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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Generalizing mkFit and its Application to HL-LHC

mkFit is an implementation of the Kalman filter-based track reconstruction algorithm that exploits both thread- and data-level parallelism. In the past few years the project transitioned from the R&D phase to deployment in the Run-3 offline workflow of the CMS experiment. The CMS tracking performs a series of iterations, targeting reconstruction of tracks of increasing difficulty after removing hits associated to tracks found in previous iterations. mkFit has been adopted for several of the tracking iterations, which contribute to the majority of reconstructed tracks. When tested in the standard conditions for production jobs, speedups in track pattern recognition are on average of the order of 3.5x for the iterations where it is used (3-7x depending on the iteration). Multiple factors contribute to the observed speedups, including vectorization and a lightweight geometry description, as well as improved memory management and single precision. Efficient vectorization is achieved with both the icc and the gcc (default in CMSSW) compilers and relies on a dedicated library for small matrix operations, Matriplex, which has recently been released in a public repository. While the mkFit geometry description already featured levels of abstraction from the actual Phase-1 CMS tracker, several components of the implementations were still tied to that specific geometry. We have further generalized the geometry description and the configuration of the run-time parameters, in order to enable support for the Phase-2 upgraded tracker geometry for the HL-LHC and potentially other detector configurations. The implementation strategy and high-level code changes required for the HL-LHC geometry are presented. Speedups in track building from mkFit imply that track fitting becomes a comparably time consuming step of the tracking chain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Three-step colloidal gelation revealed by time-resolved x-ray photon correlation spectroscopy

The gelation of PEGylated gold nanoparticles dispersed in a glycerol–water mixture is probed in situ by x-ray photon correlation spectroscopy. Following the evolution of structure and dynamics over 10 4 s, a three-step gelation process is found. First, a simultaneous increase of the Ornstein–Zernike length ξ and slowdown of dynamics is characterized by an anomalous q-dependence of the relaxation times of τ ∝q -6 and strongly stretched intermediate scattering functions. After the structure of the gel network has been established, evidenced by a constant ξ, the dynamics show aging during the second gelation step accompanied by a change toward ballistic dynamics with τ ∝ q -1 and compressed correlation functions. In the third step, aging continues after the arrest of particle motion. Our observations further suggest that gelation is characterized by stress release as evidenced by anisotropic dynamics once gelation sets in.

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

New method for level-lifetime measurements with thick scintillators

Level lifetimes provide key insight into the structure of atomic nuclei and serve as stringent tests of theoretical descriptions. Though several methods for determining level lifetimes exist for both reaction measurements and decay studies, here the focus is on techniques involving the direct measurement of time differences between population and subsequent depopulation of excited states. The techniques presented herein are broadly applicable across multiple timing ranges, but the approach is specifically described for the βγ timing method. A multi-step, amplitude-dependent time walk correction was employed to address the data analysis complications that arise from using thick scintillators for electron detection. Further, additional corrections for the depth of the interaction must also be performed when the parent isotope has been implanted into the detector. Techniques are presented for performing these time walk and depth of interaction corrections. Subsequently, a new Monte Carlo method utilizing measured detector responses obtained from the data, coupled with chi-square minimization, is presented for extracting excited state lifetimes ≳ 100 picoseconds. The framework of this Monte Carlo method is developed for the decay of a state in 68 Zn with a known 1.6 ps half life, which is considered prompt given the detection sensitivity of the technique, and then benchmarked using two other excited states in neutron-rich Ni isotopes with 120(34) ps and 1.05(3) ns half lives. Using this new method which takes into account the thick scintillator used, these same half lives were measured to be 135(10) ps and 1.04(24) ns, respectively. The overall good agreement demonstrates the validity of the technique.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗
DOE OSTI2025

An Arbitrary Time Interval Generator Base on Vernier Clocks with 0.67 ps Adjustable Steps Implemented in FPGA

In TDC testing and timing system implementations, it is often necessary to generate signal pulses with finely adjustable time intervals. In delay cell–based schemes, the adjustment resolution is constrained by the propagation delay of the cells—typically 15–20 ps per step—and is sensitive to temperature and supply voltage variations. This document presents a fully digital approach that uses two vernier clocks, generated by two stages of cascaded phase-locked loops (PLLs) with a slight frequency difference, to achieve adjustable timing intervals through accumulated phase differences. The scheme was validated on two families of low-cost FPGA devices, achieving adjustable step sizes of 0.67 ps and 0.97 ps.

Wu, Jin-yuan [Fermilab] (ORCID:0000000344329521)↗
DOE OSTI2022

Capturing the interactions between ice sheets, sea level and the solid Earth on a range of timescales: a new “time window” algorithm

Retreat and advance of ice sheets perturb the gravitational field, solid surface and rotation of the Earth, leading to spatially variable sea-level changes over a range of timescales $\textit{O}$ (10 0–6 years), which in turn feed back onto ice-sheet dynamics. Coupled ice-sheet–sea-level models have been developed to capture the interactive processes between ice sheets, sea level and the solid Earth, but it is computationally challenging to capture short-term interactions $\textit{O}$ (10 0–2 years) precisely within longer $\textit{O}$ (10 3–6 years) simulations. The standard forward sea-level modelling algorithm assigns a uniform temporal resolution in the sea-level model, causing a quadratic increase in total CPU time with the total number of input ice history steps, which increases with either the length or temporal resolution of the simulation. In this study, we introduce a new “time window” algorithm for 1D pseudo-spectral sea-level models based on the normal mode method that enables users to define the temporal resolution at which the ice loading history is captured during different time intervals before the current simulation time. Utilizing the time window, we assign a fine temporal resolution $\textit{O}$ (10 0–2 years) for the period of ongoing and recent history of surface ice and ocean loading changes and a coarser temporal resolution $\textit{O}$ (10 3–6 years) for earlier periods in the simulation. This reduces the total CPU time and memory required per model time step while maintaining the precision of the model results. We explore the sensitivity of sea-level model results to the model temporal resolution and show how this sensitivity feeds back onto ice-sheet dynamics in coupled modelling. We apply the new algorithm to simulate sea-level changes in response to global ice-sheet evolution over two glacial cycles and the rapid collapse of marine sectors of the West Antarctic Ice Sheet in the coming centuries and provide appropriate time window profiles for each application. The time window algorithm reduces the total CPU time by ~ 50 % in each of these examples and changes the trend of the total CPU time increase from quadratic to linear. This improvement would increase with longer simulations than those considered here. Our algorithm also allows for coupling time intervals of annual temporal scale for coupled ice-sheet–sea-level modelling of regions such as West Antarctica that are characterized by rapid solid Earth response to ice changes due to the thin lithosphere and low mantle viscosities.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Machine-Learning-Based Rotating Detonation Engine Diagnostics: Evaluation for Application in Experimental Facilities

Real-time monitoring of combustion behavior is a crucial step toward actively controlled rotating detonation engine (RDE) operation in laboratory and industrial environments. Various machine learning methods have been developed to advance diagnostic efficiencies from conventional postprocessing efforts to real-time methods. Here this work evaluates and compares conventional techniques alongside convolutional neural network (CNN) architectures trained in previous studies, including image classification, object detection, and time series classification, according to metrics affecting diagnostic feasibility, external applicability, and performance. Real-time, capable diagnostics are deployed and evaluated using an altered experimental setup. Image-based CNNs are applied to externally provided images to approximate dataset restrictions. Image classification using high-speed chemiluminescence images and time series classification using high-speed flame ionization and pressure measurements achieve classification speeds enabling real-time diagnostic capabilities, averaging laboratory-deployed diagnostic feedback rates of 4–5 Hz. Object detection achieves the most refined resolution of 20 μs in postprocessing. Image and time series classification require the additional correlation of sensor data, extending their time-step resolutions to 80 ms. Comparisons show that no single diagnostic approach outperforms its competitors across all metrics. This finding justifies the need for a machine learning portfolio containing a host of networks to address specific needs throughout the RDE research community.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Network-Wide Traffic Signal Control Using Bilinear System Modeling and Adaptive Optimization

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

42 ENGINEERING↗
DOE OSTI2026

Towards time-resolved MicroED grid preparation using mix-and-inject gas dynamic virtual nozzles

Recent progress in gas dynamic virtual nozzle (GDVN) technologies in combination with high-brilliance synchrotron and X-ray free-electron lasers (XFELs) has allowed the visualization of protein dynamics in crystallo by mixing macromolecular protein crystals with a substrate using tunable mixing times on the order of milliseconds to seconds prior to serial X-ray diffraction data collection. This has become the method of choice for high-resolution structure determination of intermediate states. However, such experiments require large counts of crystals of proper sizes for high-resolution data collection, and premium beam times for screening efforts. Cryogenic microcrystal electron diffraction (MicroED) represents a complementary technique that may be a more accessible avenue for time-resolved nanocrystallography compared with serial X-ray diffraction experiments. MicroED can produce full diffraction datasets from just a few submicrometre-thick crystals, and the approach is more readily accessible, requiring standard cryogenic transmission electron microscopy (TEM) equipment available at many universities and institutes. Cryogenic MicroED, like other forms of cryo-EM, begins with rapidly freezing biological material on electron microscopy grids. In the case of MicroED, micro- to nano-crystals (<500 nm thick) are deposited onto electron microscopy grids and plunge-frozen for subsequent electron diffraction data collection. Here, we have incorporated GDVN technology developed originally for XFEL experiments into the freezing process as a first step towards time-resolved studies. We describe the limited deposition efficiency of the model MicroED protein proteinase K on TEM grids using GDVNs, preceding sample vitrification and successful MicroED data collection. We discuss both the initial results from such experiments and the methodological challenges in developing this approach into a reliable workflow for millisecond-to-second time-resolved structural studies of macromolecules. Our results promise a strategy to deposit crystals on grids using GDVNs and determine high-resolution structures by MicroED, constituting a first step towards development of time-resolved MicroED experiments.

MicroED↗
DOE OSTI2024

The Role of Nonequilibrium Solvent Effects in Enhancing Direct CO 2 Capture at the Air–Aqueous Amino Acid Interface

Direct air capture (DAC) technologies are limited by the poor understanding of the dynamic role of interfaces in modulating the chemisorption of CO 2 from air into solutions. While the reactivity of aqueous amine-based solvents in the bulk environment is strongly inhibited by nonequilibrium solvent effects, promoting DAC at interfaces posits a possibility to reduce the coupling with the solvent and significantly accelerate DAC. Building on an experimentally proven concept to bring an anionic glycine absorbent to the interface through ion-pairing interactions with a positively charged surfactant, we establish the fundamental time scales for key elementary steps involved in DAC with rate theory and enhanced-sampling ab initio molecular dynamics simulations. Here, we elucidate the mechanism by which water influences the free energy barriers and dynamical crossing-recrossing of those barriers, affecting the reaction rates. We find that water reorganizes to partially dehydrate [-NH 2 ], facilitating S N 2-based CO 2 conversion to a zwitterion, which then releases a proton via overhydration of [-NH 2 ]. The low-density interfacial water favors dehydration over overhydration, leading to a comparatively higher barrier (slower kinetics) for proton release. The barrier-recrossing events neutralize this effect, letting both steps occur at the same time scale (sub-microseconds) and making the overall DAC process faster at the interface than in the bulk water. Such an understanding of environment-sensitive solvent effects on the reaction kinetics will help design tailored interfaces for enhanced CO 2 capture kinetics via control of solvation and ion paring.

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

Extremely large pressure swing adsorption processes for flue gas treatment

The current disclosure provides systems and methods for multiple beds undergoing a feed step at the same time with the same feed flow rate and multiple beds undergoing a light reflux step at the same time with the same light reflux flow rate to process a gas stream in a multi-bed, multi-unit vacuum swing adsorption (VSA) process using reasonably sized beds.

Ritter, James A.↗
DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reversible inhibition and reactivation of electron transfer in photosystem I

In photosystem I (PSI) complexes at room temperature light induced electron transfer can proceed down multiple protein-cofactor branches, and the process can be an order of magnitude faster on one branch compared to the other. One factor that might contribute to this branch asymmetry is a tryptophan amino acid at position 673 on the psaB protein. This amino acid is located between two of the pigments involved in electron transfer on the psaB protein branch. The corresponding residue on the psaA protein branch is a glycine amino acid. Microsecond time-resolved step-scan FTIR difference spectroscopy at 77 K has been used to study isolated PSI complexes from wild type and a mutant where the tryptophan residue was changed to phenylalanine. Photoaccumulated FTIR difference spectra indicate changes in the protein structure upon mutation. In the mutant we also find that the electron transfer processes is inhibited following long periods of repetitive flash illumination at room temperature. This is due to double protonation of the pigment involved in electron transfer. However, we show that we can restore electron transfer functionality by incubating the light-treated mutant PSI samples in the presence of newly added (not protonated) pigment.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Model-Free Building Temperature Control and Power Allocation Under Measurement Time Delays

Taking a step towards a greener planet has created an increased need for a higher integration of renewable energy resources into the electric grid. Nonetheless, the intermittency and uncertainty associated with renewable generation have slowed down this integration. Demand response (DR) has been recently adopted to address this challenge by utilizing demand side flexibility and enabling the participation of many grid-interactive efficient buildings (GEBs). However, existing DR methods require significant modeling and/or training efforts and are computationally expensive. To address the aforementioned issues, we propose a model-free control (MFC)-based strategy that is robust to the time delays in the temperature measurements of the thermostatically controlled loads (TCLs). It assigns to each GEB a local controller to maintain the TCLs’ temperatures within desired comfort levels, while the load aggregator (LA) allocates the assigned reference power provided by the distribution system operator (DSO) to support a specific grid service, such as demand peak reduction, load shifting, balancing supply and demand, and consuming the solar photovoltaic power locally. We investigate the effects of such loss of information on the local control action as well as on meeting the power allocation constraint. We conclude that, for an appropriate choice of design parameters, the proposed MFC controller is satisfactorily robust to measurement time delays.

Telsang, Bhagyashri↗
DOE OSTI2021

Mechanism and dynamics of fatty acid photodecarboxylase

Photoenzymes are rare biocatalysts driven by absorption of a photon at each catalytic cycle; they inspire development of artificial photoenzymes with valuable activities. Fatty acid photodecarboxylase (FAP) is a natural photoenzyme that has potential applications in the bio-based production of hydrocarbons, yet its mechanism is far from fully understood. RATIONALE To elucidate the mechanism of FAP, we studied the wild-type (WT) enzyme from Chlorella variabilis (CvFAP) and variants with altered active-site residues using a wealth of techniques, including static and time-resolved crystallography and spectroscopy, as well as biochemical and computational approaches. RESULTS A 1.8-Å-resolution CvFAP x-ray crystal structure revealed a dense hydrogen-bonding network positioning the fatty acid carboxyl group in the vicinity of the flavin adenine dinucleotide (FAD) cofactor. Structures solved from free electron laser and low-dose synchrotron x-ray crystal data further highlighted an unusual bent shape of the oxidized flavin chromophore, and showed that the bending angle (14°) did not change upon photon absorption (step 1) or throughout the photocycle. Calculations showed that bending substantially affected the energy levels of the flavin. Structural and spectroscopic analysis of WT and mutant proteins targeting two conserved active-site residues, R451 and C432, demonstrated that both residues were crucial for proper positioning of the substrate and water molecules and for oxidation of the fatty acid carboxylate by 1 FAD* (~300 ps in WT FAP) to form FAD ∙– (step 2). Time-resolved infrared spectroscopy demonstrated that decarboxylation occured quasi-instantaneously upon this forward electron transfer, consistent with barrierless bond cleavage predicted by quantum chemistry calculations and with snapshots obtained by time-resolved crystallography. Transient absorption spectroscopy in H 2 O and D 2 O buffers indicated that back electron transfer from FAD ∙– was coupled to and limited by transfer of an exchangeable proton or hydrogen atom (step 3). Unexpectedly, concomitant with FAD ∙– reoxidation (to a red-shifted form FAD RS ) in 100 ns, most of the CO 2 product was converted, most likely into bicarbonate (as inferred from FTIR spectra of the cryotrapped FAD RS intermediate). Calculations indicated that this catalytic transformation involved an active-site water molecule. Cryo-Fourier transform infrared spectroscopy studies suggested that bicarbonate formation (step 4) was preceded by deprotonation of an arginine residue (step 3). At room temperature, the remaining CO 2 left the protein in 1.5 μs (step 4'). The observation of residual electron density close to C432 in electron density maps derived from time-resolved and cryocrystallography data suggests that this residue may play a role in stabilizing CO 2 and/or bicarbonate. Three routes for alkane formation were identified by quantum chemistry calculations; the one shown in the figure is favored by the ensemble of experimental data. CONCLUSION Finally, we provide a detailed and comprehensive characterization of light-driven hydrocarbon formation by FAP, which uses a remarkably complex mechanism including unique catalytic steps. We anticipate that our results will help to expand the green chemistry toolkit.

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

Mathematical Framework Underlying the In Situ Electrochemical Diagnosis of Adsorbed Intermediates Formed during Redox Reactions at Electrode Surfaces

Previously, we have presented an electrochemical technique wherein an electroactive tracer species is employed to probe the rate-limiting factors governing redox reactions at an electrode surface. In this technique, the electrode is first held potentiostatically to facilitate a redox process (step 1), and then the potential is released to open circuit conditions (step 2) so as to monitor the time-dependent re-equilibration of the electrode potential in the presence of the tracer. The time-dependent potential response in step 2 has been shown to contain information about diffusion—limited or desorption—limited steps, enabling in situ probing of the electrochemistry at the electrode surface during step 1. In the present contribution, a theoretical model governing the transient response in step 2 is developed for two limiting cases: diffusion—limited and desorption—limited recovery of the electrode potential. Mathematical modeling shows that, during re-equilibration, the step 2 potential transient corresponding to a case where step 1 involves surface adsorbed species which undergo desorption in step 2 exhibits a much longer time constant than that when re-equilibration occurs under diffusion limitations. The mathematical framework presented herein provides a sound fundamental basis for applying the aforementioned technique to studying adsorption-desorption processes during electrochemistry. Also, technique limitations are presented in light of the modeling findings.

25 ENERGY STORAGE↗
DOE OSTI2025

Modeling Volumetric Energy Deposition-driven Rayleigh-Taylor Instability

The goal of this work is to simulate a volumetric energy deposition (VED) driven Rayleigh-Taylor instability (RTI). Efforts will focus on simulating effects observed in two-fluid VED-driven RTI experiments. The VED triggers the RTI by changing the density of the fluids through time, hence a variable Atwood number is achieved. While initially stable (heavier fluid on the bottom), the microwave heating creates a density inversion and leads to a RTI. We hope to explore the mechanisms in VED-driven RTI and see how initial perturbations change the dynamics of growth. This work will primarily focus on early-time behavior but will also include steps towards simulating late-time nonlinear behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An iterative dynamic chemical stiffness removal method for reacting flow simulations

Abstract An iterative dynamic chemical stiffness removal method (IDCSR) based on quasi-steady-state approximation (QSSA) is proposed. The IDCSR method is built on a previously developed non-iterative method which has proved to work well for small timestep sizes. A novel iterative procedure is designed in IDCSR to enable explicit time integration of stiff chemistry at relatively large timestep sizes relevant to practical reacting flow simulations. The effectiveness of the iterative procedure is first demonstrated with a toy problem and homogeneous auto-ignition with fixed integration step sizes, showing that larger timestep sizes can be allowed for explicit time integration using IDCSR compared with the previous non-iterative method. IDCSR is then compared with existing explicit chemistry solvers for simulations of homogeneous auto-ignition and shows similar or lower computational cost but significantly higher accuracy across a wide range of timestep sizes. IDCSR is further combined with an automatic adaptive time-stepping scheme for simulations of 0-D homogeneous auto-ignition and a 2-D laminar lifted n -dodecane jet flame. For the 0-D auto-ignition simulations, IDCSR is shown to reduce both the error (by 43%–90%) and computational cost (by 6–15 times) compared with existing explicit solvers, while achieving speed-up factors of up to 400 compared with VODE for a wide range of timestep sizes and reaction mechanisms. For the 2-D jet flame simulations, speed-up factors of 15 and 31 for chemistry integration, and 5 and 9 for overall simulation, are achieved by IDCSR compared with CVODE with and without analytic Jacobian, respectively.

Xu, Chao (ORCID:0000000153074159)↗