Generalized decomposition theory of finite sequential machines
Generalized decomposition theory of finite sequential machines
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Generalized decomposition theory of finite sequential machines
This document describes several navigation studies for low-altitude Earth satellites. The use of Global Positioning System Navigation Package data for LANDSAT-5 orbit determination is evaluated. In addition, a navigation analysis for the proposed Tracking and Data Aquisition System is presented. This analysis, based on simulations employing one-way Doppler data, is used to determine the agreement between the Research and Development Goddard Trajectory Determination System and the Sequential Error Analysis Program results. Properties of several geopotential error models are studied and an exploratory study of orbit smoother process noise is presented.
When porting sequential applications to parallel computer architectures, the program developer will typically go through several cycles of source code optimization and performance analysis. We have started a project to develop an environment where the user can jointly navigate through program structure and performance data information in order to make efficient optimization decisions. In a prototype implementation we have interfaced the CAPO computer aided parallelization tool with the Paraver performance analysis tool. We describe both tools and their interface and give an example for how the interface helps within the program development cycle of a benchmark code.
The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never factored during the optimization retaining its original sparsity. One of SAND's disadvantages is the increase in the number of design variables and in the associated number of constraint gradient evaluations. If SAND is to be an acceptable player in the optimization field, it is essential to investigate the efficiency of the method and to present a possible cure for any inherent deficiencies.
The Exabiome project seeks to improve the understanding of microbiomes through the development of methods for accelerating metagenomic science using exascale computing. This article gives an overview of scientific impact of the three components of the project: metagenome assembly, protein family detection, and comparative analysis of metagenomes. Exabiome developed MetaHipMer, the only metagenome assembler capable of scaling to full exascale systems. MetaHipMer has enabled ground-breaking assemblies on the Frontier supercomputer, with many scientific benefits, such as the discovery of rare species and viral genomes. To investigate protein families, Exabiome developed two exascale tools, PASTIS and HipMCL. Together, these can utilize exascale resources to understand the functional diversity of billions of dark matter proteins and novel protein families. For comparative analysis, Exabiome developed kmerprof, a tool that can be used to compare huge metagenomes for many different scientific purposes, for example, grouping human microbiomes according to body location.
The results of a detailed investigation of the distribution of stresses in aluminum and composite panels subjected to uniform end shortening are presented. The focus problem is a rectangular panel with two longitudinal stiffeners, and an inner stiffener discontinuous at a central hole in the panel. The influence of the stiffeners on the stresses is evaluated through a two-dimensional global finite element analysis in the absence or presence of the hole. Contrary to the physical feel, it is found that the maximum stresses from the glocal analysis for both stiffened aluminum and composite panels are greater than the corresponding stresses for the unstiffened panels. The inner discontinuous stiffener causes a greater increase in stresses than the reduction provided by the two outer stiffeners. A detailed layer-by-layer study of stresses around the hole is also presented for both unstiffened and stiffened composite panels. A parallel equation solver is used for the global system of equations since the computational time is far less than that using a sequential scheme. A parallel Choleski method with up to 16 processors is used on Flex/32 Multicomputer at NASA Langley Research Center. The parallel computing results are summarized and include the computational times, speedups, bandwidths, and their inter-relationships for the panel problems. It is found that the computational time for the Choleski method decreases with a decrease in bandwidth, and better speedups result as the bandwidth increases.
Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.
Bronze and bronze-derived, mixed metal oxides are materials of growing interest for lithium-ion battery anodes due to their high-rate capabilities and the potential for high energy densities via multielectron redox. We report on the synthesis and electrochemical properties of the tetragonal tungsten bronzetype phase Nb 8 W 9 O 47 and our investigation into the structural evolution of this phase upon lithium (de)intercalation, with particular attention to how it relates to the fast-cycling capabilities. Electrochemical cycling shows Nb 8 W 9 O 47 can achieve greater than one Li + per transition metal at rates of C/2 or slower and maintains a capacity equivalent to 0.65 Li + per transition metal at a rate of 20C. Sequential Rietveld analysis of operando X-ray diffraction data reveals anisotropic changes to the unit cell parameters during discharge, accompanied by an off-centering of the transition metals within their octahedral environments. While higher capacities can be accessed below 1.2 V, cells discharged to 1.0 V exhibit a significant expansion of the unit cell volume and reduced Coulombic efficiencies. This report suggests that rigid crystal structures incapable of undergoing polyhedral rotational deformations can instead exploit displacive distortions of the transition metal redox center to enable fast Li-ion cycling with minimal atomic rearrangements.
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