Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence analysis”

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

Analysis of the transient response of shell structures by numerical methods.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Geers, T. L.↗

The effects of spherical geometry on baroclinic instability

A baroclinic stability analysis is performed for a simple family of zonal shear profiles over a sphere, using a two-layer, quasi-geostrophic model. The stability properties and the structure of the most unstable waves are qualitatively similar to those on a beta-plane. However, the spherical geometry plays a major role in locating some of the important features of the most unstable waves. In particular, the locations of the maximum wave amplitude, maximum eddy heat fluxes, and maximum convergence of the eddy angular momentum flux are all well correlated with the location of the maximum excess of the vertical shear over the minimum value necessary for local instability on a sphere. Consequently the eddy momentum flux tends to generate a mid-latitude jet even if there is no preexisting mid-latitude jet in the basic state zonal flow. These findings suggest some of the elements needed for parameterizing the meridional variations of baroclinic eddy fluxes accurately.

Moura, A. D.↗

Factorization and the synthesis of optimal feedback gains for distributed parameter systems

An approach based on Volterra factorization leads to a new methodology for the analysis and synthesis of the optimal feedback gain in the finite-time linear quadratic control problem for distributed parameter systems. The approach circumvents the need for solving and analyzing Riccati equations and provides a more transparent connection between the system dynamics and the optimal gain. The general results are further extended and specialized for the case where the underlying state is characterized by autonomous differential-delay dynamics. Numerical examples are given to illustrate the second-order convergence rate that is derived for an approximation scheme for the optimal feedback gain in the differential-delay problem.

Milman, Mark H.↗

Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks

Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or clusters of genes with common activity profiles may overlook the most critical features of cellular information processing which normally determine how signal specificity is established and maintained in living cells. Copyright 2000 Academic Press.

Review↗

Modeling gas–shell mixing in ICF with separated reactants

Mixing between fuel and shell materials in ICF implosions can affect implosion dynamics and even prevent ignition. We use data from a series of separated reactant experiments on the National Ignition Facility to calibrate and test the predictive power of gas–shell mix models. Two models are used to estimate fuel–shell mix: a Reynolds-averaged turbulence model and molecular diffusion. Minor uncertainties in capsule manufacture, experimental conditions, and values for mix model parameters produce significant variation in simulation results. Using input/output pairs from 1D simulations, we train Gaussian process surrogate models to predict experimental quantities of interest. The surrogates are used to construct posteriors for mix model parameters by marginalizing over uncertainties in capsule manufacture and experimental conditions. Mix models are calibrated with a subset of experimental data (neutron yields, ion temperature, and bang time) and tested using the remaining data. In general, both the diffusion and turbulence model correctly predict experimental DT and TT neutron yields. Despite having more free parameters, the turbulence model underpredicts ion temperature at high convergence ratio. Furthermore, the simpler diffusion model correctly predicts these temperatures, suggesting nonhydrodynamic gas–shell mix. The computational model consistently overpredicts DD neutron yield, indicating possible shortcomings outside of the mix model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Role of Subcloud Mesoscale Convergence in Sculpting Convective Updraft Width and Depth

The initiation of deep moist convection is governed in part by the horizontal width of updrafts near cloud base, which limits the deleterious effects of entrainment-driven dilution on buoyant thermals ascending through the free troposphere. However, the factors controlling cloud-base updraft width, which in turn dictates cloud depth, are not well understood. We track the evolving three-dimensional structure of the mesoscale subcloud forcing for vertical motion and near-cloud thermodynamic ingredients within a high-resolution ensemble of simulations of seven realistic daytime orographic convection initiation events to determine their relative roles in controlling cloud width and depth. Statistical analysis of approximately 5000 cloudy updraft samples indicates that the most important contributors to the width of cloudy updrafts across the ensemble are the depth and magnitude of the subcloud mesoscale ascent. However, the depth achieved by clouds is more consistently predicted by the near-cloud ambient relative humidity within the lower to middle free troposphere and convective available potential energy. Therefore, although the width of cloudy updrafts may be partly set at low levels by the mesoscale vertical mass and moisture flux, the likelihood of deep moist convection is governed by the generation of positive buoyancy within cumulus thermals and entrainment-driven dilution that reduces it. The persistence of the low-level mesoscale vertical forcing locally consolidates and vertically transports boundary layer moisture, helping to reduce updraft dilution. However, these factors vary in relative impacts on cloudy updrafts across individual cases, indicating multiple pathways for deep convection initiation.

Convective storms↗

Mechanisms of Alkali Ionic Transport in Amorphous Oxyhalides Solid State Conductors

Amorphous oxyhalides have attracted significant attention due to their relatively high ionic conductivity (1 mS cm –1 ), excellent chemical stability, mechanical softness, and facile synthesis routes via standard solid‐state reactions. These materials exhibit an ionic conductivity that is almost independent of the underlying chemistry, in stark contrast to what occurs in crystalline conductors. In this work, we employ machine learning interatomic potentials to construct large‐scale molecular dynamics trajectories encompassing hundreds of nanoseconds to obtain statistically converged transport properties. We find that the amorphous state consists of chain fragments of metal‐anion tetrahedra of various lengths. By analyzing the residence time of alkali cations migrating around tetrahedrally‐coordinated metals, we find that oxygen anions limit alkali diffusion. By computing the full Einstein expression of the ionic conductivity, we demonstrate that the alkali transference number of these materials is strongly influenced by distinct‐particles correlations, while alkali transport is dictated by uncorrelated self‐diffusion. By extending this analysis to chemical compositions AMX 2.5 O 0.75 , spanning different alkaline (A = Li, Na, K), metallic (M = Al, Ga, In), and halogen (X = Cl, Br, I) species, we clarify why the diffusion properties of these materials remain largely insensitive to variations in atomic isovalent chemistry.

amorphous materials↗

A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in turn provides us with information about the nature of dark energy. Conventional methods generate shear maps from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser–Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations—an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly scaling shear map construction alternative using a scalable Gaussian process prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest neighbors and fits hyperparameters using batched leave-one-out cross-validation. This work is the first step toward a full, scalable mass mapping method. We work in a simplified regime where we validate our method by interpolating and analyzing maps given noisy point-estimate data from all three shear fields, taken from a suite of N -body ray-tracing simulations. We also show that we can perform these operations at the scale of billions of galaxies on high-performance computing platforms.

79 ASTRONOMY AND ASTROPHYSICS↗

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2

The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.

Source record↗

An Experimental and Numerical Study of a Supersonic Burner for CFD Model Development

A laboratory scale supersonic burner has been developed for validation of computational fluid dynamics models. Detailed numerical simulations were performed for the flow inside the combustor, and coupled with finite element thermal analysis to obtain more accurate outflow conditions. A database of nozzle exit profiles for a wide range of conditions of interest was generated to be used as boundary conditions for simulation of the external jet, or for validation of non-intrusive measurement techniques. A set of experiments was performed to validate the numerical results. In particular, temperature measurements obtained by using an infrared camera show that the computed heat transfer was larger than the measured value. Relaminarization in the convergent part of the nozzle was found to be responsible for this discrepancy, and further numerical simulations sustained this conclusion.

Magnotti, G.↗

Cloud based tool for analysis of chemical kinetic mechanisms

The size and complexity of chemical kinetic models used to simulate combustion of hydrocarbon fuels continue to increase with our improved understanding of the underlying physical mechanisms, along with the improved ability to utilize such models as the result of increased computational power and efficiency. As mechanisms grow beyond thousands of species and tens of thousands of reactions, it becomes increasingly difficult to manually check for errors and physical inconsistencies. In this work, we present several automated methods to check for such issues in the specification of chemical reaction models. First, we demonstrate how discontinuities in thermodynamic data can cause simulation difficulties manifested as long wall-clock times and convergence failures. To correct this type of problem, we describe an automated method for refitting thermodynamic parameters. We also outline several methods to check the timescales of reaction rate coefficients to ensure physical consistency. All the methods are made available through a web-based tool (https://combustiontools.llnl.gov) intended to aid mechanism developers and users to improve the accuracy and performance of fuel models used by the combustion community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cluster Expansion Analysis of Atomic Order in Li-Ion Battery Cathode Material LiCo y Ni 1-y O 2

A modified cluster-expansion treatment was developed recently to analyze atomic order in LiCo y Ni 1-y O 2 , a model cathode material for Li-ion batteries. In this treatment, referred to as a “spin-atom” cluster expansion, the occupant of a lattice site is identified by its spin state as well as its atomic species. Further, Effective Cluster Interaction (ECI) coefficients are derived from a large training data set (i.e., the set of atomic arrangements for which DFT calculations are performed) which is filtered by an anomaly detection algorithm to eliminate poorly converged DFT calculations. The cluster expansion incorporates Li-Ni (LN) exchange as well as intralayer Co-Ni (CN) exchange. Monte Carlo simulations based on the cluster expansion were applied to the Ni-rich part of the phase diagram. The simulations predict a miscibility gap between y = 0.05 and y = 0.65.

25 ENERGY STORAGE↗

Epistemology of voltage control in DER-rich power system

Despite the recent development of several scalable, robust, and resilient control approaches with superior convergence properties considering an increasing penetration of distributed energy resources (DERs), cognitive oversights often simplify several aspects of the cyber–physical power system in the controller development. Here, following the identification of the limitations of classical controller definitions, we justify alternative definitions of voltage control approaches classifiers considering three inter-disciplinary domains: (i) power system, (ii) optimization and decision-making, and (iii) networking and cyber-security, to develop a taxonomy for helping in real-world comparative performance analysis and deployability of these controllers. We observe that classical and introduced domain-based definitions together can better classify the control algorithms.

24 POWER TRANSMISSION AND DISTRIBUTION↗

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗

Mode spectrum characteristics and onset of the low-shear MHD stability regime

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q 0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q 0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q 0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

First-principles computations of the Stark shift of a defect-bound exciton: The case of the T center in silicon

The T center in silicon has recently drawn a lot of attention for its potential in quantum information science. The sensitivity of the zero-phonon line (ZPL) to electrical field was recently investigated by a combination of different experimental methods but there are still few first principles studies on the Stark shift of the T center. Dealing with the defect-bound exciton nature of the excited state is particularly challenging using density functional theory because of the large spatial delocalization associated with the wavefunction. Here, in this work, we tackle this issue by performing a convergence study over the supercell size. We obtain an exciton binding energy of 28.5 meV, in good agreement with experimental results. We then calculate the Stark shift through the dipole moment change of the ZPL transition of the T center using the modern theory of polarization formalism and find a modest linear coefficient of Δ⁢𝜇=0.79⁢D along X and Δ⁢𝜇=0.03⁢𝐷 along Y. We discuss our results in light of the recent experimental measurements of the Stark shift. Our analysis suggests that bound-exciton defects could be particularly sensitive to local field effect as a result of their large spatial extent.

color centers↗

FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment (Final Report)

This report documents the FY25 Theory and Simulation Performance Target (TSPT) of developing an integrated modeling framework for fusion reactor design and assessment (FREDA). Over Q1-Q4, new capabilities were developed across both plasma and engineering domains and demonstrated on an example representation of a Compact Advanced Tokamak with a Dual Cooled Lead Lithium blanket. This represents a first-of-a-kind demonstration of coupled core-to-wall-to-engineering for a reactor. Self-consistent CESOL workflows were applied to provide core, pedestal, and SOL prediction; new modules were developed for energetic particle stability (FAR3D) and transport (TGLF-EP) analysis; and boundary plasma modeling (SOLPS-ITER, BOUT++/Hermes-3) was expanded to evaluate wall and divertor heat fluxes and interface with engineering thermal analysis. A parameterized CAD tool, TRACER, was expanded to generate medium-fidelity divertor, blanket, and coil geometries; OpenFOAM and Diablo workflows were applied for first-wall and divertor thermal analyses with helium cooling; and reduced-order models were created for high-mass-flux divertor cooling. Magnet multiphysics capabilities were verified between Elmer, Diablo, and a new MFEM-based solver, and workflows enable stress, thermal, and neutron-fluence analysis of TF coils with neutronics-driven heating. Nuclear and blanket analysis workflows were demonstrated, including tritium breeding, transport, and CFD-informed thermo-mechanical assessment. Preliminary multi-fidelity uncertainty quantification workflows were applied to boundary modeling codes and shown to achieve variance reductions with fewer high-fidelity boundary simulations. Key findings highlight the challenges of resolving the ITEP gap to find suitable balance between wall and divertor loads, neutron heating, and practical limits of PFC cooling. Next step priorities are to develop automated workflows to check boundary code convergence and detachment, implement tighter physics-engineering CAD provenance tracking, and inclusion of plasma-material interface models for SLAG and tungsten cracking behavior. Collectively, these developments establish sophisticated capabilities for predictive, multi-fidelity, whole-device modeling that integrates plasma physics, materials, magnets, and nuclear engineering to guide pathways to viable Fusion Pilot Plant design points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗