SEARCH · Engineering Papers

Results for “Numerical Representation”

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.

SourceResearch connectionFrom yearThrough year

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

At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2019

A Classical Field Theory Formulation for the Numerical Solution of Time Harmonic Electromagnetic Fields

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the “curl-curl” equation for the fields. We present a variational formulation which solves for the four-potential instead, based on classical field theory. Borrowing from quantum electrodynamics, we modify the Lagrangian by adding an implicit gauge-fixing term. This reformulation explicitly accounts for Gauss’ law through the coupling between $\phi$ and $\rho$ , and enables the use of nodal basis functions instead of edge elements for time-harmonic problems. Here, we demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional covariant field description, provides a highly general, robust numerical framework.

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

Simulating county-level crop yields in the Conterminous United States using the Community Land Model: The effects of optimizing irrigation and fertilization

Representing agricultural systems explicitly in Earth system models is important for understanding the water-energy-food nexus under climate change. In this study, we applied Version 4.5 of the Community Land Model (CLM) at a 0.125 degree resolution to provide the first county-scale validation of the model in simulating crop yields over the Conterminous United States (CONUS). We focused on corn and soybean that are both important grain crops and biofuel feedstocks (corn for bioethanol; soybean for biodiesel). We find that the default model substantially under- or over-estimate yields of corn and soybean as compared to the US Department of Agriculture (USDA) census data, with corresponding county-level root-mean square error (RMSE) of 45.3 Bu/acre and 12.9 Bu/acre, or 42% and 38% of the US mean yields for these crops, respectively. Based on the numerical experiments, the lack of proper representation of agricultural management practices, such as irrigation and fertilization, was identified as a major cause for the model's poor performance. After implementing an irrigation management scheme calibrated against county-level US Geological Survey (USGS) census data, the county-level RMSE for corn yields reduced to 42.6 Bu/acre. We then incorporated an optimized fertilizer scheme in rate and timing, which is achieved by the constraining annual total fertilizer amount against the USDA data, considering the dynamics between fertilizer demand and supply and adopting a calibrated fertilizer scheduling map. The proposed approach is shown to be effective in increasing the fertilizer use efficiency for corn yields, with county-level RMSE reduced to 23.8 Bu/acre (or 22% of the US mean yield). In regions with similar annual fertilizer applied as in the default, the improvements in corn yield simulations are mainly attributed to application of longer fertilization periods and consideration of the dynamics between fertilizer demand and supply. For soybean which is capable of fixing nitrogen to meet nitrogen demand, the reduced positive bias to 6.9 Bu/acre (or 21% of the country mean) was mainly attributed to consideration of the dynamic interactions between fertilizer demand and supply. Although large bias remains in terms of the spatial pattern (i.e. high county-level RMSE), mainly due to limited performance over the Western US, our results show that optimizing irrigation and fertilization can lead to promising improvement in crop and soybean yield simulations in terms of the mean and variability especially over the Mid-west corn belt, and subsequent evapotranspiration (ET) estimates. Finally, this study demonstrates the CLM4.5 capability for predicting crop yields and their interactions with climate, and highlights the value of continued model improvements and development to understand biogeophysical and biogeochemical impacts of land use and land cover change using an Earth system modeling framework.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Modeling of Precipitation over Africa: Progress, Challenges, and Prospects

In recent years, there has been an increasing need for climate information across diverse sectors of society. This demand has arisen from the necessity to adapt to and mitigate the impacts of climate variability and change. Likewise, this period has seen a significant increase in our understanding of the physical processes and mechanisms that drive precipitation and its variability across different regions of Africa. By leveraging a large volume of climate model outputs, numerous studies have investigated the model representation of African precipitation as well as underlying physical processes. These studies have assessed whether the physical processes are well depicted and whether the models are fit for informing mitigation and adaptation strategies. This paper provides a review of the progress in precipitation simulation over Africa in state-of-the-science climate models and discusses the major issues and challenges that remain.

CMIP6↗

DOE OSTI2014

Assessment of model assumptions and budget terms of the unsteady flamelet equations for a turbulent reacting jet-in-cross-flow

An a priori analysis of the flamelet model for diffusion flames is conducted to systematically assess model assumptions that are associated with the asymptotic expansion, the omission of higher-order expansion terms, the consideration of preferential diffusion effects, and the one-dimensional flamelet representation. For this, a recent direct numerical simulation database of a reacting hydrogen/air jet-in-cross-flow (JICF) by Grout et al. [15,16] is used. The full flamelet equation for temperature, exact to the order of the Eulerian transport equation and general to different definitions of the mixture fraction, is derived. Analysis of mixture fraction conditioned profiles of temperature and scalar dissipation rate along the jet trajectory identified different ignition and flame stabilization scenarios on the windward and leeward sides of the reacting JICF. A balance analysis of the temperature flamelet equation is conducted to quantify contributions in flame-aligned and flame-orthogonal directions. Consistent with the flamelet assumption, it is shown that terms arising from scalar diffusion, heat-release, and species-diffusion-induced enthalpy flux are the dominant contributions, while the flame-aligned preferential diffusion promotes entrainment of heat into the flamelet structure. Finally, for the current JICF-configuration, it is found that contributions along the flame-orthogonal direction are on average negligible.

42 ENGINEERING↗

DOE OSTI2022

Rethinking the ill-posedness of the spectral function reconstruction — Why is it fundamentally hard and how Artificial Neural Networks can help

Reconstructing hadron spectral functions through Euclidean correlation functions are of the important missions in lattice QCD calculations. However, in a Källen–Lehmann (KL) spectral representation, the reconstruction is observed to be ill-posed in practice. It is usually ascribed to the fewer observation points compared to the number of points in the spectral function. In this paper, by solving the eigenvalue problem of continuous KL convolution, we show analytically that the ill-posedness of the inversion is fundamental and it exists even for continuous correlation functions. We discussed how to introduce regulators to alleviate the predicament, in which include the Artificial Neural Networks (ANNs) representations recently proposed by the Authors in another study. The uniqueness of solutions using ANNs representations is manifested analytically and validated numerically. Reconstructed spectral functions using different regularization schemes are also demonstrated, together with their eigen-mode decomposition. We observe that components with large eigenvalues can be reliably reconstructed by all methods, whereas those with low eigenvalues need to be constrained by regulators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Automation of the guiding center expansion

We report on the use of the recently developed Mathematica package VEST (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous non-unique forms or representations. (2) The procedure proceeds entirely in cartesian position and velocity coordinates, thereby producing manifestly gyrogauge invariant results; the commonly used perpendicular unit vector fields e{sub 1},e{sub 2} are never even introduced. (3) It is easy to apply in the derivation of higher-order contributions to the guiding center transformation without fear of human error. Our code therefore stands as a useful tool for exploring subtle issues related to the physics of toroidal momentum conservation in tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Thermodynamic stability of a spin microemulsion in Rashba spin-orbit-coupled bosons

Recent finite-temperature numerical simulations have unveiled a quantum “spin” microemulsion analog, found by raising the temperature of a stripe supersolid phase in a Rashba spin-orbit coupled Bose gas. This microemulsion state is a highly correlated, isotropic normal fluid where atoms self-arrange based on their internal pseudospin into patterns that resemble bicontinuous microemulsions. This finding leaves several open questions regarding the broader accessibility of this phase in experiments. Here, we use equilibrium finite-temperature numerical simulations based on a coherent-state path integral representation to perform a computational investigation into the thermodynamic stability of the spin microemulsion state. Numerical simulations emphasize the requirement of a nearly, but not perfectly, isotropic spin-orbit coupling in order to achieve the microemulsion phase in cold-atom experiments. Moreover, the microemulsion state exists independent of miscibility of the pseudospin components and for a wide range of pseudospin population imbalance, suggesting a high degree of flexibility in choosing the atom and hyperfine states in an experimental realization. Lastly, we demonstrate this feasibility by mimicking a Rashba spin-orbit-coupled 87 Rb experiment in an isotropic harmonic trap, where we confirm the microemulsion's existence via its density profile and equilibrium quasimomentum distribution.

Complex Langevin dynamics↗

DOE OSTI2021

Real-Frequency Response Functions at Finite Temperature

Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020), B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998), J. Vičičevic and M. Ferrero, Phys. Rev. B 101, 075113 (2020)], we show that the diagrammatic Monte Carlo technique allows us to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system’s action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. Finally, for illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).

3-dimensional systems↗

DOE OSTI2025

Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. Here, in this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

decoherence↗

DOE OSTI2025

Kolmogorov-Arnold wavefunctions

Here, this work investigates Kolmogorov-Arnold network-based (KAN) wave-function Ansätz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural-network-based Ansätz . We also introduce a novel approach for handling strong short-range potentials—a persistent challenge for many numerical techniques—which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.

1-dimensional systems↗

DOE OSTI2025

Toward particle accelerator machine state embeddings as a modality for large language models

Understanding and diagnosing the state of a particle accelerator requires navigating high-dimensional control system data, often involving hundreds of interdependent parameters. We propose a novel multimodal embedding framework that jointly learns representations of machine states from both numerical control system readouts and natural language descriptions. This enables the translation of complex machine conditions into human-readable summaries while maintaining fidelity to the underlying physical system. The obtained embeddings are subsequently adapted to an open-weights large language model via cross-attention conditioning. We demonstrate a first implementation trained on European XFEL machine state data. This work covers the embedding model architecture, training methodology, and presents initial examples demonstrating the model's capabilities in action. Due to the general concept of machine state, the model can be easily adapted to other facilities and control system environments.

Accelerator Physics↗

DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗

DOE OSTI2023

How numerical tracers and water isotope ratios help us better understand the hydrological cycle and its representation in Earth system models [Slides]

Outline: Water isotope ratios and fractionation; Isotope tracers in Earth system models; Generalized "process-oriented" water tracers in Earth system models; Opportunities in E3SM. Water isotope ratio data are rapidly becoming more available, providing a critical link between models and observations, as well as providing new opportunities to improve process representations (e.g., T/ET partitioning, cloud processes, partitioning of streamflow, coastal or urban impacts on hydrology, etc.)

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1973

An analytical and numerical study of the Martian planetary boundary layer over slopes.

A one-dimensional model of the Martian planetary boundary layer over sloping terrain is analyzed under a variety of conditions. Analytical results for the steady and diurnal components of the temperature and wind fields are found when a Boussinesq model with a Newtonian cooling law is considered. These results form a basis for understanding the numerical results which include more realistic representations for the heating and parametrizations for the eddy transfer of momentum and heat. The diurnal boundary layer thickness is determined primarily by radiative processes, and the amplitudes of the wind and temperature oscillations are found to depend in an important way on the latitude and slope magnitude. Typically, oscillations in the temperature of plus or minus 15 K and in the upslope wind of plus or minus 25 m/sec are found 1 km above a Martian slope of 0.005.

Blumsack, S. L.↗

NASA NTRS1982

Solutions of the compressible Navier-Stokes equations using the integral method

The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.

Elrefaee, M. M.↗

NASA NTRS1983

The impact of CFD on development test facilities - A National Research Council projection

The results of a National Research Council study on the effect that advances in computational fluid dynamics (CFD) will have on conventional aeronautical ground testing are reported. Current CFD capabilities include the depiction of linearized inviscid flows and a boundary layer, initial use of Euler coordinates using supercomputers to automatically generate a grid, research and development on Reynolds-averaged Navier-Stokes (N-S) equations, and preliminary research on solutions to the full N-S equations. Improvements in the range of CFD usage is dependent on the development of more powerful supercomputers, exceeding even the projected abilities of the NASA Numerical Aerodynamic Simulator (1 BFLOP/sec). Full representation of the Re-averaged N-S equations will require over one million grid points, a computing level predicted to be available in 15 yr. Present capabilities allow identification of data anomalies, confirmation of data accuracy, and adequateness of model design in wind tunnel trials. Account can be taken of the wall effects and the Re in any flight regime during simulation. CFD can actually be more accurate than instrumented tests, since all points in a flow can be modeled with CFD, while they cannot all be monitored with instrumentation in a wind tunnel.

Korkegi, R. H.↗

NASA NTRS1991

Theoretical models for duct acoustic propagation and radiation

The development of computational methods in acoustics has led to the introduction of analysis and design procedures which model the turbofan inlet as a coupled system, simultaneously modeling propagation and radiation in the presence of realistic internal and external flows. Such models are generally large, require substantial computer speed and capacity, and can be expected to be used in the final design stages, with the simpler models being used in the early design iterations. Emphasis is given to practical modeling methods that have been applied to the acoustical design problem in turbofan engines. The mathematical model is established and the simplest case of propagation in a duct with hard walls is solved to introduce concepts and terminologies. An extensive overview is given of methods for the calculation of attenuation in uniform ducts with uniform flow and with shear flow. Subsequent sections deal with numerical techniques which provide an integrated representation of duct propagation and near- and far-field radiation for realistic geometries and flight conditions.

Eversman, Walter↗