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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Model Parameter Development for Complex Materials: Species-Specific Diffusion Barriers in 316 Stainless Steel from Systematic DFT Calculations

Vacancy-mediated diffusion barriers in 316 stainless steel have been systematically calculated using density functional theory to provide essential parameters for mesoscale microstructure evolution models. A statistical sampling approach employing 210 nudged elastic band calculations across multiple special quasi-random structures captures the effects of local chemical environments in this concentrated alloy. The computational methodology addresses challenges specific to chemically disordered systems, including proper magnetic treatment throughout multi-step calculations and validation against experimental structural properties. The calculated activation barriers reveal clear species-dependent diffusion behavior with the hierarchy Ni >> Fe ˜ Cr >> Mo. Nickel exhibits the highest barriers (0.74–1.31 eV, mean 1.045 eV), confirming its role as the slowest-diffusing major component. Iron and chromium show similar moderate barriers averaging 0.587 eV and 0.522 eV, respectively. Remarkably, molybdenum demonstrates exceptionally low barriers (0.12–0.28 eV, mean 0.194 eV), suggesting much higher mobility than previously recognized and potentially significant implications for precipitation kinetics and microstructure evolution. The barrier ranges remain consistent across different 316 SS compositions, supporting parameter transferability for modeling applications. The overall mean barrier of 0.64 eV provides a practical approximation for phase field simulations, while species-specific values enable detailed treatments of diffusion-controlled processes. This systematic approach establishes a validated framework for generating diffusion parameters in other concentrated alloys where experimental data are limited, while providing the first systematic set of species-specific barriers for predictive modeling of 316 stainless steel microstructure evolution.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Structural and Dynamical Relationships of Ca 2+ and H 2 O in Smectite/ 2 H 2 O Systems

We present an X-ray diffraction and multi-nuclear ( 2 H and 43 Ca) NMR study of Ca-exchanged hectorite (a smectite clay) that provides important new insight into molecular behavior at the smectite-H 2 O interface. Variable-temperature 43 Ca MAS NMR and controlled humidity XRD indicate that Ca 2+ occurs as proximity-restricted outer-sphere hydration complexes between –120 and +25 °C in a two-layer hydrate and at T ≤ –50 °C in a 2:1 water/solid paste. Changes in the 43Ca NMR peak width and position with temperature are more onsistent with diffusion-related processes than with dynamics involving metal-surface interactions such as site exchange. The 2 H NMR signal between –50 and +25 °C for a two-layer hydrate of Ca-hectorite is similar to that of Na- and other alkali metal hectorites and represents 2 H 2 O molecules experiencing anisotropic motion describable using the 2 H C 2 /C 3 jump model we proposed previously. 2 H T 1 relaxation results for Ca- and Na-hectorite are well fit with a fast-exchange limit, rotational diffusion model for 2 H 2 O dynamics, yielding GHz-scale rotational reorientation rates compatible with the C 3 component of the C 2 /C 3 hopping model. The apparent activation energy for 2 H 2 O rotational diffusion in the two-layer hydrate is greater for Ca-hectorite than Na-hectorite (25.1 vs. 21.1 kJ/mol), consistent with the greater affinity of Ca 2+ for H 2 O. The results support the general principle that the dynamic mechanisms of proximity-restricted H 2 O are only weakly influenced by the cation in alkali metal and alkaline earth metal smectites and provide critical evidence that the NMR resonances of charge-balancing cations in smectites become increasingly influenced by diffusion-like dynamic processes at low temperatures as the charge density of the unhydrated cation increases.

2H NMR↗
DOE OSTI2016

Effective defect diffusion lengths in Ar-ion bombarded 3C-SiC

Above room temperature, SiC exhibits pronounced processes of diffusion and interaction of radiation-generated point defects. Here, we use the recently developed pulsed ion beam method to measure effective defect diffusion lengths in 3C-SiC bombarded in the temperature range of 25–200 °C with 500 keV Ar ions. Results reveal a diffusion length of ~10 nm, which exhibits a weak temperature dependence, changing from 9 to 13 nm with increasing temperature. Lastly, these results have important implications for understanding and predicting radiation damage in SiC and for the development of radiation-resistant materials via interface-mediated defect reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Preparation of Diffusion Couples for Irradiation and High Temperature Testing of Representative TRISO PyC/SiC

Understanding the release of fission products from intact tristructural-isotropic (TRISO) coated particle fuel during normal and off-normal service is necessary to ensuring safe and efficient reactor operation. Planar diffusion couples have been fabricated to determine the diffusion kinetics of select fission product species (Ag, Ag+Pd, Eu, and Sr) in pyrocarbon (PyC) and silicon carbide (SiC) materials which are representative of TRISO fuel. Obtaining accurate diffusion coefficients for these systems in representative materials will allow for higher fidelity inputs for fuel performance models. Three different diffusion couple variants have been produced which include a Baseline, PyC, and SiC variant. The Baseline variant serves as an example of representative PyC and SiC layers as the layer properties mimic those found in TRISO fuel from the second Advanced Gas Reactor Fuel Qualification and Development Program. The PyC and SiC variants include variation in the respective layer properties to understand the impact of PyC density and SiC grain size on fission product diffusion. The diffusion couples were designed to allow for exploration of neutron irradiation on diffusion reflecting in reactor behavior as well as high temperature thermal diffusion reflecting diffusive transport during off-normal conditions. The methodology for selecting the diffusion couple design, refinement of the individual variant layer properties, and the complete process for diffusion couple construction are summarized in this report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Atomistic simulations to reveal HIP-bonding mechanisms of Al6061/Al6061

Molecular dynamics simulations were employed to understand the diffusion bonding process during hot isostatic pressing (HIP) of Al6061/Al6061 alloy. Simulations of the HIP process reveal atomistic phenomena that are difficult or unlikely to be observed experimentally and provide useful insights into the mechanism of diffusion and bonding. Here, the results reveal that at the start of the HIP process, a massive incursion of oxygen atoms occurs from the pre-existing γ-Al 2 O 3 to the 6061 region across the interphase interface. These oxygen atoms interact with the enriched Mg atom layer present at the existing γ-Al 2 O 3 and 6061 matrix to form a secondary complex Mg 2 Al 2 O 5 phase. Diffusion calculations also show that transport of atoms due to the applied pressure is 4–5 orders of magnitude higher than would occur in the absence of HIP conditions. The Mg 2 Al 2 O 5 phase also provides efficient pathways for the rapid transport of Mg atoms. Because of the higher diffusion coefficients observed for Mg within the phase, Mg atoms can move more swiftly compared to their diffusion within other phases such as γ-Al 2 O 3 . This accelerated mobility facilitates the rapid movement of Mg atoms across the interface, leading to changes in the local composition and the potential growth of the Mg 2 Al 2 O 5 phase.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Ion-Exchange Interdiffusion Model with Potential Application to Long-Term Nuclear Waste Glass Performance

Ion exchange is an integral mechanism influencing the corrosion of glasses. Due to the formation of alteration layers in aqueous conditions, it is difficult to conclusively deconvolute the process of ion exchange from other processes, principally dissolution of the glass matrix. Therefore, we have developed a method to isolate alkali diffusion that involves contacting glass coupons with a solution of 6 LiCl dissolved in functionally inert dimethyl sulfoxide. Here, we employ the method at temperatures ranging from 25 to 150 °C with various glass formulations. Glass compositions include simulant nuclear waste glasses, such as SON68 and the international simple glass (ISG), glasses in which the nature of the alkali element was varied, and glasses that contained more than one alkali element. An interdiffusion model based on Fick’s second law was developed and applied to all experiments to extract diffusion coefficients. The model expands established models of interdiffusion to the case where multiple types of alkali sites are present in the glass. Activation energies for alkali ion exchange were calculated and the results are in agreement with those obtained in glass strengthening experiments but are nearly five times higher than values reported for diffusion-controlled processes in nuclear waste glass corrosion experiments. A discussion of the root causes for this apparent discrepancy is provided. The interdiffusion model derived from laboratory experiments is expected to be useful for modeling glass corrosion in a geological repository when the silicon concentration is high.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Impact of implanted phosphorus on the diffusivity of boron and its applicability to silicon solar cells

Boron diffusivity reduction in extrinsically doped silicon was investigated in the context of a process combination consisting of BBr{sub 3} furnace diffusion and preceding Phosphorus ion implantation. The implantation of Phosphorus leads to a substantial blocking of Boron during the subsequent Boron diffusion. First, the influences of ion implantation induced point defects as well as the initial P doping on B diffusivity were studied independently. Here, it was found that not the defects created during ion implantation but the P doping itself results in the observed B diffusion retardation. The influence of the initial P concentration was investigated in more detail by varying the P implantation dose. A secondary ion mass spectrometry (SIMS) analysis of the BSG layer after the B diffusion revealed that the B diffusion retardation is not due to potential P content in the BSG layer but rather caused by the n-type doping of the crystalline silicon itself. Based on the observations the B diffusion retardation was classified into three groups: (i) no reduction of B diffusivity, (ii) reduced B diffusivity, and (iii) blocking of the B diffusion. The retardation of B diffusion can well be explained by the phosphorus doping level resulting in a Fermi level shift and pairing of B and P ions, both reducing the B diffusivity. Besides these main influences, there are probably additional transient phenomena responsible for the blocking of boron. Those might be an interstitial transport mechanism caused by P diffusion that reduces interstitial concentration at the surface or the silicon/BSG interface shift due to oxidation during the BBr{sub 3} diffusion process. Lifetime measurements revealed that the residual (non-blocked) B leads to an increased dark saturation current density in the P doped region. Nevertheless, electrical quality is on a high level and was further increased by reducing the B dose as well as by removing the first few nanometers of the silicon surface after the BBr{sub 3} diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Coupled chemo-mechanical modeling of point-defect diffusion in a crystal plasticity fast Fourier transform framework

Below the yield strength and at moderate-to-high homologous temperatures, the inelastic deformation of metals is mostly governed/rate-controlled by vacancy diffusion-mediated processes. As a function of grain size, stress, temperature and dislocation content, vacancies (or atoms) can adopt preferential diffusion paths across grain interiors, along grain boundaries, or towards and along dislocations, resulting in climb and self-climb. In the steady state and under constant load, grain boundary and grain bulk vacancy diffusion-mediated plasticity have been described in seminal works by Coble and by Nabarro and Herring, respectively. Yet, the interplay between all aforementioned potential diffusion pathways has not been comprehensively mapped. This work presents a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework, which considers the coupling between the diffusion-mediated plasticity mechanisms. In the proposed approach, the kinetics and kinematics of plastic deformation due to vacancy diffusion along grain boundaries and grain bulk, as well as the exchange between grain boundaries and bulk are described explicitly. A homogenization approach at the voxel level is further introduced to simultaneously consider bulk and grain boundary diffusion in a numerically efficient fashion. The new formulation predicts the expected strain rate dependencies and the scaling of the steady-state creep rate with respect to grain size, temperature, and stress. Finally, the model predicts the transition from grain bulk to grain boundary-dominated diffusion with reduction in grain size, a significant step towards capturing transitions in deformation behavior without any phenomenological or ad-hoc adjustments.

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

Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model

We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection– dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. * * to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell- shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.

Bimolecular reactions, incomplete mixing, Stochast↗
DOE OSTI2022

A reaction–diffusion model for grayscale digital light processing 3D printing

We report that digital light processing (DLP) 3D printing is an additive manufacturing process that utilizes light patterns to photopolymerize a liquid resin into a solid. Due to the accuracy of modern digital micromirror devices (DMD) and recent advances in resin chemistry, it is now possible to create functionally graded structures using different light intensity values, also known as grayscale DLP (g-DLP). Different intensities of light lead to differences in the polymer crosslinking density after curing, which ultimately produces a part with gradients of material properties. However, g-DLP is a complicated process. First, the DLP printing is a highly coupled chemical and physical process that involves light propagation, chemical reactions, species diffusion, heat transfer, volume shrinkage, and changes in mechanical behaviors of the curing resin. Second, in g-DLP, light gradients create strong in plane gradients of chemical species concentrations in the curing liquid resin due to the strong dependence of light intensity on the rate of monomer crosslinking. Furthermore, light gradients through the depth create concentration gradients due to the degree of cure dependent light absorption and the use of photoabsorbers. These complex physical features of the printing process must be understood in order to properly control printing parameters such as light exposure time, printing speed, and grayscale variations to achieve accurate mechanical properties. In this paper, a photopolymerization reaction–diffusion model is developed and used in conjunction with experiments to investigate the coupled effects of light propagation, chemical reaction rates, and species diffusion during g-DLP 3D printing. The model is implemented numerically utilizing the finite difference method and simulation results are compared to experimental findings of simple printed structures. The agreement between experimental and model predictions of simple quantities of interest, such as geometric feature sizes, shows that the model can capture the overcure due to free-radical and other species diffusion during printing when grayscale patterns are employed. This model lays the groundwork for future extensions that can incorporate more complex coupled physics such as heat transfer, volume shrinkage, and material property evolution, which are critically important in utilizing g-DLP 3D printing for the fabrication of high-performance parts which excellent geometric and material property tolerances.

36 MATERIALS SCIENCE↗
DOE OSTI2017

The Effects of Interplanetary Transport in the Event-intergrated Solar Energetic Particle Spectra

Previous investigations on the energy spectra of solar energetic particle (SEP) events revealed that the energy spectra observed at 1 au often show double power laws with break energies from one to tens of MeV/nuc. In order to determine whether the double power-law features result from the SEP source or the interplanetary transport process from the Sun to 1 au, we separately analyze the SEP spectra in the decay phase, during which the transport effect is minimum. In this paper, we reported three events observed by the Interplanetary Monitory Platform 8 spacecraft, which occurred on 1977 September 19, November 22, and 1979 March 1. For the first two events, the event-integrated spectra of protons possess double power-law profiles with break energies in a range of several MeV to tens of MeV, while the spectra integrated in the decay (reservoir) phase yield single power laws. Moreover, a general trend from a double power law at the rising phase to a single power law at the decay phase is observed. For the third event, both the event-integrated and the reservoir spectra show double power-law features. However, the difference between the low- and high-energy power-law indices is smaller for the reservoir spectrum than the event-integrated spectrum. These features were reproduced by solving the 1D diffusion equation analytically and we suggest that the transport process, especially the diffusion process, plays an important role in breaking the energy spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Quantal diffusion approach for multinucleon transfer processes in the 58,64 Ni + 208 Pb reactions: Toward the production of unknown neutron-rich nuclei

In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power. Purpose: This article aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni + 208 Pb at E c.m. = 268 MeV and 58 Ni + 208 Pb at E c.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++. Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Effect of Sulfide Concentration on the Corrosion and Cavitation Erosion Behavior of a Manganese-Aluminum Bronze in 3.5% NaCl Solution

The effect of sulfide concentration on the corrosion and cavitation erosion behavior of a cast manganese-aluminum bronze (MAB) alloy in 3.5% NaCl solution was investigated. The electrochemical results showed that when the sulfide concentration exceeded 50 ppm, hydrogen evolution reaction dominated the cathodic process because of the very negative corrosion potential of MAB, and the formation of a copper sulfide film on MAB was a diffusion-controlled process. The mass loss rate of MAB after longer-term immersion was ordered by the sulfide concentration as: 20/50 ppm > 100 ppm > zero > 200 ppm. In the 200 ppm sulfide solution, the mass loss rate of MAB was the lowest, because of the formation of a thin and homogeneous copper sulfide film. In the other sulfide solutions, the formation of a less-protective film with both oxides and sulfides resulted in higher mass loss rate of MAB. Moreover, selective phase corrosion occurred at the β and κ phases in solutions with sulfide addition less than 100 ppm. For all solutions, it was the mechanical attack that dominated cavitation erosion degradation. The cavitation erosion–corrosion synergy was lower in high sulfide solutions, because the corrosion products on MAB could reduce the mechanical impact under cavitation erosion.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Nonlinear Structure of the Diffusing Gas-Metal Interface in a Thermonuclear Plasma

Here, we describe the theoretical structure of the plasma diffusion layer that develops from an initially sharp gas-metal interface. The layer dynamics under isothermal and isobaric conditions is considered so that only mass diffusion (mixing) processes can occur. The layer develops a distinctive structure with asymmetric and highly nonlinear features. On the gas side of the layer the diffusion coefficient goes nearly to zero, causing a sharp “front,” or well defined boundary between mix layer and clean gas with similarities to the Marshak thermal waves. Similarity solutions for the nonlinear profiles are found and verified with full ion kinetic code simulations. A criterion for plasma diffusion to significantly affect burn is given.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

The Great Solar Active Region NOAA 12192: Helicity Transport, Filament Formation, and Impact on the Polar Field

The solar active region (AR), NOAA 12192, appeared in 2014 October as the largest AR in 24 years. Here we examine the counterintuitive nature of two diffusion-driven processes in the region: the role of helicity buildup in the formation of a major filament, and the relationship between the effects of supergranular diffusion and meridional flow on the AR and on the polar field. Quantitatively, calculations of current helicity and magnetic twist from Helioseismic and Magnetic Imager (HMI) vector magnetograms indicate that, though AR 12192 emerged with negative helicity, positive helicity from subsequent flux emergence, consistent with the hemispheric sign-preference of helicity, increased over time within large-scale, weak-field regions such as those near the polarity inversion line (PIL). Morphologically, Atmospheric Imaging Assembly observations of filament barbs, sigmoidal patterns, and bases of Fe xii stalks initially exhibited signatures of negative helicity, and the long filament that subsequently formed had a strong positive helicity consistent with the helicity buildup along the PIL. We find from full-disk HMI magnetograms that AR 12192's leading positive flux was initially closer to the equator but, owing either to the region’s magnetic surroundings or to its asymmetric flux density distribution, was transported poleward more quickly on average than its trailing negative flux, contrary to the canonical pattern of bipole flux transport. This behavior caused the AR to have a smaller effect on the polar fields than expected and enabled the formation of the very long neutral line where the filament formed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Effect of Primary Carbides on the Sharpness of Kitchen Knives Made of 8Cr13MoV Steel

Although there are many primary carbides in the cutting edge of knives made of high-carbon martensitic steel, the effect of primary carbides on the sharpness of knives has not been clarified. In this paper, the evolution of primary carbides during the production process of 8Cr13MoV steel was presented. The effect of size and amount of primary carbides on the sharpness of knives was studied via employing rolling forging and diffusion annealing process, respectively. Results indicated that primary carbides easily fell off from cutting edge during cutting process, which would decrease the wear resistance of knives. The refinement of primary carbides could not only improve the wear resistance of cutting edge, but also weaken the fluctuation of sharpness during the service process of knives. By decreasing the amount of primary carbides, the wear resistance of knives would increase effectively, which improved the cutting performance effectively. Reducing the amount of primary carbides and refining the primary carbides in cutting edge were both effective ways to improve the sharpness of knives.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Measurement of minority carrier diffusion lengths in GaAs nanowires by a nanoprobe technique

Minority carrier diffusion lengths in both p-type and n-type GaAs nanowires were studied using electron beam induced current by means of a nanoprobe technique without lithographic processing. The diffusion lengths were determined for Au/GaAs rectifying junctions as well as axial p-n junctions. By incorporating a thin lattice-matched InGaP passivating shell, a 2-fold enhancement in the minority carrier diffusion lengths and one order of magnitude reduction in the surface recombination velocity were achieved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

97 MATHEMATICS AND COMPUTING↗