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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dehydration kinetics of nanoconfined water in beryl probed by high temperature single crystal synchrotron X-ray diffraction

Understanding changes in material properties through external stimuli plays a key role in validating the expected performance of materials and engineering material properties in a controlled manner. Here, we introduce a fundamental protocol to deduce dehydration reactions kinetics of water confined in nanopore channels, with the cyclosilicate beryl as the scaffold of interest, using time-resolved synchrotron X-ray diffraction (SXRD), in the temperature interval of 298–1038 K. The temperature-dependent intensity (I) of the strongest reflection (112) was used as the crystallite variable. An estimation of an isobaric thermal crystallite coefficient, k, analogous with the isobaric thermal expansion coefficient, established the rate of relative crystallization as a function of temperature, $\frac{∂I}{∂T}$. A plot of lnk and $\frac{1}{T}$ gives rise to two kinetic steps, indicating a slow dehydration stage up to ~ 700 K and a fast dehydration stage up to the investigated temperature 1038 K. The crystal structure of beryl determined up to 1038 K, in temperature increment as small as 10 K, indicates the presence of channel ions Na and Fe and a gradual decrease of water upon heating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Optimal thermodynamic conditions to minimize kinetic by-products in aqueous materials synthesis

Abstract Phase diagrams offer substantial predictive power for materials synthesis by identifying the stability regions of target phases. However, thermodynamic phase diagrams do not offer explicit information regarding the kinetic competitiveness of undesired by-product phases. Here we propose a quantitative and computable thermodynamic metric to identify synthesis conditions under which the propensity to form kinetically competing by-products is minimized. We hypothesize that thermodynamic competition is minimized when the difference in free energy between a target phase and the minimal energy of all other competing phases is maximized. We validate this hypothesis for aqueous materials synthesis through two empirical approaches: first, by analysing 331 aqueous synthesis recipes text-mined from the literature; and second, by systematic experimental synthesis of LiIn(IO 3 ) 4 and LiFePO 4 across a wide range of aqueous electrochemical conditions. Our results show that even for synthesis conditions that are within the stability region of a thermodynamic Pourbaix diagram, phase-pure synthesis occurs only when thermodynamic competition with undesired phases is minimized.

Wang, Zheren (ORCID:0000000227429451)↗
DOE OSTI2020

Kinetics of the benzyl + HO 2 and benzoxyl + OH barrierless association reactions: fate of the benzyl hydroperoxide adduct under combustion and atmospheric conditions

Radical–radical association reactions are challenging to address theoretically due to difficulties finding the bottleneck that variationally minimizes the reactive flux. For this purpose, the variable reaction coordinate (VRC) formulation of the variational transition state theory (VTST) represents an appropriate tool. Here, we revisited the kinetics of two radical–radical association reactions of importance in combustion modelling and poly-aromatic hydrocarbon (PAH) chemistry by performing VRC calculations: benzyl + HO 2 and benzoxyl + OH, both forming the adduct benzyl hydroperoxide. Our calculated rate constants are significantly lower than those previously reported based on VTST calculations, which results from a more efficient minimization of the reactive flux through the bottleneck achieved by the VRC formulation. Both reactions show different trends in the variation of their rate constants with temperature. We observed that if the pair of single occupied molecular orbitals (SOMOs) of the associating radicals show a similar nature, i.e. similar character, and thereby a small energy gap, a highly stabilized transition state structure is formed as the result of a very efficient SOMO–SOMO overlap, which may cancel out the free energy bottleneck for the formation of the adduct and result in large rate constants with a negative temperature dependence. This is the case of the benzoxyl and OH radical pair, whose SOMOs show O 2p nature with an energy gap of 20.2 kcal mol –1 . On the other hand, the benzyl and HO 2 radical pair shows lower rate constants with a positive temperature dependence due to the larger difference between both SOMOs (a 28.9 kcal mol –1 energy gap) as a consequence of the contribution of the multiple resonance structures of the benzyl radical. The reverse dissociation rate constants were also calculated using multi-structural torsional anharmonicity partition functions, which were not included in previous work, and the results show a much slower dissociation of benzyl hydroperoxide. Our work may help to improve kinetic models of interest in combustion and PAH formation, as well as to gain further understanding of radical–radical association reactions, which are ubiquitous in different environments.

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

Kinetics and mechanisms of polycondensation reactions between aryl halides and bisphenol A

Aryl chlorides (ArCl) or aryl fluorides (ArF) were used in polycondensation reactions to form poly(arylene ether sulfone)s (PAES). Interestingly, the kinetics of the ArF reaction fit a third-order rate law, which is attributed to the activation of the carbon–fluorine bond by two potassium cations (at least one bound to phenolate), which form a three-body complex. Here, the ArCl monomer follows a second-order rate law, where a two-body complex forms at the initial state of the aromatic nucleophilic substitution (S N Ar) pathway. These metal cation-activated complexes act as intermediates during the attack by the nucleophile. This finding was reproduced with either the potassium or the sodium counterion (introduced via potassium carbonate or sodium carbonate). Through a combination of experimental analysis of reaction kinetics and computational calculations with density functional theory (DFT) methods, the present work extends the fundamental understanding of polycondensation mechanisms for two aryl halides and highlights the importance of the CX–metal interaction(s) in the S N Ar reaction, which is translational to other ion-activated substitution reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Unexpected electrochemical behavior of an anolyte redoxmer in flow battery electrolytes: solvating cations help to fight against the thermodynamic–kinetic dilemma

Redoxmers are redox-active molecules that can store energy in electrolytes for redox flow batteries (RFBs), and their electrochemical properties are significantly affected by the choice of supporting electrolytes. Herein, we use 2,1,3-benzothiadiazole (BzNSN) as a model system to scrutinize the supporting electrolyte impact. By systemically varying the components of supporting salts, BzNSN not only shows substantial redox potential shifts but also exhibits varying electrochemical stabilities. Specifically, changing the size of cations can effectively alter the coordination between the supporting salt and BzNSN species. From Li + , Na + , K + , to NEt 4 + , the redox potential of BzNSN shifts negatively, from -1.63 V to -1.82 V vs. Ag/Ag + . Molecular dynamics and density functional theory simulations revealed that smaller cations, like Li + , are closer to the charged BzNSN when coordinated, implying stronger coordination, while larger cations, like K + and NEt 4 + , are farther away. Interestingly, the large cation electrolytes also lead to much improved electrochemical stability, evidenced by the extraordinarily enhanced kinetic lifetime from electron paramagnetic resonance measurement. This study demonstrates the first example of tuning an anolyte redoxmer toward a concurrent improvement of lowered redox potentials AND enhanced calendar lives via solvation means, which is usually constrained by the thermodynamic–kinetic relation.

2,1,3-benzothiadiazole↗
DOE OSTI2021

Mechanism and kinetics of the oxidation of 1,3-butadien-1-yl (n-C 4 H 5 ): a theoretical study

Here, ab initio CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) calculations of the C 4 H 5 O 2 potential energy surface have been combined with Rice–Ramsperger–Kassel–Marcus Master Equation (RRKM-ME) calculations of temperature- and pressure-dependent rate constants and product branching ratios to unravel the mechanism and kinetics of the n-C 4 H 5 + O 2 reaction. The results indicate that the reaction is fast, with the total rate constant being in the range of 3.4–5.6 × 10 –11 cm 3 molecule –1 s –1 . The main products include 1-oxo-n-butadienyl + O and acrolein + HCO, with their cumulative yield exceeding 90% at temperatures above 1500 K. Two conformers of 1-oxo-n-butadienyl + O are formed via a simple mechanism of O 2 addition to the radical site of n-C 4 H 5 followed by the cleavage of the O–O bond proceeding via a van der Waals C 4 H 5 O∙∙∙O complex. Alternatively, the pathways leading to acrolein + HCO involve significant reorganization of the heavy-atom skeleton either via formal migration of one O atom to the opposite end of the molecule or its insertion into the C1–C2 bond. Not counting thermal stabilization of the initial peroxy adducts, which prevails at low temperatures and high pressures, all other products share a minor yield of under 5%. Rate constants for the significant reaction channels have been fitted to modified Arrhenius expressions and are proposed for kinetic modeling of the oxidation of aromatic molecules and 1,3-butadiene. As a secondary reaction, n-C 4 H 5 + O 2 can be a source for the formation of acrolein observed experimentally in oxidation of the phenyl radical at low combustion temperatures, whereas another significant (secondary) product of the C 6 H 5 + O 2 reaction, furan, could be formed through unimolecular decomposition of 1-oxo-n-butadienyl. Both the n-C 4 H 5 + O 2 reaction and unimolecular decomposition of its 1-oxo-n-butadienyl primary product are shown not to be a substantial source of ketene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Initiator-dependent kinetics of lyotropic liquid crystal-templated thermal polymerization

In this study, we examine the polymerization kinetics with different thermal initiators in lamellar and hexagonal lyotropic liquid crystal (LLC) structures directed by Pluronic L64. Ammonium persulfate is used to initiate the polymerization from the water phase, whereas azobisisobutyronitrile and benzoyl peroxide are employed to commence the reaction through the monomer phase. While the mesophase structure remains intact for all the initiation systems, the kinetics of polymerization and conversion vary significantly. The obtained differential scanning calorimetry (DSC) results reveal that, under same conditions, initiation from water (IFW) system results in enhanced reaction rates as well as higher monomer conversions compared to initiation from oil (IFO) one. Higher termination rate in LLC nanoconfinements induces lower reaction rates in IFO system. Moreover, our work on different LLC structures show that the effect of nanoconfinement on polymerization rate can be minimized through IFW. Chemorheology not only confirms the results obtained from DSC, but also shows that, in similar monomer conversions, the polymers obtained from IFW system exhibit an improved mechanical properties over the samples produced though IFO process.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Thermodynamic stability versus kinetic accessibility: Pareto fronts for programmable self-assembly

A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. Additionally, the tradeoff disappears when the number of particle types reaches a value m *, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic–kinetic tradeoff. However, we argue, by contrasting our coarse-grained model's predictions with those of Brownian dynamics simulations, that particles with short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Catalytic co-pyrolysis of LDPE and PET with HZSM-5, H-beta, and HY: experiments and kinetic modelling

In this study, the catalytic pyrolysis of low-density polyethylene (LDPE), polyethylene terephthalate (PET) and their mixture (1 : 1 wt/wt) with three zeolite catalysts (HZSM-5, H-beta, HY) was investigated using a thermogravimetric analyzer (TGA) and a Pyroprobe® micro-reactor coupled to a gas chromatograph mass spectrometer (Py-GC/MS). The TGA results demonstrated that during pyrolysis at 10 °C min –1 , on average, zeolite catalysts decreased the maximum decomposition temperature by 149 °C for LDPE while only decreasing by 8 °C for PET. The derivative thermogravimetric (DTG) curve evidenced interactions when the two polymers were catalytically co-pyrolyzed for all the three catalysts. A lumped nth order reaction scheme was able to accurately model both non-catalytic and catalytic pyrolysis and co-pyrolysis by using the least squares fitting approach for determining the kinetic parameters. The kinetic model was able to model well the interaction effects observed during catalytic co-pyrolysis of LDPE and PET with HZSM-5, H-beta, and HY (Fit% Wt% > 96%, Fit% DTG > 94%). Py-GC/MS experiments for the catalytic fast pyrolysis of LDPE revealed that HZSM-5 resulted in the highest selectivity to aromatic hydrocarbons (31.6%) and HY resulted in the highest selectivity to gasoline range C 5 –C 10 paraffins and olefins (40.9%). Catalytic fast pyrolysis of PET showed high selectivity to benzene for all the catalysts (>43%) and that HZSM-5 resulted in the highest selectivity to polyaromatic hydrocarbons (24.7%). Finally, the catalytic fast co-pyrolysis of LDPE and PET revealed interaction effects for all the three catalysts evidenced by a positive synergy% for alkylated benzenes (3–142%) and polyaromatics (105–187%) with a concomitant negative synergy% for benzene (24–36%) and C 5 –C 10 paraffins and olefins (27–53%).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Kinetics of the reaction of ferrous ions with hydroxyl radicals in the temperature range 25–300 °C

Here, the kinetics and mechanism of the reaction between OH radicals and ferrous ions in the temperature range 25–300 °C were studied using pulse radiolysis. At temperatures <150 °C the rate of reaction is essentially independent of temperature, while at temperatures >150 °C the activation energy is 45.8 ± 3.0 kJ mol —1 . The change in activation energy is attributed to a change in the dominant mechanism from hydrogen atom transfer (HAT) to dissociative ligand interchange. The kinetic isotope effect (KIE) was measured by repeating experiments in heavy water. A value of 2.9 was measured at room temperature where HAT is the dominant mechanism. The KIE decreases to zero at temperatures > 150 °C as ligand interchange becomes dominant and the O–H bond is no longer involved in the reaction.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Kinetic pathways of fast lithium transport in solid electrolyte interphases with discrete inorganic components

The transport of lithium ions in the solid electrolyte interphase (SEI) has been previously accepted to proceed in two steps: a fast pore diffusion through the outer, porous organic layer followed by a slow knock-off or vacancy diffusion in the inner, dense inorganic layer. The second step is believed to be the rate-limiting step during fast-charging. In this study, we have intentionally constructed a thicker SEI (SEI-rich) structure on the surface of monoclinic Nb 2 O 5 (H-Nb 2 O 5 ) by adding LiNO 3 into a conventional ethylene carbonate based electrolyte. The electrochemical performance of two electrodes, one SEI-rich and one with few SEI (SEI-lean), was found to be almost the same, including their fast-charging capability and cycling stability, despite the significant difference in their SEI structure. Importantly, analysis using cryogenic scanning/transmission electron microscopy showed the discrete decoration of individual inorganic particles (e.g., Li 2 O) and amorphous species (LiN x O y /organic components) over the surface of H-Nb 2 O 5 . These discrete inorganic particles are in contradiction to the formation of dense inner inorganic layer, which has been commonly postulated. Based on these findings, we propose a new mechanism for Li ion transport through the SEI: one-step pore diffusion, without the second step slow diffusion. This one-step pore diffusion process provides an extremely fast Li ion transport, and effectively removes the kinetic limitation of Li ion transport in the SEI for fast charging. Finally, these results strongly suggest that the influence of SEI structure on the transport kinetics of lithium ions is much less significant than previously accepted. These results offer a new understanding of possible lithium ion transport pathway within SEI and may have implications for the future designs of fast-charging battery materials.

25 ENERGY STORAGE↗
DOE OSTI2026

High-pressure neutron powder diffraction study of an arsenolite deuterium inclusion compound: structure and formation kinetics

High-pressure variable-temperature neutron powder diffraction was employed to investigate the synthesis and structural properties of arsenolite (As 4 O 6 ), a cubic arsenic( III ) oxide polymorph, and its inclusion compound with deuterium. The compound forms with the stoichiometry As 4 O 6 ·2D 2 , consistent with earlier findings. At 295 K and 1.96(2) GPa, D 2 molecules occupy the 16c site (0, 0, 0) and are aligned along the <111> direction. The diffraction data suggest that the D 2 molecules at this site become rotationally disordered upon decompression to 0.78(2) GPa at 120 K, while no occupancy is observed at the 8a position (⅛, ⅛, ⅛) under any of the studied conditions. The kinetic data of the high-pressure inclusion compound synthesis at 1.56(2) and 1.96(2) GPa were analyzed using the Avrami model. The Avrami exponent, 0.135(16), remains invariant with pressure, demonstrating that the reaction topochemistry is unaffected by compression. Similarly, the reaction rates, 0.29(3) and 0.23(3) min −0.135 at 1.56(2) and 1.96(2) GPa, respectively, exhibit negligible pressure dependence and suggest a surprisingly low activation volume of 1.6 cm 3 mol −1 for the reaction. These results provide detailed insight into the structural dynamics and kinetics of deuterium inclusion in arsenolite under high pressure.

Guńka, Piotr A. [Warsaw University of Technology (↗
DOE OSTI2025

Decoupling electrode kinetics to elucidate reaction mechanisms in alkaline water electrolysis

Alkaline water electrolysis (AWE) presents key advantages, including reduced material costs, enhanced operational stability, and compatibility with non-precious metal catalysts, positioning it as a scalable route for hydrogen production. In this study, we introduce a minimally invasive single-cell configuration incorporating a reference electrode via diaphragm extension to form an internal ion channel. This setup, combined with an interfaced potentiostat and auxiliary electrometer, enables real-time, independent monitoring of anode and cathode behavior, offering high-resolution electrochemical diagnostics. While it is well established that the hydrogen evolution reaction (HER) exhibits sluggish kinetics in alkaline media, our study reveals that this limitation persists even in practical AWE systems where nickel-based substrates are used as electrodes. This observation is supported by both experimental data and voltage breakdown modeling. Arrhenius-type analysis reveals that localized electric fields induced by catalysts shift the reaction kinetics from classical Butler–Volmer behavior toward a Marcus-like regime, where interfacial molecular dynamics and bimolecular charge transfer dominate. We propose a semi-empirical model and a surficial reaction mechanism to describe these dynamics. This work underscores the critical need for cathode innovation and provides a rational framework for designing advanced catalysts and electrode architectures to optimize AWE performance.

08 HYDROGEN↗
DOE OSTI2025

Synthesis challenges, thermodynamic stability, and growth kinetics of La–Si–P ternary compounds

Although many new compounds have been recently predicted with the help of machine learning, the successful experimental synthesis of these compounds remains challenging. Computational insights about the thermodynamic stability and phase formation kinetics among the ground state and competing metastable phases are highly desirable to rationalize and attempt to overcome synthesis challenges experimentally. In this work, we explore synthetic challenges within ternary La–Si–P compounds through feedback between experimental and computational studies. We discuss the experimental challenges in forming three computationally predicted ternary phases (La 2 SiP, La 5 SiP 3 , and La 2 SiP 3 ). To understand the synthetic challenges, we performed molecular dynamics (MD) simulations using an accurate and efficient artificial neural network machine learning (ANN-ML) interatomic potential. We study the phase stability and formation kinetics of these ternary phases in relation to the reported and synthesized La 2 SiP 4 phase. While the growth of the La 2 SiP 4 phase can be reproduced by our MD simulation, our results indicate that the rapid formation of a Si-substituted LaP crystalline phase is a major barrier to the synthesis of the predicted La 2 SiP, La 5 SiP 3 , and La 2 SiP 3 ternary compounds, agreeing well with experimental observations. Our simulations also suggest that there is a narrow temperature window in which the La 2 SiP 3 phase can be grown from the solid–liquid interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Structural and kinetic characterization of an acetoacetyl-Coenzyme A: acetate Coenzyme A transferase from the extreme thermophile Thermosipho melanesiensis

Family 1 Coenzyme A transferases (CtfAB) from the extremely thermophilic bacterium, Thermosipho melanesiensis, has been used for in vivo acetone production up to 70°C. This enzyme has tentatively been identified as the rate-limiting step, due to its relatively low-binding affinity for acetate. However, existing kinetic and mechanistic studies on this enzyme are insufficient to evaluate this hypothesis. Here, kinetic analysis of purified recombinant T. melanesiensis CtfAB showed that it has a ping-pong bi-bi mechanism typical of Coenzyme A (CoA) transferases with Km values for acetate and acetoacetyl-CoA of 85 mM and 135 μM, respectively. Product inhibition by acetyl-CoA was competitive with respect to acetoacetyl-CoA and non-competitive with respect to acetate. Crystal structures of wild-type and mutant T. melanesiensis CtfAB were solved in the presence of acetate and in the presence or absence of acetyl-CoA. These structures led to a proposed structural basis for the competitive and non-competitive inhibition of acetyl-CoA: acetate binds independently of acetyl-CoA in an apparent low-affinity binding pocket in CtfA that is directly adjacent to a catalytic glutamate in CtfB. Similar to other CoA transferases, acetyl-CoA is bound in an apparent high-affinity binding site in CtfB with most interactions occurring between the phospho-ADP of CoA and CtfB residues far from the acetate binding pocket. This structural-based mechanism also explains the organic acid promiscuity of CtfAB. High-affinity interactions are predominantly between the conserved phospho-ADP of CoA, and the variable organic acid binding site is a low-affinity binding site with few specific interactions.

Biochemistry & Molecular Biology↗
DOE OSTI2020

Kinetic simulations of anomalous resistivity in high-temperature current carrying plasmas

Anomalous resistivity caused by lower hybrid drift instabilities (LHDIs) has been extensively studied in the literature, and has been invoked to explain the rates of magnetic diffusion and plasma profile evolution in the low-density plasma periphery of theta and screw pinch plasmas. In this article, we present a fully kinetic simulation study of LHDIs with a realistic mass ratio using the particle-in-cell code Chicago over a large range of drift speeds, 0.5 < v$^{2}_{di}$/v$^{2}_{ti}$ < 14.5, plasma β, β ≥ 2×10 –5 , and temperature ratios, 0.1 < T e /T i < 10. The resistivity quantified from the simulations is compared with the analytic estimates from the literature and a generalized resistivity expression is presented, which can be applied over the entire range of plasma environments that were simulated in this study. This expression uses the amplitude of the LHDI fluctuations resulting from instability saturation by electron resonance broadening rather than plateau formation, current relaxation, or ion trapping. The generalized resistivity expression is appropriate for full-scale fluid simulations that encounter a large range of plasma conditions, and has better agreement with the resistivity quantified from kinetic simulations than previous expressions in the literature, particularly at low plasma β. Anomalous resistivity has also been considered as an explanation of the rapid magnetic field dissipation during magnetic reconnection events at large plasma β. At a large β, the magnetic field fluctuations of LHDIs can dominate the electrostatic fluctuations and this article investigates enhanced collisionality due to the nonlinear magnetic force, δJ×δB/c.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Deep learning surrogate model for kinetic Landau-fluid closure with collision

In this work, the kinetic Landau-fluid (LF) closure with collision and periodic boundary condition is used in the development of the deep learning (DL) surrogate model. A classical neural network, namely, feedforward neural network or sometimes termed multilayer perceptron, is constructed and trained to learn the kinetic LF closure in the static limit and arbitrary mean free path in configuration space. The preliminary relation between best hyperparameters and critical parameters for data generation is found. Compared with the numerical approach (non-Fourier method) of the LF closure, the deep learning surrogate model shows an order of magnitude of improvement in terms of accuracy. Perhaps most importantly, the surrogate model closure has been integrated for the first time with fluid simulations. Our DL-enabled fluid simulations, for the first time, give the correct Landau damping rate for a wide range of wave vectors, while the Hammett–Perkins closure cannot produce the correct damping rate. We correctly connect the collisionless Hammett–Perkins closure and collisional Braginskii closure to reproduce the intrinsic nonlocal feature of the heat flux with DL techniques. We address the most concerning error accumulation problem and find that simulations with the deep learning surrogate model are as good as, if not better than, simulations with the analytic closure in terms of long-term numerical stability in the linear Landau damping test.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗