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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2022

On the Convergence of Inexact Predictor-Corrector Methods for Linear Programming

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

Dexter, Gregory↗
DOE OSTI2019

4D spatiotemporal evolution of liquid spray using kilohertz-rate x-ray computed tomography

Four-dimensional (x, y, z, t) x-ray computed tomography was shown in an optically complex spray using an imaging system consisting of three x-ray sources and three high-speed detectors. The x-ray sources consisted of high-flux rotating anode x-ray tube sources that illuminated the spray from three lines of sight. The absorption along each absorption path was collected using a CsI phosphor plate and imaged by a high-speed intensified CMOS camera at 20 kHz. The radiographs were converted to a quantitative equivalent path length (EPL) of liquid using a variable attenuation coefficient to account for beam hardening. Moreover, the EPL data were then reconstructed using the algebraic reconstruction technique into high-speed time sequences of the threedimensional liquid mass distribution.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

An Algebra of Machine Learners with Applications

Machine learning (ML) methods are increasingly being applied to solve complex, data-driven problems in diverse areas, by exploiting the physical laws derived from first principles such as thermal hydraulics and the abstract laws developed recently for data and computing infrastructures. These physical and abstract laws encapsulate, typically in compact algebraic forms, the critical knowledge that complements data-driven ML models. We present a unified perspective of these laws and ML methods using an abstract algebra (A;⊕,Ⓧ), wherein the performance estimation and classification tasks are characterized by the additive ⊕ operations, and the diagnosis, reconstruction, and optimization tasks are characterized by the difference Ⓧ operations. This abstraction provides ML codes and their performance characterizations that are transferable across different areas. We describe practical applications of these abstract operations using examples of throughput profile estimation tasks in data transport infrastructures, and power-level and sensor error estimation tasks in nuclear reactor systems.

Rao, Nageswara↗
DOE OSTI2022

MAPPRAISER: A massively parallel map-making framework for multi-kilo pixel CMB experiments

Forthcoming cosmic microwave background (CMB) polarized anisotropy experiments have the potential to revolutionize our understanding of the Universe and fundamental physics. The sought-after, tale-telling signatures will be however distributed over voluminous data sets which these experiments will collect. These data sets will need to be efficiently processed and unwanted contributions due to astrophysical, environmental, and instrumental effects characterized and efficiently mitigated in order to uncover the signatures. This poses a significant challenge to data analysis methods, techniques, and software tools which will not only have to be able to cope with huge volumes of data but to do so with unprecedented precision driven by the demanding science goals posed for the new experiments. A keystone of efficient CMB data analysis is solvers of very large linear systems of equations. Such systems appear in very diverse contexts throughout CMB data analysis pipelines, however they typically display similar algebraic structures and can therefore be solved using similar numerical techniques. Linear systems arising in the so-called map-making problem are one of the most prominent and common ones. In this work we present a massively parallel, flexible and extensible framework, comprised of a numerical library, MIDAPACK, and a high level code, MAPPRAISER, which provide tools for solving efficiently such systems. Here, the framework implements iterative solvers based on conjugate gradient techniques: enlarged and preconditioned using different preconditioners. We demonstrate the framework on simulated examples reflecting basic characteristics of the forthcoming data sets issued by ground-based and satellite-borne instruments, executing it on as many as 16,384 compute cores. The software is developed as an open source project freely available to the community at: https://github.com/B3Dcmb/midapack.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Deformation of Lie–Poisson algebras and chirality

Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian symmetric spectra: If λ is an eigenvalue of the linearized generator, -λ and $\barλ$ (hence, -$\barλ$) are also eigenvalues—the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a singular equilibrium point (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes chirality. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Z. Yoshida et al., Phys. Lett. A 381, 2772–2777 (2017)]. To elucidate how chiral spectra are generated, we study the three-dimensional Lie–Poisson systems and classify the prototypes of singularities that cause symmetry breaking. The central idea is the deformation of the underlying Lie algebra; invoking Bianchi’s list of all three-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra s o ( 3 ) , yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Generalized Bootstrap AMG and AIR-AMG for coupled PDE systems with a focus on spacetime discretizatoins

The Pennsylvania State University (“Subcontractor”) has worked on the design of new algebraic, parallel, multilevel methods that obtain the full space and time solution of systems of PDEs. In particular, the PI and his collaborators explored semi-intrusive approaches based on algebraic multigrid (AMG). The focus of the research has been on the development of these techniques for the Euler equations in 1d and 2d. The overall research focused on the development of adaptive AIR (approximate ideal restriction) AMG solvers for these problems. The PI also explored the use of smoothed aggregation and root-node energy-based AMG solvers for these problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets $δp$. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present in this paper normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring of the Muon g-2 Experiment at Fermilab (E989) is investigated.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. In conclusion, scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Algebraic approach to fractional quantum Hall effect

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓ B ~ 1, where q is the wave number at which the system is probed, and ℓ B is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing

We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state |x&rang; that is proportional to the solution of the system of linear equations $A\overrightarrow{x} = \overrightarrow{b}$. The time complexities of our algorithms are O(κ 2 log(κ)/ε) and O(κ log(κ)/ε), where κ is the condition number of A and ε is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of A, the projector onto the initial state |b&rang;, and single-qubit Pauli operators. The algorithms are conceptually simple and easy to implement. They are not obtained from equivalences between the gate model and adiabatic quantum computing. They do not use phase estimation or variable-time amplitude amplification, and do not require large ancillary systems. We discuss a gate-based implementation via Hamiltonian simulation and prove that our second algorithm is almost optimal in terms of κ. Like previous methods, our techniques yield an exponential quantum speed-up under some assumptions. Our results emphasize the role of Hamiltonian-based models of quantum computing for the discovery of important algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Accelerating Scientific Computing in the Post-Moore’s Era

Novel uses of graphical processing units for accelerated computation revolutionized the field of high-performance scientific computing by providing specialized workflows tailored to algorithmic requirements. As the era of Moore’s law draws to a close, many new non–von Neumann processors are emerging as potential computational accelerators, including those based on the principles of neuromorphic computing, tensor algebra, and quantum information. While development of these new processors is continuing to mature, the potential impact on accelerated computing is anticipated to be profound. We discuss how different processing models can advance computing in key scientific paradigms: machine learning and constraint satisfaction. Significantly, each of these new processor types utilizes a fundamentally different model of computation, and this raises questions about how to best use such processors in the design and implementation of applications. While many processors are being developed with a specific domain target, the ubiquity of spin-glass models and neural networks provides an avenue for multi-functional applications. Furthermore, this also hints at the infrastructure needed to integrate next-generation processing units into future high-performance computing systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multi-material hydrodynamics with algebraic sharp interface capturing

A finite volume method for Eulerian multi-material hydrodynamics with sharp interface capturing is presented here. The pressure-temperature non-equilibrium multi-material system with finite-rate pressure relaxation in mixed-cells is considered here. This pressure closure facilitates material-property-dependent pressure relaxation, rather than instantaneous pressure equilibration, which in turn allows the use of unsplit high-order time-integrators. A modified tangent of hyperbola for interface capturing (THINC) method is used to reconstruct multi-material (> 2) interfaces, on three-dimensional unstructured meshes. A simple modification which extends the THINC reconstruction to interfaces between more than two materials is proposed. It is demonstrated that the modified THINC can capture multi-material interfaces within 2–4 tetrahedral cells. Since no geometric reconstructions are required by the THINC method, the presented multi-material method is algorithmically simple, and computationally efficient. Consistent reconstructions of conserved quantities at material interfaces ensure that conservation and closure laws are satisfied at the discrete level. Through a suite of test problems solved on unstructured meshes, it is demonstrated that the presented method is a promising candidate for accurate and efficient multi-material hydrodynamics computations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Improving solve time of aggregation-based adaptive AMG

In this paper, we propose improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Scalable algorithms for three-field mixed finite element coupled poromechanics

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 x 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. In conclusion, the performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

42 ENGINEERING↗
DOE OSTI2017

Operator bases, S-matrices, and their partition functions

Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where S-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. Here in this paper we use the S-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation). We introduce a partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the S-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries. In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to n = 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of n-point amplitudes. We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the S- matrix in the form of soft limits. The most naÏve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations. Finally, although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Porting hypre to heterogeneous computer architectures: Strategies and experiences

We report that linear systems are occurring in many applications, and solving them can take a large amount of the total simulation time. The high performance library hypre provides a variety of interfaces and linear solvers, including various multigrid methods, that have achieved good scalability on a variety of homogeneous parallel computer architectures. Heterogeneous architectures with nodes that have both CPUs and accelerators provide new challenges, since they require more fine-grained parallelism and reduced data movement between different memories on a single node as well as across nodes. We will discuss our experiences and strategies to port hypre to heterogeneous computers with accelerators, including the design of a new memory model, the use of abstractions, the BoxLoop macros in the structured and semi-structured interfaces, and the restructuring of algebraic multigrid (AMG) into modular components. We present numerical experiments comparing CPU and GPU performance for several test problems.

97 MATHEMATICS AND COMPUTING↗