZV. Viral sequence data were mapped to the reference sequence using minimap2. Prior to mapping, DNA sequencing reads were filtered for length and quality, barcodes were removed, and alignment identity calculated. Following further assessments, statistics were compared across multiple sequencing experiments and are being used to determine the success of the protocols. Forward work will include the incorporation of herpes simplex virus 1 (HSV-1) and Epstein-Barr virus (EBV) primers as well as the validation of results to the terrestrial qPCR standard assay. Upon full validation of the developed method, saliva will be collected from 20 healthy subjects and spiked with viral DNA. These samples will be split and assayed with the MinION and standard qPCR assay.

Hang N Nguyen↗

EVEREST: Pixel Level Decorrelation of K2 Light Curves

We present EPIC Variability Extraction and Removal for Exoplanet Science Targets (EVEREST), an open-source pipeline for removing instrumental noise from K2 light curves. EVEREST employs a variant of pixel level decorrelation to remove systematics introduced by the spacecraft’s pointing error and a Gaussian process to capture astrophysical variability. We apply EVEREST to all K2 targets in campaigns 0–7, yielding light curves with precision comparable to that of the original Kepler mission for stars brighter than K(sub p) ≈ 13, and within a factor of two of the Kepler precision for fainter targets. We perform cross-validation and transit injection and recovery tests to validate the pipeline and compare our light curves to the other de-trended light curves available for download at the MAST High Level Science Products archive. We find that EVEREST achieves the highest average precision of any of these pipelines for unsaturated K2 stars. The improved precision of these light curves will aid in exoplanet detection and characterization, investigations of stellar variability, asteroseismology, and other photometric studies. The EVEREST pipeline can also easily be applied to future surveys, such as the TESS mission, to correct for instrumental systematics and enable the detection of low signal-to-noise transiting exoplanets. The EVEREST light curves and the source code used to generate them are freely available online.

Catalogs↗

Using Meteorological Data to Evaluate Worldwide PV Degradation Rates

Here we automate the process to enable the creation of world maps for specific PV durability metrics. The end goal is to create a tool for the creation of world maps predicting the sensitivity of modules to degradation to inform the development and utilization of module testing standards and to provide information to module designers. TMY (Typical Meteorological Year) Data was aggregated from sites around the world to render insight into factors contributing to the degradation of solar modules. The focus of aggregating data was to create a single dataset to work with utilizing Solar Irradiance values combined with Ambient Temperature, Relative Humidity, Wind Speed and Dew-Point Temperature.

14 SOLAR ENERGY↗

Mesoscale Modeling of Dislocation Cell Structure Evolution and Radiation-Induced Segregation in Additively Manufactured Austenitic Stainless Steel

Structural alloys under irradiation develop radiation-induced segregation (RIS) at point defect sinks, which lead to undesired changes in the alloy's properties. Additively manufactured austenitic stainless steels are expected to yield a distinct response to irradiation damage owing to their unique as-printed dislocation cell structure. In this talk, we present the development of a mesoscale model for dislocation cell structure evolution coupled with RIS using the MOOSE framework. The evolution of network dislocations within spatially distinct cells and cell walls are modeled using climb-mediated edge annihilation and generation processes. Starting with initial microstructures of as-printed non-equilibrium segregations at dislocation cell walls, our 2D and 3D simulations explore the effects of irradiation temperature, dose rate, dislocation sink bias, and specimen thickness on microstructure evolution. The results will be compared against experimental characterizations of in-situ and ex-situ ion-irradiated samples, and the implications of evolving cell structure on irradiation damage response will be discussed.

additive manufacturing↗

Modeling and control of flexible space platforms with articulated payloads

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Graves, Philip C.↗

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗

Theoretical-Numerical Study of Feasibility of Use of Winglets on Low Aspect Ration Wings at Subsonic and Transonic Mach Numbers to Reduce Drag

A numerical design study was conducted to assess the drag reduction potential of winglets installed on a series of low aspect ratio wings at a design point of M=0.8, C sub L=0.3. Wing-winglet and wing-alone design geometries were obtained for wings of aspect ratios between 1.75 and 2.67, having leading edge sweep angles between 45 and 60 deg. Winglet length was fixed at 15% of wing semispan. To assess the relative performance between wing-winglet and wing-alone configurations, the PPW nonlinear extended small disturbance potential flow code was utilized. This model has proven to yield plausible transonic flow field simulations for the series of low aspect ratio configurations selected. Predicted decreases in pressure drag coefficient for the wing-winglet configurations relative to the corresponding wing-alone planform are about 15% at the design point. Predicted decreases in wing-winglet total drag coefficient are about 12%, relative to the corresponding wing-alone design. Longer winglets (25% of the wing semispan) yielded decreases in the pressure drag of up to 22% and total drag of up to 16.4%. These predicted drag coefficient reductions are comparable to reductions already demonstrated by actual winglet designs installed on higher aspect ratio transport type aircraft.

Kuhlman, John M.↗

Absolute Calibration of the AXAF Telescope Effective Area

The prelaunch calibration of AXAF encompasses many aspects of the telescope. In principle, all that is needed is the complete point response function. This is, however, a function of energy, off-axis angle of the source, and operating mode of the facility. No single measurement would yield the entire result. Also, any calibration made prior to launch will be affected by changes in conditions after launch, such as the change from one g to zero g. The reflectivity of the mirror and perhaps even the detectors can change as well, for example by addition or removal of small amounts of material deposited on their surfaces. In this paper, we give a broad view of the issues in performing such a calibration, and discuss how they are being addressed in prelaunch preparation of AXAF. As our title indicates, we concentrate here on the total throughput of the observatory. This can be thought of as the integral of the point response function, i.e. the encircled energy, out ot the largest practical solid angle for an observation. Since there is no standard x-ray source in the sky whose flux is known to the -1% accuracy we are trying to achieve, we must do this calibration on the ground. we also must provide a means for monitoring any possible changes in this calibration from pre-launch until on-orbit operation can transfer the calibration to a celestial x-ray source whose emission is stable. In this paper, we analyze the elements of the absolute throughput calibration, which we call Effective Area. We review the requirements for calibrations of components or subsystems of the AXAF facility, including mirror, detectors, and gratings. We show how it is necessary to calibrate this ground-based detection system at standard man-made x-ray sources, such as electron storage rings. We present the status of all these calibrations, with indications of the measurements remaining to be done, even though the measurements on the AXAF flight optics and detectors will have been completed by the time this paper is presented. We evaluate progress toward the goal of making 1% measurements of the absolute x-ray flux from astrophysical sources, so that comparisons can be made with their emission at other wavelengths, in support of observations such as the Sunyaev-Zeldovitch effect, which can give absolute distance measurements independent of the traditional distance measuring techniques in astronomy.

Kellogg, E.↗

Dark Energy Survey Year 3 results: $w$CDM cosmology from simulation-based inference with persistent homology on the sphere

We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density thresholds. For the first time, we apply spherical persistent homology to galaxy survey data through the algorithm TopoS2, which is optimized for curved-sky analyses and HEALPix compatibility. Employing a simulation-based inference framework with the Gower Street simulation suite, specifically designed to mimic DES Y3 data properties, we extract topological summary statistics from convergence maps across multiple smoothing scales and redshift bins. After neural network compression of these statistics, we estimate the likelihood function and validate our analysis against baryonic feedback effects, finding minimal biases (under $0.3σ$) in the $Ω_\mathrm{m}-S_8$ plane. Assuming the $w$CDM model, our combined Betti numbers and second moments analysis yields $S_8 = 0.821 \pm 0.018$ and $Ω_\mathrm{m} = 0.304\pm0.037$-constraints 70% tighter than those from cosmic shear two-point statistics in the same parameter plane. Our results demonstrate that topological methods provide a powerful and robust framework for extracting cosmological information, with our spherical methodology readily applicable to upcoming Stage IV wide-field galaxy surveys.

Prat, J. [Nordita; Royal Inst. Tech., Sodertalje; ↗

Topological electronic properties of silicon

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. Further, This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a nodal-chain insulator. Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. Similar to nodal-chain semimetals, we find drumheadlike states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.

36 MATERIALS SCIENCE↗