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

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At least 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Viscoelastic Stresses in the Plates Containing Inclusions with Cracks

We study viscoelastic stresses in the plates containing inclusions weakened by cracks by the method of boundary integral equations and the Laplace integral transformation. The case in which the rheological relations between stresses and strains are written in the differential form is analyzed in detail. To solve the boundary problem of viscoelasticity, we use the well-known approach in which the corresponding problem of the theory of elasticity is studied by replacing the differential operators with constant quantities. The solution of the auxiliary problem is obtained by the method of boundary integral equations reduced to a system of algebraic equations. After replacing the elastic quantities in this system by the corresponding differential operators, we solve the system obtained as a result by using the Laplace integral transformation and then applying the improved numerical-analytic inversion formula adapted to this class of problems.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Superconformal Algebraic Approach to Hadron Structure

Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physics is also suitable to describe nonperturbative QCD observables based on structure functions, such as GPDs, which are not amenable to a first-principle computation. The formalism is also successful in the description of form factors, the nonperturbative behavior of the strong coupling and diffractive processes. We also discuss in this article how the framework can be extended rather successfully to the heavy-light hadron sector.

de Teramond, Guy F.↗
DOE OSTI2014

Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

On positive geometry and scattering forms for matter particles

We initiate the study of positive geometry and scattering forms for tree-level amplitudes with matter particles in the (anti-)fundamental representation of the color/flavor group. As a toy example, we study the bi-color scalar theory, which supplements the bi-adjoint theory with scalars in the (anti-)fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. In addition, we discuss the duality between color factors and wedge products, or "color is kinematics", for amplitudes with matter particles as well.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver

Here, a numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain $\mathcal{C}=\Omega\times[0,\infty)$ following. The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $\Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $\Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyl's law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions suggest that the approach is quasi-optimal in terms of complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Semi-implicit continuum kinetic modeling of weakly collisional parallel transport in a magnetic mirror

We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code COGENT. The numerical scheme employs a Jacobian-free Newton–Krylov method with algebraic multigrid preconditioning to overcome the severe time step limitations imposed by strong mirror forces in fully explicit schemes. Applied to parameters relevant to the Wisconsin HTS Axisymmetric Mirror experiment, the IMEX approach enables time steps up to 2.5×10 4 times larger than those permitted by explicit methods, resulting in a 2500× speedup in 1D–2V simulations of parallel transport with kinetic ions and Boltzmann electrons. Additionally, a reduced bounce-averaged model for a square mirror is implemented to support the computationally intensive fully kinetic simulations. The bounce-averaged formulation is used to evaluate the numerical convergence of the velocity-space discretization algorithms and to assess the role of the collision model by comparing simulations employing the nonlinear Fokker–Planck and the simplified Lenard–Bernstein–Dougherty collision operators.

Collision theories↗
DOE OSTI2016

SU-G-BRA-08: Diaphragm Motion Tracking Based On KV CBCT Projections with a Constrained Linear Regression Optimization

Purpose: To develop a novel strategy to extract the respiratory motion of the thoracic diaphragm from kilovoltage cone beam computed tomography (CBCT) projections by a constrained linear regression optimization technique. Methods: A parabolic function was identified as the geometric model and was employed to fit the shape of the diaphragm on the CBCT projections. The search was initialized by five manually placed seeds on a pre-selected projection image. Temporal redundancies, the enabling phenomenology in video compression and encoding techniques, inherent in the dynamic properties of the diaphragm motion together with the geometrical shape of the diaphragm boundary and the associated algebraic constraint that significantly reduced the searching space of viable parabolic parameters was integrated, which can be effectively optimized by a constrained linear regression approach on the subsequent projections. The innovative algebraic constraints stipulating the kinetic range of the motion and the spatial constraint preventing any unphysical deviations was able to obtain the optimal contour of the diaphragm with minimal initialization. The algorithm was assessed by a fluoroscopic movie acquired at anteriorposterior fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients. The automatic tracing by the proposed algorithm and manual tracking by a human operator were compared in both space and frequency domains. Results: The error between the estimated and manual detections for the fluoroscopic movie was 0.54mm with standard deviation (SD) of 0.45mm, while the average error for the CBCT projections was 0.79mm with SD of 0.64mm for all enrolled patients. The submillimeter accuracy outcome exhibits the promise of the proposed constrained linear regression approach to track the diaphragm motion on rotational projection images. Conclusion: The new algorithm will provide a potential solution to rendering diaphragm motion and ultimately improving tumor motion management for radiation therapy of cancer patients.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Modifying AMG Coarse Spaces with Weak Approximation Property to Exhibit Approximation in Energy Norm

Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation property (WAP) which is a necessary and sufficient condition for uniform two-grid convergence. Here, this paper studies a modification of such coarse spaces so that the modified ones provide approximation in energy norm. Our modification is based on the projection in energy norm onto an orthogonal complement of original coarse space. This generally leads to dense modified coarse space matrices, which is hence computationally infeasible. To remedy this, based on the fact that the projection involves inverse of a well-conditioned matrix, we use polynomials to approximate the projection and, therefore, obtain a practical, sparse modified coarse matrix and prove that the modified coarse space maintains computationally feasible approximation in energy norm. We present some numerical results for both PDE discretization matrices as well as graph Laplacian ones, which are in accordance with our theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Discrete Nonlinear Schrödinger-Type Hierarchy, Its Finite-Dimensional Reduction Analysis, and the Numerical Integration Scheme

We investigate the procedures of discretization of the integrable nonlinear Schrödinger dynamical system, well known as the Ablowitz–Ladik equation, the corresponding symplectic structures, and the finite-dimensional invariant reductions. We develop an efficient scheme of invariant reduction of the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter. We construct a finite set of recurrence algebraic regular relations that allows one to generate solutions of the discrete nonlinear Schrödinger dynamical system and discuss the related functional spaces of solutions. Finally, we analyze the Fourier-transform approach to the study of the set of solutions of the discrete nonlinear Schrödinger dynamical system and its functional-analytic aspects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗
DOE OSTI2023

Fast truncated SVD of sparse and dense matrices on graphics processors

We investigate the solution of low-rank matrix approximation problems using the truncated singular value decomposition (SVD). For this purpose, we develop and optimize graphics processing unit (GPU) implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work takes advantage of the fact that the two methods are composed of very similar linear algebra building blocks, which can be assembled using numerical kernels from existing high-performance linear algebra libraries. Furthermore, the experiments with several sparse matrices arising in representative real-world applications and synthetic dense test matrices reveal a performance advantage of the block Lanczos algorithm when targeting the same approximation accuracy.

Computer Science↗
DOE OSTI2018

Brochure on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence [Slides]

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Improving scalability of electronic structure code for molecular simulations in the presence of environment

A scalable density functional electronic code with Gaussian basis set, called UTEP-NRLMOL, is developed to perform simulations of molecular systems in the presence of the environment with particular attention to the memory requirements. In the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for density functional calculations scale as N*N, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure codes hinder their efficient usage of these platforms. We have introduced new scaling and parallelization paradigms using MPI-3 shared-memory functionality combined with usage of sparse algebra and storage of matrices in sparse format. This extends the range of applicability of the UTEP-NRLMOL code to large systems over 10,000 atoms, or using up to 67,000 basis functions, and making use of HPC architectures using over 6,000 processors utilizing all available cores. We have also interfaced code with effective fragment potential and polarizable continuum model libraries. The code was used in simulations of several applications which are published in reputed scientific journals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Celestial gluon amplitudes from the outside in

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D ‘gluon’ operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Pion and Kaon Valence-quark Parton Quasidistributions

Algebraic Ansatze for the Poincare-covariant Bethe-Salpeter wave functions of the pion and kaon arc used to calculate their light-front wave functions, parton distribution amplitudes, parton quasidistribution amplitudes, valence parton distribution functions, and parton quasidistribution functions (PqDFs). The light-front wave functions arc broad, concave functions, and the scale of flavor-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the s- and u-quark sectors. Parton quasidistribution amplitudes computed with longitudinal momentum P z = 1.75 GeV provide a semiquantitatively accurate representation of the objective parton distribution amplitude, but even with P z = 3 GeV, they cannot provide information about this amplitude's end point behavior. On the valence-quark domain, similar outcomes characterize PqDFs. Lastly, in this connection, however, the ratio of kaon-to-pion u-quark PqDFs is found to provide a good approximation to the true parton distribution function ratio on 0.4 ≲ x ≲ 0.8, suggesting that with existing resources computations of ratios of parton quasidistributions can yield results that support empirical comparison.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Effects of Hot Streak and Phantom Cooling on Heat Transfer in a Cooled Turbine Stage Including Particulate Deposition

The objective of this research effort was to develop a validated computational modeling capability for the characterization of the effects of hot streaks and particulate deposition on the heat load of modern gas turbines. This was accomplished with a multi-faceted approach including analytical, experimental, and computational components. A 1-year no cost extension request was approved for this effort, so the total duration was 4 years. The research effort succeeded in its ultimate objective by leveraging extensive experimental deposition studies complemented by computational modeling. Experiments were conducted with hot streaks, vane cooling, and combinations of hot streaks with vane cooling. These studies contributed to a significant body of corporate knowledge of deposition, in combination with particle rebound and deposition studies funded by other agencies, to provide suitable conditions for the development of a new model. The model includes the following physical phenomena: elastic deformation, plastic deformation, adhesion, and shear removal. It also incorporates material property sensitivity to temperature and tangential-normal velocity rebound cross-dependencies observed in experiments. The model is well-suited for incorporation in CFD simulations of complex gas turbine flows due to its algebraic (explicit) formulation. This report contains model predictions compared to coefficient of restitution data available in the open literature as well as deposition results from two different high temperature turbine deposition facilities. While the model comparisons with experiments are in many cases promising, several key aspects of particle deposition remain elusive. The simple phenomenological nature of the model allows for parametric dependencies to be evaluated in a straightforward manner. This effort also included the first-ever full turbine stage deposition model published in the open literature. The simulations included hot streaks and simulated vane cooling. The new deposition model was implemented into the CFD model as a wall boundary condition, with various particle sizes investigated in the simulation. Simulations utilizing a steady mixing plane formulation and an unsteady sliding mesh were conducted and the flow solution of each was validated against experimental data. Results from each of these simulations, including impact and capture distributions and efficiencies, were compared and potential reasons for differences discussed in detail. The inclusion of a large range of particle sizes allowed investigation of trends with particle size, such as increased radial migration and reduced sticking efficiency at the larger particle sizes. The unsteady simulation predicted lower sticking efficiencies on the rotor blades than the mixing plane simulation for the majority of particle sizes. This is postulated to be due to the preservation of the hot streak and cool vane wake through the vane-rotor interface (which are smeared out circumferentially in the mixing-plane simulation). The results reported here represent the successful implementation of a novel deposition model into validated vane-rotor flow solutions that include a non-uniform inlet temperature profile and simulated vane cooling.

42 ENGINEERING↗
DOE OSTI2023

Fermion geometry and the renormalization of the Standard Model Effective Field Theory

The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

A 2-categorical state sum model

It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗