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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

High-Resolution South American Wind Resource Data Downscaled with Generative Machine Learning Conditioned on Near-Surface Observations

High-resolution historical wind data was developed for the entirety of South America using the innovative Super-Resolution for Renewable Resource Data (sup3r) machine learning framework. The publicly available Sup3rWind South America dataset represents a significant advancement in wind resource data generation, leveraging generative machine learning conditioned on near-surface observations from the Meteorological Assimilation Data Ingest System (MADIS) to efficiently and accurately downscale coarse reanalysis data from the European Centre for Medium-Range Weather Forecasts (ERA5). This approach produces fine-scale, spatially and temporally coherent wind and meteorological fields hundreds of times more computationally efficient than traditional numerical weather modeling methods, enabling access to high-fidelity wind information across both continental and offshore regions. Sup3rWind South America builds on the earlier Sup3rWind Ukraine dataset through improvements in model architecture and outputs conditioned on near-surface observation inputs. As with the Ukraine data release, this dataset includes wind speed, wind direction, temperature, relative humidity, and pressure at a horizontal resolution of ~2 km, representing a 15x spatial enhancement relative to the 31 km ERA5 grid. Wind speed and direction are provided at 5-minute resolution, a 12x temporal refinement compared to the hourly ERA5 data, while temperature, relative humidity, and pressure remain at hourly resolution. The data covers all years from 2005 to 2024. Before downscaling, ERA5 inputs were bias-corrected using long-term monthly means and a limited number of quality-controlled observations to align large-scale statistics with regional conditions. The resulting dataset is the first publicly available high-resolution timeseries wind record that provides full spatial coverage of South America. Model validation demonstrates strong agreement with observations across several statistical metrics, consistent with other state-of-the-art high-resolution wind resource datasets. The potential applications of Sup3rWind South America span renewable energy resource assessment, energy system modeling, and grid resilience analysis. The 20-year record and high spatial and temporal resolution support accurate estimation of long-term energy yield and the economic feasibility of potential wind development sites. Continuous coverage across both continental and offshore regions enables comprehensive site prospecting within exclusive economic zones. The 2 km, 5-minute resolution data provide the spatial and temporal variability required for power system simulation, operational planning, and regional risk assessments.

17 WIND ENERGY↗
DOE OSTI2019

High temperature oxidation and microstructural evolution of cold spray chromium coatings on Zircaloy-4 in steam environments

Oxidation kinetics and microstructural evolution of cold sprayed Cr coatings on Zircaloy-4 at 1130–1310 °C in flowing steam at atmospheric pressure have been studied. The study is aimed at understanding of the response of Cr coated Zr-alloy under a steam environment and high temperatures pertinent to design basis accidents (DBAs) and beyond design basis accidents (BDBAs) in light water reactors (LWRs). Surface morphology, microstructure, and phases of post-oxidation test samples were characterized using Scanning Electron Microscopy (SEM), x-ray diffraction (XRD), and Scanning Transmission Electron Microscopy (STEM). Growth kinetics of the Cr-oxide scale and interdiffusion layers between the Cr coating and the Zr-alloy substrate were quantified from cross-sectional SEM images. Cross-sectional analysis showed that the Cr coatings offered a 50 times reduction in oxidation rate over bare Zircaloy-4 in a 1310 °C steam environment. Oxidation kinetics at 1130 °C followed parabolic law (i.e., n ~ 0.5 in power law kinetics) but at 1230 °C and 1310 °C the value of n was suppressed to below 0.5 possibly due to the volatilization of Cr species at the two highest temperatures. Interdiffusion at coating/substrate interface resulted in formation of a brittle Cr 2 Zr or Zr(Fe, Cr) 2 intermetallic compound layer on the order of micrometer in thickness and scattered Cr-rich precipitates were observed well below the interface within the Zr-alloy substrate after cooling. These experimental results could provide data to LWR system simulation codes for better estimation of coping time in the event of accidents.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An extended methodology for automated calculations of non-Boltzmann kinetic sequences: H + C 2 H 2 + X and combustion impact

It is generally assumed in phenomenological kinetic models that bimolecular reactions only occur between species whose rovibrational energy follows a Boltzmann (thermal) distribution. That is, any complexes initially formed in non-Boltzmann distributions are assumed to be thermalized by energy-transferring collisions prior to bimolecular reactions. Given the high mole fractions of reactive species, X, in combustion environments, reactive collisions of the complexes with X often occur on the same timescale as energy-transferring collisions – yielding sequences proceeding through non-Boltzmann intermediates across multiple potential energy surfaces. Recent studies have shown that such non-Boltzmann kinetic sequences can have substantial impact on the global reactivity in combustion systems. Simulations of these non-Boltzmann reaction sequences, which can be described in phenomenological kinetic models via chemically termolecular reactions, require that rovibrational excitation from one potential energy surface be carried over to the next. Here this paper presents an extended theoretical and computational methodology that couples multiple master equations and derives rate constants for phenomenological reactions describing the conversion of thermal reactants to thermal products for use in phenomenological kinetic schemes. The methodology is then implemented using in-house scripts for non-Boltzmann sequences involving C2H$^*_3$ + X (with X = O 2 , H, and OH) where C 2 H$^*_3$ is formed via H + C 2 H 2 association – which were identified as having strong potential for influencing combustion predictions in a recent study. The results reveal that non-Boltzmann reaction sequences for X = O 2 (the primary focus of this paper) significantly alters the total conversion rate from H + C 2 H 2 to products and product branching fractions from those of thermal sequential pathways. Furthermore, the present results demonstrate that non-Boltzmann reaction sequences have significant impact – as high as an order of magnitude – on predicted ignition delay times. Similarly, they yield significantly different dependence of ignition delay times with temperature and O 2 mole fraction – yielding signatures that are likely observable experimentally.

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

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗
DOE OSTI2020

Passivating Nucleobases Bring Charge Transfer Character to Optically Active Transitions in Small Silver Nanoclusters

DNA-wrapped silver nanoclusters (DNA–AgNCs) are known for their efficient luminescence. However, their emission is highly sensitive to the DNA sequence, the cluster size, and its charge state. To get better insights into photophysics of these hybrid systems, simulations based on density functional theory (DFT) are performed. Our calculations elucidate the effect of the structural conformations, charges, solvent polarity, and passivating bases on optical spectra of DNA–AgNCs containing five and six Ag atoms. It is found that inclusion of water in calculations as a polar solvent media results in stabilization of nonplanar conformations of base-passivated clusters, while their planar conformations are more stable in vacuum, similar to the bare Ag5 and Ag6 clusters. Cytosines and guanines interact with the cluster twice stronger than thymines, due to their larger dipole moments. In addition to the base–cluster interactions, hydrogen bonds between bases notably contribute to the structure stabilization. While the relative intensity, line width, and the energy of absorption peaks are slightly changing depending on the cluster charge, conformations, and base types, the overall spectral shape with five well-resolved bands at 2.5–5.5 eV is consistent for all structures. Independent of the passivating bases and the cluster size and charge, the low energy optical transitions at 2.5–3.5 eV exhibit a metal to ligand charge transfer (MLCT) character with the main contribution emerging from Ag-core to the bases. Cytosines facilitate the MLCT character to a larger degree comparing to the other bases. However, the doublet transitions in clusters with the open shell electronic structure (Ag5 and Ag6 + ) result in appearance of additional red-shifted (<2.5 eV) and optically weak band with negligible MLCT character. The passivated clusters with the closed shell electronic structure (Ag5 + and Ag6) exhibit higher optical intensity of their lowest transitions with much higher MLCT contribution, thus having better potential for emission, than their open shell counterparts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Structure–Thermodynamic Relationship of a Polysaccharide Gel (Alginate) as a Function of Water Content and Counterion Type (Na vs Ca)

Biofilms are the predominant mode of microbial life on Earth, and so a deep understanding of microbial communities-and their impacts on environmental processes-requires a firm understanding of biofilm properties. Because of the importance of biofilms to their microbial inhabitants, microbes have evolved different ways of engineering and reconfiguring the matrix of extracellular polymeric substances (EPS) that constitute the main non-living component of biofilms. This ability makes it difficult to distinguish between the biotic and abiotic origins of biofilm properties. An important route toward establishing this distinction has been the study of simplified models of the EPS matrix. This study builds on such efforts by using atomistic simulations to predict the nanoscale (≤10 nm scale) structure of a model EPS matrix and the sensitivity of this structure to interpolymer interactions and water content. To accomplish this, we use replica exchange molecular dynamics (REMD) simulations to generate all-atom configurations of ten 3.4 kDa alginate polymers at a range of water contents and Ca–Na ratios. Simulated systems are solvated with explicitly modeled water molecules, which allows us to capture the discrete structure of the hydrating water and to examine the thermodynamic stability of water in the gels as they are progressively dehydrated. Our primary findings are that (i) the structure of the hydrogels is highly sensitive to the identity of the charge-compensating cations, (ii) the thermodynamics of water within the gels (specific enthalpy and free energy) are, surprisingly, only weakly sensitive to cation identity, and (iii) predictions of the differential enthalpy and free energy of hydration include a short-ranged enthalpic term that promotes hydration and a longer-ranged (presumably entropic) term that promotes dehydration, where short and long ranges refer to distances shorter or longer than ~0.6 nm between alginate strands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Evaluating cloud feedbacks and rapid responses in the ACCESS model

A cloud feedback diagnostic package is implemented in the Australian Community Climate and Earth-System Simulator General Circulation Model, based on the methodology of “cloud radiative kernels.” Using separate increased sea surface temperature and CO 2 experiments, both the “rapid response” cloud contribution to forcing and temperature-mediated cloud feedbacks are analyzed. Under increased temperature and CO 2 changes, temperature-mediated cloud radiative feedback dominates over the rapid response in the final radiative response. Cloud feedback is positive in both long and short wave, with short wave dominating global values. Contributing most to this are low to mid-level clouds, of medium-to-high optical thickness. As a means of illustration of the methodology, a number of key parameters related to clouds, precipitation, and convection that are typically used in “tuning” in the model are modified. These changes result in substantial impacts on the model's current climate, but only modest changes to rapid response and feedbacks occur globally, regionally, and as a function of cloud optical thickness and height. This limited set of experiments shows that cloud adjustments and feedbacks in this model are robust under these changes, lending confidence that both model climate change projections and the conclusions of attribution studies are not overly sensitive to such parameterization tuning. Of course, a considerably larger set of experiments would be needed to demonstrate that feedbacks and rapid response are robust under the wider set of tuning adjustments commonly undertaken.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Mixed‐Phase Clouds Over the Southern Ocean as Observed From Satellite and Surface Based Lidar and Radar

Abstract This study investigates the occurrence of mixed‐phase clouds (MPC, i.e., cloud layers containing both liquid and ice water at sub‐freezing temperatures) over the Southern Ocean (SO) using space‐ and surface‐based lidar and radar observations. The occurrence of supercooled clouds is dominated by geometrically thin (<1 km) layers that rarely contain ice. We diagnose layers that are geometrically thicker than 1 km to contain ice ~65% and ~4% of the time from below by surface remote sensors and from above by orbiting remote sensors, respectively. We examine the discrepancy in MPC occurrence statistics as diagnosed from below and above the cloud layer. From above, we find that MPC occurrence has a gradient associated with the Antarctic Polar Front near 55°S with a rare occurrence of satellite‐derived MPC south of that latitude. In contrast, surface sensors find ice in 33% of supercooled liquid water layers. We infer using observing system simulation experiments and data analysis that space‐based lidar cannot identify the occurrence of MPC except when secondary ice‐forming processes operate in convection that is, sufficiently strong to loft ice crystals to cloud tops. We conclude that the CALIPSO phase statistics of MPC have a severe low bias in MPC occurrence. Based on surface‐based statistics in the SO, we present a parameterization of the frequency of MPC as a function of cloud top temperature that differs substantially from that used in recent climate model simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Stress Testing California's Hydroclimatic Whiplash: Potential Challenges, Trade‐Offs and Adaptations in Water Management and Hydropower Generation

Abstract Inter‐annual precipitation in California is highly variable, and future projections indicate an increase in the intensity and frequency of hydroclimatic “whiplash.” Understanding the implications of these shocks on California's water system and its degree of resiliency is critical from a planning perspective. Therefore, we quantify the resilience of reservoir services provided by water and hydropower systems in four basins in the western Sierra Nevada. Using downscaled runoff from 10 climate model outputs, we generated 200 synthetic hydrologic whiplash sequences of alternating dry and wet years to represent a wide range of extremes and transitional conditions used as inputs to a water system simulation model. Sequences were derived from upper (wet) and lower (dry) quintiles of future streamflow projections (2030–2060). Results show that carryover storage was negatively affected in all basins, particularly in those with lower storage capacity. All basins experienced negative impacts on hydropower generation, with losses ranging from 5% to nearly 90%. Reservoir sizes and inflexible operating rules are a particular challenge for flood control, as in extremely wet years spillage averaged nearly the annual basins' total discharge. The reliability of environmental flows and agricultural deliveries varied depending on the basin, intensity, and duration of whiplash sequences. Overall, wet years temporarily rebound negative drought effects, and greater storage capacity results in higher reliability and resiliency, and lesser volatility in services. We highlight potential policy changes to improve flexibility, increase resilience, and better equip managers to face challenges posed by whiplash while meeting human and environmental needs.

Environmental Sciences & Ecology↗
DOE OSTI2016

Plasma diagnostics in spherical tokamaks with silicon charged-particle detectors

Detection of charged fusion products, such as protons and tritons resulting from D(d, p) t reactions, can be used to determine the position and time dependent fusion reaction rate profile in spherical tokamak plasmas with neutral beam heating. We have developed a prototype instrument consisting of 6 ion-implanted-silicon surface barrier detectors combined with collimators in such a way that each detector can accept 3 MeV protons and 1 MeV tritons and thus provides a curved view across the plasma cross section. The combination of the results from all six detectors will provide information on the spatial distribution of the fusion reaction rate. The expected time resolution of about 1 ms makes it possible to study changes in the reaction rate due to slow variations in the neutral beam density profile, as well as rapid changes resulting from MHD instabilities. Details of the new instrument, its data acquisition system, simulation results, and electrical noise testing results are discussed in this paper. First experimental data are expected to be taken during the current experimental campaign at NSTX-U.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Long-lived polaritonic coherence and polaron decoupling effects in 2D electronic spectra

Molecular polaritons, formed by coupling molecular excitons with cavity photons, offer a promising platform for exploring quantum phenomena. A key challenge is understanding how these hybrid states maintain coherence in the presence of environmental vibrations. Here, we show theoretically that collective coupling of many molecular excitons in a cavity can protect polariton coherence from phonon-induced decoherence. Under realistic conditions, the coherence time can extend up to 200 fs at room temperature, compared with 15 fs for typical molecular systems. Simulations of two-dimensional electronic spectra reveal prolonged oscillations between upper and lower polariton states, and reduced vibrational coupling as indicated by changes in the nodal line slope of the lower polariton peak. These findings provide guidance for experimental efforts to realize long-lived polaritons, such as coupling CdSe nanoplatelets to optical cavities.

2D electronic spectroscopy↗
DOE OSTI2025

Modeling household-level party composition behavior for multiparty activities: a random parameter nested logit modeling approach

This study presents findings of a household-level party composition model for multiparty activities. It exploits data from a comprehensive Household Travel Survey conducted by Chicago Metropolitan Agency of Planning. The study estimates a random parameter nested logit model to capture households’ unobserved preference heterogeneity and non-proportional substitution patterns in terms of activity party composition for multiparty activities. A wide variety of household demographics, activity attributes and residential neighborhood characteristics are examined in this paper. The magnitude of the impacts of the determinants are tested in this study by analyzing the elasticity of the variables, which suggests that household demographics and attributes of the multiparty activities have significant effects on the household-level activity party composition. Residential neighborhood characteristics, although somewhat less impactful, still play a meaningful role. This model will be implemented within the POLARIS transportation systems simulator to improve the activity generation modeling workflow, and the prediction accuracy of various activity-travel components.

activity party composition↗
DOE OSTI2026

AI-supported mini-labs: combining smartphone-based experiments and multimodal AI

Multimedia learning has always been a topic in physics education—whether through specialized digital data acquisition systems, simulations, or animations. Due to increasing digitalization, more and more media from our everyday lives have also found their way into education in recent decades. This contribution introduces a conceptual framework and illustrative examples for AI-supported experimentation in physics education. It does not yet present empirical data but outlines directions for forthcoming classroom studies evaluating learning outcomes and engagement.

generative AI↗
DOE OSTI2021

Integrating crop growth models with remote sensing for predicting biomass yield of sorghum

Abstract Plant phenotypes are often descriptive, rather than predictive of crop performance. As a result, extensive testing is required in plant breeding programmes to develop varieties aimed at performance in the target environments. Crop models can improve this testing regime by providing a predictive framework to (i) augment field phenotyping data and derive hard-to-measure phenotypes and (ii) estimate performance across geographical regions using historical weather data. The goal of this study was to parameterize the Agricultural Production Systems sIMulator (APSIM) crop growth models with remote-sensing and ground-reference data to predict variation in phenology and yield-related traits in 18 commercial grain and biomass sorghum hybrids. Genotype parameters for each hybrid were estimated using remote-sensing measurements combined with manual phenotyping in West Lafayette, IN, in 2018. The models were validated in hybrid performance trials in two additional seasons at that site and against yield trials conducted in Bushland, TX, between 2001 and 2018. These trials demonstrated that (i) maximum plant height, final dry biomass and radiation use efficiency (RUE) of photoperiod-sensitive and -insensitive forage sorghum hybrids tended to be higher than observed in grain sorghum, (ii) photoperiod-sensitive sorghum hybrids exhibited greater biomass production in longer growing environments and (iii) the parameterized and validated models perform well in above-ground biomass simulations across years and locations. Crop growth models that integrate remote-sensing data offer an efficient approach to parameterize larger plant breeding populations.

Yang, Kai-Wei↗
DOE OSTI2023

Recombination smooths the time-signal disrupted by latency in within-host HIV phylogenies

Within-host HIV evolution involves several features that may disrupt standard phylogenetic reconstruction. One important feature is re-activation of latently integrated provirus, which has the potential to disrupt the temporal signal, leading to variation in the branch lengths and apparent evolutionary rates in a tree. Yet, real within-host HIV phylogenies tend to show clear, ladder-like trees structured by the time of sampling. Another important feature is recombination, which violates the fundamental assumption that evolutionary history can be represented by a single bifurcating tree. Thus, recombination complicates the within-host HIV dynamic by mixing genomes and creating evolutionary loop structures that cannot be represented in bifurcating trees. In this paper, we develop a coalescent-based simulator of within-host HIV evolution that includes latency, recombination, and effective population size dynamics that allows us to study the relationship between the true, complex genealogy of within-host HIV evolution, encoded as an Ancestral Recombination Graph (ARG), and the observed phylogenetic tree. To compare our ARG results to the familiar phylogeny format, we calculate the expected bifurcating tree after decomposing the ARG into all unique site trees, their combined distance matrix, and the overall corresponding bifurcating tree. While latency and recombination separately disrupt the phylogenetic signal, remarkably, we find that recombination recovers the temporal signal of within-host HIV evolution caused by latency by mixing fragments of old, latent genomes into the contemporary population. In effect, recombination averages over extant heterogeneity, whether it stems from mixed time-signals or population bottlenecks. Further, we establish that the signals of latency and recombination can be observed in phylogenetic trees despite being an incorrect representation of the true evolutionary history. Using an Approximate Bayesian Computation method, we develop a set of statistical probes to tune our simulation model to nine longitudinally-sampled within-host HIV phylogenies. Because ARGs are exceedingly difficult to infer from real HIV data, our simulation system allows investigating effects of latency, recombination, and population size bottlenecks by matching decomposed ARGs to real data as observed in standard phylogenies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Driven responses of periodically patterned superconducting films

Here, we simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density J c , the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f 0 , which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Cellulose nanofibrils and nanocrystals in confined flow: Single-particle dynamics to collective alignment revealed through scanning small-angle x-ray scattering and numerical simulations

Nanostructured materials made through flow-assisted assembly of proteinaceous or polymeric nanosized fibrillar building blocks are promising contenders for a family of high-performance biocompatible materials in a wide variety of applications. Optimization of these processes relies on improving our knowledge of the physical mechanisms from nano- to macroscale and especially understanding the alignment of elongated nanoparticles in flows. Here, we study the full projected orientation distributions of cellulose nanocrystals (CNCs) and nanofibrils (CNFs) in confined flow using scanning microbeam SAXS. For CNCs, we further compare with a simulated system of dilute Brownian ellipsoids, which agrees well at dilute concentrations. However, increasing CNC concentration to a semidilute regime results in locally arranged domains called tactoids, which aid in aligning the CNC at low shear rates, but limit alignment at higher rates. Similarly, shear alignment of CNF at semidilute conditions is also limited owing to probable bundle or flock formation of the highly entangled nanofibrils. Finally, this work provides a quantitative comparison of full projected orientation distributions of elongated nanoparticles in confined flow and provides an important stepping stone towards predicting and controlling processes to create nanostructured materials on an industrial scale.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Reaction rates for a generalized reaction-diffusion master equation

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗