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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Scalability under a Power Bound using the GREMLINs Framework

With the move towards exascale, system and software developers will have to deal with issues of extreme parallelism. The system properties affected most by the increase in node and core count are the shared resources on node and across the system. The increase in parallelism leads to reduced memory and bandwidth when regarding individual cores. Since power is a limiting factor for supercomputers, and power is not fully utilized in current systems, overprovisioning compute resources is a viable approach to maximized power utilization. To maximize system performance in regard to these changing conditions, it is necessary to understand how resource restrictions impact performance and system behavior. For the purpose of understanding anticipated system properties the GREMLINs Framework was developed. The framework gives the opportunity to add power restrictions, hinder memory properties and introduce faults to study resilience, among others. These features give the opportunity to use current petascale technology to study problems system designers and software developers will have to face when moving towards exascale and beyond. This work describes the initial release of the GREMLINs Framework, developed for this work, and shows how it can be used to study the scaling behavior of proxy applications. These proxy applications represent a selection of HPC workloads important to the scientific community. The proxy applications studied are AMG2013, an algebraic multi-grid linear system solver, CoMD, a classical molecular dynamics proxy application and NEKBONE, an application that uses a high order spectral element method to solve the Navier-Stokes equations. The main interest of these studies lies in analysis regarding their power behavior at scale under a power bound. These findings show how the GREMLINs Framework can help systems and software designers to attain better application performance and can also be used as basis for CPU power balancing tools to use power more efficiently.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Localized Pisot Matrices and Joint Approximations of Algebraic Numbers

A development of the simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions is proposed. To this end, localized Pisot matrices are constructed, whose eigenvalues with moduli less than one are contained in an interval of small length. Such Pisot matrices generate continued fractions whose convergents are arbitrarily close to the best approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point method has been the centerpiece of nonlinear programming tools used in science and engineering, its reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement it effectively on hardware accelerators. HiOp optimization package attempts to provide an implementation of the interior point method suitable for hardware accelerators by compressing the original sparse problem to produce an underlying linear problem that is dense and of manageable size. Implementations of dense linear solvers are more mature and utilize hardware accelerators better than their sparse counterparts. There is a number of important domain problems, such as optimal power flow analysis for power grids, where the sparse problem can be effectively compressed and deploying dense linear solver within the interior point method can improve performance. Here we describe a portable implementation of HiOp optimization engine, which uses a linear solver from Magma library and runs entirely on hardware accelerators. To compress the problem, HiOp uses customized mixed dense-sparse linear algebra. All HiOp kernels are implemented using Umpire and RAJA portability libraries. We describe details of the implementation and discuss trade-offs between performance, portability and development cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Architectures and random properties of symplectic quantum circuits

Parametrized and random unitary (or orthogonal) n-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformations would attract similar attention. However, this is not the case, as $\mathbb{SP}(d/2)$—the group of d × d unitary symplectic matrices—has thus far been overlooked. In this work, we aim at starting to fill this gap. We begin by presenting a universal set of generators $\mathcal{G}$ for the symplectic algebra $\mathfrak{sp}(d/2)$, consisting of one- and two-qubit Pauli operators acting on neighboring sites in a one-dimensional lattice. Here, we uncover two critical differences between such set, and equivalent ones for unitary and orthogonal circuits. Namely, we find that the operators in $\mathcal{G}$ cannot generate arbitrary local symplectic unitaries and that they are not translationally invariant. We then review the Schur–Weyl duality between the symplectic group and the Brauer algebra, and use tools from Weingarten calculus to prove that Pauli measurements at the output of Haar random symplectic circuits can converge to Gaussian processes. As a by-product, such analysis provides us with concentration bounds for Pauli measurements in circuits that form t-designs over $\mathbb{SP}(d/2)$. To finish, we present tensor-network tools to analyze shallow random symplectic circuits, and we use these to numerically show that computational-basis measurements anti-concentrate at logarithmic depth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Computer-aided detection of clustered microcalcifications in multiscale bilateral filtering regularized reconstructed digital breast tomosynthesis volume

Purpose: Develop a computer-aided detection (CADe) system for clustered microcalcifications in digital breast tomosynthesis (DBT) volume enhanced with multiscale bilateral filtering (MSBF) regularization. Methods: With Institutional Review Board approval and written informed consent, two-view DBT of 154 breasts, of which 116 had biopsy-proven microcalcification (MC) clusters and 38 were free of MCs, was imaged with a General Electric GEN2 prototype DBT system. The DBT volumes were reconstructed with MSBF-regularized simultaneous algebraic reconstruction technique (SART) that was designed to enhance MCs and reduce background noise while preserving the quality of other tissue structures. The contrast-to-noise ratio (CNR) of MCs was further improved with enhancement-modulated calcification response (EMCR) preprocessing, which combined multiscale Hessian response to enhance MCs by shape and bandpass filtering to remove the low-frequency structured background. MC candidates were then located in the EMCR volume using iterative thresholding and segmented by adaptive region growing. Two sets of potential MC objects, cluster centroid objects and MC seed objects, were generated and the CNR of each object was calculated. The number of candidates in each set was controlled based on the breast volume. Dynamic clustering around the centroid objects grouped the MC candidates to form clusters. Adaptive criteria were designed to reduce false positive (FP) clusters based on the size, CNR values and the number of MCs in the cluster, cluster shape, and cluster based maximum intensity projection. Free-response receiver operating characteristic (FROC) and jackknife alternative FROC (JAFROC) analyses were used to assess the performance and compare with that of a previous study. Results: Unpaired two-tailedt-test showed a significant increase (p < 0.0001) in the ratio of CNRs for MCs with and without MSBF regularization compared to similar ratios for FPs. For view-based detection, a sensitivity of 85% was achieved at an FP rate of 2.16 per DBT volume. For case-based detection, a sensitivity of 85% was achieved at an FP rate of 0.85 per DBT volume. JAFROC analysis showed a significant improvement in the performance of the current CADe system compared to that of our previous system (p = 0.003). Conclusions: MBSF regularized SART reconstruction enhances MCs. The enhancement in the signals, in combination with properly designed adaptive threshold criteria, effective MC feature analysis, and false positive reduction techniques, leads to a significant improvement in the detection of clustered MCs in DBT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points $a, b \in \mathbb{D}$. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces $H^2_t := \{ f \in H^2 : tf(b)\}$ where $t \in \mathbb{C} \cup \{\infty\}$. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Equivariant Verlinde Formula from Fivebranes and Vortices

We study complex Chern–Simons theory on a Seifert manifold M 3 by embedding it into string theory. We show that complex Chern–Simons theory on M 3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in fourdimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern–Simons theory on Σ × S 1 and (4) index of a spin c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the “equivariant Verlinde algebra” for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern–Simons theory on Σ × S 1 and (4) the equivariant index of a spinc Dirac operator on the moduli space of Higgs bundles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Asymptotic entanglement transformation between W and GHZ states

We investigate entanglement transformations with stochastic local operations and classical communication in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory. Results well-known in that field imply that GHZ states can be transformed into W states at rate 1 for any number of parties. As a generalization, we find that the asymptotic conversion rate from GHZ states to Dicke states is bounded as the number of subsystems increases and the number of excitations is fixed. By generalizing constructions of Coppersmith and Winograd and by using monotones introduced by Strassen, we also compute the conversion rate from W to GHZ states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Reduced models for ETG transport in the tokamak pedestal

This paper reports on the development of reduced models for electron temperature gradient (ETG) driven transport in the pedestal. Model development is enabled by a set of 61 nonlinear gyrokinetic simulations with input parameters taken from pedestals in a broad range of experimental scenarios. The simulation data have been consolidated in a new database for gyrokinetic simulation data, the multiscale gyrokinetic database (MGKDB), facilitating the analysis. The modeling approach may be considered a generalization of the standard quasilinear mixing length procedure. The parameter η, the ratio of the density to temperature gradient scale length, emerges as the key parameter for formulating an effective saturation rule. With a single order-unity fitting coefficient, the model achieves an error of 15%. A similar model for ETG particle flux is also described. We also present simple algebraic expressions for the transport informed by an algorithm for symbolic regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Fractonic coset construction for spontaneously broken translations

We study the homogeneous breaking of spatial translation symmetry concomitantly with the spontaneous breaking of other internal and spacetime symmetries, including dilations. We use the symmetry-breaking pattern as the only input to derive, via the coset construction, general effective field theories for the symmetry-originated modes associated with Goldstone’s theorem, namely the Nambu-Goldstone candidates. Through explicit computations, we show that integrating out the explicit massive Nambu-Goldstone candidates or imposing symmetric constraints, namely the inverse Higgs constraints, to express massive modes in terms of the massless ones leads to physically distinct effective field theories. This sensitivity to the chosen method can be traced back to the homogeneous breaking of translations, the homogeneous aspect of the breaking induces a mixing between internal and spacetime symmetries at the level of the Lie algebra. This, in turn, leads to subtle discussions about the inverse Higgs constraints, in particular that they lead to a loss of generality in our specific examples. The derived general effective field theories also give rise to a broad class of theories exhibiting emergent enhanced shift symmetries, which constrain the mobility of the modes. The latter are referred to as fractonic modes. Published by the American Physical Society 2025

Chavda, Ameya (ORCID:0000000211731605)↗
DOE OSTI2018

Geometric and algebraic structures associated with the channel quantization problem

We consider the use of surfaces as topological spaces in order to provide an answer to the quantization problem of a discrete memoryless channel (DMC). The aim is to identify the geometric and algebraic properties of the surface associated with the embedding of such a DMC. The procedure is based on the following steps: knowing the complete bipartite graph associated with a given DMC: (1) to determine the minimum and the maximum genus of the corresponding surfaces in which the given graph is embedded; (2) knowing the genus, to specify the roots as the elements of a Farey sequence of a planar algebraic curve; (3) to determine the solutions of a second-order Fuchsian differential equation as the generators of the corresponding Fuchsian group. We consider the cases of the hypergeometric and Heun equations, with three and four regular singular points, respectively. By means of this procedure, the fundamental region associated with the Fuchsian group is identified and this is the region where the planar algebraic curve is uniformized. A generalization of the quantization problem related to an m-ary input n-ary output symmetric channel viewed as a complete bipartite graph K{sub m,n}, by use of the embedding of this channel in compact surfaces is straightforward.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Narain to Narnia

We generalize the holographic correspondence between topological gravity coupled to an abelian Chern–Simons theory in three dimensions and an ensemble average of Narain’s family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi–Yau sigma-models and not always for the minimal models. Here, we conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max , while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr , which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L max > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2 ] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2 ]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr .

36 MATERIALS SCIENCE↗
DOE OSTI2013

Xyce(™) Parallel Electronic Simulator

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

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