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Results for “generation equation”

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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Approximating the trajectory attractor of the 3D Navier-Stokes system using various α-models of fluid dynamics

We study the limit as α→0+ of the long-time dynamics for various approximate α-models of a viscous incompressible fluid and their connection with the trajectory attractor of the exact 3D Navier-Stokes system. The α-models under consideration are divided into two classes depending on the orthogonality properties of the nonlinear terms of the equations generating every particular α-model. We show that the attractors of α-models of class I have stronger properties of attraction for their trajectories than the attractors of α-models of class II. We prove that for both classes the bounded families of trajectories of the α-models considered here converge in the corresponding weak topology to the trajectory attractor A{sub 0} of the exact 3D Navier-Stokes system as time t tends to infinity. Furthermore, we establish that the trajectory attractor A{sub α} of every α-model converges in the same topology to the attractor A{sub 0} as α→0+. We construct the minimal limits A{sub min}⊆A{sub 0} of the trajectory attractors A{sub α} for all α-models as α→0+. We prove that every such set A{sub min} is a compact connected component of the trajectory attractor A{sub 0}, and all the A{sub min} are strictly invariant under the action of the translation semigroup.Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Herbicide, fertilization, and planting density effects on intensively managed loblolly pine early stand development

Production forestry in the southeast US has been partially transitioned to intensively managed short rotations (~10 years), in which multiple silvicultural interventions are performed during forest development. Understanding the responses to silvicultural practices and continued refinement of site-specific recommendations is critical to sustainably maximize forest production. We evaluated the effects of silvicultural practices (herbicide, fertilization, and planting density) on growth, stand homogeneity, and above- and belowground biomass accumulation and partitioning of loblolly pine (Pinus taeda) throughout early stand development (age 5 years) in the southeastern US. Five treatments with eight replications each were tested: no herbicide and no fertilization (C); herbicide only (H); herbicide and half-reduced fertilization rate (R); herbicide and full fertilization (F); and increased stand density (60+ %; 1346 vs. 2152 trees per hectare) with herbicide and full fertilization rate (D). Allometric equations generated from destructive harvests were applied to annual diameter measurements to estimate plot-level biomass and allocation. Herbicide was crucial to promote stand uniformity and increase yield (~600+ % stem biomass compared with C at age 5). Aboveground biomass was similar in R and F treatments, which was ~25% higher than in H at age 5. Increasing planting density along with multiple herbicide and fertilizer applications yielded higher biomass without compromising individual tree size (diameter and height). There was little effect of silviculture practices on allocation patterns. Our results parallel what was found for fertilization with herbicide from a number of loblolly stands under similar conditions and indicate a ~28% volume gain with fertilization during early stand development. Similarly, our results were consistent with other studies implementing similar differences in planting density and suggest a ~26% volume gain through early stand development with an initial 60% increase in planting density. Furthermore, our study helps to understand complex relationships between production and silvicultural practices during early stand development and demonstrates that silvicultural prescriptions can be optimized to increase sustainability of production forestry

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A methodology for decay heat characterization in molten salt reactors

Accurate decay heat prediction in molten salt reactors (MSRs) faces dual challenges: complex operational uncertainties and the need for interpretable models compatible with engineering workflows. This work presents a hybrid machine learning and segmented polynomial methodology that addresses both requirements through three key innovations. First, a modular data architecture encodes MSR-specific operational parameters (power density: 1-100 W cm -3 , humidity: 0-0.1 wt %, air ingress: 0-0.1 mol %) with uncertainty-aware temporal discretization spanning 15 orders of magnitude. Second, region-optimized machine learning models achieve 92.3 % root mean square error (RMSE) reduction over conventional polynomials while maintaining physical interpretability through automated piecewise equation generation. Third, dual front-end interfaces accelerate safety analyses — a Jupyter environment enables researchers to explore 10,000+ parameter combinations via interactive widgets, while a Streamlit web application reduces design iteration cycles through production-grade visualization tools. Operational deployment demonstrates prediction times of only a couple hundred milliseconds for 10 4 years decay profiles, enabling real-time optimization of spent fuel container designs.

42 - ENGINEERING↗
DOE OSTI2024

Physics informed neural network can retrieve rate and state friction parameters from acoustic monitoring of laboratory stick-slip experiments

Various machine learning (ML) and deep learning (DL) techniques have been recently applied to the forecasting of laboratory earthquakes from friction experiments. The magnitude and timing of shear failures in stick-slip cycles are predicted using features extracted from the recorded ultrasonic or acoustic emission (AE) signals. In addition, the Rate and State Friction (RSF) constitutive laws are extensively used to model the frictional behavior of faults. In this work, we use data from shear experiments coupled with passive acoustic (variance, kurtosis, and AE rate) interleaved with active source ultrasonic monitoring (transmitted wave amplitude) to develop physics-informed neural network (PINN) models incorporating the RSF law and AE rate generation equation with wave amplitude serving as a proxy for friction state variable. This PINN framework allows learning RSF parameters from stick-slip experiments rather than measuring them through a series of velocity step experiments. We observe that when the stick-slip cycles are irregular, the PINN models outperform the data-driven DL models. Transfer learning (TL) PINN models are also developed by pre-training on data collected at one normal stress level followed by forecasting shear failures and retrieving RSF parameters at other stress levels (i.e., with different recurrence intervals) after retraining on a limited amount of new data. Our findings suggest that TL models perform better compared to standalone models. Both standalone and TL PINN-estimated RSF parameters and their ground truth values show excellent agreements thus demonstrating that RSF parameters can be retrieved from laboratory stick-slip experiments using the corresponding acoustic data and that the transmitted wave amplitude provides a good representation of the evolving frictional state during stick-slips.

58 GEOSCIENCES↗
DOE OSTI2012

Linear dimensions and volumes of human lungs

TOTAL LUNG Capacity is defined as “the inspiratory capacity plus the functional residual capacity; the volume of air contained in the lungs at the end of a maximal inspiration; also equals vital capacity plus residual volume” (from MediLexicon.com). Within the Results and Discussion section of their April 2012 Health Physics paper, Kramer et al. briefly noted that the lungs of their experimental subjects were “not fully inflated.” By definition and failure to obtain maximal inspiration, Kramer et. al. did not measure Total Lung Capacity (TLC). The TLC equation generated from this work will tend to underestimate TLC and does not improve or update total lung capacity data provided by ICRP and others. Likewise, the five linear measurements performed by Kramer et. al. are only representative of the conditions of the measurement (i.e., not at-rest volume, but not fully inflated either). While there was significant work performed and the data are interesting, the data does not represent a maximal situation, a minimal situation, or an at-rest situation. Moreover, while interesting, the linear data generated by this study is limited by the conditions of the experiment and may not be fully comparative with other lung or inspiratory parameters, measures, or physical dimensions.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

High thermodynamic stability of parametrically designed helical bundles

Here we describe a procedure for designing proteins with backbones produced by varying the parameters in the Crick coiled coil–generating equations. Combinatorial design calculations identify low-energy sequences for alternative helix supercoil arrangements, and the helices in the lowest-energy arrangements are connected by loop building. We design an antiparallel monomeric untwisted three-helix bundle with 80-residue helices, an antiparallel monomeric right-handed four-helix bundle, and a pentameric parallel left-handed five-helix bundle. The designed proteins are extremely stable (extrapolated ΔG fold > 60 kilocalories per mole), and their crystal structures are close to those of the design models with nearly identical core packing between the helices. The approach enables the custom design of hyperstable proteins with fine-tuned geometries for a wide range of applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Towards Exascale Astrophysics of Mergers and Supernovae (TEAMS)

The major goals of the TEAMS project are (i) to improve the modeling of many of the suggested astrophysical sites of the r‐process, as well as some potential p‐process sites, (ii) to use our models to support and guide the experimental efforts at FRIB and similar facilities, and (iii) to use our tools to cement our understanding of the roles that massive stars play in galactic chemical evolution. As part of the TEAMS project, Mezzacappa (UTK, Reddy (UW), Surman (ND), and Steiner (UTK) are (i) generating equations of state and neutrino opacities for simulations of core‐collapse supernovae and neutron star mergers which are more faithful to current understanding of the nucleon‐nucleon interaction, (ii) integrating those new equations of state and neutrino opacities into new simulation codes being developed, (iii) performing detailed nuclear reaction network post‐processing to determine abundances from simulations and (iv) quantifying the impact of nuclear physics uncertainties on r‐process abundances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1973

Backlund transformation for solutions of the Korteweg-de Vries equation

We present a Backlund transformation operating on solutions of the Korteweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.

Wahlquist, H. D.↗
NASA NTRS1977

Mask analysis program

Program uses minimal core and time resources and performs following analysis functions: artwork verification, device identification, nodal analysis, capacitance calculation, and logic equation generation. For data base simplicity, program processing operates on mask data which has been coverted from its original form to orthogonal rectangles.

Martin, M.↗
NASA NTRS1976

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Putney, B. H.↗
NASA NTRS1975

Use of multiple-stage remote sensing techniques to develop forest stocking equations

Portions of a forest supporting density levels that affect natural resource yields must be quantified to estimate the operational feasibility of a proposed management system. Estimates of average parameters do not necessarily provide complete knowledge, particularly with frequently skewed forest parameters. Instead, another statistic, the portion of a forest supporting minimum density levels would be useful to set realistic limits to the implementation of management systems and to establish priorities for operational programs. Such a statistic can be obtained from solutions of forest stocking equations generated by applications of multiple-stage remote sensing techniques.

Bisson, H. R.↗
NASA NTRS1981

CADAT integrated circuit mask analysis

CADAT System Mask Analysis Program (MAPS2) is automated software tool for analyzing integrated-circuit mask design. Included in MAPS2 functions are artwork verification, device identification, nodal analysis, capacitance calculation, and logic equation generation.

Source record↗
NASA NTRS1980

Grid generation for general three-dimensional configurations

A suitable grid system for complex three dimensional configurations such as wing/body/nacelle shape for the solution of nonlinear transonic flow problems was constructed. Two approaches were explored based on Thompson's body fitted coordinate concept. The most general approach was to divide the computational domain into multiple rectangular blocks where the configuration itself was also represented by a set of blocks whose structure follows the natural lines of the configuration. The block structured grid system was adaptable to complex configurations and gives good grid quality near physical corners. However, it introduced algorithm issues for the flow solution concerning the treatment of nonanalytic grid block boundaries and nonstandard grid cells. These issues were explored in relation to the grid generation. A more limited approach treats a wing/body configuration with only a single rectangular block in computational space. The issues involving nonstandard cells were avoided, but other limitations on grid resolution appear. Both a linear and a nonlinear system of grid generation equations were developed including methods of grid control.

Lee, K. D.↗
NASA NTRS1980

Numerical generation of two-dimensional orthogonal curvilinear coordinates in an Euclidean space

A noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves was developed. The basic generating equation is the Gaussian equation for an Euclidean space which is solved analytically. The method is applied in many cases and these test results demonstrate that the proposed method can be readily applied to a wide variety of problems. The method can also be used for simply connected regions only by obtaining the solution of the linear equation under the changed boundary conditions.

Warsi, Z. U. A.↗
NASA NTRS1982

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Sorenson, R. L.↗