Search NASA⌕ Search

SEARCH · Search NASA

Results for “Model Predictive Control”

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 865 records · Page 48

NREL RSF Measured Data 2011

Modern buildings are complex energy systems that must be controlled for energy efficiency. The Research Support Facility (RSF) at the National Renewable Energy Laboratory (NREL) has hundreds of controllers -- computers that communicate with the building's various control systems -- to control the building based on tens of thousands of variables and sensor points. These control strategies were designed for the RSF's systems to efficiently support research activities. Many events that affect energy use cannot be reliably predicted, but certain decisions (such as control strategies) must be made ahead of time. NREL researchers modeled the RSF systems to predict how they might perform. They then monitor these systems to understand how they are actually performing and reacting to the dynamic conditions of weather, occupancy, and maintenance. This submission includes the Measured Energy Data from the RSF Systems Model. The data includes a csv with measured data from NREL's Research and Support Facility (RSF) for 2011. The dataset contains hourly data for: Total Cooling (kW)- Total Heating (kW)- Total Mechanical (kW)- Total Lighting (kW)- Total Plug Loads (kW)- Total Data Center (kW)- Total Building (kW)- PV (kW)- Building Net (kW). Energy Model data and Weather data related to the RSF Systems Model can be found in the "Related Datasets" section of this submission.

2011↗

Prediction of The TREAT Facility Power and Temperature of Sirius-2c Nuclear Propulsion Fuel Experiment

This paper presents simulation results of the Sirius-2c full power experiment that was performed at the TREAT facility to support experiment modeling and transient analysis of the NASA-sponsored Sirius series of experiments for nuclear thermal propulsion applications. We presents a novel approach to predict the control rod motion and power of the reactor and the temperature of the specimen during transient experiments using the Griffin and Bison packages of the Multiphysics Object Oriented Simulation Environment (MOOSE). First, the model predicts the transient rod motion that results in the desired reactor power shape. Then, the temperature of the specimen is predicted based on the power deposited in the specimen. The prediction results are in good agreement with the measured reactor power and control rod position and over-predicted the specimen temperature which is mainly related to specimen surface emissivities. The reactor reaches a peak power of 80 MW and a specimen temperature of 2500 K and considering the right specimen emissivities the predicted temperature is in an excellent agreement with the measured values. This model can be utilized in helping and supporting the design and optimization a new experiments that are going to be irradiated in the TREAT facility.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Maximization of the annual energy production of wind power plants by optimization of layout and yaw-based wake control: Maximization of wind plant AEP by optimization of layout and wake control

This paper presents a wind plant modeling and optimization tool that enables the maximization of wind plant annual energy production (AEP) using yaw-based wake steering control and layout changes. The tool is an extension of a wake engineering model describing the steady-state effects of yaw on wake velocity profiles and power productions of wind turbines in a wind plant. To make predictions of a wind plant's AEP, necessary extensions of the original wake model include coupling it with a detailed rotor model and a control policy for turbine blade pitch and rotor speed. This enables the prediction of power production with wake effects throughout a range of wind speeds. We use the tool to perform an example optimization study on a wind plant based on the Princess Amalia Wind Park. In this case study, combined optimization of layout and wake steering control increases AEP by 5%. The power gains from wake steering control are highest for region 1.5 inflow wind speeds, and they continue to be present to some extent for the above-rated inflow wind speeds. The results show that layout optimization and wake steering are complementary because significant AEP improvements can be achieved with wake steering in a wind plant layout that is already optimized to reduce wake losses.

17 WIND ENERGY↗

Developing Multi-Gene CRISPRa/I Programs to Accelerate DBTL Cycles in ABF Hosts Engineered for Chemical Production (CRADA 468)

Bacterial metabolism is comprised of large and complex gene networks that can produce valuable chemical products. Sophisticated organism engineering efforts are required to optimize production of high-value compounds from these networks. In principle, synthetic multi-gene transcriptional programs could be constructed to reengineer these networks for efficient industrial chemical production. In practice, however, our incomplete ability to understand and model the underlying networks, combined with our limited ability to predictably control the expression of multiple genes makes achieving this goal difficult. To overcome these challenges, we will combine new CRISPR-Cas multi-gene expression programs with computational modeling, machine learning, and multi-omics data to enhance the efficacy of design-build-test-learn (DBTL) cycles. For industrially promising microorganisms in early stages of development, creating technologies for rapidly engineering complex multi-gene programs could be transformative for accelerating data- and model-driven strain design. New CRISPR-Cas tools allow programmable gene activation (CRISPRa) or repression (CRISPRi) at multiple genes simultaneously, using the catalytically inactive Cas9 protein (dCas9) with guide RNAs that recognize DNA targets through predictable Watson-Crick base pairing. To enable accelerated DBTL cycles, we will combine these technologies with advanced Agile BioFoundry (ABF) capabilities for multi-omics data collection and machine learning. We will demonstrate the immediate applicability of these tools by rapidly improving the production of an industrial aromatic in multiple ABF organisms. We recently identified and optimized new transcriptional activators that can be linked to programmable CRISPR-Cas DNA binding domains to activate gene expression in E. coli. We can now use these CRISPRa tools as generalizable trans-acting regulators for combinatorial multi-gene expression tuning that can be easily transferred to new pathways and networks without additional genome engineering. We anticipate these tools will also transfer to new hosts. We have recently found that CRISPRa systems developed in E. coli can be readily ported to Pseudomonas putida, suggesting that multi-gene CRISPRa/i programs for diverse ABF organisms may be within reach.

59 BASIC BIOLOGICAL SCIENCES↗

Abiotic transformation of high explosives by freshly precipitated iron minerals in aqueous Fe¹¹ solutions

Zerovalent iron barriers have become a viable treatment for field-scale cleanup of various ground water contaminants. While contact with the iron surface is important for contaminant destruction, the interstitial pore water within and near the iron barrier will be laden with aqueous, adsorbed and precipitated FeII phases. These freshly precipitated iron minerals could play an important role in transforming high explosives (HE). Our objective was to determine the transformation of RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), and TNT (2,4,6-trinitrotoluene) by freshly precipitated iron FeII/FeIII minerals. This was accomplished by quantifying the effects of initial FeII concentration, pH, and the presence of aquifer solids (FeIII phases) on HE transformation rates. Results showed that at pH 8.2, freshly precipitated iron minerals transformed RDX, HMX, and TNT with reaction rates increasing with increasing FeII concentrations. RDX and HMX transformations in these solutions also increased with increasing pH (5.8-8.55). By contrast, TNT transformation was not influenced by pH (6.85-8.55) except at pH values <6.35. Transformations observed via LC/MS included a variety of nitroso products (RDX, HMX) and amino degradation products (TNT). XRD analysis identified green rust and magnetite as the dominant iron solid phases that precipitated from the aqueous FeII during HE treatment under anaerobic conditions. Geochemical modeling also predicted FeII activity would likely be controlled by green rust and magnetite. These results illustrate the important role freshly precipitated FeII/FeIII minerals in aqueous FeII solutions play in the transformation of high explosives.

54 ENVIRONMENTAL SCIENCES↗

Theoretical Investigation of H₂ Oxidation on the Sr 2 Fe 1.5 Mo 0.5 O 6 (001) Perovskite Surface Under Anodic Solid Oxide Fuel Cell Conditions

Periodic density functional theory (DFT) calculations and microkinetic modeling are used to investigate the electrochemical oxidation of H₂ fuel on the (001) surface of Sr 2 Fe 1.5 Mo 0.5 O 6 (SFMO) perovskite under anodic solid oxide fuel cell conditions. Three surface models with different Fe/Mo ratios in the topmost layer-identified by ab initio thermodynamic analysis-are used to investigate the H₂ oxidation mechanism. A microkinetic analysis that considers the effects of anode bias potential suggests that a higher Mo concentration in the surface increases the activity of the surface toward H₂ oxidation. At operating voltage and anodic SOFC conditions, the model predicts that water desorption is rate-controlling and that stabilizing the oxygen vacancy structure increases the overall rate for H₂ oxidation. Although we find that Mo plays a crucial role in improving catalytic activity of SFMO, under fuel cell operating conditions, the Mo content in the surface layer tends to be very low. On the basis of these results and in agreement with previous experimental observations, a strategy for improving the overall electrochemical performance of SFMO is increasing the Mo content or adding small amounts of an active transition metal, such as Ni, to the surface to lower the oxygen vacancy formation energy of the SFMO surface.

Environmental Molecular Sciences Laboratory↗

Predicting the Evolution of Shallow Cumulus Clouds With a Lotka‐Volterra Like Model

Abstract In numerical weather prediction and climate models, boundary‐layer clouds are controlled by a wide range of subgrid‐scale processes. However, understanding the nature of these processes and their role in the evolution of the cloud size distribution as a whole has been elusive. To address this issue, we adopt a novel empirical framework from the field of population dynamics to model the evolution of cloud size statistics by using the shallow cumulus properties obtained from a large‐eddy simulation (LES). Our approach involves representing the cloud size distribution and the total cloud area using a revised Lotka‐Volterra model and ridge linear model, respectively. The physical interpretation of the total cloud area and coefficients obtained from the optimization of the models reveals three stages probably interpreted by dominant processes: the formation of new clouds, the growth of single clouds, and a steady state with organized transitions involving the growth and decay of multiple clouds. Furthermore, we showcase the potential of this framework to serve as a component of scale‐aware parameterizations of shallow‐convective clouds in atmospheric models.

54 ENVIRONMENTAL SCIENCES↗

CO 2 absorption from simulated flue gas in a bubble column

Carbon dioxide (CO 2 ) absorption from power plant generated flue gas is studied for CO 2 emissions reduction. Amino acid alkaline solvents have the potential to reduce the energy required for solvent regeneration. Here, we focus on CO 2 absorption by amino acid alkaline solvents in a bubble column. Important parameters characterizing the reactor, e.g., bubble size, liquid-phase dispersion coefficient, and gas holdup, are experimentally determined. A theoretical model based upon transient mass and energy balances for the chemical species involved is presented. Simulation results are compared to experimental data. The model can be used to predict, optimize, and control CO 2 absorption in industrial-scale applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling and control of plasma rotation for NSTX using neoclassical toroidal viscosity and neutral beam injection

A model-based feedback system is presented to control plasma rotation in a magnetically confined toroidal fusion device, to maintain plasma stability for long-pulse operation. This research uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three-dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical constraints on the actuators and the available measurements of rotation.

feedback control↗

Full-Scale Field Test of Wake Steering

Wind farm control, in which turbine controllers are coordinated to improve farmwide performance, is an active field of research. One form of wind farm control is wake steering, in which a turbine is yawed to the inflow to redirect its wake away from downstream turbines. Wake steering has been studied in depth in simulations as well as in wind tunnels and scaled test facilities. This work performs a field test of wake steering on a full-scale turbine. In the campaign, the yaw controller of the turbine has been set to track different yaw misalignment set points while a nacelle-mounted lidar scans the wake at several ranges downwind. The lidar measurements are combined with turbine data, as well as measurements of the inflow made by a highly instrumented meteorological mast. In conclusion, these measurements are then compared to the predictions of a wind farm control-oriented model of wakes.

17 WIND ENERGY↗

Irradiation Vehicles for Evaluating SiC/SiC Cladding Bowing Under Neutron Flux Gradients

Silicon carbide fiber–reinforced silicon carbide matrix (SiC/SiC) composites are among the most promising candidates for long term accident-tolerant nuclear fuel cladding. A key challenge related to their deployment is lateral bowing caused by differential radiation-induced swelling under dose or temperature gradients, which could obstruct coolant flow or interfere with control rod/blade movements. Although previous modeling efforts have predicted bowing behavior in light-water reactor (LWR) environments, experimental validation remains limited, especially at prototypic LWR temperatures. This study addresses that gap by irradiating six reduced-length SiC/SiC cladding tubes (~600 mm) in the High Flux Isotope Reactor (HFIR) at ~300°C, which is representative of LWR conditions. The tubes will be housed in a sealed vessel with an inert gas gap to maintain target temperatures and prevent direct coolant contact. Arranged in three pairs, each set will receive a different radiation dose (low, medium, high), with the central pair receiving ~0.1 displacements per atom (dpa)—the expected dose for peak bowing. The experiment will determine the dose-dependent bowing behavior and validate predictive finite element models. In this work, the tubes are freely suspended from pins to allow for unconstrained bowing; however, we present a concept for introducing localized constraints to represent grid spacer effects. Post-irradiation examination will include swelling measurements and profilometry to assess bowing and compare the results with model predictions. This work aims to confirm the conditions under which maximum bowing occurs so as to improve the reliability of SiC/SiC performance models in nuclear applications.

Russell, Nick [ORNL] (ORCID:0000000296099820)↗

Nonlinear and 3D plasmas. Final report

The project objectives are to characterize the nonlinear properties of edge instabilities in fusion plasmas from the standpoint of MHD and extended MHD models of plasmas and to develop, as much as possible, simplified models that may be useful for prediction and control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗

PAPER STUDY EVALUATIONS OF THE INTRODUCTION OF SMALL COLUMN ION EXCHANGE WASTE STREAMS TO THE DEFENSE WASTE PROCESSING FACILITY

The objective of this paper study is to provide guidance on the impact of Monosodium Titanate (MST) and Crystalline Silicotitanate (CST) streams from the Small Column Ion Exchange (SCIX) process on the Defense Waste Processing Facility (DWPF) flowsheet and glass waste form. A series of waste processing scenarios was evaluated, including projected compositions of Sludge Batches 8 through 17 (SB8 through SB17), MST additions, CST additions to Tank 40 or to a sludge batch preparation tank (Tank 42 or Tank 51, referred to generically as Tank 51 in this report), streams from the Salt Waste Processing Facility (SWPF), and two canister production rates. A wide array of potential glass frit compositions was used to support this assessment. The sludge and frit combinations were evaluated using the predictive models in the current DWPF Product Composition Control System (PCCS). The results were evaluated based on the number of frit compositions available for a particular sludge composition scenario. A large number of candidate frit compositions (e.g., several dozen to several hundred) is typically a good indicator of a sludge composition for which there is flexibility in forming an acceptable waste glass and meeting canister production rate commitments. The MST and CST streams will significantly increase the concentrations of certain components in glass, such as Nb{sub 2}O{sub 5}, TiO{sub 2}, and ZrO{sub 2}, to levels much higher than have been previously processed at DWPF. Therefore, several important assumptions, described in detail in the report, had to be made in performing the evaluations. The results of the paper studies, which must be applied carefully given the assumptions made concerning the impact of higher Ti, Zr, and Nb concentrations on model validity, provided several observations: (1) There was difficulty in identifying a reasonable number of candidate frits (and in some cases an inability to identify any candidate frits) when a waste loading of 40% is targeted for Sludge Batches 8, 16, and 17, regardless of the addition of SCIX or SWPF streams. This indicates that the blending strategy for these sludge batches should be reevaluated by Savannah River Remediation (SRR). (2) In general, candidate frits were available to accommodate CST additions to either Tank 40 or Tank 51. A larger number of candidate frits were typically available for the sludge batches when CST is added to Tank 51 rather than Tank 40, meaning that more compositional flexibility would be available for frit selection and DWPF operation. Note however that for SB8 and SB17, no candidate frits were available to accommodate CST going to Tank 40 with and without SWPF streams. The addition of SWPF streams generally improves the number of candidate frits available for processing of a given sludge batch. (3) The change in production rate from 40 Sludge Receipt and Adjustment Tank (SRAT) batches per year (i.e., the current production rate) to 75 SRAT batches per year, without SWPF streams included, had varied results in terms of the number of candidate frits available for processing of a given sludge batch. Therefore, this variable is not of much concern in terms of incorporating the SCIX streams. Note that the evaluation at 75 SRAT batches per year (approximately equivalent to 325 canisters per year) is more conservative in terms of the impact of SCIX streams as compared to a production rate of 400 canisters per year. Overall, the outcome of this paper study shows no major issues with the ability to identify an acceptable glass processing window when CST from the SCIX process is transferred to either Tank 40 or Tank 51. The assumptions used and the model limitations identified in this report must be addressed through further experimental studies, which are currently being performed. As changes occur to the planned additions of MST and CST, or to the sludge batch preparation strategy, additional evaluations will be performed to determine the potential impacts. As stated above, the issues with Sludge Batches 8, 16, and 17 should be further evaluated by SRR. A review of Chemical Process Cell (CPC) processing identified no changes to the recommendations from the previous review of the SCIX process impacts. Recommendations for testing were made during the previous review to evaluate the impact of CST on the rheological properties of DWPF process streams and evaluate the impact of CST on catalytic hydrogen generation during CPC processing.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Comparing Calibration Algorithms for the Rapid Characterization of Pretreated Corn Stover Using Near-Infrared Spectroscopy

Rapid characterization of biomass composition is a key enabling technology for biorefineries—the ability to measure the chemical composition of biomass materials entering the biorefinery as well as the composition of key process intermediate streams would allow real-time process control and the development of robust models to predict process performance. The utility of near-infrared (NIR) spectroscopy for rapid characterization requires multivariate algorithms for building calibration models. The most prevalent algorithm used for building calibration models using NIR spectra is the linear modeling algorithm Partial Least Squares Regression (PLS). Nonlinear regression algorithms (which are typically more computationally intensive than linear modeling approaches) have gained popularity in recent years due to their ability to solve a wide variety of classification and regression problems and the dramatic increase in available computational resources. In this work, we demonstrate that a calibration model can predict the composition of corn stover process intermediate samples pretreated with three different treatments—hot water (HW), dilute acid (DA), and deacetylation followed by dilute acid (DDA). We quantitatively compare three different algorithms for building prediction models based on near-infrared spectroscopy—partial least squares (PLS), support vector machines (SVM), and random forests (RF). We demonstrate the utility of improving model performance by accounting for instrument performance variability using repeated measurements of standard materials (e.g., the “repeatability file” strategy) and investigate its performance with nonlinear regression techniques, and we discuss methods for quantifying the uncertainties of specific predictions among the three methods.

09 BIOMASS FUELS↗

Coupled Biotic-Abiotic Processes Control Biogeochemical Cycling of Dissolved Organic Matter in the Columbia River Hyporheic Zone

A critical component of assessing the impacts of climate change on watershed ecosystems involves understanding the role that dissolved organic matter (DOM) plays in driving whole ecosystem metabolism. The hyporheic zone—a biogeochemical control point where ground water and river water mix—is characterized by high DOM turnover and microbial activity and is responsible for a large fraction of lotic respiration. Yet, the dynamic nature of this ecotone provides a challenging but important environment to parse out different DOM influences on watershed function and net carbon and nutrient fluxes. We used high-resolution Fourier-transform ion cyclotron resonance mass spectrometry to provide a detailed molecular characterization of DOM and its transformation pathways in the Columbia river watershed. Samples were collected from ground water (adjacent unconfined aquifer underlying the Hanford 300 Area), Columbia river water, and its hyporheic zone. The hyporheic zone was sampled at five locations to capture spatial heterogeneity within the hyporheic zone. Our results revealed that abiotic transformation pathways (e.g., carboxylation), potentially driven by abiotic factors such as sunlight, in both the ground water and river water are likely influencing DOM availability to the hyporheic zone, which could then be coupled with biotic processes for enhanced microbial activity. The ground water profile revealed high rates of N and S transformations via abiotic reactions. The river profile showed enhanced abiotic photodegradation of lignin-like molecules that subsequently entered the hyporheic zone as low molecular weight, more degraded compounds. While the compounds in river water were in part bio-unavailable, some were further shown to increase rates of microbial respiration. Together, river water and ground water enhance microbial activity within the hyporheic zone, regardless of river stage, as shown by elevated putative amino-acid transformations and the abundance of amino-sugar and protein-like compounds. This enhanced microbial activity is further dependent on the composition of ground water and river water inputs. Our results further suggest that abiotic controls on DOM should be incorporated into predictive modeling for understanding watershed dynamics, especially as climate variability and land use could affect light exposure and changes to ground water essential elements, both shown to impact the Columbia river hyporheic zone.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Integration of Photovoltaics into Building Energy Usage through Advanced Control of Rooftop Unit

This paper presents a computational approach to forecast photovoltaic (PV) power in kW based on a neural network linkage of publicly available cloud cover data and on-site solar irradiance sensor data. We also describe a control approach to utilize rooftop air conditioning units (RTUs) to support renewable integration. The PV forecasting method is validated using data from a rooftop PV panel installed on the Distributed Energy, Communications, and Controls (DECC) laboratory at Oak Ridge National Laboratory. The validation occurs in multiple phases to ensure that each component of the approach is the best representation of the actual expected output. The control of the RTU is based on model predictive methods.

Starke, Michael R↗

Finite Element Analysis on Spread for In-plane Roll-bending Process

The in-plane roll-bending process is a special wedge rolling with a configuration of two conical rolls which can form strips into open ring products. The spread of a ring is usually not considered in previous radius predicting models by Yang et al. and Xian et al. However, the spread increases to 10% for a ring with average reduction of 56%, and there is a discrepancy between the predicted radius and the experiment. Spread analysis/calculation has become an urgent problem in radius prediction and precision control of unequal deformation in this process. A finite element (FE) model considering spread effect is established and evaluated by experiments. A comparison between the predicted results with/without considering spread by FE analysis and experiments is carried out. The result shows that the predicted results considering spread are much closer to the experiments than those without considering spread effect. Based on the FE simulation, the spread characteristics of the ring with two types of cross section (including partly and entirely compressed cross section) are investigated. It is found that, there exist three spread regions, including outer positive region, middle negative region and inner positive region for the partly compressed ring; and there are outer positive region and inner negative region for the entirely compressed ring. The spread mostly happens at the outer positive region for both types of ring. The effects of process parameters, such as wedge angle, bite location, friction coefficient and rotational speed of roll, on spread for three aluminum alloys, 3A21O, 5A02O and 2A12T4, are investigated. The results indicate that the spread decreases with an increase in wedge angle, whereas increases with the growth of bite location; the spread remains stable with increasing friction coefficient and fluctuates within 3%-8% with a rise in rotational speed of roll. The spread of the partly compressed ring is less than 6%; large spread (larger than 6%) occurs when the ring is entirely compressed; the spread may reach a maximum value of 18.8% for material 5A02O.

36 MATERIALS SCIENCE↗