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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Tailoring the Gating Effect of Organic Cage via a Porous Liquid Approach

Porous liquids (PLs) represent a new frontier in material design combining the merits of solid porous host and liquid phase in gas separation and catalysis. Herein, the PL construction approach is harnessed to tailor the gating effect of organic cages toward enhanced gas separation. A type-II fluorinated PL (F-PL) is developed via liquifying a fluorinated organic cage (F-cage) by a fluorinated ionic liquid (F-IL). The F-cage is featured by a small window size (≈5.1 Å), high surface area, good stability under highly ionic conditions, and abundant fluorine moieties. The F-IL possesses high steric hindrance (bulky cation) and structure similarity with the F-cage (fluorinated alkyl chain in the anion). The existing status structure integrity of F-cage in F-IL upon F-PL formation is illustrated via spectroscopy and X-ray-based techniques. The existence of rigid voids in F-PL is illustrated by positron annihilation lifetime spectroscopy (PALS) and the improved gas uptake capacity than F-IL via pressure-swing CO 2 uptake isotherms (0–40) bar. Further, the comparison of the gas uptake behavior (CO 2 , N 2 , CH 4 , and Xe) of F-PL and F-cage, combining the computational simulation, highlights that the PL construction can be leveraged to tune the window size of porous scaffolds, leading to enhanced gas selectivity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Investigating the effect of heterogeneities across the electrode|multiphase polymer electrolyte interfaces in high-potential lithium batteries

Polymer electrolytes hold great promise for safe and high-energy batteries comprising solid or semi-solid electrolytes. Multiphase polymer electrolytes, consisting of mobile and rigid phases, exhibit fast ion conduction and desired mechanical properties. However, fundamental challenges exist in understanding and regulating interactions at the electrode|electrolyte interface, especially when using high-potential layered oxide active materials at the positive electrode. Here we demonstrate that depletion of the mobile conductive phase at the interface contributes to battery performance degradation. Molecular ionic composite electrolytes, composed of a rigid-rod ionic polymer with nanometric mobile cations and anions, serve as a multiphase platform to investigate the evolution of ion conductive domains at the interface. Chemical and structural characterizations enable the visualization of concentration heterogeneity and spatially resolve the interfacial chemical states over a statistically significant field of view for buried interfaces. We report that concentration and chemical heterogeneities prevail at electrode|electrolyte interfaces, leading to phase separation in polymer electrolytes. In conclusion, understanding the hidden roles of interfacial chemomechanics in polymer electrolytes enables us to design an interphase tailoring strategy based on electrolyte additives to mitigate the interfacial heterogeneity and improve battery performance.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lattice vacancy migration barriers in Fe-Ni alloys, and an indication as to why Ni atoms diffuse slowly: A first-principles study

Lattice vacancy migration barriers in ferromagnetic Fe 𝑥 ⁢Ni 1−𝑥 alloys (0.4 ≤ 𝑥 ≤ 0.6) are accurately quantified within the framework of ab initio electronic structure calculations using the nudged elastic band (NEB) method. Both the atomically disordered (A1) fcc phase, as well as the atomically ordered, tetragonal L⁢1 0 phase—which is under consideration as a material for a rare-earth-free gap magnet for advanced engineering applications—are investigated. Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, we find that Ni-vacancy interchanges encounter significantly higher energetic barriers than do Fe-vacancy interchanges. We contend that this aspect is a key factor in determining the differences in mobility between Fe and Ni atoms in this ferromagnetic alloy. Moreover, we are able to interpret these findings in terms of the ferromagnetic alloy's underlying spin-polarized electronic structure. Specifically, we report a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarization around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. These results give atomic-scale insight into the longstanding experimental observation that Ni exhibits remarkably slow atomic diffusion in Fe-Ni alloys.

density functional theory↗
DOE OSTI2025

Subsurface fluvial sediments beneath InSight on Mars from geophysical constraints

Subsurface structure investigation on Mars is crucial for understanding its geological evolution and past hydrological conditions. Elysium Planitia (EP), located near the hypothesized ancient ocean shorelines, could contain clues for past water activity and paleoclimate. Here we present better-constrained subsurface models beneath InSight extending to ~800 m depth, obtained from joint inversion of seismic and seismoacoustic coupling data, and use the well-resolved subsurface structure to explore the lithological profile through rock physics models. The derived subsurface lithology agrees well with local geological context and exhibits a shallow 60-m-thick low-rigidity layer consistent with hydrated sedimentary materials. Despite possible contributions of aeolian and volcanic deposits, we favor the interpretation that the low-rigidity layer originated from fluvial activity in EP during the Hesperian or Hesperian-to-Amazonian epoch, as supported by adjacent paleo-shoreline morphology observations. These results hint at a period of warmer paleoclimate at low latitudes, possibly during high-obliquity phases of Mars’ rotational axis.

58 GEOSCIENCES↗
DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗
DOE OSTI2025

Chemically and mechanically recyclable polyester-based multilayer plastics

Approximately 100 million tons of multilayered plastics (MLPs) are produced each year worldwide but are not recycled due to their complex structure. Here, this work aims to design polyester-based multilayer plastics (80–100 % polyester) that provide barrier performance comparable to typical 9–12-layer commercial MLPs, while also enabling both chemical recycling (back to parent monomer) and mechanical recycling (grind-and-melt reprocessing). Such dual recyclability is not achievable with non-polyester multilayers, such as all-polyolefin systems. Furthermore, we emphasize how the multilayer architecture was tailored to balance barrier properties, mechanical integrity, and end-of-life recyclability for both flexible and rigid packaging applications. Two main categories of polyester-based MLPs are reported; in the first type, poly(butylene adipate-co-terephthalate) (PBAT)-70 % polyglycolic acid (PGA) is used as middle barrier layer, while in second type, middle barrier layer is Ethylene-vinyl alcohol (EVOH) copolymers. Polyethylene terephthalate (PET) was used as a structural layer, while either PBAT or poly(butylene succinate) (PBS) was used to enable thermal sealing and serve as the product contact layer. These MLPs are recycled by both chemical and mechanical recycling processes. Techno-economic analysis (TEA) shows that MLPs incorporating EVOH as barrier layer have similar or lower selling costs (0.32 $\$$/m 2 ) than commercial MLPs. Life cycle assessment (LCA) indicates EVOH-based MLPs have a lower carbon footprint and lower energy consumption relative to commercial MLP benchmarks. This work offers simplified MLPs that are easy to manufacture and ready to recycle, which will significantly reduce environmental impact of MLP packaging while also providing a cost-effective and practical solution for industry.

Barrier properties↗
DOE OSTI2024

Enhanced Activity from Coordinatively Unsaturated and Dynamic Zeolite-Bound Organoscandium Species

Scandium borohydride grafted into the micropores of the faujasite zeolite HY30 catalyzes the C–H borylation of benzene, whereas silica-grafted species are inactive. This catalytic activity may originate from grafting at a Brønsted acid site leading to a more electron-deficient rare earth center. Herein, we apply multinuclear double-resonance nuclear magnetic resonance (NMR) experiments to probe the structure and dynamics of zeolite- and silica-bound scandium borohydride complexes. The experiments reveal that scandium centers located within the zeolite micropores, in proximity to Al-created Brønsted sites, are more dynamic than rigid scandium sites grafted on silanols. Through a combination of NMR and molecular dynamics simulations, we show that the coordination of the scandium in the zeolite is labile, with the metal exchanging between two binding sites. As a result, the weak electron donation from the support that enables the movement of the Sc center leads to the formation of an undercoordinated metal center that cannot exist on silica, ultimately leading to the new catalytic activity of the species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Chain entanglements enable regeneration of high-performance thermosets

Thermoset plastics underpin structural materials, electronics and transportation, yet the permanent covalent networks that prevent flow and provide dimensional stability also make them difficult to recycle without sacrificing performance. In this work we show that high-performance thermosets can be built around dense chain entanglements, the physical interlacing of long polymer strands, rather than dense permanent crosslinks, with only a small number of selectively cleavable junctions preserving connectivity. Long, rigid, entangled polyolefin backbones generated by frontal polymerization form glassy polymers with high stiffness, high toughness and excellent creep suppression yet can be fully deconstructed into soluble, linear oligomers. Varying oligomer length and end-group chemistry enables their reuse as re-entangling building blocks that regenerate thermosets with thermal and mechanical properties that remain unchanged across generations. The strategy further extends to high-temperature fibre-reinforced composite matrices and additively manufactured structures, establishing chain entanglement as a design principle for durable, regenerable thermosets.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗
DOE OSTI2025

Hierarchical domain structures in buckled ferroelectric free sheets

Flat elastic sheets tend to display wrinkles and folds. From pieces of clothing down to two-dimensional crystals, these corrugations appear in response to strain generated by sheet compression or stretching, thermal or mechanical mismatch with other elastic layers, or surface tension. Extensively studied in metals, polymers and, — more recently — in van der Waals exfoliated layers, with the advent of thin single crystal freestanding films of complex oxides, researchers are now paying attention to novel microstructural effects induced by bending ferroelectric-ferroelastics, where polarization is strongly coupled to lattice deformation. Here we show that wrinkle undulations in BaTiO3 sheets bonded to a viscoelastic substrate transform into a buckle delamination geometry when transferred onto a rigid substrate. Using spatially resolved techniques at different scales (Raman, scanning probe and electron microscopy), we show how these delaminations in the free BaTiO3 sheets display a self-organization of ferroelastic domains along the buckle profile that strongly differs from the more studied sinusoidal wrinkle geometry. Moreover, we disclose the hierarchical distribution of a secondary set of domains induced by the misalignment of these folding structures from the preferred in-plane crystallographic orientations. Our results disclose the relevance of the morphology and orientation of buckling instabilities in ferroelectric free sheets, for the stabilization of different domain structures, pointing to new routes for domain engineering of ferroelectrics in flexible oxide sheets.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Determination of Intermolecular Distances in Dilute Solutions of Macroions and Their Direct Correlations with Self-Assembly and Macrophase Transitions

Here, this work demonstrates new attempts to determine the intermolecular distances between charged macroionic solutes in their dilute solutions, which regulate the solute’s microphase (self-assembly) and macrophase transitions. Small-angle X-ray scattering (SAXS) and analytical ultracentrifuge (AUC) techniques were applied to determine the intermolecular distances for the 2.42 nm-sized, spherical uranyl peroxide molecular cluster {U 60 } in their self-assembled states in dilute aqueous solution and concentrated phases, respectively. The counterion-mediated attraction among {U 60 } leads to characteristic, inter-{U 60 } distances in solutions, which increase gradually with decreasing the strength of introduced counterions (e.g., lower valency). The gradual increment of inter-{U 60 } distance demonstrates a nice correlation with the macroscopic phase transitions of {U 60 }, from single crystals to concentrated fluids containing rigid 2-D sheets, then to dilute solutions containing a small amount of standalone, floating 2-D sheets of {U 60 }, and finally to dilute solutions containing a limited amount of self-assembled single-layered, spherical blackberry structures of different sizes from the bending of more flexible 2-D sheets.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Additive manufacturing of carbon fiber-reinforced thermoset composites via in-situ thermal curing

Fiber-reinforced polymer composites are lightweight structural materials widely used in the transportation and energy industries. Current approaches for the manufacture of composites require expensive tooling and long, energy-intensive processing, resulting in a high cost of manufacturing, limited design complexity, and low fabrication rates. Here, we report rapid, scalable, and energy-efficient additive manufacturing of fiber-reinforced thermoset composites, while eliminating the need for tooling or molds. Use of a thermoresponsive thermoset resin as the matrix of composites and localized, remote heating of carbon fiber reinforcements via photothermal conversion enables rapid, in-situ curing of composites without further post-processing. Rapid curing and phase transformation of the matrix thermoset, from a liquid or viscous resin to a rigid polymer, immediately upon deposition by a robotic platform, allows for the high-fidelity, freeform manufacturing of discontinuous and continuous fiber-reinforced composites without using sacrificial support materials. This method is applicable to a variety of industries and will enable rapid and scalable manufacture of composite parts and tooling as well as on-demand repair of composite structures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Robotics for Systems Integration in Buildings - Pilot Study of Viable Approaches to Install Hygrothermal and Rigid Electrical Systems: Preprint

The Industrialized Construction Innovation (ICI) team at the National Renewable Energy Laboratory (NREL) has been exploring the use of robotics to integrate hygrothermal, mechanical, electrical, and plumbing systems in prefabricated building assemblies (offsite construction) and 3D Printed buildings (onsite construction). Such multi-system integration tasks often require specialized robots and custom end-effectors for handling a range of rigid and non-rigid building components. This paper begins with a brief overview of the current state of robotics in construction, followed by a pilot study exploring the use of robotics to integrate a simple prototype multi-trade wall assembly composed of structural studs, hygrothermal layer, wall finishing, and electrical fixtures. The study was funded by the Department of Energy's (DOE) Advanced Materials and Manufacturing Technologies Office (AMMTO). Insights about the implementation of design for manufacturing and assembly (DfMA) principles in designing the prototype wall for robotic assembly, and selection of appropriate robotic end effector hardware for handling these components are included. Detailed comparison of computational toolpath simulations of the robotic assembly process and real-life demonstration of the same is presented. Finally, limitations and lessons learned from this study along with future research recommendations for robotic assembly of more complex multi-trade assemblies, including potential scenarios such as robotic outfitting of facilities in extra-terrestrial environments is included.

advanced manufacturing↗
DOE OSTI2024

Robotics for Systems Integration in Buildings: Pilot Study of Viable Approaches to Install Hygrothermal and Rigid Electrical Systems

The Industrialized Construction Innovation (ICI) team at the National Renewable Energy Laboratory (NREL) has been exploring the use of robotics to integrate hygrothermal, mechanical, electrical, and plumbing systems in prefabricated building assemblies (off-site construction) and 3D-printed buildings (on-site construction). Such multisystem integration tasks often require specialized robots and custom end effectors to handle a range of rigid and nonrigid building components. This paper begins with a brief overview of the current state of robotics in construction, followed by a pilot study exploring the use of robotics to integrate a simple prototype multitrade wall assembly composed of structural studs, hygrothermal layer, wall finishing, and electrical fixtures. The study was funded by the US Department of Energy's (DOE's) Advanced Materials and Manufacturing Technologies Office (AMMTO). Insights about the implementation of design for manufacturing and assembly (DfMA) principles in designing the prototype wall for robotic assembly, and selection of appropriate robotic end-effector hardware to handle these components are included. Detailed comparison of computational toolpath simulations of the robotic assembly process and real-life demonstration of the same are presented. Finally, limitations and lessons learned from this study are included, along with future research recommendations for robotic assembly of more complex multitrade assemblies, including potential scenarios such as robotic outfitting of facilities in extraterrestrial environments.

advanced manufacturing↗
DOE OSTI2026

Machine Learning Interatomic Potentials for Modeling Framework Flexibility and Water Uptake in NbOFFIVE-1-Ni Metal–Organic Framework

Metal–organic frameworks (MOFs), with their distinctive porous structures and tunable chemical properties, have shown immense promise in the separation and storage of gases. Currently, the accurate simulation of their adsorptive properties remains challenging, especially for systems where the molecules fit very tightly into the pores. Traditional simulation methods often approximate the frameworks as rigid and do not account for the framework flexibility seen in materials such as NbOFFIVE-1-Ni. First-principles molecular dynamics (FPMD) simulations offer the desired accuracy in modeling this flexibility but are limited by their extensive computational demands, rendering them impractical for long simulations. Conversely, classical force field-based simulations offer computational efficiency but lack the necessary accuracy. Here, to break this accuracy-efficiency trade-off, we have developed machine learning interatomic potentials trained on energies and forces from FPMD to model the framework flexibility of NbOFFIVE-1-Ni in the presence of water over nanosecond time scales. Furthermore, by integrating MLIP-driven molecular dynamics (MLIP-MD) with grand canonical Monte Carlo (GCMC) simulations, we further incorporated framework flexibility into adsorption predictions, yielding water adsorption isotherms that better align with experimental data compared to those of conventional GCMC simulations. These advances offer new opportunities for the design and optimization of MOFs in gas storage and separation applications.

adsorption↗
DOE OSTI2025

Catching Fullerenes: Synthesis of Molecular Nanogloves

Abstract Herein, we report the synthesis of a new series of rigid, all meta ‐phenylene, conjugated deep‐cavity molecules, displaying high binding affinity towards buckyballs. A facile synthetic approach with an overall combined yield of approximately 53% in the last two steps has been developed using a templating strategy that combines the general structure of resorcin[4]arene and [12]cyclo‐ meta ‐phenylene. These two moieties are covalently linked via four acetal bonds, resulting in a glove‐like architecture. 1 H NMR titration experiments reveal fullerene binding affinities ( K a ) exceeding ≥10 6 M −1 . The size complementarity between fullerenes and these scaffolds maximizes CH⋯π and π⋯π interactions, and their host:guest adduct resembles a ball in a glove, hence their name as nanogloves. Fullerene recognition is tested by suspending carbon soot in a solution of nanoglove in 1,1,2,2‐tetrachloroethane, where more than a dozen fullerenes are observed, ranging from C 60 to C 96 .

Mirzaei, Saber [Department of Chemistry Rice Unive↗
DOE OSTI2024

The structural basis for 2′−5′/3′−5′-cGAMP synthesis by cGAS

Abstract cGAS activates innate immune responses against cytosolic double-stranded DNA. Here, by determining crystal structures of cGAS at various reaction stages, we report a unifying catalytic mechanism. apo-cGAS assumes an array of inactive conformations and binds NTPs nonproductively. Dimerization-coupled double-stranded DNA-binding then affixes the active site into a rigid lock for productive metal•substrate binding. A web-like network of protein•NTP, intra-NTP, and inter-NTP interactions ensures the stepwise synthesis of 2′−5′/3′−5′-linked cGAMP while discriminating against noncognate NTPs and off-pathway intermediates. One divalent metal is sufficient for productive substrate binding, and capturing the second divalent metal is tightly coupled to nucleotide and linkage specificities, a process which manganese is preferred over magnesium by 100-fold. Additionally, we elucidate how mouse cGAS achieves more stringent NTP and linkage specificities than human cGAS. Together, our results reveal that an adaptable, yet precise lock-and-key-like mechanism underpins cGAS catalysis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗