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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 OSTI2016

Development of Solvent Extraction Approach to Recycle Enriched Molybdenum Material

Argonne National Laboratory, in cooperation with Oak Ridge National Laboratory and NorthStar Medical Technologies, LLC, is developing a recycling process for a solution containing valuable Mo-100 or Mo-98 enriched material. Previously, Argonne had developed a recycle process using a precipitation technique. However, this process is labor intensive and can lead to production of large volumes of highly corrosive waste. This report discusses an alternative process to recover enriched Mo in the form of ammonium heptamolybdate by using solvent extraction. Small-scale experiments determined the optimal conditions for effective extraction of high Mo concentrations. Methods were developed for removal of ammonium chloride from the molybdenum product of the solvent extraction process. In large-scale experiments, very good purification from potassium and other elements was observed with very high recovery yields (~98%).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Energy-Storing Cryogenic Carbon Capture™ for Utility and Industrial-scale Processes (Final Report)

This project leverages work completed under funding from previous U.S. Department of Energy (DOE) projects and other sources of funding around the Cryogenic Carbon Capture Process™ (CCC). The purpose of this project is to further develop a perturbation of the CCC process that stores energy called the Cryogenic Carbon Capture™ Energy Storing (CCC-ES) process. The successful completion of the tasks in this project has prepared the CCC-ES process for scaling and developed initial plans and a feasibility analysis for an engineering-scale or small-commercial scale system that can store at least 10 MWh of energy. The specific areas of work in this project are: (1) Develop a conceptual, site-specific integrated process flow diagram: Sustainable Energy Solutions (SES) developed a conceptual, site-specific plan including a process flow diagram for integrating CCC-ES at a specific location. The proposed system was based on a typical engineering-scale CCC system designed to capture 30-50 metric tonnes of CO 2 per day (TPD), with modifications and additional changes and equipment put in place to add the energy storage element to the system. The 30-50 TPD scale corresponds to the required 10 MWh of stored energy. This task includes updating simulation software for transient analysis. SES also coordinated with the Jim Bridger Power Plant in Point of Rocks, Wyoming to get site-specific data. Using these data, SES completed site-specific preliminary process flow diagrams, estimated capital and operating costs for the CCC-ES system, and used the upgraded software package to estimate the primary figures of merit. (2) Complete a technoeconomic analysis (TEA): SES completed a full-scale TEA of the CCC-ES system to meet specific success criteria. This TEA used process information from the host site selected above. (3) Technology and data gap assessment for the CCC-ES process: As part of the technology gap assessment, SES performed an assessment of the best alternative energy storage solutions including figures of merit and operational strengths and weaknesses. SES then compared the proposed system with a discussion of how it addresses the weaknesses of alternative systems, showing for example a cost of stored energy at less than $50/MWh and with a roundtrip efficiency of greater than 95%. This assessment includes technical and other risk analyses and technology gaps with research and development needs to commercialize the process by 2030. Finally, work includes a commercialization roadmap/development pathway outlining the major milestones to move to a commercially operating CCC-ES system. (4) Phase II pre-FEED project plan: SES completed a project plan for the Phase II pre-FEED analysis using the same host site as in the Phase I conceptual study.

03 NATURAL GAS↗
DOE OSTI2016

Manufacturing demonstration of microbially mediated zinc sulfide nanoparticles in pilot-plant scale reactors

The thermophilic anaerobic metal-reducing bacterium Thermoanaerobacter sp. X513 efficiently produces zinc sulfide (ZnS) nanoparticles (NPs) in laboratory-scale ( ≤24-L) reactors. To determine whether this process can be up-scaled and adapted for pilot-plant production while maintaining NP yield and quality, a series of meso-scale experiments were performed using 100-l and 900-l reactors. Pasteurization and N 2 -sparging replaced autoclaving and boiling for deoxygenating media in the transition from small-scale to pilot-plant reactors. Consecutive 100-L batches using new or recycled media produced ZnS NPs with highly reproducible ~2 nm average crystallite size (ACS) and yields of ~0.5g L -1 , similar to small-scale batches. The 900-L pilot plant reactor produced ~ 320 g ZnS without process optimization or replacement of used medium; this quantity would be sufficient to form a ZnS thin film with ~120 nm thickness over 0.5 m width 13 km length. At all scales, the bacteria produced significant amounts of acetic, lactic and formic acids, which could be neutralized by the controlled addition of sodium hydroxide without the use of an organic pH buffer, eliminating 98% of the buffer chemical costs. In conclusion, the final NP products were characterized using XRD, ICP-OES, FTIR, DLS, and C/N analyses, which confirmed the growth medium without organic buffer enhanced the ZnS NP properties by reducing carbon and nitrogen surface coatings and supporting better dispersivity with similar ACS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

A Multilevel Approach For SolvingLarge-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one ofthe promising candidates for useful quantum computation,particularly in the context of finding approximate solutionsto Quadratic Unconstrained Binary Optimization (QUBO)problems. However, the existing quantum processing units(QPUs) are of relatively small size, and canonical mappingsof QUBO via the Ising model require one qubit per vari-able, rendering direct large-scale optimization infeasible.In classical optimization, a general strategy for addressingmany large-scale problems is via multilevel/multigrid meth-ods, where the large target problem is iteratively coarsenedand the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentallytest how existing QPUs perform when used as a sub-solverwithin such a multilevel strategy. To this aim, we com-bine and extend (via additional classical processing steps)the recently proposed Noise-Directed Adaptive Remapping(NDAR) and Quantum Relax&Round (QRR) algorithms.We first demonstrate the effectiveness of our heuristicextensions on Rigetti’s superconducting transmon deviceAnkaa-2. We find approximate solutions to10instances offully connected82-qubit Sherrington-Kirkpatrick graphswith random integer-valued coefficients obtaining normal-ized approximation ratios (ARs) in the range∼0.98−1.0,and the same class with real-valued coefficients (ARs∼0.94−1.0). Then, we implement the extended NDAR andQRR algorithms as subsolvers in the multilevel algorithmfor6large-scale graphs with at most∼27,000variables.In practice, the QPU (with classical post-processing steps)is used to find approximate solutions to dozens of at most82-qubit problems, which are iteratively used to constructthe global solution. We observe that quantum optimizationresults are competitive in terms of the quality of solutionswhen compared to classical heuristics used as subsolverswithin the multilevel approach.Reproducibility: source code and data are available at[TBA upon acceptance]

quantum computing↗
DOE OSTI2020

Laboratory-Scale Melter Systems for Simulated and Real AP-107 Tank Waste - 20483

The Hanford Waste Treatment and Immobilization Plant (WTP) will process and stabilize waste that is stored in underground tanks on the Hanford Site. At the WTP, the tank waste will be combined with glass-forming and modifying additives to form an aqueous and solid mixture called melter feed, which will then be vitrified in joule-heated melters. A small-scale melter system, the continuous laboratory-scale melter (CLSM), is designed to operate with a continuous feeding process while periodically pouring glass product and collecting off-gas. Two CLSMs were constructed: one in a non-radioactive environment for processing waste simulants and another in a fume hood capable of handling radioactive material for processing actual Hanford tank waste. The waste sample received for vitrification in the CLSM was from Hanford tank 241-AP-107. Approximately 12 liters of melter-feed slurry was vitrified into 7 kilograms of glass product over the course of 10 hours of charging to the CLSM. The partitioning of technetium-99 in the product streams was used to calculate the technetium-99 recovery and help determine when the vitrification process had reached a steady state. The average single-pass retention of technetium-99 in the glass product was then calculated for the processing of AP-107 waste in the CLSM system. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Time-resolved spray characterization via unified optical flow and binarization technique

This work leverages an unsupervised machine learning and advanced image processing techniques to characterize the breakup of fuel sprays in a small-scale combustor under reacting conditions, providing valuable insights into near-nozzle flow phenomenology. The proposed methodology integrates an improved optical flow model on a convolutional neural network to extract flow vectors with a binarization technique to assess droplets’ size and shape across the region of interest. The velocimetry approach demonstrates superior performance compared to a state-of-the-art optical flow model when applied to high-speed X-ray phase contrast spray images, achieving more accurate and reliable flow predictions. Moreover, breakup processes are quantified by breakup length and sphericity in accordance with velocity estimations, allowing a more complete characterization of the flow. This study establishes a robust methodology for analyzing spray morphology and primary breakup in compact combustors, contributing valuable means of understanding and optimizing fuel spray behavior in advanced combustion systems.

42 ENGINEERING↗
DOE OSTI2021

Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow

The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Here, two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w = (0.298, 0.284, 0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β = (0.5, 0.7, 0.99), somewhat higher than the w = 0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w = 1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w = 0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.

58 GEOSCIENCES↗
NASA NTRS2019

A Model for Energy Buildup and Eruption Onset in Coronal Mass Ejections

Coronal mass ejections (CMEs) and eruptive flares (EFs) are the most energetic explosions in the solar system. Their underlying origin is the free energy that builds up slowly in the sheared magnetic field of a filament channel. We report the first end-to-end numerical simulation of a CME/EF, from zero-free-energy initial state through filament channel formation to violent eruption, driven solely by the magnetic-helicity condensation process. Helicity is the topological measure of linkages between magnetic flux systems, and is conserved in the corona, building up inexorably until it is ejected into interplanetary space. Numerous investigations have demonstrated that helicity injected by small-scale vortical motions, such as those observed in the photosphere, undergoes an inverse cascade from small scales to large, “condensing” at magnetic-polarity boundaries. Our new results verify that this process forms a filament channel within a compact bipolar region embedded in a background dipole field, and show for the first time that a fast CME eventually occurs via the magnetic-breakout mechanism. We further show that the trigger for explosive eruption is reconnection onset in the flare current sheet that develops above the polarity inversion line: this reconnection forms flare loops below the sheet and a CME flux rope above, and initiates high-speed outward flow of the CME. Our findings have important implications for magnetic self organization and explosive behavior in solar and other astrophysical plasmas, as well as for understanding and predicting explosive solar activity.

filaments↗
DOE OSTI2013

SMALL-SCALE LOCAL PHENOMENA RELATED TO THE MAGNETIC RECONNECTION AND TURBULENCE IN THE PROXIMITY OF THE HELIOPAUSE

We study processes related to magnetic reconnection and plasma turbulence occurring in the presence of the heliopause (HP) and the heliospheric current sheet. It is shown that the interaction of plasmoids initiated by magnetic reconnection may provide connections between the inner and outer heliosheath and lead to an exchange of particles between the interstellar medium and the solar wind plasma shocked at the heliospheric termination shock. The magnetic reconnection may also cause plasma density and magnetic field compressions in the proximity of the HP. We argue that these phenomena could possibly be detected by the Voyager spacecraft approaching and crossing the HP. These results could clarify the concepts of the ''magnetic highway'' and the ''heliosheath depletion region'' recently proposed to explain recent Voyager 1 observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Third data release of the Hyper Suprime-Cam Subaru Strategic Program

This work presents the third data release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP), a wide-field multi-band imaging survey with the Subaru 8.2 m telescope. HSC-SSP has three survey layers (Wide, Deep, and UltraDeep) with different area coverages and depths, designed to address a wide array of astrophysical questions. This third release from HSC-SSP includes data from 278 nights of observing time and covers about 670 deg 2 in all five broad-band filters (grizy) at the full depth (~26 mag at 5σ depending on filter) in the Wide layer. If we include partially observed areas, the release covers 1470 deg 2 . The Deep and UltraDeep layers have ~80% of the originally planned integration times, and are considered done, as we have slightly changed the observing strategy in order to compensate for various time losses. There are a number of updates in the image processing pipeline. Of particular importance is the change in the sky subtraction algorithm; we subtract the sky on small scales before the detection and measurement stages, which has significantly reduced the number of false detections. Thanks to this and other updates, the overall quality of the processed data has improved since the previous release. However, there are limitations in the data (for example, the pipeline is not optimized for crowded fields), and we encourage the user to check the quality assurance plots as well as a list of known issues before exploiting the data. The data release website is https://hsc-release.mtk.nao.ac.jp.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

High Precision, Absolute Total Column Ozone Measurements from the Pandora Spectrometer System: Comparisons with Data from a Brewer Double Monochromator and Aura OMI

We present new, high precision, high temporal resolution measurements of total column ozone (TCO) amounts derived from ground-based direct-sun irradiance measurements using our recently deployed Pandora single-grating spectrometers. Pandora's small size and portability allow deployment at multiple sites within an urban air-shed and development of a ground-based monitoring network for studying small-scale atmospheric dynamics, spatial heterogeneities in trace gas distribution, local pollution conditions, photochemical processes and interdependencies of ozone and its major precursors. Results are shown for four mid- to high-latitude sites where different Pandora instruments were used. Comparisons with a well calibrated double-grating Brewer spectrometer over a period of more than a year in Greenbelt MD showed excellent agreement and a small bias of approximately 2 DU (or, 0.6%). This was constant with slant column ozone amount over the full range of observed solar zenith angles (15-80), indicating adequate Pandora stray light correction. A small (1-2%) seasonal difference was found, consistent with sensitivity studies showing that the Pandora spectral fitting TCO retrieval has a temperature dependence of 1% per 3K, with an underestimation in temperature (e.g., during summer) resulting in an underestimation of TCO. Pandora agreed well with Aura-OMI (Ozone Measuring Instrument) satellite data, with average residuals of <1% at the different sites when the OMI view was within 50 km from the Pandora location and OMI-measured cloud fraction was <0.2. The frequent and continuous measurements by Pandora revealed significant short-term (hourly) temporal changes in TCO, not possible to capture by sun-synchronous satellites, such as OMI, alone.

Ozone↗
DOE OSTI2013

Bench-Scale Silicone Process for Low-Cost CO 2 Capture: Manufacturing Plan for Aminosilicone-based CO 2 Absorption Material

A commercially cost effective manufacturing plan was developed for GAP-1m, the aminosilicone-based part of the CO 2 capture solvent described in DE-FE0007502, and the small-scale synthesis of GAP-1m was confirmed. The plan utilizes a current intermediate at SiVance LLC to supply the 2013-2015 needs for GE Global Research. Material from this process was supplied to GE Global Research for evaluation and creation of specifications. GE Global Research has since ordered larger quantities (60 liters) for the larger scale evaluations that start in first quarter, 2013. For GE’s much larger future commercial needs, an improved, more economical pathway to make the product was developed after significant laboratory and literature research. Suppliers were identified for all raw materials.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Industrial biomanufacturing: The future of chemical production

The current model for industrial chemical manufacturing employs large-scale megafacilities that benefit from economies of unit scale. However, this strategy faces environmental, geographical, political, and economic challenges associated with energy and manufacturing demands. We review how exploiting biological processes for manufacturing (i.e., industrial biomanufacturing) addresses these concerns while also supporting and benefiting from economies of unit number. Key to this approach is the inherent small scale and capital efficiency of bioprocesses and the ability of engineered biocatalysts to produce designer products at high carbon and energy efficiency with adjustable output, at high selectivity, and under mild process conditions. The biological conversion of single-carbon compounds represents a test bed to establish this paradigm, enabling rapid, mobile, and widespread deployment, access to remote and distributed resources, and adaptation to new and changing markets.

Science & Technology - Other Topics↗
DOE OSTI2013

Large-scale magnetic structure formation in three-dimensional magnetohydrodynamic turbulence

The inverse cascade of magnetic helicity in three-dimensional magnetohydrodynamic (3D-MHD) turbulence is believed to be one of the processes responsible for large-scale magnetic structure formation in astrophysical systems. In this work, we present an exhaustive set of high-resolution direct numerical simulations of both forced and decaying 3D-MHD turbulence, to understand this structure formation process. It is first shown that an inverse cascade of magnetic helicity in small-scale driven turbulence does not necessarily generate coherent large-scale magnetic structures. The observed large-scale magnetic field, in this case, is severely perturbed by magnetic fluctuations generated by the small-scale forcing. In the decaying case, coherent large-scale structures form similarly to those observed astronomically. Based on the numerical results, the formation of large-scale magnetic structures in some astrophysical systems is suggested to be the consequence of an initial forcing that imparts the necessary turbulent energy into the system, which, after the forcing shuts off, decays to form the large-scale structures. This idea is supported by representative examples, e.g., clusters of galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2013

The Iterative Design Process in Research and Development: A Work Experience Paper

The iterative design process is one of many strategies used in new product development. Top-down development strategies, like waterfall development, place a heavy emphasis on planning and simulation. The iterative process, on the other hand, is better suited to the management of small to medium scale projects. Over the past four months, I have worked with engineers at Johnson Space Center on a multitude of electronics projects. By describing the work I have done these last few months, analyzing the factors that have driven design decisions, and examining the testing and verification process, I will demonstrate that iterative design is the obvious choice for research and development projects.

Sullivan, George F. III↗
DOE OSTI2024

Reactive transport modeling of the Aquifer Thermal Energy Storage (ATES) system at Stockton University, New Jersey during seasonal operations

Hydrogeochemical processes associated with Aquifer Thermal Energy Storage (ATES) operations can often impact the system performance owing to mineral precipitation either at the wellbore or in the aquifer owing to changes in temperature and fluid disequilibria. Although failure of ATES systems due to mineral precipitation ("fouling") is common, predictive reactive-transport models have rarely been applied to plan their design and operation. Here, the objective of this study is to develop a reactive-transport model by coupling thermal, hydrological, and chemical (THC) processes to evaluate effects of introduced atmospheric oxygen on water chemistry, mineral precipitation/dissolution, porosity, and permeability changes associated with an ATES system at Stockton University (New Jersey, USA). The THC model builds on a Thermal-Hydrological-Mechanical (THM) model of the site that evaluated system failure owing to possible fracturing in the caprock or around the wellbore. The causes of the system failure are not known – potential causes include hydraulic fracturing owing to elevated pump pressures that took place, a flow pathway created by one of the boreholes, or a pre-existing natural hydrologic connection between the upper unconfined aquifer and the ATES aquifer, any of which could have led to oxygenated water entering the reservoir and causing the observed Fe-oxide fouling on well screens. The THC model is used to evaluate some of the hypotheses and observations regarding system failure owing to geochemical processes. The reactive-transport code TOUGHREACT V4 was used to model the THC processes during seasonal heating and cooling operations at the Stockton ATES site over 6 years of operation. In the THC simulations, the primary effects on geochemistry were observed when the injection water is saturated with atmospheric oxygen. Simulations show greater precipitation of goethite near the cold wells as compared to the warm wells. Although volume fractions of Fe-hydroxides were relatively small, the model was aimed at processes in the aquifer at the scale of meters and larger rather than at the scale of mm or cm (i.e., a well screen). Kaolinite is the dominant precipitating phase, also around the cold wells. Illite dissolves near the cold wells and precipitates near the warm wells. There is a net decrease in the porosity near the cold wells and increase near the warm wells, although a slight amount of thermal contraction near the cold wells and expansion near the warm wells is responsible for a significant proportion of the porosity change. Owing to the coarse discretization of the numerical grid near the wells (compared to the screen thickness) the magnitude of permeability changes at the wellbore are likely underestimated. The reactive transport model in this study can be used for characterization of aquifers, optimizing the operational parameters (temperature, pressure, pH etc.), and planning of mitigation strategies for ATES systems.

15 GEOTHERMAL ENERGY↗
DOE OSTI2011

Effective Pore-Scale Dispersion Upscaling with the Correlated Continuous Time Random Walk Approach

We propose a general framework for upscaling dispersion in porous media. A key challenge of the upscaling procedure is to relate the temporal evolution of spreading to the small scale velocity field properties. The representation of the Lagrangian velocity transition process as a Markovian process in space provides a simple way to quantify complex correlation properties, i.e. non-Gaussian velocity distributions. The resulting effective transport model is a correlated CTRW. We use this framework to upscale pore scale dispersion for a periodic pore geometry. The correlated CTRW model is defined by the transit time distribution across one pore and the transition probability density quantifying the correlation between successive transit times. The latter is of central importance since it accounts for incomplete mixing at the pore throats. The predictions of the correlated CTRW model are in good agreement with the pore scale simulations over the pre-asymptotic and asymptotic regimes. We investigate the representation of this effective dispersion model in phase space (position, velocity) in a form similar to a Boltzmann transport equation.

multiscale modeling, dimension reduction, transpor↗
DOE OSTI2016

Stochastic behavior of nanoscale dielectric wall buckling

The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗