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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Phase-based design of CO 2 capture, transport, and storage infrastructure via SimCCS 3.0

The design of optimal infrastructure is essential for the deployment of commercial and large-scale carbon capture and storage (CCS) technology. During the design process, it is important to consider CO 2 capture and storage locations and CO 2 transportation pipelines to minimize the total project cost. SimCCS, first introduced in 2009, is an integrated open-source tool to optimize CCS infrastructure. The core CCS infrastructure design problem in SimCCS is structured as a mixed-integer linear programming problem by selecting the optimal pipeline routes, searching CO 2 source capture and storage locations, and determining the corresponding CO 2 amounts to meet desired capture targets. Multiple important and practical features have been developed to the latest version of SimCCS, SimCCS 3.0 . One of these features is phase-based modeling which enables users to dynamically design the CCS infrastructure. We demonstrate the phased-based modeling capability using two CCS infrastructure optimization case studies. The results from these case studies reveal that the phase-based modeling capability in SimCCS is particularly useful to optimize the dynamic deployment of CCS projects.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene

Here, we introduce a multi-reward reinforcement learning (RL) approach to train a flexible bond-order potential (BOP) for 2D phosphorene based on ab initio training data sets. Our approach is based on a continuous action space Monte Carlo tree search algorithm that is general and scalable and presents an efficient multiobjective optimization scheme for high-dimensional materials design problems. As a proof-of-concept, we deploy this scheme to parametrize multiple structural and dynamical properties of 2D phosphorene polymorphs. Our RL-trained BOP model adequately captures the structure, energetics, transformation barriers, equation of state, elastic constants, and phonon dispersions of various 2D P polymorphs. We use this model to probe the impact of temperature and strain rate on the phase transition from black (α-P) to blue phosphorene (β-P) through molecular dynamics simulations. A decrease in critical strain for this phase transition with increase in temperature is observed, and the underlying atomistic mechanisms are discussed.

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

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Design of Phase-Change Thermal Storage Device in a Heat Pump for Building Electric Peak Load Shaving: Preprint

Replacing carbon-intensive fossil fuel heating systems with electric heat pumps powered by renewables is a promising approach to decarbonize the building sector. However, one of the technical barriers of this approach is the large scale of heat demand, which will put excessive stress on the electricity grid. Integrating thermal energy storage (TES) into the heating systems can help alleviate this problem, by shifting thermal load and thus shaving peaks in the building electric load. Therefore, it is critical to understand how to design a thermal storage device in a heat pump for peak load shaving. In this study, we developed a numerical model for a cascaded vapor compression heat pump system integrating a phase change thermal storage device. This novel system can control the net thermal charging and discharging rate of the TES independently from the building's thermal load, which allows for precise control of electric power use. In the current study, we controlled the system to shave building electric peak load during a cold winter morning, and to charge TES during the relatively warm afternoon while still providing space heating. We used the model to evaluate the system performance with and without peak shaving. We also investigated the effect of PCM transition Tt on the peak reduction and electric energy saving potentials. The results show that peak shaving scheme effectively reduces the peak electric power consumption during a predefined discharge time window. When comparing to the no shaving case, for PCM Tt = 10 degrees C, the peak electric load reduction is 23.5%. When comparing to an air-source heat pump with back up electric heater, as Tt increases from 0 to 20 degrees C, the peak reduction increases from 46.1% to 50.9%. Integrating PCM Tt = 10 degrees C with peak shaving leads to the 45.5% of electric energy saving, which is the highest among the three transition temperatures.

electric energy saving↗
DOE OSTI2020

Advanced Intra-Cycle Detection of Pre-Ignition Events through Phase-Space Transforms of Cylinder Pressure Data

The widespread adoption of boosted, downsized SI engines has brought pre-ignition phenomena into greater focus, as the knock events resulting from pre-ignitions can cause significant hardware damage. Much attention has been given to understanding the causes of pre-ignition and identify lubricant or fuel properties and engine design and calibration considerations that impact its frequency. This helps to shift the pre-ignition limit to higher specific loads and allow further downsizing but does not fundamentally eliminate the problem. Real-time detection and mitigation of pre-ignition would thus be desirable to allow safe engine operation in pre-ignition-prone conditions. This study focuses on advancing the time of detection of pre-ignition in an engine cycle where it occurs. Furthermore, phase space transforms through time-delay embedding of cylinder pressure and principal component analysis were applied to same-cycle detection of pre-ignition and shown to enable detection on the order of a crank degree earlier than deviation in cylinder pressure can be identified through direct statistical observation of the pressure data. Additionally, it appears that the deviation of the trajectory in phase space may offer the opportunity to extend this method to further extend the detection window and allow more time for mitigation actions to occur.

42 ENGINEERING↗
DOE OSTI2022

The cosmological moduli problem and naturalness

Nowadays, the cosmological moduli problem (CMP) comes in three parts: 1. potential violation of Big-Bang nucleosynthesis (BBN) constraints from late decaying moduli fields, 2. the moduli-induced gravitino problem wherein gravitinos are overproduced and their decays violate BBN or dark matter overproduction bounds and 3. the moduli-induced lightest SUSY particle (LSP) overproduction problem. Also, the CMP may be regarded as either a problem or else a solution to scenarios with dark matter over- or under-production. We examine the cosmological moduli problem and its connection to electroweak naturalness. We calculate the various two-body decay widths of a light modulus field into MSSM particles and gravitinos within general supersymmetric models. We include both phase space and mixing effects. We examine cases without and with helicity suppression of modulus decays to gravitinos (cases 1 & 2) and/or gauginos (cases A & B). For case B1, we evaluate regions of gravitino mass m 3/2 vs. modulus mass mΦ parameter space constrained by BBN, by overproduction of gravitinos and by overproduction of neutralino dark matter, along with connections to naturalness. For this case, essentially all of parameter space is excluded unless mΦ ≳ 2.5 × 10 3 TeV with mΦ< 2m 3/2 For a potentially most propitious case B2 with Φ decay to Higgs and matter turned off, then modulus branching fractions to SUSY and to gravitinos become highly suppressed at large m Φ . But since the modulus number density increases faster than the branching fractions decrease, there is still gross overproduction of neutralino dark matter. We also show that in this scenario the thermally produced gravitino problem is fixed by huge entropy dilution, but non-thermal gravitino production from moduli decay remains a huge problem unless it is kinematically suppressed with m Φ < 2m 3/2 . In a pedagogical appendix, we present detailed calculations of modulus field two-body decay widths.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A physics-driven Σ-Y atomization model for heavy-duty engine simulations

The atomization of a liquid jet is a multi-scale and multi-physics problem of interest for many engineering applications. Particularly, it drives the fuel-oxidizer mixing and dictates the efficiency of combustion engines. High-fidelity multi-phase simulations remain challenging due to the excessive computational cost required to capture all the atomization scales. Thus, atomization models are necessary to represent sub-grid liquid structures. Here, in this work, a modified Σ-Y model in the context of Eulerian-Lagrangian Spray Atomization (ELSA) is used to transport the surface area density of the spray. The model's predictive performance is assessed under various operating conditions relevant to heavy-duty engines using the Engine Combustion Network (ECN) Spray C and Spray D research-grade injectors. The classic droplet collision formulation of the Σ-Y model alone does not replicate the response of the measured spray surface area to changes in injector, ambient pressure, and injection pressure, requiring individual tuning of the model's parameters. Instead, a transition between dense and dilute spray breakup mechanisms is proposed in terms of the average droplet spacing. The collision breakup mechanism represents the dilute spray, whereas the droplet size in the dense spray is driven by a competition between the integral scale of turbulence and the balance between the turbulent kinetic energy and the surface energy of the droplets. Such an approach minimizes the requirements for model tuning. Moreover, the role of the constants of a compressible standard k-ε RANS model is assessed in the injector's internal flow and external spray simulation framework, and an updated set is proposed. The results are validated against x-ray radiography and Ultra-Small Angle X-ray Scattering (USAXS) data and highlight the predictive capabilities of the proposed physics-driven Σ-Y model, which is compatible with engine simulation turnaround times.

42 ENGINEERING↗
DOE OSTI2020

Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form

We propose a one-parameter family of low-dissipation centred numerical schemes for solving hyperbolic equations in conservative or non-conservative form, using finite volume or discontinuous Galerkin finite element methods. The new schemes spring out from the multi-dimensional FORCE method and are determined by a single parameter α ≥ 1. Given an increasing sequence of real numbers 1 ≤ α 1 < α 2 < . . . < α K , there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of Courant numbers 1 > c 1 > c 2 > . . . > c K > 0 and a decreasing sequence of corresponding numerical viscosity functions d 1 > d 2 > . . . > d K . For a given Courant number c k ≤ 1 there is a real number α k > 0 and a corresponding stable scheme with minimal numerical viscosity d k . The proposed schemes suit very well the family of high-order discontinuous Galerkin finite element methods and the recently proposed class of ADER-TR schemes, whose orders of accuracy define decreasing sequences of Courant numbers, as the order of accuracy increases. The centred methods of this paper are stable in 2D and 3D in the frame of simultaneous updating formulae, unlike other centred methods, such as 1D FORCE, which are not. Furthermore, the schemes are highly accurate for slowly-moving waves, which is precisely the kind of waves that traditional centred methods smear disastrously. Additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non-conservative form. Here, the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system, for the Euler equations in one and two space dimensions, and for the Baer-Nunziato equations for compressible two-phase flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Radiation portal monitor data file format for comprehensive background radiation monitoring

Radiation portal monitors (RPMs) are widely used at border security checkpoints to detect the presence of radioactive materials in people, vehicles, and cargo. Typically, RPM detection systems consist of two pillars equipped with gamma and neutron detectors. To improve detection efficiency, RPMs employ techniques such as a limited energy window, dynamic alarm thresholds, and lead shielding. However, without continuous monitoring of background radiation, signal interpretation can be compromised, because environmental factors and mechanical failures can cause fluctuations. Here, we introduce a daily file format that logs gamma background and neutron background radiation levels continuously over a 24 h period; this format is different from traditional formats that record data only when the RPM is active or occupied. The approach enables RPM operators and analysts to (1) identify and diagnose malfunctioning components, (2) adjust system settings to account for dynamic environmental factors, and (3) use the recorded data to characterize outer space phenomena. Continuous background reporting is essential for identifying issues such as faulty connections, voltage divider failures, and errors in background updates. Continuous background reporting also enables the detection of external influences, including nearby X-ray scanners, temperature fluctuations, rainfall, cosmic radiation, and lunar phase changes. These data files are designed to be easily evaluated and parsed using common tools, and a quick review by an expert is often sufficient for problem diagnosis. We anticipate that continuous background radiation monitoring and these new strategies will significantly improve the accuracy and reliability of RPM systems, reducing the rate of false alarms and enhancing overall system performance.

Background radiation monitoring↗
DOE OSTI2021

The Convective-To-Total Precipitation Ratio and the “Drizzling” Bias in Climate Models

Overestimation of precipitation frequency and duration while underestimating intensity, that is, the “drizzling” bias, has been a long-standing problem of global climate models. Here we explore this issue from the perspective of precipitation partitioning. We found that most models in the Climate Model Intercomparison Project Phase 5 (CMIP5) have high convective-to-total precipitation (PC/PR) ratios in low latitudes. Convective precipitation has higher frequency and longer duration but lower intensity than non-convective precipitation in many models. As a result, the high PC/PR ratio contributes to the “drizzling” bias over low latitudes. The PC/PR ratio and associated “drizzling” bias increase as model resolution coarsens from 0.5° to 2.0°, but the resolution's effect weakens as the grid spacing increases from 2.0° to 3.0°. Some of the CMIP6 models show reduced “drizzling” bias associated with decreased PC/PR ratio. Thus, more reasonable precipitation partitioning, along with finer model resolution should alleviate the “drizzling” bias within current climate models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Vacancies in graphene: an application of adiabatic quantum optimization

Quantum annealers have grown in complexity to the point that quantum computations involving a few thousand qubits are now possible. In this paper, with the intentions to show the feasibility of quantum annealing to tackle problems of physical relevance, we used a simple model, compatible with the capability of current quantum annealers, to study the relative stability of graphene vacancy defects. By mapping the crucial interactions that dominate carbon-vacancy interchange onto a quadratic unconstrained binary optimization problem, our approach exploits the ground state as well as the excited states found by the quantum annealer to extract all the possible arrangements of multiple defects on the graphene sheet together with their relative formation energies. Furthermore, this approach reproduces known results and provides a stepping stone towards applications of quantum annealing to problems of physical–chemical interest.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Per-Phase and 3-Phase Optimal Coordination of Directional Overcurrent Relays Using Genetic Algorithm

Penetration of the power grid by renewable energy sources, distributed storage, and distributed generators is becoming increasingly common. Increased utilization of these distributed energy resources (DERs) has given rise to additional protection coordination concerns, particularly where they are utilized in an unbalanced manner or where loading among phases is unbalanced. Digital relays such as the SEL-751 (produced by Schweitzer Engineering Laboratories, Pullman, WA, USA) series have the capability of being set on a per-phase basis. This capability is underutilized in common practice. Additionally, in optimization algorithms for determining relay settings, the time-overcurrent characteristics (TOCs) of relays are generally not treated as variables and are assigned before running the optimization algorithm. In this paper, TOC options themselves are treated as discrete variables to be considered in the optimization algorithm. A mixed integer nonlinear programming problem (MINLP) is set up where the goal is to minimize relay operating times. A genetic algorithm (GA) approach is implemented in MATLAB where two cases are considered. In the first case, the TOC and Time dial setting (TDS) of each relay is set on a three-phase basis. In the second case, per-phase settings are considered. Relay TDSs and TOCs are both considered as simultaneous discrete control variables. Despite the stochastic nature of using per-phase settings for unbalanced systems is found to generally allow for shorter operating times. However, for relatively balanced systems, it is best to use three-phase settings if computation time is of importance.

Matthews, Ronald C.↗
DOE OSTI2020

Compositional phase stability of correlated electron materials within DFT+DMFT

Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics, requiring precise computations of total energies. In this work, we employ the density functional theory plus dynamical mean-field theory (DFT+DMFT) formalism to address local correlations due to transition metal $\textit{d}$ electrons on compositional phase stability in the prototype rechargeable battery cathode material Li x CoO 2 , and detailed comparisons are made with the simpler DFT+$\textit{U}$ approach (i.e., the Hartree-Fock solution of the DMFT impurity problem). Local interactions are found to strongly impact the energetics of the band insulator LiCoO 2 , most significantly via the $E_g$ orbitals, which are partially occupied via hybridization with $\textit{O p}$ states. We find CoO 2 and Li 1/2 CoO 2 to be moderately correlated Fermi liquids with quasiparticle weights of 0.6–0.8 for the $T_{2g}$ states, which are most impacted by the interactions. Further, as compared to DFT+$\textit{U}$, DFT+DMFT considerably dampens the increase in total energy as $\textit{U}$ is increased, which indicates that dynamical correlations are important to describe this class of materials despite the relatively modest quasiparticle weights. Unlike DFT+$\textit{U}$, which can incorrectly drive Li x CoO 2 toward spurious phase separating or charge-ordered states, DFT+DMFT correctly captures the system's phase stability and does not exhibit a strong charge-ordering tendency. Most importantly, the error within DFT+$\textit{U}$ varies strongly as the composition changes, challenging the common practice of artificially tuning $\textit{U}$ within DFT+$\textit{U}$ to compensate the errors of Hartree-Fock. DFT+DMFT predicts the average intercalation voltage decreases relative to DFT, opposite to the result of DFT+$\textit{U}$, which would yield favorable agreement with experiment in conjunction with the overprediction of the voltage by the strongly constrained and appropriately normed DFT functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum Alternating Operator Ansatz (QAOA) Phase Diagrams and Applications for Quantum Chemistry

Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation is an alternative that does not require noisy optimization of parameters. Beyond adiabatic schedules, QAOA is an important method for optimization problems. In this work we modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. This modification applies physical insights used in classical approximations to construct suitable QAOA operators and initial state. We find robust qualitative behavior for QAOA as a function of the number of steps and size of the parameters, and demonstrate this behavior also occurs in standard QAOA applied to combinatorial search. To this end we introduce QAOA phase diagrams that capture its performance and properties in various limits. In particular we show a region in which non-adiabatic schedules perform better than the adiabatic limit while employing lower quantum circuit depth. We further provide evidence our results and insights also apply to QAOA applications beyond chemistry.

Kremenetski, Vladimir↗
DOE OSTI2021

Adaptive machine learning for time-varying systems: low dimensional latent space tuning

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗
DOE OSTI2024

Assessment of Storm-Associated Precipitation and Its Extremes Using Observational Data Sets and Climate Model Short-Range Hindcasts

Heavy precipitation, often associated with weather phenomena such as tropical cyclones, extratropical cyclones (ETCs), atmospheric rivers (ARs), and mesoscale convective systems (MCSs), can cause significant socio-economic loss. Here, in this study, we apply atmospheric feature trackers to quantify the contributions of these storm types in observational data sets and climate model short-range hindcasts. We generate a global hourly storm data set at 0.25° spatial resolution covering 2006–2020, based on the tracking results from TempestExtremes and Python FLEXible object TRacKeR. Our analyses show that these four storm types account for 67% of global annual mean precipitation and 82% of top 1% precipitation extremes, with MCSs mainly over the tropics, and ARs and ETCs over the midlatitudes. The percentage of precipitation contributions from these storms also show strong seasonality over many geographical locations. We further apply the tracking results to the Energy Exascale Earth System Model (E3SM) short-range hindcasts and evaluate how well these storms are simulated. The evaluation show that E3SM, with ∼1° resolution, significantly underestimates storm-associated precipitation totals and extremes, especially for MCSs in the tropics. Our analysis also suggests that model fails to capture the correct mean diurnal phases and amplitude of MCS precipitation. This phenomenon-based approach provides a better understanding of precipitation characteristics and can lead to enhanced model evaluation by revealing underlying problems in model physics related to precipitation processes associated with the heavy-precipitating storms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Squaring the fermion: The threefold way and the fate of zero modes

In this work, we investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension, we establish three fundamental no-go theorems that prove the absence of parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting noninteracting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of noninteracting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗