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At least 163 records · Page 9

Sierra/SD - Theory Manual - 4.56

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 Sierra/SD, User's Notes. 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↗

Post-Closure Inspection Report for the Tonopah Test Range and Nevada Test and Training Range, Nevada for Calendar Year 2020 (Rev. 0)

This report provides the results of the annual post-closure use restriction (UR) inspections at corrective action sites (CASs) located on the Tonopah Test Range (TTR) and Nevada Test and Training Range (NTTR). This report covers post-closure UR inspections for calendar year 2020, and includes visual inspections and repair activities completed at the following corrective action units (CAUs): • CAU 407, Roller Coaster RadSafe Area (TTR) • CAU 424, Area 3 Landfill Complexes (TTR) • CAU 453, Area 9 UXO Landfill (TTR) • CAU 487, Thunderwell Site (TTR). Note: CAU 400, Bomblet Pit and Five Points Landfill (TTR) (CASs TA-19-001-05PT, Ordnance Disposal Pit; and TA-55-00-TAB2, Ordnance Disposal Pit) no longer requires inspection and reporting, as described in the Post-Closure Inspection Report for the Tonopah Test Range and Nevada Test and Training Range, Nevada for Calendar Year 2019. Site figures are included in Appendix A. The Post-Closure Inspection Plans and Record of Technical Change modifying the requirements for each UR are included in Appendix B. The Post-Closure Inspection Checklists are included in Appendix C. Field Notes are included in Appendix D. Appendix E, Inspection Photographs, does not include photographs because none were taken during the 2020 post-closure inspections. Appendix F, Post-Closure Vegetation Monitoring Report, does not include any data because vegetation monitoring was not conducted or required at any CAU in 2020. Visual inspections were conducted according to the post-closure requirements outlined in specific CAU and CAS URs, and approved by NDEP. The annual post-closure inspections for CASs associated with CAUs 407, 424, 453, and 487 were conducted on May 20, 2020. No maintenance or repair issues were noted at CAUs 487, or at CASs associated with CAU 424 (except CASs 03-08-002-A304 and 03-08-002-A308). Maintenance items and subsequent repairs include the following: • CAU 407, CAS TA-23-001-TARC (Roller Coaster RadSafe Area): A UR sign was loose and was rehung during the inspection. • CAU 424, CAS 03-08-002-A304 (Landfill Cell A3-4): The northeast monument needed a UR sign. The UR sign was attached to the monument on August 11, 2020. • CAU 424, CAS 03-08-002-A308 (Landfill Cell A3-8): The southeast monument needed additional lava rock. The lava rock was added during the inspection. • CAU 453, CAS 09-55-001-0952 (Area 9 Landfill): Two animal burrows were noted in the western portion of the northern and southern trenches (one burrow per trench). The animal burrows were repaired on August 11, 2020.

54 ENVIRONMENTAL SCIENCES↗

Double-differential Measurements of Mesonless Charged-current Muon Neutrino Interactions on Argon with Final-State Protons using the MicroBooNE Detector

This note reports the first double-differential measurements of charged-current $ν_µ$ scattering on argon leading to final states containing zero mesons and one or more protons. This event topology (hereafter abbreviated as CC0$πNp$) is the most common at the neutrino energies typically produced by the Fermilab Booster Neutrino Beam. A detailed understanding of neutrino-argon scattering in the CC0$πNp$ channel is therefore crucial for the success of the precision neutrino oscillation analyses planned for the Short-Baseline Neutrino (SBN) program. This remains true for the upcoming Deep Underground Neutrino Experiment (DUNE), but the higher mean neutrino energy used there will ensure that more inelastic reaction modes, such as single pion production, will also play a major role. The analysis described in this note builds on a previous MicroBooNE study of the CC0$πNp$ channel which obtained the first single-differential cross-section measurements on an argon target. Since that foundational work, significant improvements have been made to MicroBooNE’s simulation software, event reconstruction algorithms, and procedure for calculating systematic uncertainties. When combined with a larger dataset (corresponding to a beam exposure of 6.79 × 10 20 protons-on-target versus 1.60 × 10 20 in Ref. [3]), these enhancements allow the important CC0$πNp$ channel to be studied in more detail. This note begins with a description of the data and simulation samples used as input to the analysis. Section 3 then defines the CC0$πNp$ signal event topology, and Section 4 describes a set of selection criteria designed to identify these events in MicroBooNE data. Binning schemes are then defined in Section 5 for two double-differential measurements of event rates. The first of these considers the momentum and scattering cosine of the outgoing muon, while the second reports the same observables for the leading proton, i.e., the final-state proton with the largest momentum. After a discussion of systematic uncertainties in Section 6, the note concludes by comparing the predictions of MicroBooNE Monte Carlo (MC) simulations to the measured double-differential distributions. These results will form the basis for a future extraction of flux-averaged double-differential CC0$πNp$ cross sections that will be immediately comparable to the theoretical predictions of multiple neutrino event generators. The selection described herein may also be used to study various other observables in CC0$πNp$ events, including those which are sensitive to correlations between leptonic and hadronic kinematics in the final state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

HarDWR - Harmonized Water Rights Records

For a detailed description of the database of which this record is only one part, please see the HarDWR meta-record. Here we present a new dataset of western U.S. water rights records. This dataset provides consistent unique identifiers for each spatial unit of water management across the domain, unique identifiers for each water right record, and a consistent categorization scheme that puts each water right record into one of 7 broad use categories. These data were instrumental in conducting a study of the multi-sector dynamics of intersectoral water allocation changes through water markets (Grogan et al., in review). Specifically, the data were formatted for use as input to a process-based hydrologic model, WBM, with a water rights module (Grogan et al., in review). While this specific study motivated the development of the database presented here, U.S. west water management is a rich area of study (e.g., Anderson and Woosly, 2005; Tidwell, 2014; Null and Prudencio, 2016; Carney et al, 2021) so releasing this database publicly with documentation and usage notes will enable other researchers to do further work on water management in the U.S. west. The raw downloaded data for each state is described in Lisk et al. (in review), as well as here. The dataset is a series of various files organized by state sub-directories. The first two characters of each file name is the abbreviation for the state the in which the file contains data for. After the abbreviation is the text which describes the contents of the file. Here is each file type described in detail: XXFullHarmonizedRights.csv: A file of the combined groundwater and surface water records for each state. Essentially, this file is the merging of XXGroundwaterHarmonizedRights.csv and XXSurfaceWaterHarmonizedRights.csv by state. The column headers for each of this type of file are: state - The name of the state the data comes from. FIPS - The two-digit numeric state ID code. waterRightID - The unique identifying ID of the water right, the same identifier as its state uses. priorityDate - The priority date associated with the right. origWaterUse - The original stated water use(s) from the state. waterUse - The water use category under the unified use categories established here. source - Whether the right is for surface water or groundwater. basinNum - The alpha-numeric identifier of the WMA the record belongs to. CFS - The maximum flow of the allocation in cubic feet per second (ft3s-1). Arizona is unique among the states, as its surface and groundwater resources are managed with two different sets of boundaries. So, for Arizona, the basinNum column is missing and instead there are two columns: surBasinNum - The alpha-numeric identifier of the surface water WMA the record belongs to. grdBasinNum - The alpha-numeric identifier of the groundwater WMA the record belongs to. XXStatePOD.shp: A shapefile which identifies the location of the Points of Diversion for the state's water rights. It should be noted that not all water right records in XXFullHarmonizedRights.csv have coordinates, and therefore may be missing from this file. XXStatePOU.shp: A shapefile which contains the area(s) in which each water right is claimed to be used. Currently, only Idaho and Washington provided valid data to include within this file. XXGroundwaterHarmonizedRights.csv: A file which contains only harmonized groundwater rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. XXSurfaceWaterHarmonizedRights.csv: A file which contains only harmonized surface water rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. Additionally, one file, stateWMALabels.csv, is not stored within a sub-directory. While we have referred to the spatial boundaries that each state uses to manage its water resources as WMAs, this term is not shared across all states. This file lists the proper name for each boundary set, by state. For those whom may be interested in exploring our code more in depth, we are also making available an internal data file for convenience. The file is in .RData format and contains everything described above as well as some minor additional objects used within the code calculating the cumulative curves. For completeness, here is a detailed description of the various objects which can be found within the .RData file: states: A character vector containing the state names for those states in which data was collected for. More importantly, the index of the state name is also the index in which that state's data can be found in the various following list objects. For example, if California is the third index in this object, the data for California will also be in the third index for each accompanying list. rightsByState_ground: A list of data frames with the cleaned ground water rights collected from each state. This object holds the the data that is exported to created the xxGroundwaterHarmonizedRights.csv files. rightsByState_surface: A list of data frames with the cleaned surface water rights collected from each state. This object holds the the data that is exported to created the xxSurfaceWaterHarmonizedRights.csv files. fullRightsRecs: A list of the combined groundwater and surface water records for each state. This object holds the the data that is exported to created the xxFullHarmonizedRights.csv files. projProj: The spatial projection used for map creation in the beginning of the project. Specifically, the World Geodetic System (WGS84) as a coordinate reference system (CRS) string in PROJ.4 format. wmaStateLabel: The name and/or abbreviation for what each state legally calls their WMAs. h2oUseByState: A list of spatial polygon data frames which contain the area(s) in which each water right is claimed to be used. It should be noted that not all water right records have a listed area(s) of use in this object. Currently, only Idaho and Washington provided valid data to be included in this object. h2oDivByState: A list of spatial points data frames which identifies the location of the Point of Diversion for the state's water rights. It should be noted that not all water right records have a listed Point of Diversion in this object. spatialWMAByState: A list of spatial polygon data frames which contain the spatial WMA boundaries for each state. The only data contained within the table are identifiers for each polygon. It is worth reiterating that Arizona is the only state in which the surface and groundwater WMA boundaries are not the same. wmaIDByState: A list which contains the unique ID values of the WMAs for each state. plottingDim: A character vector used to inform mapping functions for internal map making. Each state is classified as either "tall" or "wide", to maximize space on a typical 8x11 page. The code related to the creation of this dataset can be viewed within HarDWR GitHub Repository/dataHarmonization.

Economics↗

Interdisciplinary Approaches Improve Understanding of Cryptogenic Species: A Historical Case Study of Crayfish in Montana, USA

ABSTRACT Cryptogenic species are those that are not yet “demonstrably native or introduced” in a given area, such as crayfish in western Montana, USA. Delving into evidence from diverse fields can help clarify the status of cryptogenic species. Primary historical sources and indigenous knowledge have informed various ecological questions but are seldom used to clarify the status of cryptogenic species, especially aquatic taxa. We summarize types of evidence used to illuminate species status and offer a case study applying historical sources to cryptogenic crayfish in Montana. We searched for crayfish mentions in dictionaries of indigenous languages and primary historical documents (e.g., travel journals, newspaper accounts, early biological surveys). Early explorer accounts we examined did not mention crayfish in Montana, though they noted them in the nearby Snake River drainage of Idaho and Wyoming. The first mention of crayfish in Montana that we found was from an 1868 newspaper account, probably referencing the upper Missouri River. The species was not noted, but an 1887 article suggested signal crayfish Pacifastacus leniusculus introductions near Bozeman, where non‐native signal crayfish still persist. The earliest crayfish mention we found west of the Great Divide in Montana was from 1934 in Ninepipes and probably referred to non‐native virile crayfish ( Faxonius virilis ). Signal crayfish were not mentioned west of the Divide until a 1944 newspaper account noted their 1937 introduction to the Bitterroot River drainage. The case study demonstrates the value of historical sources in identifying the absence of species and documenting their presence or introduction during periods predating scientific data.

Kennedy, Hampton L. [USDA Forest Service, Southern↗

System efficiency of packed bed TES with radial flow vs. axial flow – Influence of aspect ratio

Here, this paper compares the net system efficiency, including thermal efficiency and pressure drop effects, of radial versus axial flow packed beds for thermal energy storage. The traditional packed bed system is a cylindrical geometry where fluid flows axially from one end to another. However, issues of thermal stratification and high-pressure drop have led to recent studies on radial flow systems. One potential benefit is the reduced pressure drop in a radial flow system. This paper compares the performance of radial flow and axial flow systems at a range of aspect ratios (AR = H/D bed ) from 0.21 to 1.92 using a numerical model where the storage volume is held constant in all cases. When the radial flow bed is at a low aspect ratio (short/wide), the thermal front is improved but the pressure drop is high. At a high aspect ratio, the velocity is reduced in radial flow, leading to decreased pressure drop but an increased spreads in the thermal front that lowers thermal efficiency. The opposite trends are noted in axial flow. Thermal efficiencies of 83–91 % were noted for radial flow, while they ranged from 85 to 94 % in axial flow. Net efficiencies including pressure drop ranged from 74 to 82 % for radial flow and 80–87 % for axial flow. In both systems, a peak net efficiency was noted between the highest and lowest aspect ratio. While some aspect ratios with radial flow outperform axial flow from a net efficiency perspective, the results show that the highest net efficiency from axial flow is higher than that from radial flow. Overall, this paper highlights the importance of innovative TES designs and their potential to improve energy efficiency.

25 ENERGY STORAGE↗

Dissolution and reprecipitation of amorphous silica in silica Rich shales induces Non-Monotonic evolution of porosity in acidic reactive environments

Advances in sustainable subsurface energy technologies are crucial for meeting our energy and resource needs for a climate-resilient future. Novel strategies to harness subsurface shale reservoirs for recovering valuable metals and for enabling CO 2 storage are influenced by the morphological and mineralogical heterogeneities of these materials. In this context, delineating the interactions of highly acidic solutions such as wet supercritical CO 2 on shales with varying mineralogy is crucial to inform the stability of caprock seal for CO 2 storage and enhancements in permeability for fluid transport, reactivity, and storage. The feedback chemical effects associated with the interactions of acidic solutions on the morphologies and mineralogies of shales have not been extensively investigated. These insights are crucial for assessing temporal changes in the reactivity and the fate of the fluids in subsurface environments. In this study, we investigate the effect of 1M HCl solution on the chemistry and morphology of three different shale samples with varying carbonate, clay and silica contents. An increase in the amorphous content, from 37% to 41.3%, of silica-rich and carbonate/clay lean shale is noted due to reactions with an acidic solution which is attributed to the dissolution of Si-bearing phases such as clays, accompanied by SiO 2 precipitation. In shales bearing high content of clays and carbonates, significant increase in the pore volumes and surface areas are noted. Non-monotonic changes in the micron-scale porosity of silica rich–carbonate/clay lean (e.g., Mowry shale) are noted using in-situ X-ray microtomography experiments. Due to the initial mobilization of silica and dissolution of carbonate/clay phases, the total porosity slightly increases from 6.7% to 10.7% followed by a decrease to similar to 4% caused by SiO 2 reprecipitation. In conclusion, these findings suggest that even though silica is less reactive in acidic environments, the changes in the amorphous and crystalline content due to dissolution and reprecipitation alter the porosity and fluid flow paths.

04 OIL SHALES AND TAR SANDS↗

Structure and Shape of Surface-Mediated Assembly of Surfactants

Achieving controls on the self-assembly of cationic and block copolymer micelles has significant implications for advancing novel material systems for energy, environmental, and biological applications and for tuning fluid flow behavior in subsurface geologic environments. While it is known that the aggregation of micelles is influenced by the composition of the surrounding fluid, the influence of a solid interface has been less explored. In this study, we probe the organization of cetyltrimethylammonium bromide (CTAB) micelles in the absence and presence of the Pluronic P123 block copolymer and quartz substrate using transmission and grazing-incidence small-angle X-ray scattering measurements and classical molecular dynamics (MD) simulations. In the absence of the quartz interface, CTAB with and without P123 molecules assemble as ellipsoid core–shell micelles. Densification of the core on adding P123 is noted from the decrease in the core radius from 15.9 to 14.6 Å. Here, the presence of a quartz substrate causes the micelles to elongate, which is noted by the emergence of a power-law slope in the low q region (<0.02 Å –1 ). Moreover, in the presence of both P123 and the quartz substrate, the micelle shape changes from ellipsoid core–shell to cylindrical core–shell, and a significantly higher number of aggregates are formed. The higher number of aggregates, and faster aggregation kinetics are linked to the organization of the solvent structures as noted from the MD simulations. These findings demonstrate the effects of adding a block copolymer and including a quartz substrate on the self-assembly of cationic (CTAB) micelles, which can be used to inform the design of functional material systems that harness surfactant chemistries.

42 ENGINEERING↗

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗

CTT: Tools for Fine Alignment of Flash X-ray Systems

The CTT code is a compilation of the python code that was prototyped in the interest of making a method for fine alignment of Flash X-ray Systems at the lab. It contains python code for interacting with LTT and running optimization loops using LTT simulations or ray tracing with RaySpace. It Includes classes for creating phantom objects and modular geometry objects in the simulations. It allows one to generate a random phantom that has been optimized to stay with a certain cubic volume and maximize the minimum distance between any two ball phantom centers in all projections. It was primarily made to work on ball phantoms which were simulated as Teflon spheres. It allows the alignment from some nominal position to some displaced position to simulate recovery of a real geometry from the nominal geometry of the system. Fine alignment can be done with the projections in LTT while a rough alignment is faster using rayspace. If rayspace works well for the use case it should be preferred since it is considerably faster and less resource intensive in general. Some Notes about using this code is that one will have to edit the imports for the files to get to the correct LTT path, LTT GUI path and to the CTT path when importing. This was made by using anaconda with python 3 on windows 10. The LTT code was stored in a anaconda environment which seemed to help the python find the LTT although it shouldn’t be necessary if you append the path in your code using sys.path.append(r'add the path you want here’). The sys.path.append method is a quick way to give your python code access to a given folder when running it (such as LTT or CTT). Note that since the code was originally made with paths for a specific machine that a new user will have to edit those paths to make it work in all the files that use the old paths. This is somewhat tedious but will be required to run the code on a new machine. The methodology used to run and make these notebooks starts with opening a command prompt as administrator in windows 10. After this one would activate the anaconda environment in the appropriate directory using “conda activate myenv” in the command prompt. After this open a jupyter-notebook using the keyword “jupyter-notebook". After that a notebook should open in a browser. Note that some libraries used may not come with anaconda so those may have to be installed. There shouldn’t be much though since the main things used are scipy, numpy, matplotlib, and LTT. LTTQuicksetup also requires some paths that will be specific to the computer so that should be changed as well.

42 ENGINEERING↗

Sierra/SD - Theory Manual 4.58

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↗

Sierra/SD - Theory Manual

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↗

Wear in particle based CSP systems from particle abrasion and attrition at high temperature

High temperature particle-based receivers offer distinct advantages over conventional molten salt receivers due to their ability to achieve temperatures above 700 ºC, direct absorption of solar energy as they fall through a beam of concentrated sunlight, and the relative ease of storage (and retrieval using a secondary working fluid) in insulated storage tanks. The use of particles, however, also raises concerns with material degradation from the flow of hot or cold particles through discharge hoppers or along the inner receiver surfaces and other system components (e.g. tubes, valves etc.), depending on operating mode of the receiver. The flow of particles over surfaces may result in loss of material from abrasive wear, impact erosion from impingement under gravitational fall and particle attrition as particles fall and move on top of each other. In the present study, the performance of candidate materials and particles were evaluated through a series of abrasion erosion and particle attrition experiments at room temperature as well as at 800 °C. Candidate materials were subject to abrasive wear from particles at low particle to material velocities inside a resistance heated kiln, and analyzed for changes in mass and surface morphology using cross-sectional scanning electron microscopy (SEM) and energy dispersive x-ray spectroscopy (EDS) tests. The wear rate for different specimens was noted to be largely driven by the strength of chromia scales built on the specimens from exposure to high temperature. Particle attrition measurements explored the susceptibility of particles to breakdown from particle to particle interaction and the generation of fines from this process. At the low velocities expected in particle based CSP plants, the particles tested exhibited near negligible breakdown. However, changes in the particle hardness at 800 ºC resulted in a significantly higher particle breakdown to sizes <40 microns raising potential environmental concerns. In addition to particle breakdown, it was also noted that the sample had oxides from the stainless steel test setup mixed in with the particles. Similar oxides can be expected to turn up in the utility scale particle based CSP plants as well. The presence of oxide was also noted to affect the solar absorptivity of the mixture compared to a clean initial specimen, potentially resulting in a change in the overall efficiency of the CSP plant.

14 SOLAR ENERGY↗

Sierra/SD - Theory Manual - 5.2

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↗

Beam Coupling Impedances of Inter-cell Section in Scorpius Linac

The following technical note is prepared for distribution to external project collaborators. An inter-cell pumping section in the Scorpius linac contains a pumping grid with slots, bellows, and vacuum plenum. The beam coupling impedances of the inter-cell section are calculated with CST Studio. Important to note that all impedance values in the tech note below should be divided by a factor of 2 to obtain the beam coupling impedances in their standard definition; see reference for details.

43 PARTICLE ACCELERATORS↗

Sierra/SD - Theory Manual - 5.4

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↗

Sierra/SD - Theory Manual - 5.6

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↗

Sierra/SD - Theory Manual - 5.8

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. This page intentionally left blank.

97 MATHEMATICS AND COMPUTING↗