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855 records · Page 15

Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner

An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.

Spectral Proper Orthogonal Decomposition

Development of a high fidelity CFD model for solvent evaporation and transport in porous structure during battery electrode drying

An efficient battery manufacturing process is the key to the mass production of Electric Vehicles (EV), in which drying is one of the most energy-intensive steps significantly influencing the battery cell performance. An accurate 3D CFD model for drying is essential for predicting the drying mechanism and optimizing its parameters. By optimizing the drying process, it is possible to reduce energy consumption and cost during battery manufacturing, minimize binder loading and maximize active material loading to achieve superior electrochemical performances and facilitate wider and faster public adoption of EV. This project aims to optimize the drying process during electrode manufacturing by leveraging high-fidelity, porous electrode simulations for solvent evaporation. By optimizing this process, we seek to reduce energy consumption during battery manufacturing, while minimizing binder loading and maximizing active material loading, with the overall goal of enhancing electrical vehicle performance.

Horner, Jeffrey Scott [Sandia National Laboratorie

Insulating ground state and 2−𝑘 magnetic structure of candidate Weyl hydrogen-atom K2⁢Mn3⁢(AsO4)3

The ideal Weyl "hydrogen-atom" semimetal exhibits only a single pair of Weyl nodes and no other trivial states at the Fermi energy. Such a material would be a panacea in the study of Weyl quasi-particles, allowing direct unambiguous observation of their topological properties. The alluaudite-like K2⁢Mn3⁢(AsO4)3 compound was recently proposed as such a material. Here, we use comprehensive experimental work and first-principle calculations to assess this prediction. We find K2⁢Mn3⁢(AsO4)3 crystallizes in the 𝐶⁢2/𝑐 symmetry with a quasi-one-dimensional Mn sublattice, growing as small needle-like crystals. Bulk property measurements reveal magnetic transitions at ≈8 and ≈4 K, which neutron scattering experiments show correspond to two distinct magnetic orders, first a partially ordered ferrimagnetic 𝐤𝟏=(0,0,0) structure at 8 K and a second transition of 𝐤𝟐=(1,0,0) at 4 K to a fully ordered state. Below the second transition, both ordering vectors are necessary to describe the complex magnetic structure with modulated spin magnitudes. Both of the best-fit magnetic structures in this work are found to break the symmetry necessary for the generation of Weyl nodes, though one of the magnetic structures allowed by 𝐤𝟏 does preserve this symmetry. However, the crystals are optically transparent and ellipsometry measurements reveal a large band gap, undermining expectations of semimetallic behavior. Density functional theory calculations predict an insulating antiferromagnetic ground state, in contrast to previous reports, and suggest potential frustration on the magnetic sublattice. Given the wide tunability of the alluaudite structure, we consider ways to push the system closer to a semimetallic state.

Taddei, Keith M [Argonne National Laboratory]

Transition from Vehicular to Structural Ionic Transport in Electrified Alkali Aqueous Solutions

A molecular understanding of the solvation and dynamics of ions under static electric fields is crucial for modelling a wide range of natural and technological processes. Yet, traditional simulation methods suffer from a trade-off that has to be made between accuracy and statistical convergence. To bridge this gap, herein we extend our recently introduced Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) approach to investigate the solvation structures and ionic transport mechanisms of electrified alkali cationic solutions. We obtain ionic conductivities for Li+, Na+ and Cs+ from the field dependence of the ionic current density in good agreement with experiment. Surprisingly, the migration mechanism is found to be strikingly different for the three ions despite their similar ionic conductivities. While Li+ conducts predominantly through vehicular migration of a stable 4-fold coordinated ion at all field strengths, Cs+ conducts strictly through a structural diffusion mechanism, where 9-12 transient first shell water coordination bonds are broken and renewed. Notably, aqueous Na+ emerges as a “Goldilocks” ion: its ion-water interactions are strong enough to maintain distinct 5-6 fold coordination shells at zero field (unlike Cs+) yet labile enough to be strongly perturbed by electric fields (unlike Li+). As a consequence, we observe an electric field-induced transition from vehicular to structural ionic transport for Na+ that is accompanied by a marked increase in the ionic current density. Our results imply that the conductance mechanism of ions with moderate ion-solvent interactions can be effectively tuned by external electric fields.

Joll, Kit

Effect of Oxidizing Impurities on the Corrosion Behavior of Structural Alloys Exposed to MgCl 2 Molten Salt Vapor

The corrosion behavior of structural alloys SS304 and IN617 when exposed to vapors of MgCl 2 molten salt at 764 °C for 100 h in an argon atmosphere was investigated as a function of the level of oxidizing impurities (e.g., NaOH) present in the salt. Increasing the concentration of oxidizing impurities in the salt caused an increase in corrosion in both structural alloys, as measured by Cr depletion layers. A poorly adhered oxide scale layer containing Mg, Al, and Cr was observed on the surface of the metals, and local attack was observed as well. The Ni-based IN617 showed lower Cr depletion and less scale formation than the Fe-based SS304. These results demonstrate that oxidizing impurities in the molten salt will impact the vapor phase corrosion for structural members exposed to the molten salt headspace. This finding is highly relevant for understanding the effects of the vapor phase in molten salt applications, including molten salt thermal energy storage, molten salt nuclear reactors, and molten salt electrochemistry.

25 ENERGY STORAGE

Entanglement Structure of Non-Gaussian States and How to Measure It

Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. Here, we present a protocol that constrains quantum states using experimentally measured correlation functions. This method enables measurement of a quantum state’s entanglement structure, opening a new route to study entanglement-related phenomena. Our approach extends Gaussian state parameterizations by systematically incorporating higher-order correlations. We show the protocol’s usefulness in conjunction with current and forthcoming experimental capabilities, focusing on weakly interacting fermions as a proof of concept. Here, the lowest nontrivial expansion quantitatively predicts early time thermalization dynamics, including signaling the onset of quantum chaos indicated by the entanglement Hamiltonian.

Fermi gases

Analysis of the Erosion of Cubic Centered and Face Centered Metallic Materials [Analyse de L'erosion de Matereaux Metalliques de Structures Cubiques Centree et Face Centree]

A generalized law of erosion, in nondimensional form, is proposed. The aforementioned explicitly gives an account of the nature and the microstructure of the material impacted, the angle of impact of the particles, and their hardness. The erosion behavior of various steels, pig iron, and cast iron is examined as well as the behavior of new ordered intermetallic materials, Fe-25% Al-(Zr, Cr, B). The concern of such alloys in an erosion-corrosion environment is shown. --- Une loi généralisée d'usure par érosion, sous forme non dimensionnelle, est proposée. Celle-ci rend compte explicitement de la nature et de la microstructure du matériau impacté, de l'angle d'impact des particules, de leur acuité at de leur durete. Le comportement à l'érosion de divers aciers et fontes est examiné ainsi que la tenue de nouveaux matériaux intermétalliques ordonnés Fe-25% Al - (Zr, Cr, B). L'interet de tels alliages dans des environnements agressifs du type érosion-corrosion est montré. Mots clés: usure, érosion, modèle, matériaux métalliques, intermétalliques Fe-Al.

A Magnée

Elucidation of Design Criteria for V‐based Redox Mediators: Structure‐Function Relationships that Dictate Rates of Heterogeneous Electron Transfer

Redox mediators are attractive solutions for addressing the stringent kinetic stipulations required for efficient energy conversion processes. In this work, we compare the electrochemical properties of four vanadium complexes, namely [V(acac) 3 ], [V 6 O 7 (OMe) 12 ], [ n Bu 4 N] 3 [V 6 O 13 (TRIS NO2 ) 2 ], and [ n Bu 4 N] 5 [V 18 O 46 (NO 3 )] in non-aqueous solutions on glassy carbon electrodes. The goal of this study is to investigate the electron transfer kinetics and diffusivity of these compounds under identical experimental conditions to develop an understanding of structure-function relationships that dictate the physicochemical properties of vanadium oxide assemblies. Complex selection was dictated by two criteria – (1) nuclearity of the transition metal complexes (2) distribution of electron density in the native electronic configuration. In conclusion, our analyses establish that electronic communication between metal centers significantly impacts charge transfer kinetics of these vanadium-based compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Cold Spray Cobalt Magnetostrictive Electromagnetic Acoustic Transducers for High Temperature Structure Monitoring

The Department of Energy’s Advanced Sensors and Instrumentation program seeks to develop and qualify advanced sensors for the nuclear industry. Reliable high temperature and high radiation sensors for detection and characterization of structural flaws in pipes, vessels, and structurally critical components is a weakness for both conventional light water reactors with coolant T-hot approaching 350oC, and for advanced reactors with T-hot temperatures in excess of 500 to 800oC. Magnetostrictive Electromagnetic Acoustic Transducers using a cold spray cobalt coating have been proposed as a sensor design that can withstand these kinds of temperatures and radiation levels to serve as online sensors to detect flaws before cracks, pits, or erosion/corrosion flaws progress to through-wall failures. This report tests cold spray cobalt as part of a magnetostrictive EMAT for high temperature service. Cobalt is known to have strong magnetostrictive properties however the effect of cold spray application is not well studied. This program was surprised to discover that cold sprayed cobalt exhibited little or no magnetostrictive behavior until it was thermally annealed. Following annealing to 650oC however, cold spray cobalt did exhibit a magnetostrictive response. Work to date prior to this milestone report publication showed that magnetostrictive EMAT was successfully tested to 400oC with an alnico permanent magnet. The program plans to extend testing with an electromagnet to higher temperatures. This follow-on work will be reported under subsequent publications or as a revision to this report.

Glass, Samuel W.

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

Overview of the Center for Advanced Space Propulsion

The mission of the Center for Advanced Space Propulsion (CASP), a Center for the Commercial Development of Space (CCDS), is to strengthen U.S. competitiveness in space technology, foster cooperative research with industry and government, assist industry in developing commercial products and services, and perform research in advanced space propulsion. Current areas of focus are (1) advanced chemical propulsion, including high area ratio nozzle performance, variable thrust engine performance, and spray combustion stability; (2) artificial intelligence propulsion applications, including health monitoring of rocket engines, fault pattern detection and diagnosis, and intelligent hypertext applications; (3) microgravity fluid management, including liquid storage and transfer, a subscale orbital fluid transfer experiment, and helical, two-phase flow; (4) electric propulsion, including magnetic annular arc thruster, ion thrustor, and electrostatic plasma accelerator; and (5) laser materials processing.

George W Garrison

Molecular dynamics based study on the effects of cation size on the local structure and diffusion in polymerized ionic liquids

We have used coarse-grained molecular dynamics simulations to understand the effect of cation size on ion diffusion in polymerized ionic liquids at temperatures well above the glass transition temperature of the polymers. We investigated dependencies of the diffusion constant on the cation radius and static dielectric constant and interpreted these results in terms of underlying structural changes, and decoupling phenomenon. We have found non-monotonic effects of the cation radius on the diffusion constant, with a maximum at an intermediate radius resulting from two different size dependent effects. Changes in the radial distribution functions characterizing spatial distribution of cations with respect to anions result in a monotonic increase in the coordination number. This yields an increase in the effective interaction energy as a function of cation radius, which can explain the decrease in the diffusion constant. This increase is counteracted at small cation radii by a corresponding increase in decoupling of cation and anion dynamics. In addition, the diffusion constant is found to increase on increasing the static dielectric constant for all radii of the cations. These results highlight the significant role of decoupling in designing polymerized ionic liquids with an enhanced diffusion constant of cations.

Gillespie, Colin [ORNL] (ORCID:0000000320287080)

Dirac Fermions and Flat Bands in Phosphorus Carbide Nanotubes: Structural and Quantum Phase Transitions in a Quasi-One-Dimensional Material

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

carbon nanotubes

Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI) 2 ], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI) 2 ], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

Science & Technology - Other Topics

Electrostatic‐Attraction‐Driven Self‐Assembled Graphene‐Disordered Rocksalt Composite Cathode for Lithium‐Ion Batteries

Disordered rocksalt cathodes hold promise for achieving high-capacity lithium-ion batteries while using low-cost, earth-abundant elements. However, their electrochemical performance remains critically limited by their poor electronic conductivity. Conventional strategies such as high-energy ball milling with excess carbon additives can improve conductivity but remain challenging to scale and often produce defects and increase surface area, thereby accelerating capacity degradation. Herein, we report an alternative approach of electrostatic-attraction-driven self-assembly to fabricate Li 1.2 Mn 0.6 Ti 0.2 O 1.8 F 0.2 (LMTOF) particles uniformly wrapped with electronically conductive graphene sheets without associated materials degradation. The graphene-wrapped LMTOF demonstrates significantly improved cycling stability (89% capacity retention after 100 cycles) and superior rate capability compared with an LMTOF-carbon composite electrode fabricated using the conventional high-energy ball-milling process. Post-cycling analysis reveals reduced oxygen evolution, suppressed unwanted side reactions, and improved structural integrity for the graphene-LMTOF composite. This work highlights the advantages of solution-based carbon wrapping and offers a scalable strategy to prepare high-performance DRX cathodes for lithium-ion batteries.

carbon composite

pi-Extended Porphyrins: The Impact of Aromatic Heterocycles on the Properties of the Largely pi-Extended Structures (Final Report_UNT_SC0016766)

Largely π-extended carbon-rich materials represent fascinating yet challenging frontiers in chemistry and materials science as it offers numerous opportunities in molecular electronics. pi-Extended porphyrins possess unique set of electronic and photophysical properties and are very attractive for a wide range of applications. However, the synthesis and functionalization of pi-extended porphyrins had been very challenging. To explore and expand this intriguing research field, it is essential to develop synthetic tools to make them accessible. Funded by the Department of Energy Basic Energy Science, my laboratory addressed these synthetic challenges by developing concise and versatile methods for pi-extended porphyrins. Significant progress has been made in multiple directions, including fusing Polycyclic Aromatic Hydrocarbons (PAH), aromatic heterocycles, antiaromatic component, and cross-conjugated component to porphyrins as well as push-pull porphyrins. The availability of these methods has made it possible to rationally design and synthesize functionalized pi-extended porphyrins. Unprecedented electronic and photophysical properties have been discovered for these pi-extended porphyrins.

36 MATERIALS SCIENCE

Hydrogen Production and Li-Ion Battery Performance with MoS2-SiNWs-SWNTs@ZnONPs Nanocomposites

This study explores the hydrogen generation potential via water-splitting reactions under UV-vis radiation by using a synergistic assembly of ZnO nanoparticles integrated with MoS2, single-walled carbon nanotubes (SWNTs), and crystalline silicon nanowires (SiNWs) to create the MoS2-SiNWs-SWNTs@ZnONPs nanocomposites. A comparative analysis of MoS2 synthesized through chemical and physical exfoliation methods revealed that the chemically exfoliated MoS2 exhibited superior performance, thereby being selected for all subsequent measurements. The nanostructured materials demonstrated exceptional surface characteristics, with specific surface areas exceeding 300 m2 g−1. Notably, the hydrogen production rate achieved by a composite comprising 5% MoS2, 1.7% SiNWs, and 13.3% SWNTs at an 80% ZnONPs base was approximately 3909 µmol h−1g−1 under 500 nm wavelength radiation, marking a significant improvement of over 40-fold relative to pristine ZnONPs. This enhancement underscores the remarkable photocatalytic efficiency of the composites, maintaining high hydrogen production rates above 1500 µmol h−1g−1 even under radiation wavelengths exceeding 600 nm. Furthermore, the potential of these composites for energy storage and conversion applications, specifically within rechargeable lithium-ion batteries, was investigated. Composites, similar to those utilized for hydrogen production but excluding ZnONPs to address its limited theoretical capacity and electrical conductivity, were developed. The focus was on utilizing MoS2, SiNWs, and SWNTs as anode materials for Li-ion batteries. This strategic combination significantly improved the electronic conductivity and mechanical stability of the composite. Specifically, the composite with 56% MoS2, 24% SiNWs, and 20% SWNTs offered remarkable cyclic performance with high specific capacity values, achieving a complete stability of 1000 mA h g−1 after 100 cycles at 1 A g−1. These results illuminate the dual utility of the composites, not only as innovative catalysts for hydrogen production but also as advanced materials for energy storage technologies, showcasing their potential in contributing to sustainable energy solutions.

Chemistry

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH