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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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DOE OSTI2024

Simulating cosmological evolution by quantum quench of an atomic Bose-Einstein condensate

In cosmological evolution, it is the homogeneous scalar field (inflaton) that drives the universe to expand isotropically and to generate standard model particles. However, to simulate cosmology, atomic gas research has focused on the dynamics of Bose-Einstein condensates (BEC) with continuously applied forces. In this paper we argue that a complementary approach needs also to be pursued; we thus consider the analog BEC experiments in a nondriven and naturally closed atomic system. We implement this using a BEC in an optical lattice which, after a quench, freely transitions from an unstable to a stable state. Furthermore, this dynamical evolution displays the counterpart “preheating,” “reheating,” and “thermalization” phases of cosmology. Importantly, our studies of these analog processes yield tractable analytic models. Additionally, of great utility to the cold atom community, such understanding elucidates the dynamics of nonadiabatic condensate preparation. Indeed, the dynamical processes discussed here are generic and in future cold atom reequilibration experiments it will be important to observe both the preheating stage, corresponding to a fragmented condensate, and the reheating stage, corresponding to a particle cloud.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Characterizing magnetized plasmas with dynamic mode decomposition

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear and computationally intensive and can be difficult to interpret, while often only approximating the true dynamics. In this work, data-driven techniques recently developed in the field of fluid dynamics are leveraged to develop interpretable reduced-order models of plasmas that strike a balance between accuracy and efficiency. In particular, dynamic mode decomposition (DMD) is used to extract spatio-temporal magnetic coherent structures from the experimental and simulation datasets of the helicity injected torus with steady inductive (HIT-SI) experiment. Three-dimensional magnetic surface probes from the HIT-SI experiment are analyzed, along with companion simulations with synthetic internal magnetic probes. A number of leading variants of the DMD algorithm are compared, including the sparsity-promoting and optimized DMD. Optimized DMD results in the highest overall prediction accuracy, while sparsity-promoting DMD yields physically interpretable models that avoid overfitting. These DMD algorithms uncover several coherent magnetic modes that provide new physical insights into the inner plasma structure. These modes were subsequently used to discover a previously unobserved three-dimensional structure in the simulation, rotating at the second injector harmonic. Finally, using data from probes at experimentally accessible locations, DMD identifies a resistive kink mode, a ubiquitous instability seen in magnetized plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Leptogenesis in parity solutions to the strong CP problem and Standard Model parameters

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, v R . For generic thermal leptogenesis, v R ≳ 10 12 GeV, unless the small observed neutrino masses arise from fine-tuning. We compute v R in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at 1σ. Future precision measurements of these parameters may provide support for the theory or, if v R is determined to be below 10 12 GeV, force modifications. However, modified cosmologies do not easily allow reductions in v R — no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for v R can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine v R to be above 10 12 GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to v R ≳ 10 13 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Reformulating a Gurson-based dynamic damage model and demonstrating improved predictive power and numerical robustness

The original Tepla (TEnsile PLAsticity) ductile damage model, based on the Gurson yield surface, has long been used to model damage evolution and material failure under dynamic loading. Unfortunately, Tepla suffered from mesh sensitivity, numerical instability, and limited predictive capability. Here, we theoretically reformulate Tepla to address these issues. We especially focus on the prediction of porosity, which is the key state variable used for modeling ductile damage, as compared to more easily measured surface velocities, which are at best an indirect measure of damage. Key model changes include separating the viscosity during volumetric void growth from underlying shear strength behavior and switching to an iterative bisection solver. The new Tepla is then calibrated on incipient spall experiments on half-hard copper and tantalum, which demonstrate its ability to simultaneously fit the model to recovered porosity distributions and measured surface velocities, a stringent test. Improved numerical behavior, such as greatly reduced mesh sensitivity, is also shown in those simulations. Finally, the new Tepla model is applied to several high-explosive loaded, sweeping wave experiments, showing the ability of the model to predict behavior on tests with significantly different loading conditions and histories than the calibration data.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Improving ChemCam LIBS long-distance elemental compositions using empirical abundance trends

The ChemCam instrument on the Curiosity rover provides chemical compositions of Martian rocks and soils using remote laser-induced breakdown spectroscopy (LIBS). The elemental calibration is stable as a function of distance for Ti, Fe, Mg, and Ca. The calibration shows small, systematically increasing abundance trends as a function of distance for Al, Na, K, and to some extent, Si. The distance effect is known to be due to a dependence with distance on the relative strengths of atomic transition lines. Emission lines representing transitions from relatively low energy levels remain intense at longer distances while emission lines representing transitions from higher energy levels decrease in intensity more rapidly as a function of distance. The multivariate algorithms used to determine elemental compositions rely on a large number of emission lines in many cases, so rather than trying to correct all emission lines, a study was made of the predicted compositions as a function of distance, in order to determine an empirical correction. Abundance trends can be well approximated by a linear trend with distance within the ranges of abundances and distances observed up to ~6 m. Data from 11 distinct geological members and data groups of the Murray formation in Gale crater, Mars, were used to form the model, selecting the members and data groups yielding the best statistics. The model was tested using data from several targets observed from two different distances, and using data from the Kimberley formation, the composition of which is significantly different from the Murray formation, showing that the model works on other compositions beyond those used to build the model. For long-distance observations up to ~6 m, corrections can be made back to an equivalent composition at the median distance of ChemCam observations (2.6 m). Finally, the model has been validated up to 6.2 m, although ChemCam is able to observe bedrock targets to >7 m, and iron meteorites to distances of >9 m.

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

Effect of a collapsing gas bubble on the shock-to-detonation transition in liquid nitromethane

We studied the shock-induced collapse of butane gas bubbles in the homogeneous explosive nitromethane (NM) to investigate the effects of hot spot formation on the detonation process. A butane bubble was injected into a sample of NM, and a shock wave from a flat plate impactor compressed the bubble, creating a localized hot spot. We measured shock and detonation wave speeds with optical velocimetry, and we used a high-speed camera to image the shock propagation and bubble collapse processes. A multiband optical fiber pyrometer measured the time-resolved thermal radiance, and we used the results and emissivity values extracted from spectral fits to estimate temperatures. We measured the characteristics of the shock-to-detonation transition in NM with and without a bubble. All experiments were performed at shock pressures near 8 GPa, where neat NM can detonate. A single bubble in this system was shown to sensitize NM, leading to a reduced run-to-detonation time. We used hydrodynamic modeling to predict shock wave propagation, the extent of chemical reaction, and subsequent temperature rise from the collapsing bubble. We used a temperature-dependent Arrhenius burn model for simulations, and it yielded much better results than reactive burn models that depend only on pressure and density.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Remote Sensing-Based Estimation of Advanced Perennial Grass Biomass Yields for Bioenergy

A sustainable bioeconomy would require growing high-yielding bioenergy crops on marginal agricultural areas with minimal inputs. To determine the cost competitiveness and environmental sustainability of such production systems, reliably estimating biomass yield is critical. However, because marginal areas are often small and spread across the landscape, yield estimation using traditional approaches is costly and time-consuming. This paper demonstrates the (1) initial investigation of optical remote sensing for predicting perennial bioenergy grass yields at harvest using a linear regression model with the green normalized difference vegetation index (GNDVI) derived from Sentinel-2 imagery and (2) evaluation of the model’s performance using data from five U.S. Midwest field sites. The linear regression model using midsummer GNDVI predicted yields at harvest with R2 as high as 0.879 and a mean absolute error and root mean squared error as low as 0.539 Mg/ha and 0.616 Mg/ha, respectively, except for the establishment year. Perennial bioenergy grass yields may be predicted 152 days before the harvest date on average, except for the establishment year. The green spectral band showed a greater contribution for predicting yields than the red band, which is indicative of increased chlorophyll content during the early growing season. Although additional testing is warranted, this study showed a great promise for a remote sensing approach for forecasting perennial bioenergy grass yields to support critical economic and logistical decisions of bioeconomy stakeholders.

09 BIOMASS FUELS↗
DOE OSTI2022

2021 Monthly Rice Production in Chinese Coastal Provinces

This paper explores the dynamics of rice production in the Chinese provinces of Liaoning, Jilin, Heilongjiang, Shanghai, Jiangsu, and Zhejiang and seeks to predict monthly rice production in the months of April through October using precipitation and Normalized Difference Vegetation Index as the predictor variables available. We utilize ridge and lasso regression models to predict the rice yield. Results indicate that a lasso regression model with an R 2 value of 0.9991501 with an adjusted R 2 value of 0.9991502 and a ridge regression model with an R 2 value of 0.9865443 with an adjusted R 2 value of 0.9870637 are possible. The lasso regression model does not account for all predictor variables while the ridge regression model does. Both models could be expanded upon to include more observations.

Tubbs, Heidi↗
DOE OSTI2024

Photoneutron Production Using an Electron Linear Accelerator for Applications in Neutron Imaging

Photoneutron production is possible using an electron linear accelerator and a target capable of generating photonuclear reactions. A short pulse neutron source can be useful for neutron imaging dynamic experiments. This study is aimed at the feasibility of photoneutron production using a 20 MeV electron linear accelerator and tungsten and depleted uranium targets of various thicknesses. MCNP6 (Monte Carlo N-Particle) code will be used to develop a computational model to estimate total neutron yield, and this will be verified at the Idaho State University’s Accelerator Center. After verification of the neutron yield and energy spectra, an additional MCNP6 model will be developed to analyze the neutron imaging processes. This study will potentially prove it is possible to conduct multi-mode imaging experiments on the anticipated Scorpius electron linear accelerator at the Nevada National Security Sites.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Organic Photovoltaic Efficiency Predictor: Data-Driven Models for Non-Fullerene Acceptor Organic Solar Cells

In the design of organic solar cells, there has been a need for materials with high power conversion efficiencies. Scharber’s model is commonly used to predict efficiency; however, it exhibits poor performance with new non-fullerene acceptor (NFA) devices, since it was designed for fullerene-based devices. In this work, an empirical model is proposed that can be a more accurate alternative for NFA organic solar cells. Additionally, many screening studies use computationally expensive methods. A model based on using semiempirical simplified time-dependent density functional theory (sTD-DFT) as an alternative method can accelerate the calculations and yield a similar accuracy. The models presented in this paper, termed organic photovoltaic efficiency predictor (OPEP) models, have shown significantly lower errors than previous models, with OPEP/B3LYP yielding errors of 1.53% and OPEP/sTD- DFT of 1.55%. As a result, the proposed computational models can be used for the fast and accurate screening of new high-efficiency NFAs/donor pairs.

14 SOLAR ENERGY↗
DOE OSTI2026

Highly boosted dielectron identification in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A new technique is developed to identify dielectrons (e$^+$e$^-$) with Lorentz boost $γ_\mathrm{L}$$\gt$ 20 that produce one single merged cluster in the electromagnetic calorimeter of the CMS detector. The identification uses two multivariate models: one for the case where both electron tracks are reconstructed, and another where only one of the tracks is reconstructed. The efficiency is determined using proton-proton collision data collected at a center-of-mass energy of 13 TeV. Boosted J/$ψ$ mesons decaying into e$^+$e$^-$ pairs are used to estimate the efficiency of the model with two tracks, yielding an overall efficiency of 80%. The Z $\to$ $μ^+μ^-γ$ events, where the photon converts into a collimated dielectron, are used for the model with a single track, yielding an efficiency of about 60%. A dedicated energy correction for dielectron candidates is also developed using B$^\pm$ $\to$ J/$ψ$K$^\pm$ $\to$ e$^+$e$^-$K$^\pm$ data.

Hayrapetyan, A. [Yerevan Phys. Inst.]↗
DOE OSTI2024

Creating Accurate Methane Emission Inventories through Data-Driven Airborne Survey Strategies: Methods and Results from the Haynesville, Anadarko, and Permian Basins

Significantly reducing methane emissions from the oil and gas sector can decrease the rate of climate change over the next two decades, buying critical time for a global energy transition. However, emissions inventories that can be used by oil and gas operators and environmental regulators to identify optimal methane emission mitigation strategies are either based on conservative emission factor methods, or are inconsistent between studies due to differences in sampling strategies or survey technologies. We developed a new approach for methane emissions survey design that yields representative basinwide methane emissions inventories by surveying a subset of total assets in a given oil and gas basin. We identify several sampling and analysis principles, including large sample sizes, balanced sampling across oil and gas production, careful survey area definition, and a unified protocol for analysis, to be vital to producing an unbiased estimate of basin-scale emissions that can be reconciled with future studies. We further present results from deploying this strategy in two oil and gas producing regions in the United States: the Haynesville Basin in Texas and Louisiana, and the Woodford Shale in the Anadarko Basin in Oklahoma. Aerial surveys were performed in 2023 using the Insight M LeakSurveyor™ technology. Preliminary results from methane emissions detected by Insight M indicate that aerially detected emissions above roughly 30 kg(CH4)/hr by themselves contribute a fractional loss rate of 1.13% of gross gas production across oil and gas operations in the Haynesville Basin, with aerially detected emissions equivalent to 2.67% of gross gas production in the Woodford Shale. We supplement these aerial estimates with modeled emissions that are below the LeakSurveyor’s survey sensitivity using a recently published inventory-based model of methane emissions, which we update for our survey areas. We then combine our aerial detections with modeled emissions to yield methane emission distributions and inventories that incorporate the full range of potential methane emissions from the smallest to the largest. These results can be used to identify the most effective methane mitigation strategies for our study areas, and can be reconciled with future methane emissions surveys that use different technologies.

Sherwin, Evan (ORCID:0000000321804297)↗
DOE OSTI2022

A Critical Review of Radiolysis Issues in Water-Cooled Fission and Fusion Reactors: Part I, Assessment of Radiolysis Models

A critical review is presented on modeling of the radiolysis of the coolant water in nuclear power reactors with emphasis on ITER. The review is presented in two parts: In Part I, we assess previous work in terms of compliance with important chemical principles and conclude that no model proposed to date is completely satisfactory, in this regard. Thus, some reactions that have been proposed in various radiolysis models are not elementary in nature and can be decomposed into two or more elementary reactions, some of which are already included in the models. These reactions must be removed in formulating a viable model. Furthermore, elementary reactions between species of like charge are also commonly included, but they can be discounted upon the basis of Coulombic repulsion under the prevailing conditions (T < 350 °C) and must also be removed. Likewise, it is concluded that the current state of knowledge with respect to radiolytic yields (i.e., G-values) is also unsatisfactory. More work is required to ensure that the yields used in radiolysis models are truly “primary” yields corresponding to a time scale of nanoseconds or less. This is necessary to ensure that the impact of the reactions that occur outside of the spurs (ionizing particle tracks in the medium) are not counted twice. In Part II, the authors review the use of the radiolysis models coupled with electrochemical models to predict the water chemistry, corrosion potential, crack growth rate in Type 304 SS, and accumulated damage in the coolant circuits of boiling water reactors, pressurized water reactors, and the test fusion reactor, ITER. Based on experience with fission reactors, the emphasis should be placed on the control of the electrochemical corrosion potential because it is the parameter that best describes the state of corrosion in coolant circuits.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Integrating multi-modal remote sensing, deep learning, and attention mechanisms for yield prediction in plant breeding experiments

In both plant breeding and crop management, interpretability plays a crucial role in instilling trust in AI-driven approaches and enabling the provision of actionable insights. The primary objective of this research is to explore and evaluate the potential contributions of deep learning network architectures that employ stacked LSTM for end-of-season maize grain yield prediction. A secondary aim is to expand the capabilities of these networks by adapting them to better accommodate and leverage the multi-modality properties of remote sensing data. In this study, a multi-modal deep learning architecture that assimilates inputs from heterogeneous data streams, including high-resolution hyperspectral imagery, LiDAR point clouds, and environmental data, is proposed to forecast maize crop yields. The architecture includes attention mechanisms that assign varying levels of importance to different modalities and temporal features that, reflect the dynamics of plant growth and environmental interactions. The interpretability of the attention weights is investigated in multi-modal networks that seek to both improve predictions and attribute crop yield outcomes to genetic and environmental variables. This approach also contributes to increased interpretability of the model's predictions. The temporal attention weight distributions highlighted relevant factors and critical growth stages that contribute to the predictions. The results of this study affirm that the attention weights are consistent with recognized biological growth stages, thereby substantiating the network's capability to learn biologically interpretable features. Accuracies of the model's predictions of yield ranged from 0.82-0.93 R 2 ref in this genetics-focused study, further highlighting the potential of attention-based models. Further, this research facilitates understanding of how multi-modality remote sensing aligns with the physiological stages of maize. The proposed architecture shows promise in improving predictions and offering interpretable insights into the factors affecting maize crop yields, while demonstrating the impact of data collection by different modalities through the growing season. By identifying relevant factors and critical growth stages, the model's attention weights provide valuable information that can be used in both plant breeding and crop management. The consistency of attention weights with biological growth stages reinforces the potential of deep learning networks in agricultural applications, particularly in leveraging remote sensing data for yield prediction. To the best of our knowledge, this is the first study that investigates the use of hyperspectral and LiDAR UAV time series data for explaining/interpreting plant growth stages within deep learning networks and forecasting plot-level maize grain yield using late fusion modalities with attention mechanisms.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Predicting Switchgrass Biomass Yields Using a Spectral Vegetation Index Derived from Multispectral Satellite Imagery

Successful scaling of perennial bioenergy crop production requires a landscape design that optimizes the benefits of finite lands for people, communities, and environments. Utilizing marginal areas is the key to sustainable bioenergy crop production (Ssegane et al., 2015, 2016). Marginal areas are often small-sized lands and unevenly distributed across the agricultural landscape (Ssegane et al., 2016); thus, a systematic, semi-automated remote sensing method is needed as an effective means of estimating bioenergy crop yields across landscapes. Argonne National Laboratory (Argonne) is currently developing a tool, Scaling Up Perennial Bioenergy Economics and Ecosystem Services Tool (SUPERBEEST), to identify marginal agricultural lands and quantify environmental and economic effects of perennial bioenergy crop production systems. The tool aims to provide users a path to foster the sustainable and productive integration of bioenergy crops in the Midwestern agricultural landscape. Reliable, cost-effective, and timely estimation of bioenergy crop yields using remote sensing would help calculate and track the success of integrated bioenergy crops in the landscape for those communities. Argonne previously conducted feasibility studies for estimating biomass yields for bioenergy feedstock, corn and perennial grass using spectral vegetation indices (SVIs)1 derived from optical imagery (Hamada et al., 2015, 2021). In both studies, SVIs, more specifically those sensitive to plant chlorophyll or nitrogen contents, showed potential for estimating or predicting biomass yields with a correlation of determination (R2) ranging from 0.54 to 0.96, indicating a value for further investigation as a viable means of quantifying bioenergy feedstock production across large landscapes. Thus, the goal of this study is to evaluate the feasibility of use of SVIs as a means of estimating or predicting switchgrass biomass yields at harvest using publicly available multispectral satellite imagery. The feasibility analysis was performed using four study areas of mature switchgrass located in Virginia. Objectives are to (1) examine the SVIs and establish their relationships with switchgrass biomass yields at harvest, (2) develop a parsimonious image processing model for predicting at-harvest yields by applying the relationships with the most promising spectral index and (3) map switchgrass yields predicted by the image processing model across the study sites. The calibration to field data will rely on switchgrass biomass yields determined by the baling method, representing a potential challenge to the analysis but an important practical aspect for future applications. With this research design, the study aimed to gain insights into enabling remote sensing-based estimation of bioenergy crop yields in a reliable, cost- effective, and timely manner across large, heterogeneous landscapes.

09 BIOMASS FUELS↗
DOE OSTI2021

Open source implementation of glued sphere discrete element method and nonspherical biomass fast pyrolysis simulation

Here, in this research, a glued-sphere Discrete Element Method (DEM) method was implemented in the open-source, Computational Fluid Dynamics (CFD) software MFiX. The implementation was verified using a cylinder-wall collision and then validated by simulating the packing and fluidization of non-spherical particles. The validated code was applied to simulate fast pyrolysis of non-spherical biomass particles in a bubbling fluidized bed. The glued sphere occupancy ratio was proposed to quantify the quality of shape resolution using glued sphere. Shape resolution showed significant influence on the packing height in the simulation of particle packing and an occupancy ratio of 80 % was recommended. Its influence is minor in fully fluidized bed but can be 8 times higher in fixed fluidized bed. Three tested heat transfer models predicted similar yields of elongated biomass fast pyrolysis. The solver developed in this research can be used to simulate other multiphase reacting flows involving non-spherical particles.

42 ENGINEERING↗
DOE OSTI2022

Forbidden scalar dark matter and dark Higgses

As experimental searches for WIMP dark matter continue to yield null results, models beyond the WIMP paradigm have proliferated in order to elude ever improving observational constraints, among them that of sub-GeV dark matter mediated by a massive vector portal (a dark photon) associated with a new dark U(1) gauge symmetry. It has been previously noted that for a significant range of the parameter space of this class of models, the annihilation of dark matter particles into a pair of dark photons can dominate the freeze-out process even when this process is kinematically forbidden for dark matter at rest — this is known as the “forbidden dark matter” (FDM) regime. Prior studies of this regime, however, assume that any “dark Higgs” associated with breaking the dark U(1) and imparting mass to the dark photon is decoupled from the dark matter and as such plays no role in the freeze-out process. In this paper, we explore the effects of a dark Higgs on sub-GeV dark matter phenomenology in this FDM regime by considering the simplest possible construction in which there exist non-trivial dark matter-dark Higgs couplings: a model with a single complex scalar DM candidate coupled directly to the dark Higgs field. We find that for a wide range of parameter space, the dark Higgs can alter the resulting relic abundance by many orders of magnitude, and that this effect can remain significant even for a small dark matter-dark Higgs coupling constant. Considering measurements from direct detection and measurements of the CMB, we further find that points in this model’s parameter space which recreate the appropriate dark matter relic abundance suffer only mild constraints from other sources at present, but may become accessible in near-future direct detection experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗