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All sources NASA NTRS DOE OSTI

DOE OSTI2024

Multi-Source Machine Learning and Thermoplastics Enhanced Aerostructure Manufacturing (mTEAM)

RTX Technology Research Center (RTRC), together with Collins Aerospace (Collins) and Oak Ridge National Laboratory (ORNL) has developed an Artificial Intelligence (AI) / Machine Learning (ML) guided solution to advance the manufacturing and assembly of high performance and lightweight thermoplastic composite (TPC) aerospace products. The solution aims to lower risk, cost and lead time for induction heating based welding and consolidation processes for TPC structure. The cost and lead time of part and material specific process development for induction welding (IW) and induction consolidation will be reduced by replacing traditional empirical methods with optimization methods that merge AI/ML and physics-based process simulations and process experiments with sensing and controls. TPC-IW process development is empirical in nature, and uncertainties in material & process behavior exist near & far from the induction coil. Physics-based simulations can be leveraged directly for process optimization but can be too computationally expensive to run in high fidelity and real time to do robust process optimization. The key impact of successful TPC induction consolidation and welding is cost & lead time reduction for part & material specific consolidation and welding recipes. This is an enabler for more rapid deployment of TPC structures via joining assembly, which can reduce energy & cost intensive usage of autoclaves & ovens. The solution aimed to advance the U.S. Department of Energy’s interests in using thermoplastics and automation in composite manufacturing for improvement of products for existing markets via increased production speeds, reduced costs, and lowered use of energy. Welded TPC structures can offer significant weight & energy savings for high-value commercial aerospace & industrial applications compared to metal & thermoset composite structures assembled by mechanical fastening and/or adhesive bonding. The project was organized into two Budget Periods. Budget Period 1 (BP1) was 15 months and its goal was to perform ML process optimization framework development & deployment on lab-coupon aerostructure components. A Go/No-Go Review was performed at the end of BP1 to verify fulfilment of key tasks & milestones to justify a Go Decision to move into the next Budget Period. Budget Period 2 (BP2) was 12 months and its goal was the deployment of the ML framework for ML process optimization of pilot industrial scale aerostructure components. The overall project aim was to develop & demonstrate ML-enhanced modeling framework that learns process-property mapping from multiple data sources at different fidelities. During BP1, the team accomplished key tasks & milestones to demonstrate the concept of multi-source ML for TPC aerostructure consolidation and assembly. First, the team completed documentation of induction based TPC heating requirements including baseline metrics to compare measured results against. Next the team completed demonstration of data generation from physics-based simulations for ML surrogate model generation and demonstrated the integration of physics-based simulation data into multi-source AI/ML algorithms. In parallel, the team established the lab-coupon scale induction welding system and completed a process to label and reduce generated data from physics-based simulation and experiments for ML surrogate models to enable multi-source ML model training & testing. To complete BP1, the team integrated physics-based simulation data and experimental data into multi-source ML algorithms. This was based on the team completing ML deployment of the induction welding on a lab system at RTRC and AI/ML deployment on existing induction welding line at Collins. ORNL visited both Collins and RTRC sites to witness the TPC induction welding process. Then, ORNL designed and constructed a new version of their vision-based sensing system better adapted to acquire process signals of the TPC induction welding process for process anomaly and defect detection. In BP2, the team accomplished key tasks & milestones to scale up multi-source ML for TPC aerostructure consolidation and assembly from the lab-coupon scale to the pilot-industrial scale. In BP2, the team demonstrated real time anomaly & defect detection via experiments performed by ORNL & RTRC. The team completed ML-optimization heating trials for TPC induction consolidation at Collins, and the team confirmed pilot industrial scale experimental data from Collins was compatible with the developed ML pipeline from RTRC. The team completed sub-element scale ML process optimization demonstration at RTRC, where the team leveraged RTRC’s robotic TPC welding setup to de-risk the ML process optimization by performing ML analysis of recorded temperatures to account for complex part features. Then, the team applied its ML-derived control strategies and ML process optimization framework at Collins to the pilot-industrial scale on a demo skin-stiffener part representative of a nacelle aerostructure fan cowl section. The key innovation is the AI/ML framework enabling effective process development of high performance, lightweight, energy efficient TPCs for composite aircraft structures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Magnetization distribution in Cu 0.6 Mn 2.4 Ge 2 ferromagnet from polarized and non-polarized neutron powder diffraction aided by density-functional theory calculations

The crystal structure and magnetic properties of Cu 0.6 Mn 2.4 Ge 2 have been re-investigated by a combination of extensive magnetic measurements and neutron scattering experiments, aided by electronic structure calculations. The material is found to be a soft ferromagnet with the ordering temperature T C = 316 K. The magnetocaloric effect evaluated from field-dependent magnetization isotherms is equal to 1.2 J/(kg·K) and 2.5 J/(kg·K) under the maximum applied magnetic field of 2 T and 5 T, respectively. The compound crystallizes in the hexagonal space group P6 3 /mmc. A complex structural disorder necessitated testing of several disorder models against the results of non-polarized and polarized neutron scattering experiments and magnetization measurements. Simulations at the density-functional theory level were also performed to identify the most robust solution that properly described the data observed. The final magnetic structure model reveals non-equal magnetic moments on the Mn1 and Mn2 atoms (2.29(9) µ B and 2.7(1) µ B , respectively) and the presence of vacancies and minor Cu substitution defects in both Mn sites. The work demonstrates how the non-polarized and polarized neutron scattering methods can be combined with electronic structure calculations to establish the microscopic structure of magnetic materials with complex crystallographic disorder.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Modeling of transient heat pipe operation

Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.

Colwell, G. T.↗

DOE OSTI2021

Phase Transformation Mechanism of Amorphous Calcium Phosphate to Hydroxyapatite Investigated by Liquid-Cell Transmission Electron Microscopy

Crystallization via phase transformation of a metastable precursor is a ubiquitous and effective strategy used by living systems to direct the growth of crystalline nanomaterials with remarkable functional properties. However, determining the exact process by which transformation occurs at the nanoscale is a difficult challenge. In this work, the recrystallization process of amorphous calcium phosphate (ACP) to hydroxyapatite (HAP) is explored by liquid-cell transmission electron microscopy. The effect of confinement in the liquid-cell is found to increase the size of ACP nanoparticles. In the presence of Mg 2+ , these large ACP nanoparticles transform to HAP by first dissolving from the interior to create a hollow structure, after which HAP forms preferentially on the surface and then subsequently in the bulk solution. We propose that the preferential dissolution within ACP particles is due to a change in the structure and/or chemistry of the ACP surface, likely associated with dehydration before crystallization of HAP. These results imply an important role of the confined environment of the liquid-cell in regulating the size of ACP particles, which then affects the surface structure and the detailed dissolution–recrystallization pathway. Moreover, we stress the key role of Mg 2+ in controlling HAP formation by stabilizing ACP via reduction in ACP solubility. This work provides a better understanding of the roles of additives and confinement during the phase transformation of ACP to HAP through dissolution and recrystallization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1988

The Calvin 28 cryptoexplosive disturbance, Cass County, Michigan: Evidence for impact origin

The Calvin 28 cryptoexplosive disturbance is an isolated, nearly circular subsurface structure of Late Ordovician age in southwestern Michigan. The structure is defined by 107 wells, is about 7.24 km in diameter and consists of a central dome, an annular depression and an encircling anticlinal rim. Seismic and geophysical well log data confirm that an intricate system of faults and structural derangement exists within the structure. Deformation decreases with depth and distance from the structure. U.S.G.S. topographic maps and aerial imagery show the structure is reflected as a subtle surface topographic rise controlling local drainage. Igneous or diapiric intrusion and solution collapse are rejected as possible origins for Calvin 28 on the basis of stratigraphic, structural and geophysical evidence. A volcanic origin is inconsistent with calculated energy requirements and an absence of igneous material. Although shock-metamorphic features are unidentified, microbreccias occur in deep wells that penetrate the structure. Morphology and structural parameters support an impact origin.

Milstein, Randall L.↗

DOE OSTI2024

Electromagnetic entrapment in gravity

Abstract We derive specific properties of electromagnetism when gravitational effects are not negligible and analyze their impact on new physics at the horizons of black holes. We show that a neutral configuration of charges in a region of high redshift, characterized by a largeg tt , produces a highly localized electromagnetic field that vanishes just beyond that region. This phenomenon implies the existence of extensive families of spacetime structures generated by electromagnetic degrees of freedom that are as compact as black holes. We construct neutral bound states of extremal black holes in four dimensions and in five dimensions, where one direction is compact. These geometries are indistinguishable from a neutral black hole, referred to asdistorted Schwarzschild, except in an infinitesimal region near its horizon where the entrapped electromagnetic structures start to manifest. The five-dimensional solutions satisfy various criteria for describing black hole microstructure: they increase in size with the Newton constant, are as compact as the Schwarzschild black hole, and have an entropy that scales likeM 2 .

Physics↗

DOE OSTI2024

Zero modes of massive fermions delocalize from axion strings

Massless chiral excitations can arise from the interactions between a fermion and an axion string, propagating along the string and allowing it to superconduct. The properties of these excitations, or zero modes, dictate how the string interacts with light and can thus have important phenomenological consequences. In this paper, we add a nowhere-vanishing Dirac mass for the fermion in the usual model of axion electrodynamics. We find that the zero modes exhibit an interesting phase structure in which they delocalize from the string’s core as the mass increases, up until a critical value past which they disappear. We study this structure from an analytic perspective, with explicit numerical solutions, and via anomaly inflow arguments. Finally, we derive the two-dimensional effective theory of the zero mode and its interactions with the four-dimensional gauge field and show how this effective theory breaks down as the zero modes delocalize.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Gas-solid reaction-based selective lithium leaching strategy for efficient LiFePO 4 recycling

As the electric-vehicle market continues to expand, LiFePO 4 (LFP) batteries, valued for their intrinsic safety and cost-effectiveness, are being increasingly utilized. However, this widespread adoption highlights the urgent need for innovative and environmentally friendly recycling methods for spent LFP batteries due to their relatively low material value and the environmental challenges associated with traditional recycling processes. Here, in this study, we present a novel selective lithium leaching technique that involves a gas–solid reaction with chlorine gas. This method achieves a remarkable leaching efficiency of 99.8 % and a selectivity of 98.8 % at 200 °C within just 10 min, without generating acidic wastewater. The resulting LiCl solution was successfully converted into Li 2 CO 3 with an excellent purity of 99.5 %, while producing NaCl solution as the only byproduct. Notably, the olivine structure of the LFP was preserved as FePO 4 after lithium leaching. The regenerated LFP demonstrated excellent performance, retaining 94.1 % of its capacity after 150 cycles, while the lithium-leached FePO 4 delivered a reversible capacity exceeding 150 mAh/g. This approach not only enhances the efficiency of LFP recycling but also paves the way for more sustainable battery technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Two-layer transient heat transfer using impulse response methods

Solutions to the inverse heat conduction problem (IHCP) are methods that can be used to quantify surface heat flux in multi-layer materials for components in which there are limited subsurface (internal) temperature measurements, such as coated components. A critical consideration is to capture high frequency fluctuations using a practical heat flux sensor. To that end, this paper highlights key parameters for calculating accurate surface heat transfer. Specifically, this research extends the available solutions to the IHCP for multi-substrate structures through an impulse response methodology. The sensitivity of the impulse method was quantified with respect to practical measurements. Further, when compared to the inverse case, the impulse method resulted in lower errors when calculating surface heat flux over a range of conditions. Overall, this work provides a foundation for deducing heat flux from a subsurface heat flux sensor while maintaining a high-frequency response.

42 ENGINEERING↗

DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Interface-engineered (AlMnCoNiZn) 3 O 4 @PPy nanocomposites for superior lithium storage: Mechanism and performance

The practical application of graphite anodes in lithium-ion batteries (LIBs) is constrained by low specific capacity (372 mAh g -1 ) and sluggish kinetics. Here, to address these limitations, our present study focuses on high-entropy oxides (HEOs), which offer high theoretical capacity and structural stability. We synthesized spinel-structured (AlMnCoNiZn) 3 O 4 nanoparticles via a solution combustion method and fabricated an (AlMnCoNiZn) 3 O 4 @polypyrrole (PPy) nanocomposite through in-situ polymerization. Our electrochemical tests demonstrate that the PPy modification significantly enhances performance. While the pristine (AlMnCoNiZn) 3 O 4 delivered 445 mAh g −1 after 100 cycles at 100 mA g −1 and 350 mAh g −1 after 1000 cycles at 1000 mA g −1 , the (AlMnCoNiZn) 3 O 4 @PPy composite achieved 695 mAh g −1 after 100 cycles and maintained 675 mAh g −1 after 1000 cycles. Furthermore, the composite improved rate capacity at 1000 mA g −1 from 211 mAh g −1 to 403 mAh g −1 . This work highlights how conductive and flexible polymer modifications can dramatically improve the electrochemical properties of HEOs. The developed (AlMnCoNiZn) 3 O 4 @PPy composite provides a promising direction for designing advanced anodes to meet next-generation energy storage demands.

Anodes material↗

DOE OSTI2020

Chain flexibility and glass transition temperatures of poly(n-alkyl (meth)acrylate)s: Implications of tacticity and chain dynamics

The relationship between chain microstructure and glass transition temperature (T g ) is complicated for poly(alkyl methacrylate)s and poly(alkyl acrylate)s. Despite intensive studies, relationships between the structures of these polymers and their properties, including solution characteristics and T g , are still controversial. Solution properties, chain conformations, including Flory's characteristic ratio (C ∞ ), persistence length (l p ), and chain diameters, and T g are reported for series of poly(n-alkyl acrylate)s and poly(n-alkyl methacrylate)s having alkyl side chain lengths (n) ranging from 1 to 10 carbons in length, with uniform and well-characterized tacticities. Chain flexibilities of both series of polymers decrease as n increases, reflecting increased hindrances to rotation about backbone bonds as side chains become longer. Conversely, the T g s for both series of polymers decrease substantially as n increases, reflecting the greater side chain mobilities of long alkyl substituents. For shorter alkyl chain lengths, T g s for the poly(n-alkyl acrylate)s are much lower than for the corresponding poly(n-alkyl methacrylate)s, a difference which has been attributed in the past to the presumed reduced chain flexibility of polymethacrylates due to the presence of the α-methyl substituent. However, contrary to such expectations, C ∞ and l p values for these two series of polymers are nearly identical at a given n value, except for the longest n-alkyl substituents. Instead, the differences in T g may be attributed to the differences in tacticity of the two series – almost ideally atactic for the poly(n-alkyl acrylate)s but high in syndiotacticity for the poly(n-alkyl methacrylate)s. The T g s for the two series of polymers approach that of polyethylene at longer alkyl chain lengths. In addition, the effects of tacticity and chain dynamics on C ∞ , l p , and T g of poly(methyl methacrylate) is discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Improved Accuracy in Semi-Experimental Structure Determination by Resolving Problems Associated with Rotation of Principal Inertial Axes of Isotopologues: Structures of 1,3-Oxazole ( c -C 3 H 3 NO)

The rotational spectrum of the normal isotopologue of 1,3-oxazole (c-C 3 H 3 NO) was observed from 43 to 750 GHz. Over 3900 transitions for the ground vibrational state are measured, assigned, and least-squares fit to sextic centrifugally distorted-rotor Hamiltonians. The measured frequencies and resulting spectroscopic constants from this extended spectral range, combined with previous measurements of the nuclear quadrupole coupling constants, will facilitate astronomical searches for oxazole across the majority of the range of modern radiotelescopes. Spectra for a set of 30 oxazole isotopologues, which include multiple isotopic substitutions of each atom, are used to determine the first semi-experimental equilibrium ($r$$^{SE}_{e}$) structure and semi-experimental substitution structure ($r$$^{SE}_{e}$), each using CCSD(T) computed values for the vibration–rotation interaction and electron-mass corrections. The large number of isotopologues, including 21 isotopologues observed for the first time, and the redundant substitutions of each atom provide sufficient spectroscopic information to determine the $r$$^{SE}_{e}$ structure with the expected high level of accuracy and precision (0.0001 or 0.0002 Å in bond distances and 0.013 to 0.025° in bond angles). In the course of this study, we analyzed a known issue for some $r$$^{SE}_{e}$ structure determinations of near-oblate asymmetric tops in which inclusion of individual isotopologues degrades the structure determination. We demonstrate that this problem primarily arises from the difference in the values of the computed vibration–rotation interaction corrections as evaluated at the computed re geometry vs the $r$$^{SE}_{e}$ geometry of the “real” molecule. Our solution to this problem substantially improves the $r$$^{SE}_{e}$ structure of oxazole and likely can be generalized to many other molecules.

Chemical structure↗

DOE OSTI2025

Side Chain Engineering of Near-IR Aza-BODIPY Dyes Enables Processable Films with High Hole Mobility in Diodes

Boron chelated azadipyrromethene (Aza-BODIPY) derivatives are promising candidates for near-infrared optoelectronic applications due to their tunable absorption, electron-deficient core, and strong π-conjugation. Here, in this work, we synthesized and studied a series of 1-naphthylethynyl-substituted aza-BODIPY molecules featuring hexyl or hexyloxy solubilizing groups at either the proximal or the distal phenyl positions. These substitutions were designed to improve the solubility, film formation, and optoelectronic properties. We found that solubilizing groups not only enabled uniform solution-processed films but also fine-tuned key properties, such as absorption onset, oxidation potential, and energy levels. Charge transport analysis showed consistently high hole mobilities (∼10 –3 cm 2 /V s) across all substituted derivatives when CuI was used as the hole transport layer, regardless of film morphology. In contrast, electron mobilities tended to be low and inconsistent, partly because of the relatively poor-quality films on the ZnO electron transport layer. Overall, we have shown that solubilizing groups enable film solution-casting and can fine-tune the properties of these near-infrared aza-BODIPY derivatives.

36 MATERIALS SCIENCE↗

DOE OSTI2022

PplD is a de-N-acetylase of the cell wall linkage unit of streptococcal rhamnopolysaccharides

The cell wall of the human bacterial pathogen Group A Streptococcus (GAS) consists of peptidoglycan decorated with the Lancefield group A carbohydrate (GAC). GAC is a promising target for the development of GAS vaccines. In this study, employing chemical, compositional, and NMR methods, we show that GAC is attached to peptidoglycan via glucosamine 1-phosphate. This structural feature makes the GAC-peptidoglycan linkage highly sensitive to cleavage by nitrous acid and resistant to mild acid conditions. Using this characteristic of the GAS cell wall, we identify PplD as a protein required for deacetylation of linkage N-acetylglucosamine (GlcNAc). X-ray structural analysis indicates that PplD performs catalysis via a modified acid/base mechanism. Genetic surveys in silico together with functional analysis indicate that PplD homologs deacetylate the polysaccharide linkage in many streptococcal species. We further demonstrate that introduction of positive charges to the cell wall by GlcNAc deacetylation protects GAS against host cationic antimicrobial proteins.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Surface-mediated spontaneous emulsification of the acylated peptide, semaglutide

Acylated peptides composed of glucagon-like peptide-1 receptor agonists modified with a fatty acid side chain are an important class of therapeutics for type 2 diabetes and obesity but are susceptible to an unusual physical instability in the presence of hydrophobic surfaces, i.e., spontaneous emulsification, also known as ouzo formation in practice. In this work, light scattering, small-angle X-ray scattering, and circular dichroism measurements are used to characterize the physical properties of the semaglutide colloidal phase, including size distribution, shape, secondary structure, internal structure, and internal composition, as a function of solution physico-chemical conditions. The existence and size of the colloids formed are successfully predicted by a classical Rayleigh model, which identifies the parameters controlling their size and formation. Colloid formation is found to be catalyzed by hydrophobic surfaces, and formation rates are modeled as an autocatalytic reaction, enabling the formation of a master curve for various surfaces that elucidates the mechanism. Surfaces differ due to differences in surface wettability, which can be correlated with Hansen solubility parameters. This work provides insights into this unusual colloidal phenomenon and guides the peptide synthesis process and drug product formulation in the pharmaceutical industry.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Self-organized patterns at the plasma–liquid anode interface in a helium glow discharge: temporal development and mechanisms

Self-organization at the plasma–liquid anode interface is a commonly observed phenomenon for atmospheric pressure glow plasmas, resulting in patterns with distinctive shapes such as circular ring, star-shaped, and gear-like structures, depending primarily on the discharge current and solution conductivity. Recent studies have shown that the electrode gap distance, solute used for liquid anode solution, and gas composition can also significantly impact pattern formation. Nonetheless, an overarching model or explanation of the key underlying mechanisms consistent with all experimentally observed trends is not yet reported. We propose a key underlying mechanism enabling pattern formation motivated by a detailed parametric study of pattern formation complemented by the temporal development of patterns and consistent with all observed trends. Pattern formation was observed to be on a time scale of 100 μs, similar to the time scales of gas heating and evaporation. It was found that a minimum water evaporation rate of (3.5 ± 0.5) × 10 –6 kg s –1 and reduced electric field in the positive column of 16.6 ± 0.4 Td is required for pattern formation in the investigated cases irrespective of solution conductivity and gas composition for NaCl solutions. Nonetheless, the presence of cations for which the corresponding metal atom has a low ionization energy was identified as a necessary condition for pattern formation. Furthermore, the reported results suggest that the presence of a small amount of metal atoms in the gas phase with low ionization energy enhances the overall ionization rate in the near anode region which triggers pattern formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Homotopy characterization of non-Hermitian Hamiltonians

We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called “point-gap” and “line-gap” schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from $\mathbb{Z}$ winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups $\mathbb{Z}_n$ (rather than $\mathbb{Z}$ Chern number). Finally, we interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗