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At least 1,063 records · Page 59

On determining important aspects of mathematical models: Application to problems in physics and chemistry

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Rabitz, Herschel↗

Design sensitivity analysis of rotorcraft airframe structures for vibration reduction

Optimization of rotorcraft structures for vibration reduction was studied. The objective of this study is to develop practical computational procedures for structural optimization of airframes subject to steady-state vibration response constraints. One of the key elements of any such computational procedure is design sensitivity analysis. A method for design sensitivity analysis of airframes under vibration response constraints is presented. The mathematical formulation of the method and its implementation as a new solution sequence in MSC/NASTRAN are described. The results of the application of the method to a simple finite element stick model of the AH-1G helicopter airframe are presented and discussed. Selection of design variables that are most likely to bring about changes in the response at specified locations in the airframe is based on consideration of forced response strain energy. Sensitivity coefficients are determined for the selected design variable set. Constraints on the natural frequencies are also included in addition to the constraints on the steady-state response. Sensitivity coefficients for these constraints are determined. Results of the analysis and insights gained in applying the method to the airframe model are discussed. The general nature of future work to be conducted is described.

Murthy, T. Sreekanta↗

SAVS: A Space Analysis and Visualization System

We propose to develop, test, demonstrate, and deliver to NASA a powerful and versatile data acquisition, manipulation, analysis and visualization system which will enhance scientific capabilities in the display and interpretation of diverse and distributed data within an integrated user-friendly environment. Our approach exploits existing technologies and combines three major elements into an easy-to-use interactive package: (1) innovative visualization software; (2) advanced database techniques; and (3) a rich set of mathematical and image processing tools. Visualization capabilities will include one-, two-, and three-dimensional displays, along with animation, compression, warping and slicing functions. Analysis tools will include generic mathematical and statistical techniques along with the ability to use large scale models for interactive interpretation of large volume data sets. Our system will be implemented on Sun and DEC UNIX workstations and on the Stardent Graphics Super computer. Our final deliverable will include complete documentation and a NASA/NSF-CDAW/SUNDIAL campaign demonstration.

Szuszczewicz, Edward P.↗

SAVS: A Space Analysis and Visualization System

We propose to develop, test, demonstrate, and deliver to NASA a powerful and versatile data acquisition, manipulation, analysis and visualization system which will enhance scientific capabilities in the display and interpretation of diverse and distributed data within an integrated user-friendly environment. Our approach exploits existing technologies and combines three major elements into an easy-to-use interactive package: (1) innovative visualization software; (2) advanced database techniques; and (3) a rich set of mathematical and image processing tools. Visualization capabilities will include one-, two-, and three-dimensinal displays, along with animation, compression, warping and slicing functions. Analysis tools will include generic mathematical and statistical techniques along with the ability to use large scale models for interactive interpretation of large volume data sets. Our system will be implemented on Sun and EC UNIX workstations and on the Stardent Graphics Supercomputer. Our final deliverable will include complete documentation and a NASA/NSF-CDAW/SUNDIAL campaign demonstration.

Szuszczewicz, Edward P.↗

Numerical Analysis of Regular Material Point Method and its Application to Multiphase Flows

The material point method (MPM) is gaining wide popularity in engineering research to model and simulate complex multiphase flow dynamics. The method relies on solving the governing equations of motion and transport in a Lagrangian framework using particles also known as material points. The fluid and kinematic properties are stored on the material points while the spatial gradient calculation and temporal integration are performed on a background grid. This Lagrangian framework allows for large deformations, easy integration of constitutive models, and direct import of complex geometries as particles. However, despite their increasing popularity, very few studies have addressed the issues of numerical resolution and stability of MPM techniques. The presence of additional factors such as the number of material points-per-cell, the location of the material points, the CFL-like condition used in time update, and the grid shape functions also increase the complexity of the error analysis when compared to other finite element methods. In this presentation, we analyze the various forms of error incurred in the application of MPM to continuum mechanics and multiphase flows. The effect of the previously mentioned factors on the error dynamics is studied. The application of these principles to canonical and industrial problems is also presented.

high pressure reverse osmosis↗

Axially grooved heat pipes - 1976

This paper summarizes the 'state-of-the-art' of axially grooved heat pipes. Applications are identified and the related heat pipe design and performance are defined. Recent developments in the analysis, design and fabrication of axially grooved hardware are also discussed. A mathematical model which predicts the hydrodynamic behavior and accounts for liquid recession, liquid/vapor shear interaction and 1-g puddle flow is also presented. Performance data for various fluids in the 100-500 K range is compared to predictions from the Groove Analysis Program (GAP). Finally, a simplified closed form solution which accounts for gravity effects, self-priming and composite pumping by the grooves as well as all of the hydrodynamic losses is also discussed.

Brennan, P. J.↗

Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems

Mathematically sound techniques are used to view a knowledge-based system (KBS) as a set of processes executing in parallel and being enabled in response to specific rules being fired. The set of processes can be manipulated, examined, analyzed, and used in a simulation. The tool that embodies this technology may warn developers of errors in their rules, but may also highlight rules (or sets of rules) in the system that are underspecified (or overspecified) and need to be corrected for the KBS to operate as intended. The rules embodied in a KBS specify the allowed situations, events, and/or results of the system they describe. In that sense, they provide a very abstract specification of a system. The system is implemented through the combination of the system specification together with an appropriate inference engine, independent of the algorithm used in that inference engine. Viewing the rule base as a major component of the specification, and choosing an appropriate specification notation to represent it, reveals how additional power can be derived from an approach to the knowledge-base system that involves analysis, simulation, and verification. This innovative approach requires no special knowledge of the rules, and allows a general approach where standardized analysis, verification, simulation, and model checking techniques can be applied to the KBS.

Hinchey, Mike↗

FRAM, Version 6.1 User Manual

This manual describes the use of version 6.1 of the FRAM gamma-ray isotopic analysis software developed in the Safeguards Science and Technology Group, NEN-1, Nuclear Engineering & Nonproliferation Division, Los Alamos National Laboratory. The software analyzes the gamma ray spectrum from plutonium-bearing items and determines the isotopic distribution of the plutonium, 241Am content, and concentration of other isotopes in the item. The software can also determine the isotopic distribution of uranium isotopes in items containing only uranium. The body of this manual describes the generic version of the code.

07 ISOTOPE AND RADIATION SOURCES↗

A Practical Solver for Scalar Data Topological Simplification

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of “signal” persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of “non-signal” pairs, while (ii) preserving the “signal” pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. Here, we also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.

97 MATHEMATICS AND COMPUTING↗

INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.

computational mathematics↗

Reduced Order Models Generation for HTGRs Pebble Shuffling Procedure Optimization Studies

This report provides an initial study for producing reduced-order models (ROMs) of pebble-bed high temperature gas reactor (HTGR) models for the purposes of design optimization. As an initial study, this work is meant to be exploratory---identifying useful workflows and methods for ROM generation---and not meant to be a catch-all analysis of HTGR ROM generation and usage for optimization. This report summarizes three tasks performed in Fiscal Year 2022: 1) the creation of HTGR model, 2) the sensitivity analysis of model design parameters, and 3) an introduction to ROM generation techniques. The representative HTGR model created in this work is a multiphysics equilibrium-core using the BlueCRAB (comprehensive reactor analysis bundle) reactor analysis application, coupling four physical phenomena: neutronics, streamline depletion, porous flow thermal hydraulics, and pebble heat conduction. Part of the model creation was identifying some design parameters and quantities of interest that are relevant in an optimization analysis and adjustable in the model. The sensitivity analysis utilized a polynomial chaos expansion methodology to compute global sensitivity metrics. This analysis showed that thermal hydraulics parameters and quantities of interest had a relatively small impact on simulation results. Finally, the ROM generation work involved exploring three different ROM methodologies: polynomial regression, a Gaussian process, and artificial neural networks. Using a cross-validation technique to characterize ROM performance, the Gaussian process and single-layer artificial neural networks showed the most promising results. Overall, this study was insightful and the lessons learned will be invaluable for the eventual development of an HTGR design optimization workflow.

97 MATHEMATICS AND COMPUTING↗

General MACOS Interface for Modeling and Analysis for Controlled Optical Systems

The General MACOS Interface (GMI) for Modeling and Analysis for Controlled Optical Systems (MACOS) enables the use of MATLAB as a front-end for JPL s critical optical modeling package, MACOS. MACOS is JPL s in-house optical modeling software, which has proven to be a superb tool for advanced systems engineering of optical systems. GMI, coupled with MACOS, allows for seamless interfacing with modeling tools from other disciplines to make possible integration of dynamics, structures, and thermal models with the addition of control systems for deformable optics and other actuated optics. This software package is designed as a tool for analysts to quickly and easily use MACOS without needing to be an expert at programming MACOS. The strength of MACOS is its ability to interface with various modeling/development platforms, allowing evaluation of system performance with thermal, mechanical, and optical modeling parameter variations. GMI provides an improved means for accessing selected key MACOS functionalities. The main objective of GMI is to marry the vast mathematical and graphical capabilities of MATLAB with the powerful optical analysis engine of MACOS, thereby providing a useful tool to anyone who can program in MATLAB. GMI also improves modeling efficiency by eliminating the need to write an interface function for each task/project, reducing error sources, speeding up user/modeling tasks, and making MACOS well suited for fast prototyping.

Sigrist, Norbert↗

Inverse Analysis with Variational Autoencoders: A Comparison of Shallow and Deep Networks

Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.

97 MATHEMATICS AND COMPUTING↗

A Simple Engineering Analysis of Solar Particle Event High Energy Tails and Their Impact on Vehicle Design

The mathematical models for Solar Particle Event (SPE) high energy tails are constructed with several di erent algorithms. Since limited measured data exist above energies around 400 MeV, this paper arbitrarily de nes the high energy tail as any proton with an energy above 400 MeV. In order to better understand the importance of accurately modeling the high energy tail for SPE spectra, the contribution to astronaut whole body e ective dose equivalent of the high energy portions of three di erent SPE models has been evaluated. To ensure completeness of this analysis, simple and complex geometries were used. This analysis showed that the high energy tail of certain SPEs can be relevant to astronaut exposure and hence safety. Therefore, models of high energy tails for SPEs should be well analyzed and based on data if possible.

Singleterry, Robert C., Jr.↗

Graph Theory and IC Component Design Analysis

Graph analysis in large integrated circuit (IC) designs is an essential tool for verifying design logic and timing via dynamic timing analysis (DTA). IC designs resemble graphs with each logic gate as a vertex and the conductive connections between gates as edges. Using DTA digital statistical correlations, graph condensation, and graph partitioning, it is possible to identify high-entropy component centers and paths within an IC design. Identification of high-entropy component centers (HECC) enables focused DTA, effectively lowering the computational complexity of DTA on large integrated circuit graphs. In this paper, a devised methodology termed IC layout subgraph component center identification (CCI) is used to identify described. CCI lowers DTA computationally complexity by condensing IC graphs into reduced subgraphs in which dominant logic functions are verified.

42 ENGINEERING↗

FRAM v.7.1

Fixed-energy Response-function Analysis with Multiple efficiency (FRAM) is a software code designed primarily for plutonium and uranium isotopic analysis. It is widely used in both the domestic and international safeguards community. FRAM can quickly and accurately determine the isotopic compositions of plutonium, uranium, and mixed oxides (MOX) when measuring with a high-purity germanium (HPGe), cadmium zinc telluride (CZT), or lanthanum bromide (LaBr3) detector. The capabilities of FRAM have been enhanced to analyze the data of the pixelated CZT detector (made by H3D) and to measure the mass of plutonium, uranium, and MOX. Both the isotopic composition and mass of the item can be quickly determined with one measurement using a gamma detector with FRAM v.7.1.

07 ISOTOPE AND RADIATION SOURCES↗

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING↗