Search NASA⌕ Search

SEARCH · Search NASA

Results for “Reference Model”

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 577 records · Page 32

Convergence of Cloud Droplet Spectral Relative Dispersion During Entrainment‐Mixing Based on Particle‐Resolved Direct Numerical Simulations

Entrainment-mixing processes critically impact cloud microphysical properties, but their effects on the relative dispersion (d) of cloud droplet size distributions (CDSDs) remain elusive. A direct numerical simulation model is initialized with different CDSDs to fill the gap. These results show that d decreases for broad CDSDs and increases for narrow ones, ultimately converging to approximately 0.5 regardless of initial CDSDs during the evaporation-dominated mixing stage. The supersaturation fluctuation and the shape of CDSDs jointly influence the convergence behavior of d. Further sensitivity tests show that the initial microphysical/dynamical/thermodynamical conditions exert negligible effects on the final converged value of d but affect the convergence rate (k). The k generally increases with increasing droplet number concentration and dissipation rate, and increases with decreasing liquid water content, relative humidity of entrained air, and mixing fraction of cloudy air. A conceptual model with two timescales is proposed; k and the timescales are negatively correlated, meaning that slow mixing and/or evaporation process results in slow convergence of d. In conclusion, this finding provides an important reference for improving understanding and parameterization of d during the entrainment-mixing processes.

54 ENVIRONMENTAL SCIENCES↗

The AI-Base NDA Catalog

The project objective was to create a catalog of NDA capabilities so that as future challenges emerge, potential solutions can be quickly identified. The initial direction was to create a custom database where we would manually add various NDA technologies. During the year, LANL leadership heavily embraced AI tools and established LANL’s Enterprise ChatGPT license. To align with this vision, instead of a database we created a custom GPT to achieve the same capability. We provided a series of references on NDA technologies, the most comprehensive of which is the 2024 “PANDA manual” which is a 700-page textbook. A custom GPT is a semi-isolated version of OpenAI’s GPT model that can be tailored to specific tasks with context documents and instructions. Anyone with a LANL ChatGPT Enterprise account can access the NDA Catalog. Since the GPT exists on the green network, only non-sensitive questions may be asked. The Catalog can be used by simply asking questions in conversational English. We have found the Catalog to be quite accurate, even for heavily technical, complex queries. The Catalog allows the user to describe a measurement problem and it will respond with potential technology solutions.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Development of Automated Atom Probe Tomography capability to study the influence of applied voltage and laser power on the final apparent composition of the analyzed specimen

This study presents the development and implementation of an autonomous Bayesian optimization (BO) framework for controlling and optimizing experimental parameters in Atom Probe Tomography (APT). Using commercial silicon needle samples as a benchmark system, we demonstrate that BO can efficiently navigate the complex parameter space of voltage and laser power to achieve target charge state ratios (specifically Si + /(Si + +Si 2+ )) with minimal experimental evaluations. Our implementation integrates Gaussian Process modeling with the CAMECA atom probe control framework, enabling autonomous adjustment of experimental conditions in real-time. Results show that the algorithm successfully converges to target ratios under different scenarios: maintaining a reference ratio, increasing the ratio (favoring Si 1+ ), and decreasing the ratio (favoring Si 2+ ). The system adapts to specimen evolution during analysis, compensating for changes in apex geometry while maintaining optimization targets. This work establishes a proof of concept for AI-driven optimization in APT, addressing the traditional challenges of manual parameter tuning and paving the way for applications to more complex materials where compositional accuracy is critical.

36 MATERIALS SCIENCE↗

Ground-Truthing: Exploratory Borehole Characterization and Modeling to Verify and Expand Techno-Economic Evaluation of Earth Source Heat at Cornell U

This report documents the successful completion of DOE award DE-EE0009255: Ground- Truthing: Exploratory Borehole Characterization and Modeling to Verify and Expand Techno- Economic Evaluation of Earth Source Heat at Cornell University . Cornell University is evaluating the technical and economic feasibility of using deep direct-use (DDU) geothermal energy, referred to locally as Earth Source Heat (ESH), to serve as a renewable energy source for campus heating. To meet this objective, Cornell drilled an approximately 3-kilometer-deep exploratory borehole: the Cornell University Borehole Observatory (CUBO), or ESH-1. The team conducted an extensive suite of geophysical, hydrologic, thermal, mechanical, and geochemical measurements to evaluate subsurface conditions and geothermal development potential. This report summarizes the well drilling and testing tasks, findings, and conclusions.

15 GEOTHERMAL ENERGY↗

PIE-Enabled Study of Aqueous Corrosion & Zr Hydriding in Cr-Coated Cladding: M3GV-23PN0101132

Chromium-coated zirconium alloy cladding is under investigation as an accident-tolerant fuel (ATF) concept to extend performance to higher burnups via improved oxidation resistance and reduced hydrogen pickup. However, hydrothermal corrosion behavior and hydrogen transport mechanisms governing in-service hydriding of these coatings remain poorly understood. In a collaborative study between Pacific Northwest National Laboratory (PNNL), Idaho National Laboratory (INL), and the University of Huddersfield, cold spray (CS) and physical vapor deposition (PVD) Cr-coated Optimized ZIRLO™ cladding samples were characterized after exposure to PWR-simulated water chemistry under both in-core (neutron irradiation) and out-of-core (aqueous-only) conditions at the MIT Research Reactor. Multi-scale characterization was performed independently at PNNL and INL to evaluate coating integrity, microstructural evolution, Cr/Zr interface chemistry, and hydride formation. Both laboratories observed a consistent divergence in hydriding behavior: out-of-core CS Cr-coated cladding exhibited elevated hydride concentrations exceeding those of uncoated cladding, whereas in-core CS samples showed substantially suppressed hydriding. In-core specimens also displayed irradiation-specific features, including nanoscale voids within the Cr coating and radiation-induced segregation clusters in the Zr substrate. CS coatings retained an interdiffusion-free Cr/Zr bond with no intermetallic layer, whereas PVD coatings exhibited inferior quality with visible cracks and pores. An automated image-based hydride quantification method systematically overestimated bulk hydrogen content relative to inert gas fusion measurements, underscoring the need for standardized sample preparation and reference standards. Interpretation of hydride nucleation and growth is complicated by the open inner-diameter of the specimens, which provides additional hydrogen pathways. The results motivate further foundational studies to support predictive models of hydrothermal corrosion and hydrogen transport in unirradiated and irradiated Cr-coated cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DESI Emission-line Galaxies: Unveiling the Diversity of [O II ] Profiles and Its Links to Star Formation and Morphology

We study the [O II ] profiles of emission-line galaxies (ELGs) from the Early Data Release of the Dark Energy Spectroscopic Instrument (DESI). To this end, we decompose and classify the shape of [O II ] profiles with the first two eigenspectra derived from principal component analysis. Our results show that DESI ELGs have diverse line profiles, which can be categorized into three main types: (1) narrow lines with a median width of ∼50 km s −1 , (2) broad lines with a median width of ∼80 km s −1 , and (3) two redshift systems with a median velocity separation of ∼150 km s −1 , i.e., double-peak galaxies. To investigate the connections between the line profiles and galaxy properties, we utilize the information from the COSMOS data set and compare the properties of ELGs, including star formation rate (SFR) and galaxy morphology, with the average properties of reference star-forming galaxies with similar stellar mass, sizes, and redshifts. Our findings show that, on average, DESI ELGs have a higher SFR and more asymmetrical/disturbed morphology than the reference galaxies. Moreover, we uncover a relationship between the line profiles, the excess SFR, and the excess asymmetry parameter, showing that DESI ELGs with broader [O II ] line profiles have more disturbed morphology and higher SFR than the reference star-forming galaxies. Finally, we discuss possible physical mechanisms giving rise to the observed relationship and the implications of our findings on the galaxy clustering measurements, including the halo occupation distribution modeling of DESI ELGs and the observed excess velocity dispersion of the satellite ELGs.

79 ASTRONOMY AND ASTROPHYSICS↗

CONUS-wide Projected Flood Frequency and Uncertainty Estimates, Version 1.0

This dataset presents a large-ensemble of CONUS-wide projected flood frequency and uncertainty estimates across ~2.7 million NHDPlusV2 river reaches over the CONUS. The framework producing this dataset leverages a multi-model, uncertainty-aware modeling framework that allows evaluating shifts in flood frequences at the stream reach level across the CONUS. CONUS-wide ensemble streamflow projections generated from hydrologic simulations driven by downscaled and bias-corrected Coupled Model Intercomparison Project Phase 6 (CMIP6) outputs are used to derive these flood frequency and uncertainty estimates over the period 1980 - 2099. A spatially consistent regional L-moment algorithm is applied across clusters defined by the US Hydrologic Unit Code Subregions (HUC4s and HUC8s) and NHDPlusV2 stream orders to estimate flood frequencies. The dataset also includes at-site based flood estimates that allow for the comparison between local and regional approach-based estimates, assess projected changes, and characterize their uncertainties. For more reliable estimation of rare flood frequencies such as 500 and 1000-year return periods, super-ensemble based estimates are also included in the dataset. This dataset is derived to support the "Impact-Informed Dam Safety Risk Assessment for Securing Hydropower Assests" project for the US Department of Energy (DOE) Hydropower and Hydrokinetic Office (H2O). For further details, refer to Kao et al. (2022), Ghimire et al. (2023), Ghimire et al. (2025), and Hosking and Wallis (1997).

Ghimire, Ganesh [ORNL] (ORCID:0000000242843941)↗

Historical and Future Windstorms in the Northeastern United States

Large-scale windstorms represent an important atmospheric hazard in the Northeastern US (NE) and are associated with substantial socioeconomic losses. Regional simulations performed with the Weather Research and Forecasting (WRF) model using lateral boundary conditions from three Earth System Models (ESMs: Geophysical Fluid Dynamics Laboratory (GFDL), Hadley Centre Global Environment Model (HadGEM) and Max Planck Institute (MPI)) are used to quantify possible future changes in windstorm characteristics and/or changes in the parent cyclone types responsible for windstorms. WRF nested within MPI ESM best represents important aspects of historical windstorms and the cyclone types responsible for generating windstorms compared with a reference simulation performed with the ERA-Interim reanalysis for the historical climate. The spatial scale and frequency of the largest windstorms in each simulation defined using the greatest extent of exceedance of local 99.9th percentile wind speeds (U > U999) plus 50-year return period wind speeds (U50,RP) do not exhibit secular trends. Projections of extreme wind speeds and windstorm intensity/frequency/geolocation and dominant parent cyclone type associated with windstorms vary markedly across the simulations. Only the MPI nested simulations indicate statistically significant differences in windstorm spatial scale, frequency and intensity over the NE in the future and historical periods. This model chain, which also exhibits the highest fidelity in the historical climate, yields evidence of future increases in 99.9th percentile 10 m height wind speeds, the frequency of simultaneous U > U999 over a substantial fraction (5–25%) of the NE and the frequency of maximum wind speeds above 22.5 ms−1. These geophysical changes, coupled with a projected doubling of population, leads to a projected tripling of a socioeconomic loss index, and hence risk to human systems, from future windstorms.

Pryor, Sara C. (ORCID:0000000348473440)↗

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Development of real-time density feedback control on MAST-U in L-mode

In this paper we report on the development and demonstration of density feedback control for MAST-U. Sinusoidal perturbations are used to measure the frequency response from a deuterium gas valve (actuator) to line-integrated core electron density measured by the interferometer (sensor). In the frequency range relevant for control design, only two system-identification experiments were needed to regress a first-order dynamic model. This control-oriented model informs the offline design of a proportional integral controller with the established loop-shaping controller design method. After offline verification of the controller implementation, control is demonstrated by experimentally tracking a staircase reference for the line-integrated electron density. This paper demonstrates the efficiency of controller design using system-identification and loop-shaping, providing reliable density control for MAST-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical implementation of the MOOSE subchannel module (SCM) algorithm

The subchannel module of moose (SCM), previously referred to as Pronghorn-SC, is a subchannel code designed to resolve single-phase flow fields and calculate the relevant flow variables, in nuclear reactor fuel-pin assemblies. The assemblies it models are: water-cooled, with bare fuel-pins in a square ducted, quadrilateral lattice and liquid-metal/water-cooled, with bare/wire-wrapped fuel pins in a hexagonal ducted, triangular lattice. Previous publications have presented the development, validation and verification of SCM. This work presents an comparative overview of the different solvers implemented within SCM. This includes the solver algorithm description, and a performance comparison. The two test cases chosen to demonstrate the solver performance were taken from the PSBT enthalpy mixing benchmark and the ORNL-19 pin benchmark.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Direct measurement of reduced exchange stiffness and its impact on magnetic vortex behavior in PyGd alloys

Thin films composed of sputtered transition metal/rare earth (TM/RE) ferrimagnets have emerged as promising building blocks for future spintronic devices, offering tunable magnetic properties critical for data storage, memory, and logic applications. However, understanding how the combination of TM and RE elements influences effective magnetic properties, such as exchange stiffness (Aex), remains challenging. Magnetic vortices provide a versatile tool for probing these properties in thin film systems. By combining magnetic imaging via soft x-ray microscopy and micromagnetic modeling, we quantify the effective exchange stiffness in PyGd ferrimagnetic disks with varying Gd concentrations. Our results indicate a reduction in Aex to below 3 pJ/m for a 20% Gd concentration when compared to reference Py, and values below 2 pJ/m for 30% Gd, reflecting weak Ni–Gd exchange coupling. These findings highlight the critical role of rare earth content in tuning the exchange stiffness. The reduced exchange stiffness facilitates a linear field response of the magnetization up to the edge of the disk, as well as significant deformations in the vortex core itself when compared to films with larger Aex. Our results are in line with, albeit lower than, recent measurements of the exchange stiffness in intermixed PyGd. This reduced exchange stiffness has implications for the development of spintronic devices based on ferrimagnetic skyrmions.

Jacob, Liyan↗

Accessible, uniform protein property prediction with a scikit-learn based toolset AIDE

Summary Protein property prediction via machine learning with and without labeled data is becoming increasingly powerful, yet methods are disparate and capabilities vary widely over applications. The software presented here, “Artificial Intelligence Driven protein Estimation (AIDE)”, enables instantiating, optimizing, and testing many zero-shot and supervised property prediction methods for variants and variable length homologs in a single, reproducible notebook or script by defining a modular, standardized application programming interface (API), i.e. drop-in compatible with scikit-learn transformers and pipelines. Availability and implementation AIDE is an installable, importable python package inheriting from scikit-learn classes and API and is installable on Windows, Mac, and Linux. Many of the wrapped models internal to AIDE will be effectively inaccessible without a GPU, and some assume CUDA. The newest stable, tested version can be found at https://github.com/beckham-lab/aide_predict and a full user guide and API reference can be found at https://beckham-lab.github.io/aide_predict/. Static versions of both at the time of writing can be found on Zenodo.

36 MATERIALS SCIENCE↗

Deep Cyber-Physical Situational Awareness for Energy Systems: A Secure Foundation for Next-Generation Energy Management

This document provides the final report for the CYPRES project. The purpose is (1) to highlight and summarize its major accomplishments and (2) to provide guidance on how its outcomes have informed and can inform important additional research and technology transfer. The goal of CYPRES was the research, development, and demonstration of a security-oriented next generation cyber-physical EMS for electric power systems that detects malicious and abnormal events through the fusion of cyber and physical data. To achieve this, the CYPRES project team researched, developed, and built a prototype of the solution, referred to as the CYPRES EMS. The CYPRES EMS is a proof-of-concept cyber-physical platform that demonstrates the management of the energy system, communications, security, and cyber-physical grid modeling and analytics. As part of the capabilities of the CYPRES EMS, the team designed and developed a suite of power system applications for monitoring, risk analyses, detection, and control that are inherently cyberaware. At its core, the project aimed to research, develop, and demonstrate a security-oriented next-generation cyber-physical Energy Management System (EMS) capable of detecting malicious and abnormal events through the innovative fusion of cyber and physical data. This approach represents a fundamental shift from traditional EMS, reimagining how critical infrastructure can be protected through unified cyber-aware and physics-aware secure data flow pipelines. The project’s cornerstone deliverable, the CYPRES EMS, serves as a proof-of-concept cyber-physical platform that revolutionizes the management of energy systems, communications, security, and cyber-physical grid modeling and analytics. This prototype implements a comprehensive suite of power system applications for monitoring, risk analyses, detection, and control, all designed with inherent cyber awareness. The system’s architecture extends from end-devices in the field through to control center applications, establishing a secure and resilient control framework that addresses the challenges posed by diverse devices of unknown trustworthiness connecting to modern power systems. Through this innovative approach to deep cyber-physical situational awareness, the CYPRES project not only advances the state-of-the-art in energy infrastructure protection but also establishes a new paradigm for how EMS can be designed, deployed, and operated in an increasingly complex threat landscape. The findings and developments from this project provide crucial insights for stakeholders across the energy sector, offering a blueprint for enhancing the reliability and resilience of our nation’s critical energy infrastructure in the face of evolving cyber threats.

24 POWER TRANSMISSION AND DISTRIBUTION↗

IRMA

IRMA (In)elastic Representation of Materials As S(α,β) evaluations IRMA turns one phonon model into three outputs that usually require three separate tool chains: an evaluated nuclear-data file, predicted neutron-scattering spectra, and scattering kernels for Monte Carlo transport. The three outputs draw on a single, consistent description of the material, so the evaluation, the spectroscopy that can validate it, and the transport that uses it always agree about the physics. Nuclear data. IRMA writes ENDF-6 File 7 thermal scattering evaluations on automatically constructed (α, β) grids. This part reimplements and generalizes NJOY's LEAPR: the classic kernels reproduce freshly generated NJOY2016 tapes digit for digit and published reference tapes to about 1e-4, and the generalized paths add the exact coherent one-phonon term, anisotropic Debye-Waller tensors, coherent elastic for arbitrary crystals, and a per-species partition for polyatomic materials. The tapes feed NJOY, AMPX, FUDGE, and every transport code downstream of them. Neutron spectroscopy. The irma.spectra forward model projects the same physics onto an instrument's kinematics and resolution: INS spectra for VISION and generic indirect geometries, and 2-D S(Q,E) powder maps for direct-geometry spectrometers, from a phonopy model or straight from a phonon DOS. It can be used to predict a proposed measurement before beam time; in analysis, it supplies the calculated single-scattering counterpart of a measured spectrum, from the same material description the evaluation was built from. Monte Carlo transport. The irma.ncrystal exporter writes per-temperature scattering kernels for the companion NCrystal plugin, so McStas, OpenMC, and other NCrystal-aware codes sample the same physics. The exported kernels carry the per-site anisotropic Debye-Waller tensors, keeping directional coherent-elastic physics that NCrystal's standard scalar treatment does not represent. With the same physics inside a transport code, an entire beamline becomes a virtual experiment: IRMA's end-to-end validation ran a custom McStas implementation of the ARCS spectrometer, assembled from the existing McVine and McStas models, against measured data. From a bare crystal structure. The irma mlip front end builds the phonon model itself: a structure file and a choice of potential are enough. Nine pretrained machine-learned interatomic potentials are supported, on a laptop CPU, with no first-principles calculation; an approximate phonon model for a new material costs minutes, not a DFT campaign, and the build emits prefilled inputs for all three outputs. The result is a good starting point rather than a finished evaluation: survey-quality physics with every parameter exposed for review. A converged atomistic calculation enters the same way, as a phonopy model, when higher fidelity is needed.

Ramic, Kemal [Oak Ridge National Laboratory (ORNL)↗

Sierra/SD – Theory Manual – 5.22

Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD, we refer the reader to User’s Manual. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer_notes manual, the user’s notes and of course the material in the open literature.

97 MATHEMATICS AND COMPUTING↗

Thermal Integration of Advanced Nuclear Reactors with a Reference Refinery, Methanol Synthesis, and a Wood Pulp Plant (Rev.1)

The present report is intended to provide process flow diagrams (PFDs) and energy and mass balance data sheets for a U.S. industrial sector subset with which nuclear heat and power could be integrated—a subset that includes the oil refining, methanol and pulp and paper industries. Coupling options for integrating nuclear energy into these industries are quantitatively outlined for reference systems, and future work will extend this analysis in greater detail. Opportunities for integrating small modular nuclear reactors (SMNRs) were investigated for each of the industrial process configurations. Aspen HYSYS and Cycle-Tempo models for a high-temperature gas-cooled reactor were developed to evaluate the proposed integration. This introductory evaluation provides a general description and assessment of the operating principles, reactor coolant core outlet temperature, and reactor size to be integrated with industry. The industrial processes of oil refining and the production of methanol, pulp and paper were simulated by using Aspen HYSYS, Aspen Plus, and the PRELIM (Petroleum Refinery Life Cycle Inventory Model) tool to develop process details. Cycle-Tempo models then extend the process modeling results to obtain net energy demands (e.g., heat, steam, and electricity) when accounting for process steam and waste heat recovery. This information is intended to foster the analysis of integrating an SMNR to decarbonize industrial facilities. The SMNR would provide reliable, competitive, and sustainable clean energy while reducing carbon emissions and other environmental impacts, such as water withdrawals, consumption, and contamination. The refining industry, exhibited in Figure ES1, is a leading consumer of fossil -fuel-based heat, power, and hydrogen in the U.S. industrial sector, generating over 164 million metric tons (MMT) of CO 2 emissions in 2023. The overall mass and energy pertaining to a generalized complex refinery in the United States is reflected in Figure ES1, along with energy metrics regarding integration with a nuclear power plant (NPP). Data sheets were developed to indicate the energy requirements for the overall refinery and each refinery process. The data sheet for the overall refinery is shown in Table ES2.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sierra/SD – Theory Manual (V.5.24)

Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD, we refer the reader to User’s Manual. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer_notes manual, the user’s notes and of course the material in the open literature.

42 ENGINEERING↗