Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “reduction”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Variability in climate change simulations affects needed long-term riverine nutrient reductions for the Baltic Sea

Changes to runoff due to climate change may influence management of nutrient loading to the sea. Assuming unchanged river nutrient concentrations, we evaluate the effects of changing runoff on commitments to nutrient reductions under the Baltic Sea Action Plan. For several countries, climate projections point to large variability in load changes in relation to reduction targets. These changes either increase loads, making the target more difficult to reach, or decrease them, leading instead to a full achievement of the target. The impact of variability in climate projections varies with the size of the reduction target and is larger for countries with more limited commitments. Finally, in the end, a number of focused actions are needed to manage the effects of climate change on nutrient loads: reducing uncertainty in climate projections, deciding on frameworks to identify best performing models with respect to land surface hydrology, and increasing efforts at sustained monitoring of water flow changes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

An evaluation of low-cost heuristics for matrix bandwidth and profile reductions

Hundreds of heuristics have been proposed to resolve the problems of bandwidth and profile reductions since the 1960s. We found 132 heuristics that have been applied to these problems in reviews of the literature. Among them, 14 were selected for which no other simulation or comparison revealed that the heuristic could be superseded by any other algorithm in the analyzed articles with respect to bandwidth or profile reduction. We also considered the computational costs of the heuristics during this process. Therefore, these 14 heuristics were selected as potentially being the best low-cost methods to solve the bandwidth and/or profile reduction problems. Results of the 14 selected heuristics are evaluated in this work. For evaluation on the set of test problems, a metric based on the relative percentage distance to the best possible bandwidth or profile is proposed. The most promising heuristics for several application areas are identified. Moreover, it was found that the FNCHC and GPS heuristics showed the best overall results in reducing the bandwidth of symmetric and asymmetric matrices among the evaluated heuristics, respectively. In addition, the NSloan and MPG heuristics showed the best overall results in reducing the profile of symmetric and asymmetric matrices among the heuristics among the evaluated heuristics, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Particle scale modeling of CuFeAlO 4 during reduction with CO in chemical looping applications

Particle scale models that couple reaction phenomena to changes in the solid-state chemistry of an oxygen carrier system are critical to the advancement of the chemical looping concept by allowing for a means to assess process scale up. This work presents an analysis of the reduction for a CuFeAlO 4 oxygen carrier with Carbon Monoxide (CO). The analysis was utilized to aid in the application of particle scale model representation of the carrier system. An experimentally driven study was conducted to provide an array of operational/parametric data sets for the analysis and their impact accessed. Quantification of the cubic spinel oxide phase and changes due to lattice oxygen depletion from reduction were explored to link the solid-state chemistry changes to the reaction progression. Reduction occurred in a multistep process as oxygen was depleted from the structure. Oxygen bound to Cu cations were the first to react with CO. As oxygen was depleted further phase re-orientation occurred resulting in an iron based aluminate (FeAl 2 O 4 ) with discrete metallic copper present. FeAl 2 O 4 was further depleted of oxygen to metallic Fe and alumina. The multistep process was emulated through the use of a multi-interface Grainy pellet model. To add to the utility of the model, the effects of product gas, CO 2 , on the reaction progression were incorporated into the description. In addition, the catalytic effects of the Boudouard reaction were examined and incorporated into the representation adding to the novelty of the work.

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

The role of current and emerging technologies in meeting Japan’s mid- to long-term carbon reduction goals

Using Japan as a proxy for a developed nation, we investigated the role of existing and nascent technologies in curbing carbon emissions. We simulated possible pathways to meeting 2030 and 2050 emission targets within the Japanese electricity supply sector using a single-region model in The Integrated MARKAL-EFOM System (TIMES). Critically, our simulations incorporate novel technologies like hydrogen electrolysers, carbon capture, photochemical water splitting, and emerging photovoltaic cells, assess long-term impacts up to the year 2100, and include life-cycle emissions and learning curves for parameters such as investment cost, efficiency, and emission coefficients. Results indicate that a hybrid approach, using nuclear power and hydrogen from renewable energy-based electrolysis, is cost-effective and provides long-term emission reduction along with energy security. Finally, nuclear, wind, solar, and hydrogen from renewables emerge as key emission reduction technologies, while natural gas with carbon capture plays a minor role in achieving emission reduction targets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Carnitine protects the nematode Caenorhabditis elegans from glucose-induced reduction of survival depending on the nuclear hormone receptor DAF-12

Besides its function in transport of fatty acids into mitochondria in order to provide substrates for β-oxidation, carnitine has been shown to affect also glucose metabolism and to inhibit several mechanisms associated with diabetic complications. In the present study we used the mev-1 mutant of the nematode Caenorhabditis elegans fed on a high glucose concentration in liquid media as a diabetes model and tested the effects of carnitine supplementation on their survival under heat-stress. Carnitine at 100 μM completely prevented the survival reduction that was caused by the application of 10 mM glucose. RNA-interference for sir-2.1, a candidate genes mediating the effects of carnitine revealed no contribution of the sirtuin for the rescue of survival. Under daf-12 RNAi rescue of survival by carnitine was abolished. RNA-interference for γ-butyrobetaine hydroxylase 2, encoding the key enzyme for carnitine biosynthesis did neither increase glucose toxicity nor prevent the rescue of survival by carnitine, suggesting that the effects of carnitine supplementation on carnitine levels were significant. Finally, it was demonstrated that neither the amount of lysosomes nor the proteasomal activity were increased by carnitine, excluding that protein degradation pathways, such as autophagy or proteasomal degradation, are involved in the protective carnitine effects. In conclusion, carnitine supplementation prevents the reduction of survival caused by glucose in C. elegans in dependence on a nuclear hormone receptor which displays high homologies to the vertebrate peroxisomal proliferator activated receptors. - Highlights: • Carnitine protects from glucose-induced reduction of stress-resistance. • Carnitine acts via the PPAR homolog DAF-12 on glucose toxicity. • Carnitine protects from glucose toxicity independent of protein degradation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Early-stage reduction of the dendritic complexity in basolateral amygdala of a transgenic mouse model of Alzheimer's disease

Alzheimer's disease is a representative age-related neurodegenerative disease that could result in loss of memory and cognitive deficiency. However, the precise onset time of Alzheimer's disease affecting neuronal circuits and the mechanisms underlying the changes are not clearly known. To address the neuroanatomical changes during the early pathologic developing process, we acquired the neuronal morphological characterization of AD in APP/PS1 double-transgenic mice using the Micro-Optical Sectioning Tomography system. We reconstructed the neurons in 3D datasets with a resolution of 0.32 × 0.32 × 1 μm and used the Sholl method to analyze the anatomical characterization of the dendritic branches. The results showed that, similar to the progressive change in amyloid plaques, the number of dendritic branches were significantly decreased in 9-month-old mice. In addition, a distinct reduction of dendritic complexity occurred in third and fourth-order dendritic branches of 9-month-old mice, while no significant changes were identified in these parameters in 6-month-old mice. At the branch-level, the density distribution of dendritic arbors in the radial direction decreased in the range of 40–90 μm from the neuron soma in 6-month-old mice. These changes in the dendritic complexity suggest that these reductions contribute to the progressive cognitive impairment seen in APP/PS1 mice. This work may yield insights into the early changes in dendritic abnormality and its relevance to dysfunctional mechanisms of learning, memory and emotion in Alzheimer's disease. - Highlights: • Neuron-level, reduction of dendritic complexity in BLA of 9-month-old AD mice. • Specific range of branch decrease in density of 6-month-old AD mice. • 3D imaging with high resolution will provide insights into brain aging.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Tuning electronic properties by oxidation-reduction reactions at graphene-ruthenium interface

Mass production of graphene is associated with the growth on catalysts used also in other chemical reactions. In this study, we exploit the oxidation-reduction to tailor the properties of single layer graphene domains with incorporated bi-layer patches on ruthenium. Using photoelectron spectromicroscopy techniques, we find that oxygen, intercalating under single layer and making it p-doped by the formation of Ru-O x , does not intercalate under the bilayer patches with n-doped upper layer, but decorates them under single layer surrounding creating lateral p-n junctions with chemical potential difference of 1.2 eV. O-reduction by thermal treatment in vacuum results in C-vacancy defects enhancing electronic coupling of remained graphene to Ru, whereas in H 2 , vacancy formation is suppressed. Also, for the domains below 15–25 μm size, after O-reduction in H 2 , graphene/Ru coupling is restored, while wrinkle pattern produced by O-intercalation is irreversible and can trap reaction products between the wrinkles and Ru surface step edges. In fact, in certain regions of bigger domains, the products, containing H 2 O and/or its fragments, remain at the interface, making graphene decoupled and undoped.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Impact of sulfation and desulfation on NO x reduction using Cu-chabazite SCR catalysts

This bench reactor study investigates the impact of gaseous sulfur on the NO x reduction activity of Cu-chabazite SCR (Cu-CHA) catalysts at SO 2 concentrations representative of marine diesel engine exhaust. After two hours of 500 ppm SO 2 exposure at 250 and 400 °C in the simulated diesel exhaust gases, the NO x reduction activity of the sulfated Cu-CHA SCR catalysts is severely degraded at evaluation temperatures below 250 °C; however, above 250 °C the impact of sulfur exposure is minimal. EPMA shows that sulfur is located throughout the washcoat and along the entire length of the sulfated samples. Interestingly, BET measurements reveal that the sulfated samples have a 20% decrease in surface area. Moreover, the sulfated samples show a decrease in NO x /nitrate absorption during NO exposure in a DRIFTS reactor which suggests that Cu sites in the catalyst are blocked by the presence of sulfur. SO 2 exposure also results in an increase in NH 3 storage capacity, possibly due to the formation of ammonium sulfate species in the sulfated samples. In all cases, lean thermal treatments as low as 500 °C reverse the effects of sulfur exposure and restore the NO x reduction activity of the Cu-CHA catalyst to that of the fresh condition.

36 MATERIALS SCIENCE↗
DOE OSTI2019

First-row transition metal polypyridine complexes that catalyze proton to hydrogen reduction

Proton reduction is a critical reaction for the efficient utilization of solar fuels and the development of a hydrogen economy. Molecular proton reduction catalysts help us to understand how hydrogenases function in nature, on one hand, and inspire us to design new practical materials on the other. This manuscript introduces the concept of electrocatalytic and photocatalytic proton (hydrogen evolution) in a homogeneous system, and then reviews recent studies on molecular proton reduction catalysts that contain 3d transition metal centers (Mn, Fe, Co, and Ni) surrounded by polypyridine ligands. The discussion focuses on the design, structure, and catalytic behavior of these metal polypyridine catalysts. Catalytic pathways, and how they are affected by complex structure, are addressed in order to offer rational suggestions for the future preparation of promising hydrogen evolution catalysts.

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

Planar, curved and twisted molecular nanographenes: Reduction-induced alkali metal coordination

Planar and curved polycyclic aromatic hydrocarbons (PAHs) attract significant attention as molecular models of fullerenes, carbon nanotubes, and graphene, thus stimulating broad investigation of chemical reactivity and materials applications of designed nanocarbon π-systems. Non-planar molecular nanographenes (NGs) recently emerge as advanced anode materials in energy storage, showing high reduction limits and enhanced alkali metal intercalation levels. However, the lack of direct structure–property correlations in such complex hybrid systems impedes their further development and utilization. With a focus on alkali-metal-induced reduction of selected PAHs, we herein review original metal binding and intercalation trends, site specific coordination, and distinct carbon framework responses to stepwise electron uptake. Small planar graphene fragments, like triphenylene and coronene, are compared to π-expanded hexabenzocoronenes, followed by the discussion of bowl-shaped corannulene, sumanene and other carbon bowls, as well as bent, warped, and twisted molecular nanographenes. The effect of size, symmetry, and framework topology along with the structural deformation of carbon backbones upon reduction are analyzed, using recent crystallographic examples of alkali-metal intercalated products. In conclusion, the revealed insights into the structures, binding, and metal intercalation in molecular nanographenes should stimulate their future applications as new functional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Kinetics of the reduction of hematite (Fe{sub 2}O{sub 3}) by methane (CH{sub 4}) during chemical looping combustion: A global mechanism

Chemical-looping combustion (CLC) has emerged as a promising technology for fossil fuel combustion which produces a sequestration ready concentrated CO{sub 2} stream in power production. A CLC system is composed with two reactors, an air and a fuel reactor. An oxygen carrier such as hematite (94%Fe{sub 2}O{sub 3}) circulates between the reactors, which transfers the oxygen necessary for the fuel combustion from the air to the fuel. An important issue for the CLC process is the selection of metal oxide as oxygen carrier, since it must retain its reactivity through many cycles. The primary objective of this work is to develop a global mechanism with respective kinetics rate parameters such that CFD simulations can be performed for large systems. In this study, thermogravimetric analysis (TGA) of the reduction of hematite (Fe{sub 2}O{sub 3}) in a continuous stream of CH{sub 4} (15, 20, and 35%) was conducted at temperatures ranging from 700 to 825{degrees}C over ten reduction cycles. The mass spectroscopy analysis of product gas indicated the presence of CO{sub 2} and H{sub 2}O at the early stage of reaction and H{sub 2} and CO at the final stage of reactions. A kinetic model based on two parallel reactions, 1) first-order irreversible rate kinetics and 2) Avrami equation describing nucleation and growth processes, was applied to the reduction data. It was found, that the reaction rates for both reactions increase with, both, temperature and the methane concentration in inlet gas.

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

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

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

Slow manifold reduction for plasma science

The classical Chapman–Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are based on controlled approximations applied to problems with multiple timescales. In this Review we develop the theory of slow manifold reduction with a plasma physics audience in mind. In particular we illustrate (a) how the slow manifold concept may be used to understand breakdown of a reduced model over sufficiently-long time intervals, and (b) how a discrete-time analogue of slow manifold theory provides a useful framework for developing implicit integrators for temporally-stiff plasma models. For readers with more advanced mathematical training we also use slow manifold reduction to explain the phenomenon of inheritance of Hamiltonian structure in dissipation-free reduced plasma models. Various facets of the theory are illustrated in the context of the Abraham–Lorentz model of a single charged particle experiencing its own radiation drag. As a culminating example we derive the slow manifold underlying kinetic quasineutral plasma dynamics up to first-order in perturbation theory. This first-order result incorporates several physical effects associated with small deviations from exact charge neutrality that lead to slow drift away from predictions based on the leading-order approximation n e = Z i n i .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Quantifying impact reduction due to avoidance, minimization and restoration for a natural gas pipeline in the Peruvian Andes

We present monitoring methods and quantitative biodiversity data to document components of the mitigation hierarchy. We estimated avoidance, minimization, restoration and impact reduction in quality hectares for the 25 m wide right of way of a 408 km natural gas buried pipeline that crosses 14 Ecological Landscape Units (ELUs) in the tropical Andes of Peru. We found that applying the mitigation hierarchy as part of a comprehensive biodiversity action plan substantially reduced impacts on biodiversity in all habitats studied. Avoidance and right of way minimization contributed to significant impact reduction. We quantified impact reduction during construction and operation on the right of way of the pipeline over a five-year period and found that restoration was the greatest contributor to reducing impacts. We documented that most ELUs have a positive restoration trajectory. We also documented how monitoring over large scale spatial scales, in combination with site-specific monitoring, generated data for management to determine restoration priorities and impact mitigation. A biodiversity action plan that incorporated the mitigation hierarchy and a science-based biodiversity monitoring and assessment program contributed to biodiversity management of the project and played an important role in minimizing and managing impacts. - Highlights: •Quantitative data for mitigation hierarchy components are presented. •Application of the mitigation hierarchy reduced impacts on biodiversity. •A biodiversity monitoring program provided data to reduce impacts.

03 NATURAL GAS↗
DOE OSTI2013

Biological Oxidation of Fe(II) in Reduced Nontronite Coupled with Nitrate Reduction by Pseudogulbenkiania sp. Strain 2002

Nitrate contamination in soils, sediments, and water bodies is a significant issue. Although much is known about nitrate degradation in these environments, especially via microbial pathways, a complete understanding of all degradation processes, especially in clay mineral-rich soils, is still lacking. The objective of this study was to study the potential of removing nitrate contaminant using structural Fe(II) in clay mineral nontronite. Specifically, the coupled processes of microbial oxidation of Fe(II) in microbially reduced nontronite (NAu-2) and nitrate reduction by Pseudogulbenkiania species strain 2002 was investigated. Bio-oxidation experiments were conducted in bicarbonate-buffered medium under both growth and nongrowth conditions. The extents of Fe(II) oxidation and nitrate reduction were measured by wet chemical methods. X-ray diffraction (XRD), scanning and transmission electron microscopy (SEM and TEM), and 57Fe-Mössbauer spectroscopy were used to observe mineralogical changes associated with Fe(III) reduction and Fe(II) oxidation in nontronite. The bio-oxidation extent under growth and nongrowth conditions reached 93% and 57%, respectively. Over the same time period, nitrate was completely reduced under both conditions to nitrogen gas (N2), via an intermediate product nitrite. Magnetite was a mineral product of nitrate-dependent Fe(II) oxidation, as evidenced by XRD data and TEM diffraction patterns. The results of this study highlight the importance of iron-bearing clay minerals in the global nitrogen cycle with potential applications in nitrate removal in soils.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2016

Observer Evaluation of a Metal Artifact Reduction Algorithm Applied to Head and Neck Cone Beam Computed Tomographic Images

Purpose and Objectives: To quantify, through an observer study, the reduction in metal artifacts on cone beam computed tomographic (CBCT) images using a projection-interpolation algorithm, on images containing metal artifacts from dental fillings and implants in patients treated for head and neck (H&N) cancer. Methods and Materials: An interpolation-substitution algorithm was applied to H&N CBCT images containing metal artifacts from dental fillings and implants. Image quality with respect to metal artifacts was evaluated subjectively and objectively. First, 6 independent radiation oncologists were asked to rank randomly sorted blinded images (before and after metal artifact reduction) using a 5-point rating scale (1 = severe artifacts; 5 = no artifacts). Second, the standard deviation of different regions of interest (ROI) within each image was calculated and compared with the mean rating scores. Results: The interpolation-substitution technique successfully reduced metal artifacts in 70% of the cases. From a total of 60 images from 15 H&N cancer patients undergoing image guided radiation therapy, the mean rating score on the uncorrected images was 2.3 ± 1.1, versus 3.3 ± 1.0 for the corrected images. The mean difference in ranking score between uncorrected and corrected images was 1.0 (95% confidence interval: 0.9-1.2, P<.05). The standard deviation of each ROI significantly decreased after artifact reduction (P<.01). Moreover, a negative correlation between the mean rating score for each image and the standard deviation of the oral cavity and bilateral cheeks was observed. Conclusion: The interpolation-substitution algorithm is efficient and effective for reducing metal artifacts caused by dental fillings and implants on CBCT images, as demonstrated by the statistically significant increase in observer image quality ranking and by the decrease in ROI standard deviation between uncorrected and corrected images.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

Catalytic N 2 O decomposition and reduction by NH 3 over Fe/Beta and Fe/SSZ-13 catalysts

Fe/zeolites are important N 2 O abatement catalysts, efficient in direct N 2 O decomposition and (selective) catalytic N 2 O reduction. In this study, Fe/Beta and Fe/SSZ-13 were synthesized via solution ion-exchange and used to catalyze these two reactions. Nature of the Fe species was probed with UV-vis, Mössbauer and EPR spectroscopies and H2-TPR. The characterizations collectively indicate that isolated and dinuclear Fe sites dominate in Fe/SSZ-13, whereas Fe/Beta contains higher concentrations of oligomeric Fe x O y species. H 2 -TPR results suggest that Fe-O interactions are weaker in Fe/SSZ-13, as evidenced by the lower reduction temperatures and higher extents of autoreduction during high-temperature pretreatments in inert gas. Kinetic measurements show that Fe/SSZ-13 has higher activity in catalytic N 2 O decomposition, thus demonstrating a positive correlation between activity and Fe-O binding, consistent with O 2 desorption being rate-limiting for this reaction. However, Fe/Beta was found to be more active in catalyzing N 2 O reduction by NH 3 . This indicates that larger active ensembles (i.e., oligomers) are more active for this reaction, consistent with the fact that both N 2 O and NH 3 need to be activated in this case. The authors from PNNL gratefully acknowledge the US Department of Energy (DOE), Energy Efficiency and Renewable Energy, Vehicle Technologies Office for the support of this work. The research described in this paper was performed in the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is operated for the US DOE by Battelle. Aiyong Wang gratefully acknowledges the China Scholarship Council for the Joint-Training Scholarship Program with the Pacific Northwest National Laboratory (PNNL). The authors from East China University of Science and Technology acknowledge National Basic Research Program of China (2013CB933200), National Natural Science Foundation of China (21577035, 21577034), Commission of Science and Technology of Shanghai Municipality (15DZ1205305) and 111 Project (B08021) for supports.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2015

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗