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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 OSTI2020

Prevalent root-derived phenolics drive shifts in microbial community composition and prime decomposition in forest soil

Phenolic compounds perform various functions in soil ranging from microbial substrate to toxin and form the basis of several plant-mediated processes. The aim of this study was to investigate how phenolics commonly exuded by tree roots influence soil organic matter (SOM) decomposition and interact with other labile forms of carbon (C) abundant in root exudates. Therefore, we performed a 38-day incubation experiment and assessed whether phenolic compounds (benzoic acid, caffeic acid and catechin) facilitated or inhibited SOM decomposition in a glucose-amended forest soil. Changes in decomposition, substrate use, fungal and bacterial community composition, and microbial abundance and activity were measured over time using 13 C-stable-isotope tracing, DNA-based molecular methods and enzyme assays. Our findings showed that phenolics inhibited microbial activity and abundance to varying degrees. Yet, benzoic acid was the only compound producing a substantial priming effect leading to a 21% increase in SOM decomposition, which was amplified in glucose-amended soils. This stimulation in microbial activity was associated with an increase in β-1,4-glucosidase activity and the bacterial genera Paraburkholderia and Caballeronia of the Burkholderiaceae family. Phenolics drove microbial community shifts in glucose-amended soils with negligible interactive effects. In conclusion, phenolic priming of SOM decomposition is associated with microbial community shifts and amplified in the presence of glucose. This evidence emphasizes the need for considering phenolics and interactions among root exudates as priming mechanisms in the rhizosphere and other soil environments where aromatics and phenolic compounds are abundant.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Ectomycorrhizal effects on decomposition are highly dependent on fungal traits, climate, and litter properties: A model-based assessment

It has been proposed that competition between ectomycorrhizal (ECM) fungi and free-living saprotrophs for resources like nitrogen (N) slows decomposition and increases the soil carbon storage in ECM ecosystems compared to arbuscular (AM) ecosystems. However, empirical evidence for the generality of such ECM effects is equivocal, and confounding mechanisms have been proposed that affect the magnitude and direction of ECM effects on soil carbon. Here, for this work, we conduct a theoretical modeling experiment, where we explicitly incorporate mycorrhizal processes into the Carbon, Organisms, Rhizosphere, and Protection in the Soil Environment (CORPSE) model. We use the model to explore the conditions under which ECM N acquisition processes can induce stronger saprotrophic N limitation and result in slower decomposition rates and greater soil organic carbon accumulation compared to AM processes. We found that the ECM fungi more strongly inhibited decomposition when litter inputs were N-depleted and relatively recalcitrant and when ECM fungi possessed a strong capacity to mine N from both recalcitrant soil organic matter and microbial necromass. Climate and seasonality also played a role as the ECM competition effect was strongest at low mean annual temperatures and when litterfall peaked seasonally. Priming effects driven by high root exudation rates in ECM-dominated systems could overwhelm the competition effect and reduce soil carbon under some circumstances. The ECM effect on decomposition in our simulations was highly context dependent. Based on our model results, we expect to see a strong ECM competition effect in temperate deciduous and boreal forests with relatively recalcitrant litter inputs, and with ECM fungi that produce oxidases and necromass-degrading enzymes. However, even a relatively strong ECM competition effect on decomposition only increased soil organic carbon accumulation by ~10%.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Thermal and Catalytic Decomposition of 2-Hydroxyethylhydrazine and 2-Hydroxyethylhydrazinium Nitrate Ionic Liquid

To develop chemical kinetics models for the combustion of ionic liquid-based monopropellants, identification of the elementary steps in the thermal and catalytic decomposition of components such as 2-hydroxyethylhydrazinium nitrate (HEHN) is needed but is currently not well understood. The first decomposition step in protic ionic liquids such as HEHN is typically the proton transfer from the cation to the anion, resulting in the formation of 2-hydroxyethylhydrazine (HEH) and HNO 3 . In the first part of this investigation, the high-temperature thermal decomposition of HEH is probed with flash pyrolysis (<1400 K) and vacuum ultraviolet (10.45 eV) photoionization time-of-flight mass spectrometry (VUV-PI-TOFMS). Next, the investigation into the thermal and catalytic decomposition of HEHN includes two mass spectrometric techniques: (1) tunable VUV-PI-TOFMS (7.4-15 eV) and (2) ambient ionization mass spectrometry utilizing both plasma and laser ionization techniques whereby HEHN is introduced onto a heated inert or iridium catalytic surface and the products are probed. The products can be identified by their masses, their ionization energies, and their collision-induced fragmentation patterns. Further, formation of product species indicates that catalytic surface recombination is an important reaction process in the decomposition mechanism of HEHN. The products and their possible elementary reaction mechanisms are discussed.

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

Effect of the Chemical States of Copper on Methanol Decomposition and Oxidation

Here, the decomposition and oxidation reactions of CH 3 OH over metallic Cu(100) and Cu 2 O-covered Cu(100) surfaces are studied using a combination of in-situ ambient-pressure X-ray photoelectron spectroscopy, Auger electron spectroscopy, and density functional theory calculations. We identify the sequential chemical transformation pathways from bond cleavage to the formation of intermediates and final products under operational conditions. Accumulative surface adsorption of CH 3 O species on metallic Cu(100) impedes the decomposition of CH 3 OH. Co-dosing on metallic Cu(100) with low pressures of 1·10 -4 Torr CH 3 OH + 1·10 -4 Torr O 2 results in partial oxidation of CH 3 OH, where the chemisorbed O ads reduces surface sites available for CH 3 O adsorption, decreasing the surface activity for CH 3 OH decomposition. In contrast, the Cu 2 O overlayer formed under the elevated pressures of 0.33 Torr CH 3 OH + 0.66 Torr O 2 promotes the total oxidation of CH 3 OH into the final products of CO 2 and H 2 O, arising from the active reaction 2 between lattice O within Cu 2 O and intermediates of CH 3 O, CH 2 O, HCOO, and CO. Despite the more favorable O-H bond scission, C-O bond scission also occurs to result in surface accumulation of CH x on metallic Cu(100), blocking active sites for decomposition reactions of CH 3 OH and CH 3 O. By comparison, the CH x species on the Cu 2 O-covered Cu(100) undergo oxidation into CO 2 and H 2 O with lattice O in the Cu 2 O overlayer, thereby freeing active sites for the total oxidation of CH 3 OH. These results highlight the distinct roles of metallic Cu and Cu 2 O in the pathways of CH 3 OH decomposition and oxidation reactions, offering practical insights for the design of Cu-based catalysts with tailored reactivity and selectivity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Intensified Soil Moisture Extremes Decrease Soil Organic Carbon Decomposition: A Mechanistic Modeling Analysis

Earth system models have predicted that there will be more frequent and severe precipitation and drought events in terrestrial ecosystems. Microbially mediated decomposition of soil organic carbon (SOC) tends to increase as soils wet and decrease as soils dry. However, the long-term SOC change under intensified moisture extremes remains poorly known as it depends on the frequency and intensity of soil drying and wetting. In this study, we explored long-term SOC dynamics under scenarios of alternating drying-wetting cycles using the Microbial-ENzyme Decomposition model, a mechanistic microbial model. The model was parameterized with 11 years of observations from a temperate deciduous broadleaf forest site, showing satisfactory model performance in both model calibration (R 2 = 0.67) and validation (R 2 = 0.69) against heterotrophic respiration. We then used the model to simulate the long-term SOC dynamics under five scenarios of alternating drying-wetting cycles with different frequencies and severities over a period of 100 years. Results showed that the changes in active microbial biomass C and the corresponding turnover rates of SOC pools were more sensitive to soil drying than soil wetting. As a result, the cumulative soil carbon emission from microbial respiration decreased by 433.7 g C m -2 after the 100-year simulation in the highest frequency and intensity moisture scenario, but was not significantly affected by the lowest frequency and intensity scenario. This study emphasizes the nonlinear response of SOC decomposition to soil moisture changes, which causes decreased decomposition by microbes under drying that is, not compensated by increased decomposition under wetting conditions.

58 GEOSCIENCES↗
DOE OSTI2024

The cluster decomposition of the configurational energy of multicomponent alloys

Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.

Chemistry↗
DOE OSTI2024

Martensite decomposition during rapid heating of Ti-6Al-4V studied via in situ synchrotron X-ray diffraction

Martensite, α‘, commonly appears in Ti-6Al-4V upon rapid cooling from above the β-transus temperature. It is known that α‘ decomposes into α and β at high temperatures but well below the β-transus temperature. Here, we study the decomposition of martensitic Ti-6Al-4V under rapid laser heating, employing in situ synchrotron X-ray diffraction. A comparison is made with post-annealed Ti-6Al-4V under heating to elucidate changes without martensite decomposition. The fast acquisition of X-ray diffraction data at 250 Hz temporally resolves the decomposition process initiated by annihilating dislocations in α‘. The recovery process is accompanied by structural changes in martensite, followed by the phase transformation to β. Thermal profiles estimated from the lattice parameter data reveal the influence of heating rates and dislocation densities on the decomposition process. Throughout the analysis of the diffraction profiles with respect to estimated temperature, we propose a straightforward method for approximating the initiation temperature of martensite decomposition.

42 ENGINEERING↗
DOE OSTI2021

Electrochemical Decomposition of Primary Alcohol Groups in Deep Eutectic Solvents

This work investigates the electrochemical decomposition of an ethylene glycol/sodium chloride electrolyte and a deep eutectic solvent (DES) comprised of ethylene glycol/choline chloride (ethaline). Understanding these reactions can help to better understand the safety risks of overcharge when these electrolytes are used in a battery and to guide the design of DES electrolytes for improved electrochemical stability. Analysis of the decomposition products was performed using a combination of coulometry, gas chromatography, mass spectrometry, and Fourier transform infrared spectroscopy. It was found that even at relatively low (mM) concentrations of water, a stoichiometric rate of hydrogen is produced under cathodic conditions in both the ethaline and EG/NaCl electrolytes. This suggest an electrochemical hydrolysis cathodic decomposition reaction that produces both hydrogen gas and hydroxyl ions. This reaction was verified in both electrolytes by also identifying the liquid phase products. Only liquid phase products were observed under anodic conditions. A suspected alcohol oxidation to aldehyde anodic decomposition reaction was confirmed through a similar analysis of products. A tertiary alcohol only DES was investigated to eliminate these decomposition paths and was found to have increased stability window compared to the primary alcohol.

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

Increasing temperatures reduce invertebrate abundance and slow decomposition

Decomposition is an essential ecosystem service driven by interacting biotic and abiotic factors. Increasing temperatures due to climate change can affect soil moisture, soil fauna, and subsequently, decomposition. Understanding how projected climate change scenarios will affect decomposition is of vital importance for predicting nutrient cycling and ecosystem health. In this study, we experimentally addressed the question of how the early stages of decomposition would vary along a gradient of projected climate change scenarios. Given the importance of biodiversity for ecosystem service provisioning, we measured the effect of invertebrate exclusion on red maple ( Acer rubrum ) leaf litter breakdown along a temperature gradient using litterbags in warming chambers over a period of five weeks. Leaf litter decomposed more slowly in the warmer chambers and in the litterbag treatment that minimized invertebrate access. Moreover, increasing air temperature reduced invertebrate abundance and richness, and altered the community composition, independent of exclusion treatment. Using structural equation models, we were able to disentangle the effects of average air temperature on leaf litter loss, finding a direct negative effect of warming on the early stages of decomposition, independent of invertebrate abundance. This result indicates that not only can climate change affect the invertebrate community, but may also directly influence how the remaining organisms interact with their environment and their effectiveness at provisioning ecosystem services. Overall, our study highlights the role of biodiversity in maintaining ecosystem services and contributes to our understanding of how climate change could disrupt nutrient cycling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Calcium is associated with specific soil organic carbon decomposition products

Abstract. Calcium (Ca) may contribute to the preservation of soil organic carbon (SOC) in more ecosystems than previously thought. Here, we provide evidence that Ca is co-located with SOC compounds that are enriched in aromatic and phenolic groups, across different acidic soil types and locations with different ecosystem properties, differing in terms of climate, parent material, soil type, and vegetation. In turn, this co-localised fraction of Ca–SOC is removed through cation exchange, and the association is then only re-established during decomposition in the presence of Ca (Ca addition incubation). Thus, this highlights a causative link between decomposition and the co-location of Ca with a characteristic fraction of SOC. Decomposition increases the relative proportion of negatively charged functional groups, which can increase the propensity for the association between SOC and Ca; in turn, this association can inhibit dissolved organic carbon export or further decomposition. We propose that this mechanism could be driven by Ca hotspots at the microscale shifting local decomposition processes and thereby explaining the co-location of Ca with SOC of a specific composition across different acidic soil environments. Incorporating this biogeochemical process into Earth system models could improve our understanding, predictions, and management of carbon dynamics in soils, as well as accounting for their response to Ca-rich amendments.

Rowley, Mike C. (ORCID:0000000224407855)↗
DOE OSTI2025

Arctic shrub and Eriophorum leaf and root decomposition, northern Alaska, 2017-2018

This data package contains litter decomposition data collected from 170 plots of rapidly expanding shrub genera (Alnus, Betula, and Salix) and a widespread sedge (Eriophorum vaginatum) along a latitudinal and temperature gradient in northern Alaska. These data were produced from a litter bag experiment that took place from July 2017 to July 2018 and include mass loss and nitrogen loss decomposition metrics for both leaf and root litters. These raw data support a submitted manuscript that examines the variability in decomposition between shrub and graminoid leaf and root litters across a 1-year experiment across the graminoid-dominated Arctic tundra and reveals how deciduous shrub expansion affects litter decomposition in tundra ecosystems. Data are presented by site (n=5) and patch (shrub or sedge plot) in csv files. The site and plot location data and environmental measurement data are provided in Fraterrigo and Chen (2020). Additional methods regarding plot distribution and environmental measurements are in Chen et al. (2020) and Fraterrigo et al. (2024).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Comparative analysis of sublimation and thermal decomposition of TATB

This experimental study investigated the effects of confinement, starting mass, and heating rate on TATB thermal decomposition and sublimation using a combined Thermo-Gravimetric Analyzer and Differential Scanning Calorimetry (TGA/DSC) instrument. The confinement of volatile products was varied using different pinhole sizes with TGA/DSC pans. The measurements showed the open pan experiments without lids/pinholes resulted in complete sublimation of TATB between 320 °C and 360 °C. The heat of sublimation was determined to be 176 kJ/mol (42 kcal /mol), consistent with literature data obtained from other experimental techniques. The use of pinholes suppressed the sublimation of TATB such that the decrease in pinhole size resulted in 1) an increase in the enthalpy of reaction and an increase in the amount of carbonaceous material remaining at the end of decomposition, and 2) convergence of the two peak temperatures corresponding to maximum heat flow and maximum weight loss. Also, a transition from a two-exotherm thermal decomposition behavior towards a single-exotherm occurred as the pinhole size was decreased for a given starting mass or as the starting mass was increased for a given pinhole size. These results indicate the kinetics of TATB sublimation, TATB thermal decomposition, and gas diffusion out of a TGA/DSC pan can all compete and result in significantly different enthalpies, amounts of remaining materials, and peak temperatures depending on the pinhole size and starting mass used in the measurements. Furthermore, the results also indicate precise control of process variables (pinhole size, starting mass, and heating rate) in TGA/DSC measurements is required for thermal safety assessment of explosives.

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

TATB thermal decomposition: Expanding the molecular profile with cryo-focused pyrolysis GC-MS

Understanding the molecular composition of high explosives during thermal decomposition is vital for predicting the sensitivity, safety, and performance of explosive materials. The thermal decomposition of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has been linked to the formation of furazans through a series of dehydration reactions of the NO2 and NH2 groups on the phenyl ring, along with breakdown into small molecules (≤120 amu). Molecular identification of compounds formed in this transformation of the furazans to light gases has been lacking. To address this, we have applied a pseudo-confined sampling system in a cryo-focused pyrolysis gas chromatography-mass spectrometry (pyGC-MS) system to molecularly identify these intermediates. By design, sublimation of TATB, which has complicated MS analyses of thermal degradation, was significantly reduced and additional compounds were identified with potential structural information. In addition to the known furazan compounds, one of these compounds forms from the loss of oxygen from benzo-trifurazan (F3) and produces an open ring structure that may be the first step in the formation of lower molecular weight furazan breakdown products. The loss of a nitro group from benzo-monofurazan (F1) was also discovered and implicates the formation of oxidizing NO2 gas in the thermal decomposition mechanism. So these findings are vital for understanding the proper heat flow from energetic materials on a molecular level, necessary when measuring enthalpy and developing decomposition models based on kinetic parameters.

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

Reaction Pathways and Energy Consumption in NH 3 Decomposition for H 2 Production by Low Temperature, Atmospheric Pressure Plasma

Pathways for NH 3 decomposition to N 2 and N 2 H 4 by atmospheric pressure nonthermal plasma are analyzed using a combination of molecular beam mass spectrometry measurements and zero-dimensional kinetic modeling. Experimental measurements show that NH 3 conversion and selectivity towards N 2 formation scale monotonically with the specific energy input into the plasma with ~ 100% selectivity to N 2 formation achieved at specific energy inputs above 0.12 J cm −3 (3.1 eV (molecule NH 3 ) −1 ). The kinetic model recovers these trends, although it underpredicts N 2 selectivity at low specific energy input. These discrepancies can be explained by the underestimation of reaction rate coefficients for reactions that consume N 2 H x species in collisions with H radicals and/or radial nonuniformities in power deposition, gas temperature, and species concentrations that are not represented by the plug flow approximation used in the model. The kinetic model shows that N 2 formation proceeds through N 2 H x decomposition pathways rather than NH x decomposition pathways in low temperature, atmospheric pressure plasma. Higher selectivity toward N 2 production can be achieved by operating at higher NH 3 conversion and with a higher gas temperature. Furthermore, the high energy cost of NH 3 decomposition by atmospheric pressure nonthermal plasma found in this work (25–50 eV (molecule NH 3 converted) −1 ; 17–33 eV (molecule H 2 formed) −1 ) is a result of the energy requirement for electron-impact dissociation of NH 3 and the significant re-formation of NH 3 by three-body recombination reactions between NH 2 and H.

Nonthermal plasma↗
DOE OSTI2019

Optimization of CCT Equations Using Calculated Grain Boundary Soluble Compositions for the Simulation of Austenite Decomposition of Steels

New CCT equations have been developed and optimized to simulate the start temperatures of the austenite decomposition process in low-alloyed steels using experimental CCT data published in the literature. Exceptionally, this optimization does not apply the nominal compositions of the steels, but the corresponding soluble compositions of the grain boundaries calculated using IDS software, depending on the reported austenitization treatments of the steels. These compositions, rather than the nominal ones, are expected to control the start of the austenite decomposition, which usually initiates at the grain boundaries. The new optimization treatment takes into account the solute microsegregation and the possible precipitate formation. Using IDS software, the new equations were validated with new experimental CCT data. Agreement was good not only for the austenite decomposition start temperatures, but also for the final phase fractions, indicating fairly reasonable predictions of phase transformation kinetics by the IDS. In addition, IDS simulations were compared with the experimental CCT data of five high-carbon steels, applying both the new equations based on grain boundary soluble compositions as well as the equations based on the nominal compositions. With the same experimental CCT data used in optimization, better agreement was obtained with the new equations, indicating the importance of determining the soluble compositions at the grain boundaries where the austenite decomposition process is likely to begin.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗