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Development of Modified Perturbation Solutions to the One-Phase Stefan Problems With a Convective Boundary

The classical Stefan problem is used to track the moving solid-liquid interface during the freezing process. Perturbation theory has often been applied to find an approximate analytical solution due to the nonlinearity of the moving interface. However, the Stefan number (i.e., the sensible over latent heat) must be small and usually less than 0.01 to assume the perturbation expansion, which in turn limits the thermal engineering applications. In this study, a modified perturbation solution is developed by adding a correction term after the leading-order solution to be valid for a much wider range of Stefan numbers (i.e., 0.01 less than or equal to Ste less than or equal to 1). Specifically, a one-phase Stefan problem is first formulated subjected to a convective boundary in the Cartesian, cylindrical, and spherical coordinate systems for inward solidification. The leading-order solution is calculated based on the regular perturbation theory, while the correction term is obtained using the Monte-Carlo method and a multi-variant regression. Results show that the correction term has a linear relationship with the Stefan number and is not significantly influenced by the Biot number. The proposed modified perturbation solution can accurately and rapidly predict the nonlinear moving interface motion for the freezing process.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗

Verification of a solvent optimization approach for postcombustion CO 2 capture using commercial alkanolamines

This work verified a phase equilibrium approach for optimization of conceptual solvents by using process simulations of commercial solvents N-methyl-diethanolamine (MDEA) and 2-amino-2-methyl-1-propanol (AMP) aqueous solution, for a conventional absorption/desorption based postcombustion CO 2 capture process. The simulated total heat/total equivalent work for the investigated tertiary/hindered amines has the same trends as those based on the phase equilibrium approach for conceptual solvents with the same heat of reactions. Moreover, the simulated CO 2 working capacities for the commercial solvents agree well with those obtained with the phase equilibrium approach for the corresponding conceptual solvents, verifying the phase equilibrium approach. Finally, results of parametric tests using the AMP aqueous solution illustrate that there is an optimal lean loading for the lean solution and an optimal temperature for the stripper inlet solvent to achieve the least total equivalent work/total heat.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

PanDA: Production and Distributed Analysis System

The Production and Distributed Analysis (PanDA) system is a data-driven workload management system engineered to operate at the LHC data processing scale. The PanDA system provides a solution for scientific experiments to fully leverage their distributed heterogeneous resources, showcasing scalability, usability, flexibility, and robustness. The system has successfully proven itself through nearly two decades of steady operation in the ATLAS experiment, addressing the intricate requirements such as diverse resources distributed worldwide at about 200 sites, thousands of scientists analyzing the data remotely, the volume of processed data beyond the exabyte scale, dozens of scientific applications to support, and data processing over several billion hours of computing usage per year. PanDA’s flexibility and scalability make it suitable for the High Energy Physics community and wider science domains at the Exascale. Beyond High Energy Physics, PanDA’s relevance extends to other big data sciences, as evidenced by its adoption in the Vera C. Rubin Observatory and the sPHENIX experiment. As the significance of advanced workflows continues to grow, PanDA has transformed into a comprehensive ecosystem, effectively tackling challenges associated with emerging workflows and evolving computing technologies. The paper discusses PanDA’s prominent role in the scientific landscape, detailing its architecture, functionality, deployment strategies, project management approaches, results, and evolution into an ecosystem.

97 MATHEMATICS AND COMPUTING↗

Supramolecular Nanosheets Assembled from Poly(ethylene glycol)- b -poly( N -(2-phenylethyl)glycine) Diblock Copolymer Containing Crystallizable Hydrophobic Polypeptoid: Crystallization Driven Assembly Transition from Filaments to Nanosheets

Supramolecular two-dimensional (2D) nanomaterials from block copolymers have received great interest for their unique structure and properties. In this work, we report the formation of ultrathin nanosheets from self-assembly of amphiphilic poly(ethylene glycol)- b -poly( N -(2-phenylethyl)glycine) (PEG- b -PNPE) diblock copolymers, which contain rigid crystallizable polypeptoid segment. The PEG- b -PNPE copolymers were synthesized via ring opening polymerization (ROP). The obtained PEG- b -PNPE diblock copolymers can spontaneously form highly ordered structures in PEG selective solvents such as water and methanol. The copolymers with short PNPE segment can directly form nanosheets in water, and the obtained 2D nanosheets have a uniform thickness of 4-5 nm. In contrast, the copolymers with relatively long PNPE segment can only assemble into nanosheets with the assistance of methanol. It is anticpated that the crystallization and π-π stacking of PNPE blocks play critical roles in the formation of the nanosheet as suggested by grazing incidence wide-angle X-ray scattering (GIWAXS). During the process of adding water into copolymer methanol solution, the nanosheets were observed to evolve from individual nanofibers, to parallel aligning nanofibers, and eventually to the nanosheet structures verified by transmission electron microscopy (TEM) and cryo-TEM characterizations. We demonstrated that the preassembled filament behave as a fundamental packing motif to align laterally and further fuse into platelet-like structures. The assembly structure evolution process was tracked by TEM, atomic force microscopy, and cryo-TEM techniques. The understandings of supramolecular 2D nanosheet formation offer a new opportunity to make hierarchical nanostructures from polypeptoids containing copolymers.

36 MATERIALS SCIENCE↗

A low power flexible dielectric barrier discharge disinfects surfaces and improves the action of hydrogen peroxide

There is an urgent need for disinfection and sterilization devices accessible to the public that can be fulfilled by innovative strategies for using cold atmospheric pressure plasmas. Here, we demonstrate a successful novel combination of a flexible printed circuit design of a dielectric barrier discharge (flex-DBD) with an environmentally safe chemical reagent for surface decontamination from bacterial contaminants. Flex-DBD operates in ambient air, atmospheric pressure, and room temperature without any additional gas flow at a power density not exceeding 0.5 W/cm 2 . The flex-DBD activation of a 3% hydrogen peroxide solution results in the reduction in the bacterial load of a surface contaminant of > 6log 10 in 90 s, about 3log 10 and 2log 10 better than hydrogen peroxide alone or the flex-DBD alone, respectively, for the same treatment time. We propose that the synergy between plasma and hydrogen peroxide is based on the combined action of plasma-generated OH · radicals in the hydrogen peroxide solution and the reactive nitrogen species supplied by the plasma effluent. A scavenger method verified a significant increase in OH · concentration due to plasma treatment. Novel in-situ FTIR absorption spectra show the presence of O 3 , NO 2 , N 2 O, and other nitrogen species. Ozone dissolving in the H 2 O 2 solution can effectively generate OH · through a peroxone process. The addition of the reactive nitrogen species increases the disinfection efficiency of the hydroxyl radicals and other oxygen species. Hence, plasma activation of a low concentration hydrogen peroxide solution, using a hand-held flexible DBD device results in a dramatic improvement in disinfection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A large molecular cluster with high proton release capacity

We present a single molecular polyoxometalate cluster (K-41[(P2W12Nb6O62)(6){Mn-3(OH)(3)(H2O)(6)}(4){Mn3Na(H2O)(16)}]center dot 26H(2)O) with controllable release of a large number of protons (similar to 40 per molecule) in its aqueous solution upon addition of a base. The deprotonation/protonation process is reversible with the clusters remaining intact. This molecule can also absorb up to 11 protons per cluster when an acid, HCl, was added to its original aqueous solution. To the best of our knowledge, such large proton absorption/release capacity along with excellent stability is unprecedented.

Zhang, Dongdi↗

Software Quality Assurance for EBR-II Fuels Irradiation and Physics Database (FIPD)

The Fuels Irradiation and Physics Database (FIPD) is an ongoing DOE project on archival of the EBR-II metal-alloy fuel irradiation experiments. As part of its use in support of license applications, the Quality Assurance Program Plan (QAPP) was drafted and endorsed by NRC in an effort to demonstrate its compliance with regulatory expectations. Software Quality Assurance (SQA) for the physics portion of FIPD is intended to qualify the calculated quantities such as fuel and cladding temperatures, neutron fluence and axially varying burnup estimates for irradiated fuel elements. This report covers the initial evaluation of SQA status of three neutron physics and thermo-fluid codes (REBUS, RCT and SE2RCT) that form the basis of calculated quantities for as-irradiated characteristics of the tested metallic fuel elements. The report also introduces an SQA plan to address the identified deficiencies. The REBUS, RCT, and SE2RCT codes are all part of the Argonne Reactor Code (ARC) code system. There is considerable knowledge and experience on REBUS and RCT but relatively less on SE2RCT. During FY2021, efforts focused on an assessment of how the data in the EBR-II Physics and Analysis DataBase (PADB) is generated with SE2RCT and used in FIPD. Additional tasks included considerations of uncertainties for power estimates in REBUS and RCT calculations and their impact on the combined RCT methodology. The RCT software usage in FIPD was assessed this year and the input/output details studied. A “requirements” document was created that identifies the key features of the RCT software being used in FIPD that need to have SQA documentation. A brief discussion on the history of RCT and its input is included in this report along with the basic SQA roadmap laid out in the requirements document. The SE2RCT software usage in FIPD is still being studied noting that there is no current manual. As part of the work done this year, two bugs were identified in the SE2RCT software which have a minor impact on the accuracy of the results it produces. No requirements document has been created, but one identified feature of SE2RCT being used that needs verification was its fuel pin temperature calculation. The work completed this year confirms that the approximations which will be included in the software verification report for SE2RCT are accurate. In addition to software quality assurance work for RCT and SE2RCT, an automated verification framework is proposed to simplify the software quality assurance process. The purpose of this framework is to streamline code verification and documentation while minimizing repetitive tasks for code developers and reviewers. The reduction of repeated input (between reference solution, software, and documentation input) throughout the SQA process reduces potential for human errors during the preparation of the supporting software quality records. The automation of the verification and documentation process proposed for this project leverages the existing verification structure already in place for the SAS4A/SASSYS-1 code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Static Irradiated ALSEP Scrub Section

The INL is studying the impacts of gamma radiolysis on the ALSEP minor actinide extraction process. This process uses an organic solvent consisting of a neutral diglycolamide extractant, N,N,N’,N’ -tetra-2- ethylhexylglycolamide (T2EHDGA), and an acidic extractant 2-ethylhexylphosphonic acid mono-2- ethylhexyl ester (HEH[EHP]) dissolved in an aliphatic diluent. The actinides and lanthanides are coextracted from relatively high nitric acid and the actinides are selectively stripped using a carboxylic acid buffered aminopolycarboxylic acid solution. Previous investigations of the radiolytic degradation processes on the ALSEP process performed at the INL focused upon the extraction section of the flowsheet. Current efforts are concerned with examining the scrub section of the ALSEP flowsheet. This report describes the static irradiations performed during the current fiscal year in support of the test loop irradiations which will be conducted later in FY-2017, and documents completion of the level four milestone (M4FT- 17IN030102012) entitled “Static Irradiated ALSEP Scrub Section.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Radioactive waste management in France: taking-up present and future challenges - 15120

The reduction of the volume and radiotoxicity of radioactive waste has been one of the key drivers for the implementation of the French nuclear program. Interactions between the nuclear industry, the administration, the competent authorities and other stakeholders including the civil society has led to a continuous evolution of the industrial facilities, practices, solutions and products to move towards waste minimization. Bringing a solution to the management of ultimate radioactive waste is clearly a requirement for the sustainable development of nuclear energy whose crucial role in the world's future energy mix has been confirmed in the past few months by several international organizations. The first question to be answered concerns the definition of radioactive waste. This notion may be seen as self-evident. It is not. For example, used fuel is considered a High Level Waste in Finland or Sweden, but a recyclable material in countries including China, France, India, Japan, Russia, and the Netherlands. In France, a definition is provided by law to clarify this notion. Indeed, the 2006 French law concerning the Sustainable Management of Radioactive Materials and Waste stipulates that 'ultimate radioactive waste shall include any radioactive waste for which no further processing is possible under current technical and economic conditions, notably by extracting their recoverable fraction or by reducing their polluting or hazardous character'. Used fuel is thus reprocessed in order to reduce the final waste volume and long term radiotoxicity, while extracting value from the recovered materials. Even if the general approach and the processes may be common for waste management, it is important to clearly make the distinction between the wastes stemming from used fuel processing or conditioning (when considered as waste), the wastes generated through the operation of nuclear power plants and fuel cycle facilities, and the waste arising from the dismantling of nuclear installations. After a brief overview of the different types of waste stemming from nuclear power generation, this paper will review solutions and processes already implemented for their safe and efficient management. It will also practically illustrate the evolution of these processes and related facilities to further gain in efficiency, notably in terms of volume reduction; the related R and D outcomes will be addressed. It will also describe the upcoming challenges in this field and the envisioned solutions to respond to them; the efficiency, the completeness and consistency of these solutions with the currently considered global framework, based on a stepwise and long term approach from waste generation to disposal, will also be analyzed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Tuning 3-D Nanomaterial Architectures Using Atomic Layer Deposition to Direct Solution Synthesis

The ability to synthesize nanoarchitected materials with tunable geometries provides a means to control their functional properties, with applications in biological, environmental, and energy fields. To this end, various bottom-up and top-down synthesis processes have been developed. However, many of these processes require prepatterning or etching steps, making them challenging to scale-up to complex, nonplanar substrates. Furthermore, the ability to integrate nanomaterials into hierarchical arrays with precise control of feature spacing and orientation remains a challenge. One approach to overcome these patterning challenges is the use of surface modification layers to guide the resulting geometry of nanomaterial architectures grown from the substrate. A powerful strategy to accomplish this is what we will refer to as “surface-directed assembly,” where the resulting geometric parameters (feature size, shape, orientation) are predetermined by the initial surface layer. In particular, the use of Atomic Layer Deposition (ALD) to form a surface layer, followed by solution-based growth processes, has the ability to synthesize architected structures with tunable geometries on complex, nonplanar surfaces. Over the past decade, we have reported a series of studies where surface-directed assembly is used to synthesize ZnO nanowires (NWs) on top of a variety of substrates. In this case, a thin film of ZnO is deposited onto the substrate using ALD, which can guide the NW diameter, spacing, and angular orientation with respect to the substrate by controlling epitaxial relationships. Furthermore, we have shown that by depositing a submonolayer overcoat of a secondary material (e.g., amorphous TiO 2 ), nucleation sites are partially blocked, which can further tune the spacing between nanowires while minimizing changes to their other geometric properties. This approach can be used to generate multilevel hierarchical structures, such as hyperbranched NW arrays with tunable control of each level of hierarchy using ALD. Finally, we have demonstrated that the tunable control of geometric parameters can be scaled-up to curved, nonplanar substrates. This highlights the power of ALD to conformally and uniformly deposit the seed layers on complex substrates with subnanometer precision. To complement these seeded hydrothermal approaches, we expanded this strategy to include conversion chemistry of the initial ALD seed layers. For example, by replacing ZnO with Al 2 O 3 as the seed layer without changing the hydrothermal growth conditions, Al–Zn layered-double hydroxide nanosheets can be formed instead of nanowires. In another example of conversion chemistry, a solution anion-exchange process was used to incorporate sulfur into ALD metal oxide films. In both of these conversion processes, the properties of the initial ALD film enabled tuning of the resulting nanostructure geometry. In this Account, we describe the use of ALD to guide the growth of diverse nanomaterial systems, with tunable control over their geometry and composition. We further show how these approaches can be used to tune functional properties for a range of applications, including superomniphobic surfaces, antibiofouling coatings, and photocatalysis. In conclusion, we conclude with an outlook on how the combination of ALD and solution synthesis can enable future directions in scalable nanomanufacturing to overcome the limitations of traditional top-down and bottom-up approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Controllable synthesis of hydroxyapatite-supported palladium nanoparticles with enhanced catalytic activity

A multi-stage electrochemical method was developed to synthesize palladium (Pd) nanoparticles supported on hydroxyapatite (HA) coatings. In the first stage, a dense coating of HA nanocrystals was synthesized from an aqueous electrolyte solution onto a titanium cathode surface through a galvanostatic process. The HA-coated titanium electrode was then used as the cathode for the electrochemical reduction of Pd2+ from aqueous solution. A synthesis approach using two sequential electrochemical reduction reactions was found to be more e ective in producing uniform coatings of Pd nanoparticles than a single stage reduction. In the first step, a higher voltage was applied to the cathode for a short time to promote the nucleation of Pd nanoparticles. A lower voltage was then applied for a longer time in the second stage to promote the growth of the Pd nanoparticles. The size and size distribution of the Pd nanoparticles were controlled by adjusting the duration of the first and second stages of electrochemical reduction. The resulting HA supported Pd nanoparticles demonstrated significantly higher catalytic activity than commercial Pd nanoparticles in the degradation of methyl orange by NaBH 4 . The high surface area and the complex oxidation states of the HA-supported Pd nanoparticles are believed to account for the enhanced catalytic activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale

The thrust of the proposal was to exploit modern data-mining tools in a way that will create a systematic, computer-assisted approach to the representation of random media -- and also to the representation of the solutions of an array of important physicochemical processes that take place in/on such media. A parsimonious representation/parametrization of the random media links directly (via uncertainty quantification tools) to good sampling of the distribution of random media realizations. It also links directly to modern multiscale computational algorithms (like the equation-free approach that has been developed in our group) and plays a crucial role in accelerating the scientific computation of solutions of nonlinear PDE models (deterministic or stochastic) in such media – both solutions in particular realizations of the random media, and estimation of the statistics of the solutions over multiple realizations (e.g. expectations).

97 MATHEMATICS AND COMPUTING↗

Use of aluminum oxide as a permeation barrier for producing thin films on aluminum substrates

Aluminum has desirable characteristics of good thermal properties, good electrical characteristics, good optical properties, and the characteristic of being nonmagnetic and having a low atomic weight (26.98 g atoms), but because of its low melting point (660 °C) and ability as a reactive metal to alloy with most common metals in use, it has been ignored as a substrate material for use in processing thin films. The author developed a simple solution to this problem, by putting a permeation barrier of alumina (Al{sub 2}O{sub 3}) onto the surface of pure Al substrates by using a standard chemical oxidation process of the surface (i.e., anodization), before additional film deposition of reactive metals at temperatures up to 500 °C for 1-h, without the formation of alloys or intermetallic compounds to affect the good properties of Al substrates. The chromic acid anodization process used (MIL-A-8625) produced a film barrier of ∼(500–1000) nm of alumina. The fact that refractory Al{sub 2}O{sub 3} can inhibit the reaction of metals with Al at temperatures below 500 °C suggests that Al is a satisfactory substrate if properly oxidized prior to film deposition. To prove this concept, thin film samples of Cr, Mo, Er, Sc, Ti, and Zr were prepared on anodized Al substrates and studied by x-ray diffraction, Rutherford ion back scattering, and Auger/argon sputter surface profile analysis to determine any film substrate interactions. In addition, a major purpose of our study was to determine if ErD{sub 2} thin films could be produced on Al substrates with fully hydrided Er films. Thus, a thin film of ErD{sub 2} on an anodized Al substrate was prepared and studied, with and without the alumina permeation barrier. Films for study were prepared on 1.27 cm diameter Al substrates with ∼500 nm of the metals studied after anodization. Substrates were weighed, cleaned, and vacuum fired at 500 °C prior to use. The Al substrates were deposited using standard electron beam cold crucible evaporation techniques, and after deposition the Er film was hydrided with D{sub 2} gas using a standard nonair exposure hydriding technique. All processing was conducted in an all metal ion pumped ultrahigh vacuum system. Results showed that e-beam deposition of films studied onto Al substrates could be successfully performed, if a permeation barrier of Al{sub 2}O{sub 3} from 500 to 1000 nm was made prior to thin film deposition up to temperatures of 500 °C for 1-h. Hydrides also, could be produced with full gas/metal atomic ratios of ∼2.0 as evidenced by the ErD{sub 2} films produced. Thus, the use of a simple permeation barrier of Al{sub 2}O{sub 3} on Al substrates prior to additional metal film deposition was proven to be a successful method of producing both thin metal films and hydride films of various types for many applications.

36 MATERIALS SCIENCE↗

Mineralogical, nanostructural, and Ca isotopic evidence for non-classical calcium phosphate mineralization at circum-neutral pH

Growth pathways of calcium (Ca) phosphate minerals are still under debate, but non-classical growth pathways, which encompass any mode of growth involving attachment of primary particles instead of monomer ions, are currently thought to dominate over classical mechanisms under a wide range of growth conditions. Cation desolvation during ion-by-ion growth is associated with the preferential uptake of isotopically light Ca in Ca-bearing phases, so the Ca isotope composition of Ca-bearing minerals can help to elucidate the dominant growth mechanism. Here, we combine stable Ca isotope analysis with mineralogical characterization and nanoscale imaging of growth features to determine for the first time the rate-dependent Ca isotope fractionation during seeded growth of hydroxyapatite (HAP) involving an octacalcium phosphate (OCP) precursor. Our data reveal that growth rates are strongly attenuated by pH, and that Ca isotope fractionation between the solid and growth solution is independent of growth rate between 1.9 × 10 -9 and 2.8 × 10 -8 mol Ca m -2 s -1 . Moreover, nanoscale images of surface topography reveal direct deposition of primary particles on the HAP seed surface following sustained growth, providing visual evidence of a non-classical growth pathway. Together, these findings support the hypothesis that hydroxyapatite growth is dominantly non-classical. The process of cluster nucleation from the bulk solution and attachment of these clusters to the seeded HAP apparently does not involve a significant kinetic isotope effect, which implies that abiogenically formed Ca-phosphates likely preserve the Ca isotope composition of the fluid from which the crystals originated.

36 MATERIALS SCIENCE↗

Aerosol Synthesis of Highly Dispersed Y{sub 3}Al{sub 5}O{sub 12}:Ce{sup 3+} Phosphor with Intense Photoluminescence

A simple method of pyrolysis of an aerosol solution of yttrium, aluminum, and cerium nitrates with the addition of urea or citric acid, followed by brief annealing, is developed to obtain a highly dispersed aluminum–yttrium garnet powder that demonstrates intense photoluminescence in the visible light region. Characterization of the synthesized samples (photoluminescence spectra, X-ray diffraction analysis, Raman spectra) showed that intense photoluminescence is achieved only in a narrow window of process conditions, namely, the concentration of nitrate solution and the concentration of citric acid or urea. The photoluminescence intensity increases upon annealing synchronously with an increase in the crystallite size, which, along with the optimal cerium concentration (~0.5 at %), is a determining factor for obtaining high-quality samples. The synthesized powders had intense photoluminescence and high optical perfection, as evidenced by the observation of whispering gallery modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Equilibrium and kinetic studies of sorption of 2.4-dichlorophenol onto 2 mixtures: bamboo biochar plus calcium sulphate (BC) and hydroxyapatite plus bamboo biochar plus calcium sulphate (HBC), in a fluidized bed circulation column

Sorption studies were carried out to investigate removal of 2.4-dichlorophenol (2.4-DCP) from aqueous solution in a fluidized bed by two types of adsorbent mixtures: BC (Bamboo char plus Calcium sulphate), and HBC (Hydroxyapatite plus Bamboo char plus Calcium sulphate); both manufactured in ball shape. The main material bamboo char was characterized by FTIR, DTA and SEM. The adsorption experiments were conducted in a fluidized bed circulation column. Adsorption, isotherms and kinetic studies were established under 180 min operating process time, at different initial 2.4-DCP solution concentrations ranging from 5–10 mg/L, and at different flow rates ranging from 0.25–0.75 L/min. The data obtained fitted well for both the Langmuir and Freundlich isotherm models; indicating favorable condition of monolayer adsorption. The kinetics of both adsorbents complies with the pseudo second-order kinetic model. BC was proven a new effective composite and low cost adsorbent which can be applied in the field of wastewater treatment, and it can also play an important role in industry water treatment

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability

This paper is devoted to the study of the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability. The notions of random fuzzy variables and fuzzy stochastic processes are developed for multivariable functions. The existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations are proved using the successive approximations method and Gronwall’s inequality for stochastic processes. The continuous dependence on the data, the boundedness, and the stability with probability one of integral solutions are established to confirm the well posedness of our model. Some computational examples are presented to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗

Outcomes from a Collaborative Approach to a Code Comparison Study for Enhanced Geothermal Systems

A code comparison study, supported by the U.S. Department of Energy, Geothermal Technologies Office, has recently been completed whose stated purpose was to test, diagnose differences, and demonstrate the state of modeling capabilities developed at national laboratories and academic institutes within the United States for modeling enhanced geothermal systems. This three-year study comprised two sets of problems; those classified as benchmark problems and those classified as challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted in hot dry rock at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995, covering two research stimulation, development and circulation phases in two separate reservoirs. Both challenge problems have specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners. Critical observations and data from the Fenton Hill experiments were varied and scattered among a number of individual experiments, and numerical simulation solutions were sought that satisfied as many observations at possible. Achieving agreement in multiple experimental observations from Fenton Hill often required participants to critically think about stimulation mechanisms involving natural and hydraulic fractures and re-evaluate their conceptual models and numerical solution approaches. This process has yielded new insights to Fenton Hill reservoirs and direction for future EGS research. The keys to the success of this study were the high quality numerical simulation tools available, the expertise of the developers and practitioners, and the collaborative approach to reporting preliminary results among the study participants. This paper describes results submitted to the challenge problems and the outcomes of a collaborative approach to conducting a code comparison study.

Enhanced Geothermal Systems, numerical simulation,↗

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