Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTEGRALS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Advanced simulation capability for environmental management, integrated tool-sets and simulator to enhance public communication - 15186

The U.S. Department of Energy (US DOE) Office of Environmental Management (EM), Office of Soil and Groundwater Remediation, is supporting multi-laboratory development of the Advanced Simulation Capability for Environmental Management (ASCEM). ASCEM is an open source and modular computing framework that incorporates new advances and tools for predicting contaminant fate and transport in natural and engineered systems. ASCEM facilitates transparent, efficient and integrated approaches to modeling and site characterization, and provides robust and standardized assessments of performance and risk for EM cleanup and closure activities. Site subsurface simulation modeling and performance assessments are complex and involve sensitivity evaluations and uncertainty quantification to better understand the risks at a site. The ASCEM tool-set was designed in close collaboration with the sites and other potential end-users (both the public and regulators) to allow better communication and understanding of these complex modeling efforts. ASCEM's integrated tool-sets provide a user interface and tools for managing work-flows, including conceptual model development, management of data and metadata for model input, sensitivity analysis, model calibration and uncertainty analysis, model execution on diverse computational platforms, and processing of model output, including visualization. The hierarchical and modular design of ASCEM HPC simulator Amanzi easily lends itself to translating this conceptual model of a site into a numerical model that can easily be spatially and temporally discretized to run on the HPC simulator. Together this integrated work-flow allows for a seamless and integrated analysis tracking all provenance information and modeling uncertainties. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Integrated Waste Feed Qualification Program for Direct LAW Feed to WTP - 16421

The Hanford Tank Waste Treatment and Immobilization Plant (WTP) is a one-of-a-kind facility being designed and constructed for DOE by Bechtel National, Inc. (BNI) and principal subcontractor URS, to process and vitrify radioactive waste stored in underground tanks at the Hanford Site. The Tank Operations Contractor (TOC), Washington River Protection Solutions (WRPS), has the responsibility to retrieve, stage, pretreat, and deliver feed directly to the WTP Low Activity Waste (LAW) Vitrification Facility. The Direct Feed LAW (DFLAW) scenario is being considered by DOE as a strategy to treat Hanford tank wastes as soon as practicable. Extensive planning is underway by One System, an effort with joint participation by WTP and TOC personnel. The initial focus of One System is to achieve the required integration to ensure the waste feed meets acceptance requirements for processing in the TOC Low Activity Waste Pretreatment System (LAWPS) and WTP LAW facilities. The integrated waste feed qualification program approach for DFLAW was defined by One System during a four-day workshop. The effort resulted in a feasible approach for integrating LAWPS and LAW feed acceptance requirements to vitrify low-activity waste while complying with facility design basis, safety basis, waste acceptance criteria, and glass product compliance. The defined qualification program will provide a systematic approach to test newly staged feed campaigns at bench-scale using actual tank waste samples. The required integration and basis for obtaining sufficient and necessary data to qualify the feed for DFLAW facilities are discussed in this paper. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Subcritical Copper-Reflected-α-phase Plutonium (SCRαP) Integral Experiment Design

A Subcritical Copper-Reflected α-phase Plutonium (SCRαP) integral benchmark experiment is proposed where multiplication will be approximated using correlated neutron data from a detector system consisting of {sup 3}He tubes inside polyethylene. Measurements will be performed on various subcritical experimental configurations consisting of a weapons-grade plutonium sphere surrounded by different Cu thicknesses. In addition to the proposed base experimental configurations with Cu, additional configurations are planned with the plutonium ball nested in various thicknesses of interleaved polyethylene spherical shells mixed in with the Cu shells. The polyethylene is intended to provide fast neutron moderation and reflection, resulting in additional measurements with differing multiplication, spectra, and nuclear data sensitivity. The proposed experiments will performed at the National Criticality Experiments Research Center (NCERC). NCERC is home to a 4.5-kg α-phase stainless steel clad plutonium sphere that is referred to as the BeRP (Beryllium-Reflected Plutonium) ball due to its historical use in a beryllium-reflected critical experiment. In 2014, similar subcritical measurements were performed with the BeRP ball surrounded by nickel and tungsten. The nickel-reflected measurements were documented as a benchmark evaluation which was accepted by the International Criticality Safety Benchmark Evaluation Project (ICSBEP). Similar to past measurements, the proposed work will help both identify deficiencies and quantify uncertainties in nuclear data and validate computational methods related to neutron multiplication inference for subcritical benchmark evaluations. Monte Carlo simulations were performed for the preliminary design of a subcritical Copper-Reflected - phase Plutonium (SCRP) integral benchmark experiment. Specifically, MCNP{sup R} version 6 was used to determine the k{sub eff} and associated nuclear data sensitivities for different preliminary configurations (reflector thickness, material type). The final experimental design process will include continuous-energy nuclear data sensitivity analysis. This will help assess the potential impact of this integral measurement as it relates to international efforts to continuously improve current libraries (ENDF, JEFF, JENDL etc) that still tend to over/under-estimate the measured results of integral experiments, sometimes significantly. Deficiencies in underlying nuclear data quantities such as Nubar have been shown to have an effect on inferred values from subcritical measurements as well. The proposed experiments and subsequent computational validation will help identify such deficiencies. It will also help validate new nuclear data evaluations, including one for Cu that was recently performed in the resolved region up to 100 MeV for {sup 65}Cu and {sup 63}Cu which is expected to improve Cu-related benchmark simulation performance. The final experimental design phase will also include simulation results that will incorporate the detectors that will be used for the subcritical measurements. For the benchmark portion of the measurements, the main detectors that are being considered are portable neutron multiplicity counters made up of {sup 3}He tubes embedded in polyethylene and lined with cadmium. These detectors employ a data acquisition system that produces list-mode data (correlated information where each event is listed sequentially) that can be analyzed using the Feynman variance-to-mean method. Other detector systems including SNAP (single {sup 3}He tube embedded in polyethylene), and a high-purity germanium (HPGe) detector are being considered for supplementary measurements only and are not intended to be used for the final benchmark measurements. Decoupling the supplementary detectors from the system eliminates any contribution to the total system multiplication, and greatly simplifies the final computational benchmark model. Therefore, an optimization of the portable neutron multiplicity counter placement in the benchmark measurements will be performed to ensure that there is minimal contribution to the total system multiplication. In addition, new temperature measurement techniques and hardware will be explored. (authors)

42 ENGINEERING↗
DOE OSTI2019

Performance Assessment Results for the Hanford Integrated Disposal Facility - 19134

In 2014, the US DOE Office of River Protection and its contractors began to develop a performance assessment for the near-surface disposal of low-level and mixed low-level waste at the Hanford Integrated Disposal Facility. The Hanford Integrated Disposal Facility is a doubly-lined landfill that was constructed between 2004 and 2006 to be the disposal facility for the vitrified low-activity waste containers that will be produced at the Hanford Waste Treatment and Immobilization Plant. The disposal facility is also expected to receive solid secondary waste produced at the Hanford Waste Treatment and Immobilization Plant and other solid wastes from site activities. The constructed facility is awaiting authorization to receive waste. Although no waste destined for the facility is currently being generated, operations cannot begin until the facility has received a Disposal Authorization Statement from US DOE and a permit modification from the State of Washington Department of Ecology. Both the Disposal Authorization Statement and permit modification require a demonstration that the system of engineered and natural features of the disposal facility will limit releases from the facility and be protective of human health and the environment for the next 1,000 to 10,000 years. Based on the analyses presented in the Integrated Disposal Facility Performance Assessment, US DOE issued a conditional Disposal Authorization Statement for the facility in June 2018. Demonstrating the long-term performance of the facility to be protective of human health and the environment was evaluated under the requirements of US DOE Order 435.1, Radioactive Waste Management. Computer simulations were performed to evaluate whether or not the disposal facility would comply with the performance objectives specified in the order. The evaluation was performed using numerical models to simulate source term releases from vitrified and cement-based waste forms. Source term releases were subsequently transported through an air pathway and a groundwater pathway to a point of compliance 100 meters from the disposed of waste. In addition, an analysis evaluating the consequences of an inadvertent intrusion into the waste was also performed. In accordance with US DoE's technical standard for performance assessments, deterministic and probabilistic analyses were performed to demonstrate that the Hanford Integrated Disposal Facility, together with the engineered features of the waste forms and natural features of the selected site, provides a reasonable expectation that the low-level waste and mixed low-level waste disposal will meet the radiological performance objectives established by US DOE. Post-closure doses to future members of the public were evaluated after the time of closure and included a 100-year period of institutional controls that limited exposure immediately following closure of the facility. Calculated doses to a future member of the public from the air pathway were below the 100 μSv/yr dose performance objective. Calculated doses to a future member of the public from all exposure pathways, including the air pathway and the groundwater pathway, were below the 250 μSv/yr dose performance objective. Doses following an inadvertent intrusion into the facility after the institutional control period were below the 5 mSv acute dose performance measure and the 1 mSv/yr chronic dose performance measure. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Towards Lightweight Data Integration Using Multi-Workflow Provenance and Data Observability

Modern large-scale scientific discovery requires multidisciplinary collaboration across diverse computing facilities, including High Performance Computing (HPC) machines and the Edge-to-Cloud continuum. Integrated data analysis plays a crucial role in scientific discovery, especially in the current AI era, by enabling Responsible AI development, FAIR, Reproducibility, and User Steering. However, the heterogeneous nature of science poses challenges such as dealing with multiple supporting tools, cross-facility environments, and efficient HPC execution. Building on data observability, adapter system design, and provenance, we propose MIDA: an approach for lightweight runtime Multi-workflow Integrated Data Analysis. MIDA defines data observability strategies and adaptability methods for various parallel systems and machine learning tools. With observability, it intercepts the dataflows in the background without requiring instrumentation while integrating domain, provenance, and telemetry data at runtime into a unified database ready for user steering queries. We conduct experiments showing end-to-end multi-workflow analysis integrating data from Dask and MLFlow in a real distributed deep learning use case for materials science that runs on multiple environments with up to 276 GPUs in parallel. We show near-zero overhead running up to 100,000 tasks on 1,680 CPU cores on the Summit supercomputer.

Santos Souza, Renan↗
DOE OSTI2020

Integrated Environmental Management System Communication at Large Sites - 20480

At a large Department of Energy-owned (DOE) site, there are challenges to communicating Environmental Management System (EMS) topics effectively. With multiple contractors and Environmental Management System scopes, as well as a large number of employees, communication preferences and possibilities vary, providing both the benefit and the challenge of differing pathways for sharing information. Additionally, data collection for site-wide environmental reporting involves numerous points of contact spread across contractors and requires organization and integrated communication. Focusing on the value of communication to enhance EMS education and awareness to drive environmental performance, we discuss the communication methods used both at a site-wide level and by individual organizations. Example methods include site-wide working group meetings, internal Share Point, site-wide surveys, collaborative reporting, weekly newsletters, and combined communication efforts with the Integrated Safety Management System (ISMS). Using external audit results to gauge employee environmental awareness and culture, we analyze the effectiveness of EMS communications. In conclusion, integration of EMS communication in alignment with the ISMS has assisted in meeting International Organization of Standardization 14001 (ISO 14001) requirements and strengthened the concept that environmental protection is part of safety for workers and the site. Increased environmental enthusiasm and awareness supports the effectiveness of EMS communication methods and positive external audit results. These results benefit other sites with EMS to gain knowledge of integrated communication efforts that increase the effectiveness of the EMS, environmental performance, and conformance with ISO 14001. By assessing the effectiveness of actual EMS communication methods, contractors will be able to take away tools to enhance environmental communication in their workplace. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Integration and assessment of component health prognostics in supervisory control systems - 291

Enhanced risk monitors (ERMs) for active components in advanced reactor concepts use predictive estimates of component failure to update, in real time, predictive safety and economic risk metrics. These metrics have been shown to be capable of use in optimizing maintenance scheduling and managing plant maintenance costs. Integrating this information with plant supervisory control systems increases the potential for making control decisions that utilize realtime information on component conditions. Such decision making would limit the possibility of plant operations that increase the likelihood of degrading the functionality of one or more components while maintaining the overall functionality of the plant. ERM uses sensor data for providing real-time information about equipment condition for deriving risk monitors. This information is used to estimate the remaining useful life and probability of failure of these components. By combining this information with plant probabilistic risk assessment models, predictive estimates of risk posed by continued plant operation in the presence of detected degradation may be estimated. In this paper, we describe this methodology in greater detail, and discuss its integration with a prototypic software-based plant supervisory control platform. In order to integrate these two technologies and evaluate the integrated system, software to simulate the sensor data was developed, prognostic models for feedwater valves were developed, and several use cases defined. The full paper will describe these use cases, and the results of the initial evaluation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Overview of Nuclear Integration Activities for Mitigation of Radiation Loads to ITER Superconducting Magnets

The Nuclear Integration Unit (NIU) is a trans-departmental team from the ITER Organization and Domestic Agencies, responsible for all nuclear integration aspects of the facility and for ensuring that systems and components are suitable for their radiation environment and satisfy all related performance requirements. This is a very challenging task namely due to the large number of systems, their still evolving designs, the intricate and far-reaching impacts of these in nuclear responses everywhere, and the complex world-wide distribution of procurement responsibilities. A sound systems engineering approach that involves all relevant experts and stakeholders, and trades-off between different performance requirements in an optimum way, needs to be taken and sustained during design evolution and construction, always with the objective of final overall project success. One of the most important current occupations of the NIU is the evaluation of, and protection from, radiation conditions to superconducting magnets during plasma operations, and particularly nuclear heating. This requires neutronic analyses in massive computer resources, with state-of-the-art methods and complex, extensive computer models. The main ITER superconducting magnet systems subject to significant nuclear loads are the toroidal field coils (TFCs) and the poloidal field coils (PFCs). These are illustrated in Fig. 1. Nuclear responses in these depend mostly on the design of all in-vessel (blankets, manifolds, divertor, in-vessel coils, port plugs), vessel and thermal shield components. Sources to consider are the 500 MW DT burning plasma (14.1 MeV neutrons) and the activated water in the in-vessel cooling system (photons up to 7 MeV from N-16 and neutrons up to 3.5 MeV from N-17). This paper discusses a snapshot of the present understanding of nuclear heat conditions in both the TFC and PFC magnets. This includes integral values and distributions, as well as best estimates from computations and conservative upper estimates by consideration of systematic effects and random uncertainties. The computer models, methods and assumptions used for evaluation of these responses are described. Nuclear integration aspects and ongoing efforts to study and implement additional shielding and other mitigating measures are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Mathematics Integrated with Computer Science through Scratch: Curricular Modules for the Middle Grades

A project funded by the National Science Foundation, Computer Science Integrated with Mathematics in Middle Schools (CSIMMS) (DRL-1640039), brought middle-school mathematics teachers together with university computer science (CS) faculty and STEM education faculty to design, develop, and test curriculum modules in which CS is integrated into instruction for middle-school general-mathematics courses. The project developed integrated math/CS curriculum modules (for grades 6, 7, and 8), complete with student tasks and teacher materials to guide classroom implementation. Across the project, sixteen teachers from four middle schools representing different school contexts (both urban and suburban, serving students from a range of demographic and socioeconomic backgrounds) participated as members of the design team and trial testers of the math/CS modules. All modules underwent multiple years of testing and refinement, with extensive input from the teachers who co-designed and implemented them. Approximately 50-100 middle-school students participated in the classes of those who taught each year. The modules in this volume feature a range of models for integrating mathematics and computer science at the 6th and 7th grade levels. All modules foreground the teaching of grade-level mathematics content, with computer science functioning to motivate and/or reinforce these ideas.

Andrews larson, Christine↗
DOE OSTI2024

Optical device having a light-emitting structure and a waveguide integrated capacitor to monitor light

Examples described herein relate to an optical device with an integrated light-emitting structure to generate light and a waveguide integrated capacitor to monitor light. The light-emitting structure may emit light upon the application of electricity to the optical device. The waveguide integrated capacitor may be formed under the light-emitting structure to monitor the light emitted by the light-emitting structure. The waveguide integrated capacitor includes a waveguide region carrying at least a portion of the light. The waveguide region includes one or more photon absorption sites causing the generation of free charge carriers relative to an intensity of the light confined in the waveguide region resulting in a change in the conductance of the waveguide region.

Srinivasan, Sudharsanan↗
DOE OSTI2025

Integrated Molten Salt Reactor Modeling Capabilities in NEAMS Thermal Hydraulics Tools

The DOE neams program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the msr concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Property Database (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and \gls{msre} demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to msr components such as the msre pump bowl. Finally, updates to SAM’s msr mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation \gls{msr}s.

42 - ENGINEERING↗
DOE OSTI2026

Case Study of Integrating High-Temperature Heat Pump with LiBr-H2O Absorption Chiller for Data Center Liquid Cooling

Data centers (DCs) are physical infrastructures that support artificial intelligence workloads. The rapid growth of artificial intelligence is putting substantial pressure on the US power grid. Most of electricity consumed by IT equipment, accounting for 50%-60% of total DC power, ultimately becomes waste heat. This heat is dissipated by DC’s cooling facilities, accounting for an additional 30%-40% of total DC power. Recovering and repurposing this waste heat offers a significant opportunity to enhance energy efficiency and reduce operating costs of DCs. One potential pathway is converting heat to cold using thermal-driven absorption chillers, therefore, reducing the power consumption in DC cooling facilities. Existing studies mainly demonstrate the technical and economic feasibility of repurposing DC’s waste heat for cooling applications but provide limited technical details on how to integrate the thermal-driven absorption chillers with DC cooling systems. In addition, the low-grade waste heat available from DCs must be upgraded to higher temperatures suitable for absorption chillers. This paper presents a case study on integrating high-temperature heat pumps with a LiBr-H2O absorption chiller to use DC waste heat for cooling. A thermodynamic model of single-effect, LiBr-H2O absorption chiller and an empirical model of high-temperature heat pumps were built. The case study considers ASHRAE W17 liquid-cooled DC, with facility service water supplied at 17.0℃ and returned at 25.3℃. The thermal behaviors of absorption chiller components were predicted for the generation temperature ranging from 75.0℃ to 115.0℃. Based on the available waste heat in the integrated system, two waste heat recovery strategies were evaluated: a facility service water-based strategy and cooling water-based strategy. Results indicated that the cooling water-based strategy achieves higher Coefficient of Performance (COPs) than the facility service water-based strategy. The relatively low cooling COPs of single-effect LiBr-H2O absorption chillers could be offset by high heating COP of high temperature heat pumps. The maximum cooling COP of absorption chiller and the overall COP of integrated systems occur at lower generation temperatures, but these conditions also yield lower cooling capacities. In practice, system operation should balance the trade-off between the COP and cooling capacity

Wang, Pengtao [ORNL] (ORCID:0000000214713429)↗
DOE OSTI2017

Effects of spatially distributed sectoral water management on the redistribution of water resources in an integrated water model

Realistic representations of sectoral water withdrawals and consumptive demands and their allocation to surface and groundwater sources are important for improving modeling of the integrated water cycle. To inform future model development, in this work we enhance the representation of water management in a regional Earth system (ES) model with a spatially distributed allocation of sectoral water demands simulated by a regional integrated assessment (IA) model to surface and groundwater systems. The integrated modeling framework (IA-ES) is evaluated by analyzing the simulated regulated flow and sectoral supply deficit in major hydrologic regions of the conterminous U.S, which differ from ES studies looking at water storage variations. Decreases in historical supply deficit are used as metrics to evaluate IA-ES model improvement in representating the complex sectoral human activities for assessing future adaptation and mitigation strategies. We also assess the spatial changes in both regulated flow and unmet demands, for irrigation and nonirrigation sectors, resulting from the individual and combined additions of groundwater and return flow modules. Results show that groundwater use has a pronounced regional and sectoral effect by reducing water supply deficit. The effects of sectoral return flow exhibit a clear east-west contrast in the hydrologic patterns, so the return flow component combined with the IA sectoral demands is a major driver for spatial redistribution of water resources and water deficits in the US. Our analysis highlights the need for spatially distributed sectoral representation of water management to capture the regional differences in interbasin redistribution of water resources and deficits.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Integrated energy-water-land nexus planning in the Colorado River Basin (Argentina)

Integrated energy-water-land (EWL) planning promotes synergies and avoids conflicts in ways that sector-specific planning approaches cannot. Many important decisions that influence emerging EWL nexus issues are implemented at regional (e.g., large river basin, electricity grid) and sub-regional (e.g., small river basin, irrigation district) scales. However, actual implementation of integrated planning at these scales has been limited. Simply collecting and visualizing data and interconnections across multiple sectors and sub-regions in a single modeling platform is a unique endeavor in many regions. This study introduces and applies a novel approach to linking together multiple sub-regions in a single platform to characterize and visualize EWL resource use, EWL system linkages within and among sub-regions, and the EWL nexus implications of future policies and investments. This integrated planning methodology is applied in the water-stressed Colorado River Basin in Argentina, which is facing increasing demands for agricultural and fossil fuel commodities. Guided by stakeholders, this study seeks to inform basin planning activities by characterizing and visualizing (1) the basin’s current state of EWL resources, (2) the linkages between sectors within and among basin sub-regions, and (3) the EWL nexus implications of planned future agricultural development activities. Results show that water scarcity, driven in part by human demands that have historically reached 60% of total surface water supply, poses a substantial constraint to economic development in the basin. The Colorado basin has the potential to serve as a testbed for crafting novel and generalizable sub-regional EWL planning approaches capable of informing the EWL planning dialogue globally.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Integrable Variable Dissipation Systems on the Tangent Bundle of a Multi-Dimensional Sphere and Some Applications

This paper is a survey of integrable cases in dynamics of a multi-dimensional rigid body under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean. The problem of the search for complete sets of transcendental first integrals of systems with dissipation is quite topical; a large number of works are devoted to it. We introduce a new class of dynamical systems that have a periodic coordinate. Due to the existence of nontrivial symmetry groups of such systems, we can prove that these systems possess variable dissipation with zero mean, which means that on the average for a period with respect to the periodic coordinate, the dissipation in the system is equal to zero, although in various domains of the phase space, either energy pumping or dissipation can occur. Based on the facts obtained, we analyze dynamical systems that appear in the dynamics of a multi-dimensional rigid body and obtain a series of new cases of complete integrability of the equations of motion in transcendental functions, which can be expressed through a finite combination of elementary functions. As applications, we study dynamical equations of motion arising in the study of the plane and spatial dynamics of a rigid body interacting with a medium and also a possible generalization of the obtained methods to the study of general systems arising in the qualitative theory of ordinary differential equations, in the theory of dynamical systems, and also in oscillation theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Improved integrability and boundedness of solutions to some high-order variational problems

We give a series of results on the improved integrability and boundedness of solutions to several high-order variational problems with strengthened coercivity. In particular, we consider the homogeneous Dirichlet problem on the minimum of integral functionals and study variational inequalities with unilateral and bilateral obstacles and with integral and gradient constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Application of hat basis functions for solving two-dimensional stochastic fractional integral equations

This article concerns with a computational scheme to solve two-dimensional stochastic fractional integral equations (2DSFIEs), numerically. In these equations, the fractional integral is considered in the Riemann–Liouville sense. The proposed method is essentially based on two-dimensional hat basis functions and its fractional operational matrices. The fractional-order operational matrices of integration are applied to reduce the solution of 2DSFIEs to the solution of a system of linear equations which can be solved using a direct method or iterative method. Some results concerning the convergence analysis associated with the proposed technique are discussed. In addition, we establish the rate of convergence of this approach for solving 2DSFIEs is O(h{sup 2}). Finally, some examples are solved using present method to indicate the pertinent features of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗