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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Rigorous Analytic Combinatorics in Several Variables in SageMath

We introduce the new [sage_acsv] package for the SageMath computer algebra system, allowing users to rigorously compute asymptotics for a large variety of multivariate sequences with rational generating functions. Using Sage's support for exact computations over the algebraic number field, this package provides the first rigorous implementation of algorithms from the theory of analytic combinatorics in several variables.

Hackl, Benjamin↗
DOE OSTI2017

SymPy: symbolic computing in Python

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions

The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require equally precise theoretical predictions to make full use of the acquired data. To match the experimental precision, second-, third- and, for certain quantities, even higher-order calculations in perturbative quantum field theory are required. To facilitate such calculations, computer software automating as many steps as possible is required. Yet, each calculation poses different challenges and thus, a high level of configurability is required. In this context we present tapir: a tool for identification, manipulation and minimization of Feynman integral families. It is designed to integrate in toolchains based on the computer algebra system FORM, the use of which is common practice in the field. tapir can be used to reduce the complexity of multi-loop problems with cut-filters, topology mapping, partial fraction decomposition and alike. Program Title:tapir CPC Library link to program files:https://doi.org/10.17632/ptc9t46xyn.1 Developer's repository link:https://gitlab.com/tapir-devs/tapir Licensing provisions: GPLv3 Programming language:python 3, C++ Nature of problem: Multi-loop computations require the automatization of a large number of different tasks related to Feynman integral topologies. Among them are the identification and minimization of integral topologies, partial fraction decomposition of topologies in the case of linearly dependent propagators as well as mapping scalar products of loop momenta to scalar functions. Solution method: The minimization of topologies is performed by comparison of their respective Nickel indices [1], even further minimization utilizes Pak's algorithm [2]. To efficiently map scalar products of loop momenta to scalar functions FORM [3] code is generated. Additional comments including restrictions and unusual features: Minimization based on Pak's algorithm slows down for many lines and scales. A coarser minimization using the Nickel indices, however, is still possible. [1]B. Nickel, D. Meiron, G.A.J. Baker, Compilation of 2-pt and 4-pt graphs for continuous spin model, Report, University of Guelph, 1977.[2]A. Pak, J. Phys. Conf. Ser. 368 (2012) 012049, https://doi.org/10.1088/1742-6596/368/1/012049, arXiv:1111.0868.[3]B. Ruijl, T. Ueda, J. Vermaseren, FORM version 4.2, arXiv:1707.06453, 7 2017.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Moments of the Boltzmann collision operator for Coulomb interactions

Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗
DOE OSTI2018

L{sup ∞} error bound of conservative compact difference scheme for the generalized symmetric regularized long-wave (GSRLW) equations

In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is O(τ{sup 2}+h{sup 4}) in the L{sup ∞}-norm for u and ρ. For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A fast and accurate modeling approach for water and steam thermodynamics with practical applications in district heating system simulation

In U.S. district heating (DH) systems, steam is the most common heat transport medium. Industry demand for new advanced modeling capabilities of complete steam DH systems is increasing; however, the existing models for water/steam thermodynamics are too slow for large system simulations because of computationally expensive algebraic loops that require the solution to nonlinear systems of equations. For practical applications, this work presents a novel split-medium approach that implements numerically efficient liquid water models alongside various water/steam models, breaking costly algebraic loops by decoupling mass and energy balance equations. New component models for steam DH systems are also presented. We implemented the models in the equation based Modelica language and evaluated accuracy and computing speed across multiple scales: from fundamental thermodynamic properties to complete districts featuring 10 to 200 buildings. Compared to district models with the IF97 water/steam model and equipment models from the Modelica Standard Library, the new implementation improves the scaling rate for large districts from cubic to quadratic with negligible compromise to accuracy. Additionally, for an annual simulation with 180 buildings, this translates to a computing time reduction from 33 to 1-1.5 h. These results are critically important for industry practitioners to simulate steam DH systems at large scales.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

Dynamic simulation↗
DOE OSTI2018

Green’s Function Coupled-Cluster Approach: Simulating Photoelectron Spectra for Realistic Molecular Systems

In this paper we present an efficient implementation for the analytical energy- dependent coupled cluster Green’s function with singles and doubles (GFCCSD) approach with our first practice being computing spectral functions of real molecular systems. Due to its algebraic structure, the presented method is highly scalable, and is capable of computing spectral function for a given molecular system in any energy region. Several typical examples have been given to demonstrate its capability of computing spectral functions not only in the valence band, but also in the core-level energy region. Satellite peaks have been observed in the inner valence band and core-level energy region where many-body effect becomes significant and single particle picture of ionization often breaks down. The accuracy test has been carried out by extensively comparing our GFCCSD results with experimental results as well as the theoretical results from other methods. It turns out GFCCSD method is able to provide qualitative or semi-quantitative level of description of ionization processes in both the core and valence regimes. To significantly improve the GFCCSD results for the main states, larger basis set can usually be employed, whereas the improvement of the GFCCSD results for the satellite states needs higher order many-body terms to be included in the GFCC implementation.

electronic structure theory↗
DOE OSTI2021

An Analog Preconditioner for Solving Linear Systems [Slides]

This presentation concludes in situ computation enables new approaches to linear algebra problems which can be both more effective and more efficient as compared to conventional digital systems. Preconditioning is well-suited to analog computation due to the tolerance for approximate solutions. When combined with prior work on in situ MVM for scientific computing, analog preconditioning can enable significant speedups for important linear algebra applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Integrating Learning and Physics based Computation for Fast Online Transient Analysis

In this work, a novel method that integrates learning and physics based computation is developed for greatly accelerating the simulation of full power system transient trajectories. To solve the dynamic algebraic equations, the method replaces the time-consuming dynamic computation for generator dynamics with trained predictors, while retaining the time-efficient algebraic computation of solving AC-power flow (PF) for power systems. In particular, a predictor is trained for each generator, and the system trajectories are computed by alternating steps of calling the predictors and solving AC-PF. The proposed method also allows fully parallelizable training strategies and a flexible trade-off between training time and testing accuracy. Comprehensive evaluations of the proposed method for transient/dynamic contingency analysis of the New York/New England 16-machine 68-bus power systems demonstrate excellent performance and significant acceleration of computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗
DOE OSTI2018

Center for Extended Magnetohydrodynamic Modeling (CEMM), Final Technical Report for UW-Madison Engineering Physics

The Center for Extended Magnetohydrodynamic Modeling (CEMM) focused on the further development, verification, validation, and application of two scientific computation programs, the NIMROD and M3D-C1 codes, for modeling macroscopic dynamics in magnetized plasma. Both NIMROD and M3D-C1 solve the mathematical equations that model two-fluid 3D magnetohydrodynamic (MHD). They are designed and optimized to be efficient and accurate for toroidal confinement physics calculations. The effort improved the fidelity of the physics models, the realism of the treatment of the surrounding vessel, coils, and other structures, the accuracy and efficiency of the algorithms, and the ability to scale calculations to thousands of processors in order to take advantage of leading-edge computers. The primary application areas of Resonant Magnetic Perturbations (RMP), Edge Harmonic Oscillations (EHO), Edge Localized Modes (ELMs), Disruption Studies, Sawteeth and Stationary States, and Kinetic MHD and Neoclassical Tearing Modes (NTM) are of concern for the international ITER experiment, which is under construction in France. The effort by the UW-Madison Engineering Physics component of CEMM improved the numerical methods in the NIMROD code with respect to modeling MHD interchange and two-fluid effects. It also improved the algorithm for solving large algebraic systems to enhance NIMROD's computational performance when running the code in parallel on increasing numbers of processor cores. The modeling efforts included a study of the nonlinear evolution of ballooning, and the findings were supported by analytical theory and computation. Numerical MHD modeling also examined the influences of two-fluid effects on ELMs and RMPs, where "two-fluid" refers to separation of electron dynamics from ion dynamics. Another related aspect considered the effects of a localized layer of electrical current density near the edge of the plasma confinement region. Two-fluid effects on resonant reconnecting instabilities were verified and applied to computations of sawtooth and drift-tearing dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Using computational singular perturbation as a diagnostic tool in ODE and DAE systems: a case study in heterogeneous catalysis

We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. Here we use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum Software Engineering (Dagstuhl Seminar 24512)

The Dagstuhl Seminar 24512 on "Quantum Software Engineering" was held from December 15 to 20, 2024. It brought together 26 participants from industry and academia from 13 different countries, including senior and junior researchers as well as practitioners in the field of Quantum Software Engineering. The aim of the seminar was to advance software engineering methods and tools for the engineering of hybrid quantum systems by promoting personal interaction and open discussion among researchers who are already working in this emerging area of knowledge. The first day of the seminar was devoted to the topic "When software engineering meets quantum mechanics", while the second day focused on "Quantum software engineering and its challenges." During both days, 16 invited presentations were given. The rest of the seminar was organized into three working groups to address the topics "Quantum Software Design, Modelling and Architecturing", "Adaptive Hybrid Quantum Systems", and "Quantum Software Quality Assurance". The seminar was a very fruitful experience for all participants both in terms of scientific outcomes and in terms of the personal relationships that were generated to jointly address future experiences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems

In this paper, we consider the balanced truncation method for model reductions in large-scale linear and time-independent dynamical systems with multi-inputs and multi-outputs. The method is based on the solutions of two large coupled Lyapunov matrix equations when the system is stable or on the computation of stabilizing positive and semi-definite solutions of some continuous-time algebraic Riccati equations when the dynamical system is not stable. Using the rational block Arnoldi, we show how to compute approximate solutions to these large Lyapunov or algebraic Riccati equations. The obtained approximate solutions are given in a factored form and used to build the reduced order model. We give some theoretical results and present numerical examples with some benchmark models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the Random Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Differential equations from unitarity cuts: nonplanar hexa-box integrals

We compute ϵ-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗