Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MATRICES”

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 901 records · Page 50

Remote detectability from entanglement bootstrap I: Kirby’s torus trick

Remote detectability is often taken as a physical assumption in the study of topologically ordered systems, and it is a central axiom of mathematical frameworks of topological quantum field theories. We show under the entanglement bootstrap approach that remote detectability is a necessary property; that is, we derive it as a theorem. Starting from a single wave function on a topologically-trivial region satisfying the entanglement bootstrap axioms, we can construct states on closed manifolds. The crucial technique is to immerse the punctured manifold into the topologically trivial region and then heal the puncture. This is analogous to Kirby’s torus trick. We then analyze a special class of such manifolds, which we call pairing manifolds. For each pairing manifold, which pairs two classes of excitations, we identify an analog of the topological S S -matrix. This pairing matrix is unitary, which implies remote detectability between two classes of excitations. These matrices are in general not associated with the mapping class group of the manifold. As a by-product, we can count excitation types (e.g., graph excitations in 3+1d). The pairing phenomenon occurs in many physical contexts, including systems in different dimensions, with or without gapped boundaries. We provide a variety of examples to illustrate its scope.

Shi, Bowen (ORCID:0000000206899964)↗

A simple coin for a 2d entangled walk

We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

To study quantum properties of the hadron wavefunction at small x, we derived the reduced density matrix for soft gluons in the CGC framework. We explicitly showed that the reduced density matrix is not diagonal in the particle number basis. The off-diagonal components are usually ignored in the conventional parton model. We thus defined the density matrix of ignorance by keeping only the part of the reduced density matrix which can be probed in a limited set of experimental measurements. We calculated Von Neumann entropy for both the reduced and ignorance density matrices. The entropy of ignorance is always greater than the entanglement entropy (computed drom the reduced density matrix) of gluons. Finally, we showed that the CGC reduced density matrix for soft gluons can be diagonalized in a thermal basis with Boltzmann weights suggesting thermalization of new quasi-particle states which we dubbed entangolons.

Duan, Haowu↗

Compiler and Runtime Approaches to Enable Large-Scale Irregular Programs. Final report, July 2013 - July 2019

While regular algorithms, characterized by operations on dense matrices and arrays, have long been the mainstay of scientific, high-performance computing, irregular algorithms, which feature unpredictable accesses to pointer-based data structures, are becoming increasingly common in high performance computing, arising in graph analysis, data mining and visualization, among other domains. Unfortunately, the defining characteristics of irregular applications, their dynamic, unpredictable, data-dependent access patterns and data layouts, make achieving high performance on large scale systems difficult. Scaling applications to peta- and exa-scale requires carefully controlling communication and data movement and placement, an inherently difficult task when access patterns and data layouts are unpredictable! Most irregular applications that attain high performance must be painstakingly hand-written and hand-tuned, with few common principles or paradigms uniting various implementations and easing future development. Despite the increasing importance of irregular applications, there is little programmer knowledge, and even less compiler ability, devoted to optimizing them. This project aims to solve these problems. By allowing programmers to write irregular applications in high level forms, with at most a few annotations highlighting key structural properties, programmers can focus on developing their algorithms and methods. The compiler and run-time system can take on the tedious task of optimizing the application for execution at large scales, and can automatically provide efficient implementations. This will provide portability and ease maintenance for existing irregular applications, but, more importantly, open up whole new domains of computational science to large-scale, high-performance simulation codes.

97 MATHEMATICS AND COMPUTING↗

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗

Numerical Experiments and Identification of Areas for Further Consideration (B639388 Subcontract Quarter II Report)

The second quarter of the project was spent carrying out numerical experiments on a variety of test matrices, using a combination of precisions, with the intent to study the numerical properties (namely, accuracy and convergence behavior) of the Conjugate Gradient (CG) method. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings. We are also currently collaborating with Steven Thomas (NREL) on the numerical stability analysis of “low-synch” Gram-Schmidt routines, for potential application within high-performance GMRES variants. This work is in progress. The subsequent quarter will be spent delving into the numerical analysis in order to provide theoretical explanation for the behavior observed in our experiments.

97 MATHEMATICS AND COMPUTING↗

TChem v2.0 - A Software Toolkit for the Analysis of Complex Kinetic Models

TChem is an open source software library for solving complex computational chemistry problems and analyzing detailed chemical kinetic models. The software provides support for: complex kinetic models for gas-phase and surface chemistry; thermodynamic properties based on NASA polynomials; species production/consumption rates; stable time integrator for solving stiff time ordinary differential equations; and, reactor models such as homogenous gas-phase ignition (with analytical Jacobian matrices), continuously stirred tank reactor, plug-flow reactor. This toolkit builds upon earlier versions that were written in C and featured tools for gas-phase chemistry only. The current version of the software was completely refactored in C++, uses an object-oriented programming model, and adopts Kokkos as its portability layer to make it ready for the next generation computing architectures i.e., multi/many core computing platforms with GPU accelerators. We have expanded the range of kinetic models to include surface chemistry and have added examples pertaining to Continuously Stirred Tank Reactors (CSTR) and Plug Flow Reactor (PFR) models to complement the homogenous ignition examples present in the earlier versions. To exploit the massive parallelism available from modern computing platforms, the current software interface is designed to evaluate samples in parallel, which enables large scale parametric studies, e.g. for sensitivity analysis and model calibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗

Development and Characterization of Cementitious Waste Forms for Immobilization of Granular Activated Carbon, Silver Mordenite, and HEPA Filter Media Solid Secondary Waste

At the Department of Energy’s Hanford site, over 53 million gallons of chemically complex and radioactive wastes have been stored in 177 underground tanks. The Hanford Tank Waste Treatment and Immobilization Plant (WTP) is under construction and is designed to treat and immobilize these wastes. During operations of WTP, solid secondary wastes (SSWs) will be generated as a result of waste treatment, vitrification, off-gas management, and supporting process activities. SSW treatment processes and resulting disposal pathways for the final disposition form of the SSW are needed to support direct feed low activity waste (DFLAW) operations and facilitate continued operation of WTP. The SSWs produced through WTP operations are expected to include used process equipment, contaminated tools and instruments, decontamination wastes, high-efficiency particulate air (HEPA) filters, carbon absorption beds (granular activated carbon, GAC), silver mordenite (AgM) and spent ion-exchange resins. These waste streams are planned to be immobilized in a cementitious waste form and disposed of either as stabilized/blended (non-debris) or encapsulated (debris) in a cementitious waste form. Accordingly, cementitious waste forms from these streams were included in the 2017 Integrated Disposal Facility (IDF) Performance Assessment (PA). The input data used to represent these SSW forms in the 2017 IDF PA involved many assumptions and associated uncertainties. This data limitation was due to the lack of material- and site-specific data available for representative SSW materials in cementitious matrices. To verify the assumed values used in the IDF PA and fill this limitation in available data, Washington River Protection Solutions, LLC (WRPS), has initiated a program targeted toward gathering site specific data relevant to Hanford SSW disposal. The work within this report is a continuation of this ongoing program.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning

In this study, we present spectral equivalence results for higher-order tensor product edge-, face- and interior-based finite elements. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the higher-order elements are spectrally equivalent to those for an assembly of lowest-order elements on the associated Gauss-Lobatto-Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗

C-NR Countroom Overview [Slides]

Perform qualitative and quantitative assay of gamma, beta, and alpha-emitting radionuclides in a variety of matrices and over a wide range of activity levels.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Validation and Demonstration of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an integrated energy system (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. The new RAVEN plugin for grid and capacity optimization (HERON) only addresses the limits that affect the production variables and the corresponding rates of variation (explicit constraints). However, other variables are subject to constraints, and the associated limits should be accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response affects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. To obtain a more accurate approximation of the nonlinear dynamic behavior, a parametric version of the dynamic mode decomposition with control (DMDc) algorithm was developed to derive the state-space representation matrices of the IES components at different scheduling parameter. Thanks to this approach, a more accurate approximation of the system response can be obtained, the limits imposed by thermal mechanical implicit constraints can be translated into power dispatch limits, and the feedbacks to HERON power dispatcher can be provided. To assess the developed methodology, a power dispatching test case composed of three power generating and storage units (Balance of Plant, Secondary Energy Source, Thermal Energy Storage) was developed. The power output of each one of the three units was optimized to meet the imposed time-dependent load demand trajectory and to maximize the IES profitability by meeting both the explicit and implicit constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Exploring Covalency in the Actinides Using Soft Donor-Based Ligands and Metal-Ligand Multiple Bonding

Closing the fuel cycle is critical to the renaissance of nuclear energy in the United States. Essential in closing the fuel cycle is identification of separation strategies for actinides and fission products from spent fuels and identification of host matrices for storage or transmutation of fission products. These issues are intensified due to the complex nature of the problem (e.g., high radiation fields, high thermal fields, long half-lives of certain fission products). The use of extractor ligands with soft donor atoms has been demonstrated to selectively sequester actinides over their lanthanide counterparts. This has been presumed to be enhanced covalent bonding between the actinide 5f orbitals and the valence ligand-based orbitals; however, the coordination chemistry and reactivity with ligands containing selenium, tellurium, phosphorus, and arsenic are underdeveloped. Additionally, compounds containing actinide-ligand multiple bonding will be explored to examine pi-bonding with 5f orbitals. Efforts will be made to develop this chemistry with neptunium as well. This research explores the unique structure, bonding, and reactivity of the actinide elements while developing the underlying fundamental science involved in the separation of actinides.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Metric Type in the Target-matrix Mesh Optimization Paradigm

The Target Matrix Optimization Paradigm (TMOP) is a method for improving the accuracy, efficiency, and robustness of numerical solutions to partial differential equations by improving the geometric quality of the computational mesh, primarily through node movement. TMOP has been successfully applied to a number applications even though the paradigm was not fully understood at the time. With this work, TMOP can be seen to be a tightly woven fabric of interconnecting ideas and concepts that provides a powerful approach to mesh optimization. The central unifying concepts in TMOP are the concept of a Target Matrix and the concept of Metric Type. Target matrices are motivated by the desire to make mesh quality improvement application-specific and, when needed, solution-adaptive. Metric type plays an essential role because it provides, through the use of typed metrics, the bridge between application-specific quality and target construction. It is shown that there are eight theoretical metric types, including the shape and shape+size types used informally in the past. It is shown further that there exist well-posed metrics corresponding to six of the eight metric types. A well-posed metric is a metric that is typed and convex, polyconvex, or invex, and further, it is a metric that simplifies target construction.

97 MATHEMATICS AND COMPUTING↗

A parallel-plate avalanche counter for the prompt fission neutron spectrum measurement

Neutrons, gamma’s, and fission fragments are among the prompt fission observables. Their precision measurements are fundamental to advance our understanding of fission and any application of fission. For our programmatic need, the χ matrix, which defines as the outgoing neutron spectrum as a function of incoming neutron energy, is sparsely populated and poorly measured for 233,235,238 U and 239,240 Pu. To improve the quality of those χ matrices, a joint LANLLLNL project was undertaken to measure their prompt fission neutron spectra at the LANSCE/WNR facility using neutron detector arrays and a charged-particle detector for the fission-fragment detection. A typical setup is shown in Fig. 1, where one of neutron detector array with a charged-particle detector is given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Clean Grid Vision: A U.S. Perspective - Chapter 3. Transmission Grid-Supporting Technologies

High renewable penetration will bring different challenges to power system reliability and stability. Reduction of inertia has been of concern for more wide-spread instable events; however, with the advanced control functionalities provided by power electronics interface and proper storage compensation, renewable generators are capable of providing wide-range of grid services that can maintain and improve grid reliability and stability matrices. Many studies and testing has demonstrated those functions and many pilot projects throughout the world had proved the concepts are working.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Modified Isotherm Modeling to Predict Cs Exchange with Crystalline Silicotitanate in Tank Waste Simulants

The U.S. Department of Energy is working to expedite processing of Hanford tank waste supernate at the Hanford Waste Treatment and Immobilization Plant. To support this goal, Washington River Protection Solutions is designing a Tank Side Cesium Removal (TSCR) system for suspended solids and cesium (Cs/ 137 Cs) removal from Hanford tank waste supernate. The ion exchange media selected for Cs removal at TSCR is crystalline silicotitanate (CST) that is manufactured in a nearly spherical form by Honeywell UOP LLC (UOP; Des Plaines, IL) as product IONSIV® R9140-B (Na form). The Zheng Anthony Miller (ZAM) isotherm model (Zheng et al. 1997) is a multicomponent ion exchange model used to predict the exchange of Group I metals onto CST. The ZAM isotherm has historically been used to predict Cs distribution values from Hanford and Savannah River Site (SRS) tank waste simulants. Figure S.1 summarizes model predictions from the ZAM isotherm that indicate poor prediction of Cs distribution values for simple and complex simulants with the engineered form of CST, IONSIV® R9140-B, and IONSIV® R9120-B where the solid line indicates a perfect fit by the model. The dotted lines indicate ±20% error. Batch contact testing with Hanford tank waste complex and simple simulants was used in conjunction with SRS simulants to experimentally determine Cs distribution values using a modification to the original isotherm model. The experimentally determined maximum Cs capacity for IONSIV® R9140-B CST in both the simple and complex matrices was found to be 0.53±0.3 mmoles Cs/g of CST. This value is not drastically different from the maximum Cs capacity of 0.58 mmoles Cs/g TAM-5 reported by Zheng et al. (1997). However, it is important to note that TAM-5 (commercially IONSIV® IE-910) is a powder. Hamm et al. (2002) determined that a dilution factor was needed to account for the Zr(OH)2 binder in the engineered form of CST. Hamm et al. determined that a dilution factor of 0.68 was appropriate to account for binder contribution and correct overprediction of Cs exchange on the engineered form of CST in ZAM calculations. This reduced the total capacity from 0.58 mmol/g with TAM-5 to 0.39 mmol/g for the engineered form of CST (Hamm et al. 2002). Despite substituting the experimentally determined maximum Cs capacity of 0.55 mmoles Cs/g for the literature-reported capacity of 0.39 mmoles Cs/g, it was determined that additional modifications to the model’s equilibrium rate constants were necessary in refining the isotherm model. The modified model overpredicted K+ uptake by the CST when compared to digested CST results described by Campbell et al. (2019). The modified model was further revised to omit three of the five K+ exchange equilibrium reactions described by ZAM to reduce the additional K+ loading seen by the model. Figure S.2 summarizes the revised model isotherm predictions plotted against measured Kd values.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Matrix Graphite Material Models In Pebbles and Compacts For Bison

The cores and reflectors in high-temperature gas-cooled reactors (HTGRs) are made of graphite materials, with the graphite acting as a moderator, a fuel host matrix, or the foundation for various structural components. This study aims to survey the models in the literature for graphite materials being used as host matrices in pebble/fuel compacts and to implement those surveyed models into Bison to conduct an early assessment of graphite's thermo-mechanical response under various reactor conditions. In this study, thermal (e.g., thermal conductivity, and specific heat capacity) and mechanical (e.g., elastic properties, thermal expansion, irradiation-induced dimensional changes, and irradiation-induced creep) material models for various graphite grades (e.g., H-451, IG-110, G-348, 2020, A3-3, and A3-27) are incorporated into Bison. Two benchmark problems are then exercised utilizing these new graphite-related capabilities: (1) modeling an Advanced Gas Reactor (AGR)-2 fuel compact, and (2) modeling the debonding of a particle-matrix interface.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗