Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Algebraic models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Variable Complexity Structural Optimization of Shells

Structural designers today face both opportunities and challenges in a vast array of available analysis and optimization programs. Some programs such as NASTRAN, are very general, permitting the designer to model any structure, to any degree of accuracy, but often at a higher computational cost. Additionally, such general procedures often do not allow easy implementation of all constraints of interest to the designer. Other programs, based on algebraic expressions used by designers one generation ago, have limited applicability for general structures with modem materials. However, when applicable, they provide easy understanding of design decisions trade-off. Finally, designers can also use specialized programs suitable for designing efficiently a subset of structural problems. For example, PASCO and PANDA2 are panel design codes, which calculate response and estimate failure much more efficiently than general-purpose codes, but are narrowly applicable in terms of geometry and loading. Therefore, the problem of optimizing structures based on simultaneous use of several models and computer programs is a subject of considerable interest. The problem of using several levels of models in optimization has been dubbed variable complexity modeling. Work under NASA grant NAG1-1808 has been concerned with the development of variable complexity modeling strategies with special emphasis on response surface techniques. In addition several modeling issues for the design of shells of revolution were studied.

Haftka, Raphael T.↗
NASA NTRS1999

Variable Complexity Structural Optimization of Shells

Structural designers today face both opportunities and challenges in a vast array of available analysis and optimization programs. Some programs such as NASTRAN, are very general, permitting the designer to model any structure, to any degree of accuracy, but often at a higher computational cost. Additionally, such general procedures often do not allow easy implementation of all constraints of interest to the designer. Other programs, based on algebraic expressions used by designers one generation ago, have limited applicability for general structures with modem materials. However, when applicable, they provide easy understanding of design decisions trade-off. Finally, designers can also use specialized programs suitable for designing efficiently a subset of structural problems. For example, PASCO and PANDA2 are panel design codes, which calculate response and estimate failure much more efficiently than general-purpose codes, but are narrowly applicable in terms of geometry and loading. Therefore, the problem of optimizing structures based on simultaneous use of several models and computer programs is a subject of considerable interest. The problem of using several levels of models in optimization has been dubbed variable complexity modeling. Work under NASA grant NAG1-2110 has been concerned with the development of variable complexity modeling strategies with special emphasis on response surface techniques. In addition, several modeling issues for the design of shells of revolution were studied.

Haftka, Raphael T.↗
DOE OSTI2024

U(1) fields from qubits: An approach via D-theory algebra

A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1 + 0 -dimensional ( 1 + 0 -D) matrix models, 1 + 1 -D sigma models and non-Abelian gauge theories in 2 + 1 and 3 + 1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU ( 3 ) field for lattice QCD and other non-Abelian 1 + 1 -D sigma models or 3 + 1 -D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1 + 1 -D sine-Gordon equation. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2021

Lowest-dimensional portals to SU( N ) exotics

New matter fields charged under the strong nuclear force would have dramatic phenomenological implications. In this work, we systematically explore how these new states, which we postulate belong to some representation of SU(3) of quantum chromo-dynamics, could interact with standard model fields: We analyze all lowest-dimensional “portal” operators for any SU(3) representation, and motivated by grand unification, we extend our results to SU( N ) for N > 3. We provide a publicly available python code, “tessellation,” that automatically constructs said lowest-dimensional portal operators for any new exotic matter field charged under SU( N ) for any N .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Reinforcement Learning-Based Approach for EMT Automation of Large-Scale PV Plants

In the pursuit of efficient and precise modeling of large-scale power systems, particularly utility-scale photovoltaic (PV) plants, Electromagnetic Transient (EMT) simulations play a crucial role. As utility-scale PV plants increase in size and complexity, traditional computational methods become inadequate, necessitating more advanced techniques. This paper highlights the progressive efforts made to accelerate EMT simulations. A novel continuous reinforcement learning (RL) strategy is explored to automate the differentiation and categorization of stiff and non-stiff differential algebraic equations (DAEs). The use of stiff and non-stiff integration methods applied to relevant parts of the DAEs assists with the speed-up of the simulations. The paper details the data acquisition, development and offline training of the RL model, leading to its validation that demonstrates a high precision in optimizing simulation methods. The proposed RL promises to significantly enhance the efficacy of EMT simulations, offering a robust framework for the future of power system analysis.

Xia, Qianxue↗
DOE OSTI2022

Black hole scattering and partition functions

When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by “renormalizing” the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev formula, fixes the reference free energy to be that on a Rindler-like region, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static BTZ, Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗
NASA NTRS1979

Application of the method of integral relations to unsteady fluid flow problems with shocks

A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.

Wadia, A. R.↗
NASA NTRS1986

Error-source effects in a high-accuracy optical finite-element processor

High-accuracy optical linear algebra processors are addressed with attention to three new aspects. These include: their application to the solution of finite-element problems; the first error-source models for component errors in such processors; and the first analysis of error sources in such processors.

Taylor, B. K.↗
NASA NTRS1984

Structural synthesis: Precursor and catalyst

More than twenty five years have elapsed since it was recognized that a rather general class of structural design optimization tasks could be properly posed as an inequality constrained minimization problem. It is suggested that, independent of primary discipline area, it will be useful to think about: (1) posing design problems in terms of an objective function and inequality constraints; (2) generating design oriented approximate analysis methods (giving special attention to behavior sensitivity analysis); (3) distinguishing between decisions that lead to an analysis model and those that lead to a design model; (4) finding ways to generate a sequence of approximate design optimization problems that capture the essential characteristics of the primary problem, while still having an explicit algebraic form that is matched to one or more of the established optimization algorithms; (5) examining the potential of optimum design sensitivity analysis to facilitate quantitative trade-off studies as well as participation in multilevel design activities. It should be kept in mind that multilevel methods are inherently well suited to a parallel mode of operation in computer terms or to a division of labor between task groups in organizational terms. Based on structural experience with multilevel methods general guidelines are suggested.

Schmit, L. A.↗
NASA NTRS1987

Precise computer controlled positioning of robot end effectors using force sensors

A major problem in space applications of robotics and docking of spacecraft is the development of technology for automated precise positioning of mating components with smooth motion and soft contact. To achieve the above objective, a design method was developed for optimally placing the closed-loop poles of a discretized robotic control system at exact prescribed locations inside the unit circle of the complex z-plane. The design method combines the merits of the pole placement and the linear quadratic design approaches. The proposed design procedure is based on the assignment of one real eigenvalue or two complex conjugate (or real) eigenvalues at each design step. The method involves solutions of simple algebraic equations and this is considered to be efficient for on-line or off-line computations. Also, two methods for the linearization of the nonlinear model of a robotic manipulator were presented. Since automatic control of multi-degree freedom robotic manipulators involves high nonlinear equations of systems, a pilot project was proposed involving the control of a one-dimensional system. This simple system can be readily implemented for testing the concepts and algorithms.

Shieh, Leang S.↗
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

Data assimilation in operator algebras

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

String membrane nets from higher-form gauging: An alternate route to 𝑝-string condensation

We present a new perspective on the $p$-string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in 3+1D that is generated by Abelian anyons in isotropic stacks of 2+1D topological orders naturally results in a 3+1D $p$-string condensed phase, providing a controlled non-perturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and one-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: in field theory, we derive the foliated field theory description of the $\mathbb{Z}_N$ X-Cube model by gauging a higher-form symmetry in stacks of 2+1D $\mathbb{Z}_N$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$-graded string-net models leads to string-membrane-nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d \geq 2$ and provides a step towards building an algebraic theory of $p$-string condensation.

Anyons↗
DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗
NASA NTRS1987

Computer-based phosphoric acid fuel cell analytical tools Descriptions and usages

Simulation models have been developed for the prediction of phosphoric acid fuel cell (PAFC) powerplant system performance under both transient and steady operation conditions, as well as for the design of component configurations and for optimal systems synthesis. These models, which are presently computer-implemented, are an engineering and a system model; the former being solved by the finite difference method to determine the balances and properties of different sections, and the latter using thermodynamic balances to set up algebraic equations that yield physical and chemical properties of the stream for one operating condition.

Lu, C.↗