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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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The quantum $\mathrm{UV}$-$\mathrm{IR}$ map for line defects in $$ \mathfrak{gl} $$(3)-type class $\mathcal{S}$ theories

We consider the quantum UV-IR map for line defects in class S theories of $\mathfrak{gl}$(3)-type. This map computes the protected spin character which counts framed BPS states with spin for the bulk-defect system. We give a geometric method of computing this map motivated by the physics of five-dimensional $\mathcal{N}$ = 2 supersymmetric Yang-Mills theory, and compute it explicitly in various examples. As a spin-off we propose a new way of computing a certain specialization of the HOMFLY polynomial for links in $\mathbb{R}^3$, as a sum over BPS webs attached to the link.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Down the rabbit hole with theories of class $ \mathcal{S} $

We review some of the properties of 3d N=4 theories obtained by dimensionally reducing theories of class S. We study 3d partition functions, and certain limits thereof, for such theories, and the properties implied for these by 3d mirror symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The moduli space of vacua of $ \mathcal{N}=2 $ class $ \mathcal{S} $ theories

We develop a systematic method to describe the moduli space of vacua of four dimensional N=2 class S theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin’s equations obtained from twisted compactification of 5d maximal Super-Yang-Mills, with local degrees of freedom at punctures given by (nilpotent) orbits. The crucial thing is the holomorphic factorization of the Seiberg-Witten curve and reduction of singularity at punctures. We illustrate our method by many examples including N=2 SQCD, T N theory and Argyres-Douglas theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Synthesis and bioassay of a new class of disubstituted 1,3,4-oxadiazoles, 1,3,4-thiadiazoles and 1,2,4-triazoles

A new class of aroylethenesulfonylmethyl styryl oxadiazoles/thiadiazoles/triazoles and arylsulfonylethenesulfonylmethyl styryl oxadiazoles/thiadiazoles/triazoles were synthesized from the synthetic intermediates E-aroylethenesulfonylacetic acid methyl ester, E-arylsulfonylethenesulfonylacetic acid methyl ester and substituted cinnamic acids adopting conventional and ultrasonication methodologies. All the synthesized compounds were obtained in higher yields and in shorter reaction times in ultrasound irradiation method when compared with conventional method. The structures of all the compounds were characterized by IR, {sup 1}H NMR, {sup 13}C NMR and mass spectra. All the title compounds were tested for antimicrobial activity. The arylsulfonylethenesulfonylmethyl styryl azoles displayed higher antimicrobial activity than the aroylethenesulfonylmethyl styryl azoles. The compounds having triazole moiety showed greater activity than those with oxadiazole and thiadiazole. Amongst all the tested compounds unsubstituted and chloro substituted arylsulfonylethenesulfonyl methyl styryl triazoles are identified as potential antimicrobial agents particularly against B. subtilis and P.chrysogenum. .

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Kalman Duality Principle for a Class of Ill-Posed Minimax Control Problems with Linear Differential-Algebraic Constraints

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and time-varying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical optimality conditions are not applicable in the general case. We construct a minimizing sequence <##> } } u }&#x005E;<!-- ^ --> } &#x03B5;<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> for the dual problem applying Tikhonov method. Finally we represent <##> } } u }&#x005E;<!-- ^ --> } &#x03B5;<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dimension of Restricted Classes of Interval Orders

Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most 3. Herein, this article shows that the same dimension bound applies to two other classes of posets: those having a representation consisting of unit intervals (but with a mixture of open and closed intervals allowed) and those having a representation consisting of closed intervals with lengths in {0,1}.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Hydrogeomorphic controls on soil carbon composition in two classes of subalpine wetlands

Wetlands play a vital role in terrestrial carbon (C) sequestration, but the sensitivity of their C stocks to disturbance remains uncertain, requiring enhanced understanding of the processes that govern C storage and removal. The unique conditions in wetlands from different hydrogeomorphic (HGM) classes likely regulate the cycling, storage and vulnerabilities of wetland soil C stocks. To determine how differences in hydrogeomorphic setting influence soil organic carbon (SOC) processing, in this study we compared C content and composition between depressional and slope wetlands located in the Colorado Rocky Mountains. Isolated depressional wetlands were characterized by seasonally declining water tables, slow discharge, high clay content, and thick organic horizons. Slope wetlands received perennial groundwater inputs and had coarser soil textures and thinner organic horizons. Seasonal snowmelt inputs coupled with low hydrologic discharge and higher clay content in depressional wetlands were predicted to sustain anoxic conditions, leading to high SOC content and chemically reduced C compounds. Depressional wetland soils had higher SOC content at depth and higher porewater DOC concentrations compared to slope wetland soils. Solid-state 13 C nuclear magnetic resonance spectroscopy demonstrated that aliphatic compounds were the dominant SOC component in depressional wetlands compared to aromatic C forms in the slope wetlands. The higher prevalence of aliphatic carbon in depressional wetland soils suggests that stored SOC is protected by anaerobic conditions to a greater extent than in the slope wetlands, and that this SOC may be more vulnerable to drying and oxic conditions associated with wetland drainage and climate change.

13C NMR↗
DOE OSTI2018

On the Stability of Toroidal Manifold for One Class of Dynamical Systems

We study the problem of stability of an invariant toroidal manifold for one class of linear extensions of a dynamical system on a torus. The obtained result is used to investigate the problem of existence of invariant manifold for a nonlinear system of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations

We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evaluation of pre-training large language models on leadership-class supercomputers

Large language models (LLMs) have arisen rapidly to the center stage of artificial intelligence as the foundation models applicable to many downstream learning tasks. However, how to effectively build, train, and serve such models for many high-stake and first-principle-based scientific use cases are both of great interests and of great challenges. Moreover, pre-training LLMs with billions or even trillions of parameters can be prohibitively expensive not just for academic institutions, but also for well-funded industrial and government labs. Furthermore, the energy cost and the environmental impact of developing LLMs must be kept in mind. Here, in this work, we conduct a first-of-its-kind performance analysis to understand the time and energy cost of pre-training LLMs on the Department of Energy (DOE)’s leadership-class supercomputers. Employing state-of-the-art distributed training techniques, we evaluate the computational performance of various parallelization approaches at scale for a range of model sizes, and establish a projection model for the cost of full training. Our findings provide baseline results, best practices, and heuristics for pre-training such large models that should be valuable to HPC community at large. We also offer insights and optimization strategies for using the first exascale computing system, Frontier, to train models of the size of GPT-3 and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP

The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for second-order cone complementarity problems proposed by Tang et al. (Comput Appl Math 33:655–669, 2014). Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by Chen et al. (Math Comput 67:519–540, 1998), and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A class of customized proximal point algorithms for linearly constrained convex optimization

In this paper, we propose a class of customized proximal point algorithms for linearly constrained convex optimization problems. The algorithms are implementable, provided that the proximal operator of the objective function is easy to evaluate. We show that, with special setting of the algorithmic scalar, our algorithms contain the customized proximal point algorithm (He et al., Optim Appl 56:559–572, 2013), the linearized augmented Lagrangian method (Yang and Yuan, Math Comput 82:301–329, 2013), the Bregman Operator Splitting algorithm (Zhang et al., SIAM J Imaging Sci 3:253–276, 2010) as special cases. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the proposed algorithms. Numerical results demonstrate that the algorithms work well for a wide range of the scalar.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On LPMHSS-based iteration methods for a class of weakly nonlinear systems

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems

In this paper, we reformulate a class of nonlinear complementarity problems as the implicit fixed-point equations. We demonstrate accelerated modulus-based matrix splitting iteration method. We show their convergence by assuming that the system matrix is positive definite or the splitting of the system matrix are H{sub +}-compatible splitting and discuss the choice of the optimal parameter. Furthermore, we give two-step accelerated modulus-based matrix splitting iteration method, which may achieve higher computing efficiency. Numerical experiments are presented to show the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗