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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 37 records · Page 2

Modeling and Validation of Irradiation Damage in Ni-based Alloys for Long-Term LWR Applications (Final Report)

As light water reactor (LWR) plant lives are extended, the need for predictive modeling tools for materials degradation increase in order to ensure safe operation and plan for component replacements. The Grizzly code, which is built on the MOOSE multi-physics simulation environment, is being developed for exactly this purpose. To extend Grizzly to include capabilities for modeling Ni-based alloys, we propose a US/UK integrated program to address thermal and irradiation-induced transformations mechanisms of Alloys 690 and 625. Alloy 690 is widely used in existing LWR plants due to its superior stress corrosion cracking (SCC) resistance compared to Alloy 600. Alloy 625 is used in more limited applications but offers the benefits of both high strength (in the aged condition) and corrosion/SCC resistance. Research has shown that both alloys can undergo phase changes due to thermal or irradiation exposure. In the precipitation-hardened condition, Alloy 625 “softens” during neutron irradiation as the strengthening precipitates decompose and metastable precipitates form. However, the nature and rates of these transformations as a function of exposure conditions are not well understood. Similarly, the effects of these thermal and irradiation-induced microstructural changes on mechanical properties require evaluation. The proposed program combines thermal and irradiation experiments, mechanical testing, microstructural characterization using state-of-the art analytical techniques, atomistic modeling, micro-and macro-scale modeling via Grizzly. This multi-pronged approach yields several benefits: 1) atomistic scale models capture the physics of the mechanisms of phase transformations, which can be generalized to other systems, 2) the modeling results (from atomistic to continuum) will be validated experimentally to ensure the predictive aspect, 3) the microstructure/property relationships captured with mechanical testing provides information at the engineering scale that is needed to validate the integration of the proposed new capability into Grizzly

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Screening Model to Predict Microalgae Biomass Growth in Photobioreactors and Raceway Ponds

A microalgae biomass growth model was developed for screening novel strains for their potential to exhibit high biomass productivities under nutrient-replete conditions in photobioreactors or outdoor ponds. Growth is modeled by first estimating the light attenuation by biomass according to Beer-Lambert’s law, and then calculating the specific growth rate in discretized culture volume slices that receive declining light intensities due to attenuation. The model requires only two physical and two species-specific biological input parameters, all of which are relatively easy to determine: incident light intensity, culture depth, as well as the biomass light absorption coefficient and the specific growth rate as a function of light intensity. Roux bottle culture experiments were performed with Nannochloropsis salina at constant temperature (23 °C) at six different incident light intensities (5, 10, 25, 50, 100, 250, and 850 μmol/m2∙ sec) to determine both the specific growth rate under non-shading conditions and the biomass light absorption coefficient as a function of light intensity. The model was successful in predicting the biomass growth rate in these Roux bottle cultures during the light-limited linear phase at different incident light intensities. Model predictions were moderately sensitive to minor variations in the values of input parameters. The model was also successful in predicting the growth performance of Chlorella sp. cultured in LED-lighted 800 L raceway ponds operated at constant temperature (30 °C) and constant light intensity (1650 μmol/m2∙ sec). Measurements of oxygen concentrations as a function of time demonstrated that following exposure to darkness, it takes at least 5 seconds for cells to initiate dark respiration. As a result, biomass loss due to dark respiration in the aphotic zone of a culture is unlikely to occur in highly mixed small-scale photobioreactors where cells move rapidly in and out of the light. By contrast, as supported also by the growth model, biomass loss due to dark respiration occurs in the dark zones of the relatively less well mixed pond cultures. In addition to screening novel microalgae strains for high biomass productivities, the model can also be used for optimizing the pond design and operation. Additional research is needed to validate the biomass growth model for other microalgae species and for the more realistic case of fluctuating temperatures and light intensities observed in outdoor pond cultures.

biomass growth model↗

A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, the rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

97 MATHEMATICS AND COMPUTING↗

Fracture Characterization in Enhanced Geothermal Systems by Wellbore and Reservoir Analysis

This report highlights the work that was done to characterize fractured geothermal reservoirs using production data. That includes methods that were developed to infer characteristic functions from production data and models that were designed to optimize reinjection scheduling into geothermal reservoirs, based on these characteristic functions. The characterization method provides a robust way of interpreting tracer and flow rate data from fractured reservoirs. The flow-rate data are used to infer the interwell connectivity, which describes how injected fluids are divided between producers in the reservoir. The tracer data are used to find the tracer kernel for each injector-producer connection. The tracer kernel describes the volume and dispersive properties of the interwell flow path. A combination of parametric and nonparametric regression methods were developed to estimate the tracer kernels for situations where data is collected at variable flow-rate or variable injected concentration conditions. The characteristic functions can be used to calibrate thermal transport models, which can in turn be used to predict the productivity of geothermal systems. This predictive model can be used to optimize injection scheduling in a geothermal reservoir, as is illustrated in this report.

15 GEOTHERMAL ENERGY↗

Decoding Zeolite Crystallization and Stage III in Nuclear Waste Glasses by Coupled Modeling and Experiments

Under specific conditions of pH and temperature, nuclear waste immobilization borosilicate glasses may exhibit a sudden acceleration in their corrosion kinetics (stage III)—a behavior that has been associated with the formation of zeolite crystals. Such accelerated dissolution may compromise the integrity of nuclear wasteforms placed in geological depositories. However, thus far, none of the available models is able to predict the thermodynamic propensity and kinetics of zeolite precipitation as a function of the solution conditions due to (i) a lack of fundamental knowledge regarding the nucleation & growth mechanisms of zeolitic phases, (ii) uncertainty regarding the compositions (types) of zeolites that may form and the rate-limiting step in their precipitation as a function of the solution conditions, and (iii) the complexities that arise due to the vast parametric space (i.e., solution chemistry, temperature, number of secondary phases, etc.) that encompass these systems under conditions of environmental exposure. To resolve these challenges, this project aimed to unambiguously identify the thermodynamic propensity for zeolite precipitation and the kinetics thereof as a function of the solution conditions (composition, pH, and temperature). To achieve this goal: 1) We identified the solution conditions and zeolite phases relevant to nuclear glass dissolution. 2) We performed a series of ab initio molecular dynamics (AIMD) simulations to compute the thermodynamic properties of a group of characteristic zeolites that features a large range of compositions, various hydration levels, a wide range of framework structures, and partial atomic site occupancies. 3) We released a first-of-a-kind self-consistent thermodynamic database that can be used to assess the kinetics and the stability fields of zeolitic phases within a Gibbs energy minimization (GEM) framework. 4) We developed a robust geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. 5) We introduced a model that predicts the dissolution kinetics of a series of borosilicate nuclear waste immobilization glasses in terms of the topology of their atomic network. 6) We investigated the roles of the solution composition on the crystallization kinetics of phillipsite zeolites and tobermorite silicate hydrates. Via PNNL’s collaboration and engagement, this project directly supports DOE’s nuclear waste immobilization activities by offering a technical, science-based foundation that will (i) facilitate predictions of the long-term corrosion rates and extents of existing nuclear waste immobilization glasses to help ensure safe and successful vitrification operations, (ii) inform the development of advanced glass formulations with enhanced durability, and, (iii) enable cost-savings that result from making more decisive and hence less conservative predictions while offering higher levels of nuclear waste embedment in smaller, more compact glass volumes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

High-throughput Fluorometric Measurement of Potential Soil Extracellular Enzyme Activities

Microbes in soils and other environments produce extracellular enzymes to depolymerize and hydrolyze organic macromolecules so that they can be assimilated for energy and nutrients. Measuring soil microbial enzyme activity is crucial in understanding soil ecosystem functional dynamics. The general concept of the fluorescence enzyme assay is that synthetic C-, N-, or P-rich substrates bound with a fluorescent dye are added to soil samples. When intact, the labeled substrates do not fluoresce. Enzyme activity is measured as the increase in fluorescence as the fluorescent dyes are cleaved from their substrates, which allows them to fluoresce. Enzyme measurements can be expressed in units of molarity or activity. To perform this assay, soil slurries are prepared by combining soil with a pH buffer. The pH buffer (typically a 50 mM sodium acetate or 50 mM Tris buffer), is chosen for the buffer's particular acid dissociation constant (pKa) to best match the soil sample pH. The soil slurries are inoculated with a nonlimiting amount of fluorescently labeled (i.e. C-, N-, or P-rich) substrate. Using soil slurries in the assay serves to minimize limitations on enzyme and substrate diffusion. Therefore, this assay controls for differences in substrate limitation, diffusion rates, and soil pH conditions; thus detecting potential enzyme activity rates as a function of the difference in enzyme concentrations (per sample). Fluorescence enzyme assays are typically more sensitive than spectrophotometric (i.e. colorimetric) assays, but can suffer from interference caused by impurities and the instability of many fluorescent compounds when exposed to light; so caution is required when handling fluorescent substrates. Likewise, this method only assesses potential enzyme activities under laboratory conditions when substrates are not limiting. Caution should be used when interpreting the data representing cross-site comparisons with differing temperatures or soil types, as in situ soil type and temperature can influence enzyme kinetics.

59 BASIC BIOLOGICAL SCIENCES↗

Role of Low Molecular Weight Polymers on the Dynamics of Silicon Anodes During Casting

This work probes the slurry architecture of a high silicon content electrode slurry with and without low molecular weight polymeric dispersants as a function of shear rate to mimic electrode casting conditions for poly(acrylic acid) (PAA) and lithium neutralized poly(acrylic acid) (LiPAA) based electrodes. Rheology coupled ultra-small angle neutron scattering (rheo-USANS) was used to examine the aggregation and agglomeration behavior of each slurry as well as the overall shape of the aggregates. The addition of dispersant has opposing effects on slurries made with PAA or LiPAA binder. With a dispersant, there are fewer aggregates and agglomerates in the PAA based silicon slurries, while LiPAA based silicon slurries become orders of magnitude more aggregated and agglomerated at all shear rates. The reorganization of the PAA and LiPAA binder in the presence of dispersant leads to a more homogeneous slurry and a more heterogeneous slurry, respectively. This reorganization ripples through to the cast electrode architecture and is reflected in the electrochemical cycling of these electrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Degrees of Rate Control at Non(pseudo)steady-State Conditions

The degrees of rate control enable identification of rate-controlling transition states and species during (pseudo-)steady-state reaction. We demonstrate a method for identifying rate-controlling transition states and species at non-(pseudo-)steady-state conditions through modification of the definitions for degrees of rate control and sensitivities by superimposing the condition that time constants of the analytical rate function are kept constant when taking the partial derivatives of rate with respect to the rate constants/free energies. In conclusion, the utility of transient degrees of rate control is demonstrated for catalytic reaction networks to rationalize features of the transient rate including extrema and discontinuities.

42 ENGINEERING↗

Galaxy Evolution in the Radio Band: The Role of Star-forming Galaxies and Active Galactic Nuclei

We investigate the astrophysics of radio-emitting star-forming galaxies and active galactic nuclei (AGNs) and elucidate their statistical properties in the radio band, including luminosity functions, redshift distributions, and number counts at sub-mJy flux levels, which will be crucially probed by next-generation radio continuum surveys. Specifically, we exploit the model-independent approach by Mancuso et al. to compute the star formation rate functions, the AGN duty cycles, and the conditional probability of a star-forming galaxy to host an AGN with given bolometric luminosity. Coupling these ingredients with the radio emission properties associated with star formation and nuclear activity, we compute relevant statistics at different radio frequencies and disentangle the relative contribution of star-forming galaxies and AGNs in different radio luminosity, radio flux, and redshift ranges. Finally, we highlight that radio-emitting star-forming galaxies and AGNs are expected to host supermassive black holes accreting with different Eddington ratio distributions and to occupy different loci in the galaxy main-sequence diagrams. These specific predictions are consistent with current data sets but need to be tested with larger statistics via future radio data with multiband coverage on wide areas, as will become routinely achievable with the advent of the Square Kilometre Array and its precursors.

79 ASTRONOMY AND ASTROPHYSICS↗

OECD MCCI project Melt Eruption Test (MET) design report, Rev. 2. April 15, 2003.

The Melt Attack and Coolability Experiments (MACE) program at Argonne National Laboratory addressed the issue of the ability of water to cool and thermally stabilize a molten core-concrete interaction when the reactants are flooded from above. These tests provided data regarding the nature of corium interactions with concrete, the heat transfer rates from the melt to the overlying water pool, and the role of noncondensable gases in the mixing processes that contribute to melt quenching. The Melt Coolability and Concrete Interaction (MCCI) program is pursuing separate effect tests to examine the viability of the melt coolability mechanisms identified as part of the MACE program. These mechanisms include bulk cooling, water ingression, volcanic eruptions, and crust breach. At the second PRG meeting held at ANL on 22-23 October 2002, a preliminary design1 for a separate effects test to investigate the melt eruption cooling mechanism was presented for PRG review. At this meeting, NUPEC made several recommendations on the experiment approach aimed at optimizing the chances of achieving a floating crust boundary condition in this test. The principal recommendation was to incorporate a mortar sidewall liner into the test design, since data from the COTELS experiment program indicates that corium does not form a strong mechanical bond with this material. Other recommendations included: (i) reduction of the electrode elevation to well below the melt upper surface elevation (since the crust may bond to these solid surfaces), and (ii) favorably taper the mortar liner to facilitate crust detachment and relocation during the experiment. Finally, as a precursor to implementing these modifications, the PRG recommended the development of a design for a small-scale scoping test intended to verify the ability of the mortar liner to preclude formation of an anchored bridge crust under core-concrete interaction conditions. This revised Melt Eruption Test (MET) plan is intended to satisfy these PRG recommendations. Specifically, the revised plan focuses on providing data on the extent of crust growth and melt eruptions as a function of gas sparging rate under well-controlled experiment conditions, including a floating crust boundary condition. The overall objective of MET is to determine to what extent core debris is rendered coolable by eruptive-type processes that breach the crust that rests upon the melt. The specific objectives of this test are as follows: (1) Evaluate the augmentation in surface heat flux during periods of melt eruption; (2) Evaluate the melt entrainment coefficient from the heat flux and gas flow rate data for input into models that calculate ex-vessel debris coolability; (3) Characterize the morphology and coolability of debris resulting from eruptive processes that transport melt into overlying water; and (4) Discriminate between periods when eruptions take the form of particle ejections into overlying water, leading to a porous particle bed, and single-phase extrusions, which lead to volcano-type structures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FY2017 ILAW Glass Corrosion Testing with the Single-Pass Flow-Through Method

The inventory of immobilized low-activity waste (ILAW) produced at the Hanford Tank Waste Treatment and Immobilization Plant (WTP) will be disposed of at the near-surface, on-site Integrated Disposal Facility (IDF). When groundwater comes into contact with the waste form, the glass will corrode and radionuclides will be released into the near-field environment. Because the release of the radionuclides is dependent on the dissolution rate of the glass, it is important that the performance assessment (PA) model accounts for the dissolution rate of the glass as a function of various conditions. To accomplish this, an IDF PA glass dissolution model based on Transition State Theory (TST) can be employed. The model is able to account for changes in temperature, exposed surface area, and pH of the contacting solution as well as the effect of silicon solution concentrations, specifically the activity of orthosilicic acid (H4SiO4), whose concentration is directly linked to the glass dissolution rate. In addition, the IDF PA model accounts for the ion exchange process. The effect of temperature, pH, H4SiO4 activity, and the rate of ion exchange can be parameterized and implemented directly into the PA rate model. The rate model parameters are derived from laboratory tests with the single-pass flow-through (SPFT) method. The provided data can be used by glass researchers to further the understanding of ILAW glass behavior, by IDF PA modelers to use the rate model parameters in PA modeling efforts, and by Department of Energy (DOE) contractors and decision makers as they assess the IDF PA program.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

The long-term corrosion performance of Alloy 22 in heated brine solutions

Long-term corrosion experiments have been performed on Alloy 22 (UNS N06022), in a series of heated brines formulated to represent evaporatively concentrated ground water, to evaluate the long-term corrosion performance of the material. These solutions included 0.5 M NaCl, in addition to two simulated concentrated ground water solutions. Under conditions where Alloy 22 was anticipated to be passive, the corrosion rate was found to be vanishingly small (i.e., below the resolution of the weight-loss technique used to quantify corrosion in this study). However, under low pH conditions where Alloy 22 was anticipated to be active, or more specifically, where the chromium oxide passive film was not thermodynamically stable, the corrosion rate was appreciable. Furthermore, under such conditions the corrosion rate was observed to be a strong function of temperature, with an activation energy of 72.9±1.8 kJ/mol. Time of Flight-Secondary Ion Mass Spectroscopy analysis of the oxide layer revealed that, while sulfur was present within the oxide for all test conditions, no accumulation was observed at or near the metal/oxide interface. Furthermore, these observations confirm that inhibition of passive film formation via sulfur accumulation does not occur during the corrosion of Alloy 22.

36 MATERIALS SCIENCE↗

FY2016 ILAW Glass Corrosion Testing with the Single-Pass Flow-Through Method

The inventory of immobilized low-activity waste (ILAW) produced at the Hanford Tank Waste Treatment and Immobilization Plant (WTP) will be disposed of at the near-surface, on-site Integrated Disposal Facility (IDF). When groundwater comes into contact with the waste form, the glass will corrode and radionuclides will be released into the near-field environment. Because the release of the radionuclides is dependent on the dissolution rate of the glass, it is important that the performance assessment (PA) model accounts for the dissolution rate of the glass as a function of various chemical conditions. To accomplish this, an IDF PA model based on Transition State Theory (TST) can be employed. The model is able to account for changes in temperature, exposed surface area, and pH of the contacting solution as well as the effect of silicon concentrations in solution, specifically the activity of orthosilicic acid (H4SiO4), whose concentration is directly linked to the glass dissolution rate. In addition, the IDF PA model accounts for the alkali-ion exchange process as sodium is leached from the glass and into solution. The effect of temperature, pH, H4SiO4 activity, and the rate of ion-exchange can be parameterized and implemented directly into the PA rate law model. The rate law parameters are derived from laboratory tests with the single-pass flow-through (SPFT) method. To date, rate law parameters have been determined for seven ILAW glass compositions, thus additional rate law parameters on a wider range of compositions will supplement the existing body of data for PA maintenance activities. The data provided in this report can be used by ILAW glass scientists to further the understanding of ILAW glass behavior, by IDF PA modelers to use the rate law parameters in PA modeling efforts, and by Department of Energy (DOE) contractors and decision makers as they assess the IDF PA program.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Critical surface for explosions of rotational core-collapse supernovae

The effect of rotation on the explosion of core-collapse supernovae is investigated systematically in three-dimensional simulations. In order to obtain the critical conditions for explosion as a function of mass accretion rate, neutrino luminosity, and specific angular momentum, rigidly rotating matter was injected from the outer boundary with an angular momentum, which is increased every 500 ms. It is found that there is a critical value of the specific angular momentum, above which the standing shock wave revives, for a given combination of mass accretion rate and neutrino luminosity, i.e., an explosion can occur by rotation even if the neutrino luminosity is lower than the critical value for a given mass accretion rate in non-rotational models. The coupling of rotation and hydrodynamical instabilities plays an important role in characterizing the dynamics of shock revival for the range of specific angular momentum that are supposed to be realistic. Contrary to expectations from past studies, the most rapidly expanding direction of the shock wave is not aligned with the rotation axis. Being perpendicular to the rotation axis on average, it can be oriented in various directions. Its dispersion is small when the spiral mode of the standing accretion shock instability (SASI) governs the dynamics, while it is large when neutrino-driven convection is dominant. As a result of the comparison between two-dimensional and three-dimensional rotational models, it is found that m ≠ 0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface.

79 ASTRONOMY AND ASTROPHYSICS↗

Plant-Nitrifier Interactions in Topsoil and Subsoil

Plants can influence soil microbes through resource acquisition and interference competition, with consequences for ecosystem function such as nitrification. However, how plants alter soil conditions to influence nitrifiers and nitrification rates remains poorly understood, especially in the subsoil. Here, coupling the 15N isotopic pool dilution technique, high throughput sequencing and in situ soil O2 monitoring, we investigated how a deep-rooted perennial grass, miscanthus, versus an adjacent shallow-rooted turfgrass reference shapes nitrifier assembly and function along 1 m soil profiles. In topsoil, the suppression of ammonia (NH3) oxidizing archaea (AOA) and gross nitrification rates in miscanthus relative to the reference likely resulted from nitrifiers being outcompeted by plant roots and heterotrophic bacteria for ammonium (NH4+). The stronger tripartite competition under miscanthus may have been caused in part by the lower soil organic matter (SOM) content, which supported lower gross nitrogen (N) mineralization, the major soil process that produces NH4+. In contrast, below 10 cm soil depth, significantly greater gross nitrification rates were observed in miscanthus compared to the reference. This was likely driven by the significantly lower oxygen (O2) in miscanthus than reference subsoil, which selected against aerobic heterotrophic bacteria but in favor of AOA. Overall, we found that plants can regulate AOA community structure and function through different mechanisms in topsoil and subsoil, with suppression of nitrification in topsoil and enhancement of nitrification in subsoil.

Field Data↗

OECD MCCI project long-term 2-D molten core concrete interaction test design report, Rev. 0. September 30, 2002.

The Melt Attack and Coolability Experiments (MACE) program at Argonne National Laboratory addressed the issue of the ability of water to cool and thermally stabilize a molten core-concrete interaction when the reactants are flooded from above. These tests provided data regarding the nature of corium interactions with concrete, the heat transfer rates from the melt to the overlying water pool, and the role of noncondensable gases in the mixing processes that contribute to melt quenching. As a follow-on program to MACE, The Melt Coolability and Concrete Interaction Experiments (MCCI) project is conducting reactor material experiments and associated analysis to achieve the following two technical objectives: (1) resolve the ex-vessel debris coolability issue through a program that focuses on providing both confirmatory evidence and test data for the coolability mechanisms identified in MACE integral effects tests, and (2) address remaining uncertainties related to long-term two-dimensional molten core-concrete interactions under both wet and dry cavity conditions. Achievement of these two objectives will demonstrate the efficacy of severe accident management guidelines for existing plants, and provide the technical basis for better containment designs for future plants. In terms of the first program objective, the Small-Scale Water Ingression and Crust Strength (SSWICS) test series has been initiated to provide fundamental information on the ability of water to ingress into cracks and fissures that form in the debris during quench, thereby augmenting the otherwise conduction-limited heat transfer process. A test plan for Melt Eruption Separate Effects Tests (MESET) has also been developed to provide information on the extent of crust growth and melt eruptions as a function of gas sparging rate under well-controlled experiment conditions. In terms of the second program objective, the project Management Board (MB) has approved startup activities required to carry out experiments to address remaining uncertainties related to long-term two-dimensional molten core-concrete interaction. In particular, for both wet and dry cavity conditions, there is uncertainty insofar as evaluating the lateral vs. axial power split during a core-concrete interaction due to a lack of experiment data. As a result, there are differences in the 2-D cavity erosion predicted by codes such as MELCOR, WECHSL, and COSACO. The first step towards generating this data is to produce a test plan for review by the Project Review Group (PRG). The purpose of this document is to provide this plan.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion

In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗