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 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Chiral spin liquid and quantum phase transition in the triangular-lattice Hofstadter-Hubbard model

Recent advances in moiré engineering motivate the study of lattice models of strongly correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular-lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120° antiferromagnetic phases. Here, we use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.

Divic, Stefan [University of Pennsylvania, Philade↗
DOE OSTI2019

skyline

skyline is a header-only C++ library for the direct solution of linear algebraic equations that are stored in skyline format. It is intended for medium-sized sparse problems with moderate bandwidth. This solution approach has historically been used for pressure network solvers and in some finite element codes. It was developed to replace legacy solver code included in the EnergyPlus building energy modeling software package, but is not limited to use by EnergyPlus.

DeGraw, Jason↗
NASA NTRS1986

Equations for Annular-Heat-Transfer Coefficients

Tables of coefficients converted to algebraic expressions. Plot of Equation for Nusselt number agrees closely with points from tabulated data. Equation for Nusselt number and those for coefficients A and B obtained by regression analysis of data. Other plots also show close agreement for radius of 0.1 and 0.2. In equation form, coefficients incorporated into mathematical models more readily than as tabular data. Equations simplify design and analysis of heat exchangers.

Yao, B.↗
NASA NTRS1995

Estimation of attitude sensor timetag biases

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Sedlak, J.↗
DOE OSTI2014

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.

Meng, Da↗
DOE OSTI2016

Comparative Performance Analysis of Coarse Solvers for Algebraic Multigrid on Multicore and Manycore Architectures

In this paper, we study the performance of a two-level algebraic-multigrid algorithm, with a focus on the impact of the coarse-grid solver on performance. We consider two algorithms for solving the coarse-space systems: the preconditioned conjugate gradient method and a new robust HSS-embedded low-rank sparse-factorization algorithm. Our test data comes from the SPE Comparative Solution Project for oil-reservoir simulations. We contrast the performance of our code on one 12-core socket of a Cray XC30 machine with performance on a 60-core Intel Xeon Phi coprocessor. To obtain top performance, we optimized the code to take full advantage of fine-grained parallelism and made it thread-friendly for high thread count. We also developed a bounds-and-bottlenecks performance model of the solver which we used to guide us through the optimization effort, and also carried out performance tuning in the solver’s large parameter space. Finally, as a result, significant speedups were obtained on both machines.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Symmetries near the horizon

We consider a nearly-AdS_2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS_2 which move bulk matter relative to the dynamical boundaries. In a two-sided system, these operators satisfy an SL(2) algebra (up to non perturbative corrections). In a semiclassical limit, these generators act like SL(2) transformations of the boundary time, or conformal symmetries of the two sided boundary theory. These can be used to define an operator-state mapping. A particular large N and low temperature limit of the SYK model has precisely the same structure, and this construction of the exact generators also applies. We also discuss approximate, but simpler, constructions of the generators in the SYK model. These are closely related to the “size” operator and are connected to the maximal chaos behavior captured by out of time order correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

A finite element algorithm for sound propagation in axisymmetric ducts containing compressible mean flow

The described investigation is concerned with he development of a finite element scheme which can be used in a study of the acoustics of aircraft-engine ducts. In the absence of suitable variational principles for acoustic fluctuations within an aircraft fan engine, an acoustic analysis must proceed directly from the differential equations which describe compressible flow. The derived equations cannot be solved algebraically. The numerical technique used for solving them makes use of a linear rectangular element of a type considered by Zienkiewicz (1971). Attention is given to aspects of element derivation, the global matrix assembly, the solution of the matrix equation, questions of acoustic attenuation, and illustrations of the potential of the current model in duct optimization.

Abrahamson, A. L.↗
NASA NTRS1986

Compliance matrices for cracked bodies

An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).

Ballarini, R.↗
NASA NTRS1976

New convergence criteria for the vortex-lattice models of the leading-edge separation

The convergence criterion for the vortex-lattice technique which deals with delta wings exhibiting significant leading-edge separation was studied. It was shown that one can predict pressure distributions without irregularities which agree fairly well with experimental data (which show some irregularities of their own) by replacing the system of discrete vortex lines with a single concentrated core. This core has a circulation equal to the algebraic sum of the circulations around the discrete lines and is located at the centroid of these lines. Moreover, there is a requirement that the position and strength of the core must converge as the number of elements increases. Because the calculation of the position and strength of the core is much less involved than the calculation of the loads, this approach has the additional desirable feature of requiring less computational time.

Kandil, O. A.↗
DOE OSTI2024

Hybrid analysis of radiative corrections to neutron decay with current algebra and effective field theory

We introduce a useful framework for high-precision studies of the neutron beta decay by merging the current algebra description and the fixed-order effective field theory calculation of the electroweak radiative corrections to the neutron axial form factor. We discuss the advantages of this hybrid method and show that it only requires a minimal amount of lattice QCD inputs to achieve a 10 –4 theory accuracy for the Standard Model prediction of the neutron lifetime and the axial-to-vector coupling ratio λ, both important to the search for physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1984

Stability of finite difference models containing two boundaries or interfaces

The stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves. Wave propagation ideas are applied to models containing two boundaires or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Various known instability phenomena are accounted for in a unified way. Results show: (1) dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface; (2) algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present; and (3) GKS-stability and P-stability can be established in certain problems by showing that all numerical reflection coefficients have modulus less than 1.

Trefethen, L. N.↗
NASA NTRS1985

Stability of finite-difference models containing two boundaries or interfaces

The stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves. Wave propagation ideas are applied to models containing two boundaries or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Various known instability phenomena are accounted for in a unified way. Results show: (1) dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface; (2) algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present; and (3) GKS-stability and P-stability can be established in certain problems by showing that all numerical reflection coefficients have modulus less than 1.

Trefethen, L. N.↗
NASA NTRS1989

A skin friction law for compressible turbulent flow

An algebraic skin friction law is derived for adiabatic, compressible, equilibrium, turbulent boundary layer flow. An outer solution in terms of the Clauser defect stream function is matched to an inner empirical expression composed of compressible laws of the wall and wake. The modified Crocco temperature-velocity relationship and the Clauser eddy viscousity model are used in the outer solution. The skin friction law pertains for all pressure gradients in the incompressible through supersonic range and for small pressure gradients in the hypersonic range. Excellent comparisons with experiment are obtained in the appropriate parameter ranges. The application to numerical computation is discussed.

Barnwell, Richard W.↗
DOE OSTI2025

Scalable multilevel Monte Carlo methods exploiting parallel redistribution on coarse levels

Here, we study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the number of MPI processes used on the finest level. The overall procedure generates coarse elements (general unstructured unions of fine grid elements) within the framework of element-based algebraic multigrid methods (or AMGe) studied previously. The AMGe-generated coarse spaces have the ability to exhibit approximation properties of the same order as the fine-level spaces since by construction they contain the piecewise polynomials of the same order as on the fine level. These approximation properties are key for the successful use of AMGe in multilevel solvers for nonlinear partial differential equations as well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen without being constrained by the number of MPI processes, as described in the present paper, allows to improve the scalability of these solvers as well as the overall MLMC method. The paper illustrates this latter fact with detailed scalability study of MLMC simulations applied to model Darcy equations with a stochastic log-normal permeability field.

AMGe↗
DOE OSTI2013

Fixman compensating potential for general branched molecules

The technique of constraining high frequency modes of molecular motion is an effective way to increase simulation time scale and improve conformational sampling in molecular dynamics simulations. However, it has been shown that constraints on higher frequency modes such as bond lengths and bond angles stiffen the molecular model, thereby introducing systematic biases in the statistical behavior of the simulations. Fixman proposed a compensating potential to remove such biases in the thermodynamic and kinetic properties calculated from dynamics simulations. Previous implementations of the Fixman potential have been limited to only short serial chain systems. In this paper, we present a spatial operator algebra based algorithm to calculate the Fixman potential and its gradient within constrained dynamics simulations for branched topology molecules of any size. Our numerical studies on molecules of increasing complexity validate our algorithm by demonstrating recovery of the dihedral angle probability distribution function for systems that range in complexity from serial chains to protein molecules. We observe that the Fixman compensating potential recovers the free energy surface of a serial chain polymer, thus annulling the biases caused by constraining the bond lengths and bond angles. The inclusion of Fixman potential entails only a modest increase in the computational cost in these simulations. We believe that this work represents the first instance where the Fixman potential has been used for general branched systems, and establishes the viability for its use in constrained dynamics simulations of proteins and other macromolecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Quasi-Optimal Elimination Trees for 2D Grids with Singularities

We construct quasi-optimal elimination trees for 2D finite element meshes with singularities. These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal. We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O N e log ⁡ N e , where N e is the number of elements in the mesh. We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.

Paszyńska, A.↗