Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linearity”

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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Two-Dimensional Non-Linear Magnetic Equivalent Circuit Model to Facilitate the Preliminary Design of a Normal Conducting Quadrupole

Normal conducting quadrupoles have been used to focus charged particle beams in synchrotrons, beam transfer lines, medical linacs, etc. for a long time. Optimization techniques based on analytical expressions combined with the use of a numerical field analysis tool exist in the literature for the design of an optimal pole tip shape. However, the initial shape and dimensions of the remaining yoke (including the pole itself and yoke base that act as the return path) are usually less well defined. This article discusses a design methodology for a normal conducting quadrupole based on a two-dimensional magnetic equivalent circuit. Here, this approach considers the geometry of the entire magnet and the non-linear behavior of the yoke material, thereby eliminating the initial iterations. The design outcome of this exercise serves as a competent starting point and can then be used to refine the pole tip, pole taper, yoke size, and add other geometrical features to achieve the required field quality, gradient, coil considerations, etc. by employing a finite element analysis tool. An example design study to demonstrate the proposed methodology is presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Canopy Structure Exhibits Linear and Nonlinear Links to Biome‐Level Maximum Light Use Efficiency

Maximum light use efficiency (ε max ) represents a plant's capacity to convert light into carbon during photosynthesis. Although prior studies have explored ε max variations between sunlit and shaded leaves or its temporal ties to canopy structure, the spatial relationship between biome-level ε max (ε biome ) and biome structure remains poorly understood. We analysed data from 320 eddy covariance sites (~855 site-years) with satellite-derived near-infrared reflectance of vegetation (NIRv) and leaf area index (LAI). We introduced NIRvN (NIRv/LAI) to isolate architectural effects from leaf quantity. Site-level ε max was calculated and aggregated by biome to derive ε biome . Results show ε biome rises nonlinearly with NIRv and LAI, saturating at high LAI, with crops and tropical evergreen forests deviating from this trend. Conversely, ε biome decreases linearly with increasing NIRvN, indicating that biomes with greater NIR scattering efficiency exhibit lower ε biome . These results enhance understanding of structural influences on carbon uptake across global biomes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Bifurcation Buckling Analysis and Non-Linear Collapse Analysis of Teardrop Shaped Vacuum Chamber

The Spallation Neutron Source (SNS) accelerator is being upgraded to increase the beam power from 1.4MW at 1GeV to 2.8MW at 1.3GeV. The currents in the middle two injection chicane magnets cannot simply be scaled up to accommodate the increased injection energy of 1.3GeV due to potential excessive H- stripping; the magnets must be replaced with longer, lower-field magnets and the associated vacuum chambers need to be redesigned. A new teardrop-shaped vacuum chamber was initially designed to accommodate the new magnets and the updated beam paths and instrumentation. This paper focuses on the structural stability study of the teardrop shape vacuum chamber based on buckling analysis. Protection against collapse from buckling according to the ASME BPVC requirement has been evaluated in depth. First, a Type-1 bifurcation buckling analysis using a linear eigenvalue solution to determine the critical load factor was performed. Subsequently, a Type-3 nonlinear collapse analysis was conducted using the static Riks method with elastic-plastic material properties and imperfections explicitly considered in the model geometry. The critical buckling load for the teardrop shape vacuum chamber was confidently estimated based upon this two-stage approach.

Jiang, Hao↗
DOE OSTI2020

Study of a linear surface wave plasma source for tin removal in an extreme ultraviolet source

Tin deposition mitigation employs hydrogen radicals and ions, formed in a hydrogen plasma, to interact with tin to form tin hydride (SnH 4 ) in the gaseous state, which is then pumped away. Surface wave plasma (SWP) technology developed at Illinois generates hydrogen radicals and ions, resulting in tin etch rates that are high enough to keep extreme ultraviolet (EUV) lithographic tools clean. An advantage of an SWP antenna is the ability to generate a high density of hydrogen radicals and hydrogen ions directly at the desired etching location. In situ etching of tin enables high availability EUV tools by maintaining high reflectivity of the multilayer mirror of the collector. Additionally, the SWP is characterized with low ion energies and low electron temperature, such that the multilayer mirror does not suffer any damage from sputtering or implantation of hydrogen ions during operation. Here, experiments elucidating the fundamental processes of tin removal are conducted by varying pressure, power, surface temperature, and gas flow rate in order to observe the etch rate behavior. Our results have shown that the presence of hydrogen ions increases etch rates because ion bombardment weakens Sn–Sn bonds, which, in turn, allows for a higher rate of chemical etching by the radicals. The ion bombardment reduces the number of radicals needed to etch a single tin atom to the range of 10 2 –10 3 . The linear SWP antenna yields plasma densities on the order of 10 17 to 10 18 m -3 and radical densities on the order of 10 18 to 10 19 m -3 , allowing for greater utilization of ion etch enhancement. Etch rates of up to 200 nm/min have been achieved. The surface temperature of the samples is an important factor in the etching process such that the decrease in the surface temperature increases the etch rates and decreases the hydrogen desorption rates. In addition, a kinetic etch model is developed to explain the behavior of etch rates as a function of surface temperature. Furthermore, results from experiments performed in an Illinois NXE:3100 chamber will be discussed.

42 ENGINEERING↗
DOE OSTI2023

Laser and optical transport line for laser-based ion beam diagnostics and control in the SNS linear accelerator

We report our recent upgrade of the laser and optical transport line for the laser-based ion beam diagnostics (laser wire) system at the linear accelerator (linac) of the Spallation Neutron Source (SNS). A new light source based on diodepumped solid-state laser amplifiers has been developed to provide near diffraction-limited laser beam with a variety of pulse structures. The free-space optical transport line has been modified to include image relay optics with remote control, which greatly improved the laser beam quality and position stability at individual measurement stations. The upgraded system enables novel beam diagnostics/control capabilities including longitudinal profile measurement and high-energy proton beam extraction from the SNS linac.

Liu, Yun↗
DOE OSTI2022

Large-Scale Optimization with Linear Equality Constraints Using Reduced Compact Representation

For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems

This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called k-distributed control, which lets the agents make control decisions based on the state information within distance k on the underlying graph. This controller can tune its degree of decentralization using the parameter k and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a subexponentially growing graph condition, the performance difference between k-distributed control and centralized optimal control becomes exponentially small in k. Finally, this result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers

Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2021

Linear polarization–direction correlations in $\gamma $-ray scattering experiments

Scattering measurements with incident linearly polarized γ rays provide information on spins, parities, and γ-ray multipolarity mixing coefficients, and, therefore, on the nuclear matrix elements involved in the transitions. Here, we present the general formalism for analyzing the observed angular correlations. The expressions are used to compute three-dimensional radiation patterns, which are important tools for optimizing experimental setups. Frequently, γ-ray transitions can proceed via two multipolarities that mix coherently. In such cases, the relative phases of the nuclear matrix elements are important when comparing results from different measurements. We discuss different phase conventions that have been used in the literature and present their relationships. Finally, we propose a basic experimental geometry consisting of detectors located at four different spatial locations. For this geometry, we present the measured anisotropies of the emitted γ rays in graphical format as an aid in the data analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

$\gamma$-ray angular correlations, distributions and linear polarization in tracking arrays

With $\gamma $-ray tracking arrays, the angular correlation and, especially, the linear polarization of $\gamma $ rays can be measured with high precision. However, because of the complexity of these spectrometers, measuring angular distributions is more involved. The techniques and associated formalisms were developed and established in the 1950s. The experimental setups of that era were relatively simple when compared to the advanced $\gamma $-ray tracking arrays available today. This paper aims to review and refine these techniques, unify the nomenclatures and, specifically, adapt them for use with the newest tracking arrays. In addition, new methods for producing the required response functions for these arrays are introduced.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

QLBT: a linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles

Abstract We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor $$R_\mathrm {AA}$$ R AA and the elliptic flow $$v_2$$ v 2 of D mesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on the D meson $$R_\mathrm {AA}$$ R AA and $$v_2$$ v 2 , we extract the heavy quark transport parameter $$\hat{q}$$ q ^ and diffusion coefficient $$D_\mathrm {s}$$ D s in the temperature range of $$1-4~T_\mathrm {c}$$ 1 - 4 T c , and compare them with the lattice QCD results and other phenomenological studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2021

Developments on two lithium vapor-box linear test-stand experiments

The lithium vapor-box divertor is a possible fusion power exhaust solution.It uses condensation pumping to create a gradient of vapor density in a divertor slot; this should allow a stable detachment front without active feedback.As initial explorations of the concept, two test stands which take the form of three connected cylindrical stainless steel boxes are being developed: one without plasma at PPPL, to test models of lithium evaporation and flow; and one for the linear plasma device Magnum-PSI (at DIFFER in Eindhoven, The Netherlands) to test the ability of a lithium vapor cloud to induce volumetric detachment and redistribute the plasma power.The first experiment uses boxes with diameters of 6 cm, joined by apertures with diameters of 2.2 cm. Up to 1 g of Li is placed in one box, which is heated to up to 600 degrees C. The Li evaporates, then flows to and condenses in the two other, cooler boxes over several minutes. The quantity of Li transported is assessed by weighing the boxes before and after the heating cycle, and is compared to the quantity predicted to flow for the box at its measured temperature using a Direct Simulation Monte Carlo code, SPARTA. With good experimental conditions, the two values agree to within 15%.The experiment on Magnum-PSI is in the conceptual design stage.The design is assessed by simulations using the code B2.5-Eunomia.They show that when the hydrogen-ion plasma beam, with n_e = 4e20 per cubic meter, T_e = 1.5 eV, and r = 1 cm, is passed through a 16 cm long, 12 Pa, 625 degree C Li vapor cloud, the plasma heat flux and pressure on the target are significantly reduced compared to the case without Li.With the Li present, the plasma is cooled by excitation of Li neutrals followed by radiation until it volumetrically recombines, lowering the heat flux from 3.7 MW/m^2 to 0.13 MW/m^2, and the pressure is reduced by 93%, largely by collisions of hydrogen ions with neutral Li.

divertor↗
DOE OSTI2023

Code for Value Decomposition Graph Network and environment for AMR on linear advection

This is the code for the paper [Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement](https://arxiv.org/abs/2211.00801), published at AAMAS 2023. It contains the implementation of a new algorithm, called Value Decomposition Graph Network (VDGN), for applying multi-agent reinforcement learning to the problem of adaptive mesh refinement (AMR). It also contains the implementation of a multi-agent environment for AMR on a linear advection problem. VDGN is the first learning algorithm to display anticipatory refinement behavior in AMR, and it outperforms local error threshold-based heuristic strategies.

Yang, Jiachen↗
DOE OSTI2023

Graph Neural Networks and Applied Linear Algebra v.1.0

SAND2024-01365O The Graph Neural Networks and Applied Linear Algebra is companion software for the educational article with the same title. The software provides illustrative examples of graph neural networks in Matlab and Python. These stand-alone algorithms are for educational purposes. The software also includes graph neural network-based algorithms for a trainable Jacobi iteration as well as diffusion coefficient estimation. The software provides human-interpretable implementations of Graph Neural Networks in Matlab and Python. These implementations are not optimized for performance and instead emphasize readability. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2023

Interpretable, Extensible Linear Regression Model for Electron Density Prediction

This code allows us to generate a model to predict ground state electron densities directly from atomic structure thereby bypassing the need to perform direct DFT calculations. It is based on many body correlation descriptors defined in https://arxiv.org/abs/2004.14442 (IM release numbers: LLNL-JRNL- 808791 and LLNL-JRNL-840698). The code reads in electron densities, in CHGCAR format used by the DFT code VASP, calculates many-body correlation descriptors based on atoms surrounding a grid point and then uses linear regression to obtain the fitting parameters.

Kumar, Shashikant↗