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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Evans, Tyrus M. Marsht, Andrew W. Uzodinma, Jaylon Mazumdar, Yi Chen Guildenbecher, Daniel R. Georgia Inst Technol Guggenheim Sch Aerosp Engn Atlanta GA 30332 USA Georgia Inst Technol Woodruff Sch Mech Engn Atlanta GA 30332 USA Sandia Natl Labs Engn Sci Ctr POB 5800 Albuquerque NM 87185 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

In extreme supersonic, hypersonic, or explosive environments, the presence of gas-phase shocks cause coherent imaging distortions and inhibit object tracking. In this work, we aim to remove these distortions by measuring the relative phase of the light using digital phase-sensitive holography techniques including a two-step phase-shifting technique and a single-shot polarization phase-shifting technique. Once the phase of the shock-wave is acquired, the distortion is numerically canceled from the image and the un-distorted object image is recovered. This work discusses the theory, provides simulation results, and presents preliminary experimental data showing how this concept can be applied to remove shock-wave phase distortions created by supersonic air jets.

关键词： Shock Waves Polarization numerical algorithms Laser Energy Microscopy Continuous Wave Lasers Combustion System Image Registration Multiphase Flows Frequency Domain

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Theoretical formulation and numerical implementation of electromagnetic and thermomechanical loading processes in solids

Theoretical formulation and numerical implementation of elec...

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作者： Thomas, Jesse D. University of Michigan

学位级别：Ph.D.

The electromagnetic-thermal-mechanical process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. One of the several advantages of this technique is the considerable ductility increase observed in several metals, particularly aluminum. In this research two important aspects of this process are addressed: the influence of the sheet metal's constitutive response on ductility and the consistent formulation of the fully coupled electromagnetic-mechanical problem. The first part of the work addresses the necking localization of a metal sheet during an electromagnetic process. A "weak band" model is used to predict the onset of necking of a thin sheet under plane stress and in-plane electric currents, an idealization of the local conditions in unconstrained electromagnetic loading. This work finds that EMF increases ductility over quasistatic techniques, due to the material's strain-rate sensitivity, and details how the material constitutive response and process characteristics affect ductility. The general theory is subsequently applied to freely expanding electromagnetically loaded aluminum tubes. Necking strains are measured in tubes of various geometries that are loaded by different forming coils and electric currents. The experimental results show reasonable agreement with the corresponding theoretical forming limit predictions, which indicate a two to three fold increase in the forming limits with respect to the quasistatic case. The second part of the work pertains to predictive modeling of EMF processes. Recent works do not consistently account for the coupling between electromagnetic fields and finite deformations. Typically, separate solutions to the electromagnetic and finite strain mechanical problems are combined in lock-step. The present work employs a fully coupled Lagrangian (reference configuration) least-action variational principle. This principle forms

关键词： Electromagnetic-thermal-Mechanical Processes Continuum Mechanics High Strain Rate Ductility numerical algorithms Variational Calculus Thesis

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DeepStability: A Study of Unstable numerical Methods and Their Solutions in Deep Learning 22

DeepStability: A Study of Unstable Numerical Methods and The...

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ACM/IEEE 44th International Conference on Software Engineering (ICSE)

作者： Kloberdanz, Eliska Kloberdanz, Kyle G. Le, Wei Iowa State Univ Dept Comp Sci Ames IA 50011 USA Cape Privacy Ames IA USA

ISBN: (纸本)9781450392211

Deep learning (DL) has become an integral part of solutions to various important problems, which is why ensuring the quality of DL systems is essential. One of the challenges of achieving reliability and robustness of DL software is to ensure that algorithm implementations are numerically stable. DL algorithms require a large amount and a wide variety of numerical computations. A naive implementation of numerical computation can lead to errors that may result in incorrect or inaccurate learning and results. A numerical algorithm or a mathematical formula can have several implementations that are mathematically equivalent, but have different numerical stability properties. Designing numerically stable algorithm implementations is challenging, because it requires an interdisciplinary knowledge of software engineering, DL, and numerical analysis. In this paper, we study two mature DL libraries PyTorch and Tensorflow with the goal of identifying unstable numerical methods and their solutions. Specifically, we investigate which DL algorithms are numerically unstable and conduct an in-depth analysis of the root cause, manifestation, and patches to numerical instabilities. Based on these findings, we launch DeepStability, the first database of numerical stability issues and solutions in DL. Our findings and DeepStability provide future references to developers and tool builders to prevent, detect, localize and fix numerically unstable algorithm implementations. To demonstrate that, using DeepStability we have located numerical stability issues in Tensorflow, and submitted a fix which has been accepted and merged in.

关键词： numerical stability deep learning numerical algorithms

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numerical solution of eigenvalue problems for Hamiltonian systems

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Advances in Computational Mathematics 1994年第2期2卷 155-184页

作者： Marletta, Marco Department of Mathematics and Computer Science University of Leicester Leicester LE1 7RH University Road United Kingdom

This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here;to the best of the author's knowledge, these are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written in Pfort-verified Fortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f. © 1994 J.C. Baltzer AG, Science Publishers.

关键词： AMS(MOS) subject classification: 65L15 eigenvalue problems Hamiltonian systems mathematical software numerical algorithms

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An improved two-terminal numerical algorithm for fault location estimation considering shunt capacitance

An improved two-terminal numerical algorithm for fault locat...

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General Meeting of the Power-Engineering-Society

作者： Kim, H. H. Lee, C. J. Radojevic, Z. M. Park, J. B. Shin, J. R. Konkuk Univ Dept Elect Engn Seoul 143701 South Korea

ISBN: (纸本)9781424404926

This paper presents a new two-terminal numerical algorithm for fault location estimation using the synchronized phasor in time-domain. The proposed algorithm is also based on the synchronized voltage and current phasor measured from the PMUs(Phasor Measurement Units) installed at both ends of the transmission lines. In this paper the algorithm is given with-out shunt capacitance and with shunt capacitance using, Pi -model and estimated using DFT(Discrete Fourier Transform) and the LES(Least Error Squares Method). The algorithm uses a very short data window and classification for real-time transmission line protection. To test the validity, of the proposed algorithm, the Electro-Magnetic Transient Program(EMTP) and MATLAB is used.

关键词： numerical algorithms fault location time-domain with-out/with shunt capacitance protection

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Comparison of analytical and numerical estimations of laser beam spreading in a turbulent atmosphere 25

Comparison of analytical and numerical estimations of laser ...

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25th International Symposium On Atmospheric and Ocean Optics - Atmospheric Physics

作者： Konyaev, Petr Kanev, Feodor VE Zuev Inst Atmospher Opt Tomsk Russia

ISBN: (数字)9781510631694

ISBN: (纸本)9781510631694

Two possible methods to solve scalar parabolic wave equation describing beam propagation in a randomly inhomogeneous medium have been compared in the article. The analytical approach was based on additive approximation, while numerically the equation was solved by the split-step Fourier algorithm. As was shown calculation of the beam radius with the use of both methods provides approximately the same results in the interval of weak fluctuations of the index of refraction. Increase of distortion intensity leads to divergence of data obtained analytically and in computer simulations. This disagreement can be explained by intrinsic limitations of additive approximation evolving in the regime of strong amplitude-phase fluctuations.

关键词： Atmospheric turbulence numerical algorithms split-step Fourier method wave optics laser beams

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Predicting the past: Mathematical models and numerical methods in molecular phylogenetics

Predicting the past: Mathematical models and numerical metho...

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作者： Stoltz, Stephanus Marnus University of Otago

学位级别：博士

Molecular phylogenetics is the study of phylogenies and processes of evolution by the analyses of DNA or amino acid sequence data. In this thesis we describe a computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. The new diffusion approach coupled with state-of-the-art numerical algorithms allow for analyses of datasets containing hundreds or even thousands of individuals. We demonstrate the scale of analyses possible using a SNP data sampled from 399 fresh water turtles in 41 populations. The method, which we call Snapper, is the successor of the coalescent based method Snapp. A reanalysis of soybean SNP data demonstrates that the two methods are hard to distinguish in practice. We also describe a Bayesian methodology for inferring niches of present and ancestral species of plants from environmental measurements and estimated phylogenies. Fitting the phylogenetic niche model to three conifer species endemic to New Zealand confirms that viable ancestral niches can be inferred. Lastly, in anticipation of even larger genomic datasets we look into graphical processing units as computational tools for efficient model fitting. We introduce a new graphical processing unit based algorithm designed to fit long chain Hidden Markov models, applying this approach to an Hidden Markov model for nonvolcanic tremor events. Our implementation resulted in a 1000-fold increase in speed over the standard single processing algorithm, allowing for a full Bayesian inference of model parameters.

关键词： PDEs Phylogenetics Bayesian inference SNPs Species trees numerical algorithms

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Dynamic interaction between pantograph and rigid overhead lines using a coupled FEM - multibody procedure

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MECHANISM AND MACHINE THEORY 2016年 97卷 100-111页

作者： Bautista, A. Montesinos, J. Pintado, P. Univ Castilla La Mancha Dept Mech Engn ETSI Ind E-13071 Ciudad Real Spain Electrificac & Estudios Ferroviarios Albacete 02008 Spain

Most studies on the interaction between pantograph and overhead contact systems refer to the conventional catenary composed of contact and messenger wires and droppers, whereas the literature related to the interaction with rigid overhead conductor rails is limited. This paper presents an algorithm capable of simulating the interaction between a catenary represented as a Finite Element Model and a pantograph modeled as a multibody linkage. The algorithm will be proven to be accurate and efficient. The procedure has been used to simulate the interaction in different scenarios as a tool to optimize the design of the infrastructure as well as the configuration of the pantograph. The piece of software produced can consider interaction of one or two pantographs with one or two overhead lines in transition sections. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Rigid overhead conductor rail Pantograph FEM Multibody Dynamic interaction numerical algorithms

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Serrated flow in NaI:Tl scintillator crystals

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Journal of Materials Science & Technology 2023年第22期153卷 120-127页

作者： Jamieson Brechtl Xie Xie Rui Feng Gongyao Wang Charles Melcher Mariya Zhuravleva Peter K.Liaw The Bredesen Center for Interdisciplinary Research and Graduate Education The University of TennesseeKnoxvilleTN 37996USA Department of Materials Science and Engineering The University of TennesseeKnoxvilleTN 37996USA Scintillation Materials Research Center The University of TennesseeKnoxvilleTN 37996USA

The serrated-flow behavior is an important phenomenon that unveils material-deformation mechanisms,as reported for various kinds of *** doped with Tl(NaI:Tl)is unique among scintillation ma-terials in that the structure contains glide planes that are linked to serration *** the present work,single crystals of NaI:Tl were subjected to room-temperature compression experiments at different strain *** serrated flow was observed,and complexity and multifractal analyses were performed to analyze the serration *** findings revealed that the strain rate had a pronounced effect on the complexity and multifractality of the serrated flow,similar to what has been found in other alloy *** results also indicate that there may be a strong link between the complexity of the serrated flow behavior and the heterogeneity of the underlying *** is expected that the present work could be a step toward a better understanding of the deformation behavior and forgeability of NaI:Tl single crystals.

关键词： Dislocations Ceramic material Mechanical testing numerical algorithms Scintillator

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numerical METHODS FOR UNCERTAINTY ANALYSIS IN DYNAMICAL SYSTEMS

NUMERICAL METHODS FOR UNCERTAINTY ANALYSIS IN DYNAMICAL SYST...

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作者： KYUNGEUN KIM Texas A&M University

学位级别：硕士

The current methods for uncertainty analysis in dynamical systems are restricted in terms of computational cost and evaluation domain since they either use grid points or work only along trajectories. To break through these problems we present a new method: the Rothe & maximum-entropy method which follows the steps below. A deterministic dynamical system with initial value uncertainties can be analyzed via the uncertainty propagation which is based on the Liouville equation in the form of the first-order linear partial differential equation. On this equation we conduct a semi-discretization in time via A-stable rational approximations of consistency order k and this yields the stationary spatial problem. This spatial problem now can be solved by the spatial discretization scheme: we propose the maximum-entropy approximation which provides unbiased interpolations even with fewer number of scattered points. Through these steps we finally obtain a system of linear equations for the evolution of the probability density function u t, which can be easily solved in several ways. This method can provide more efficiency in terms of computation time thanks to using fewer number of scattered points instead of grid points. Also, it enables the constant tracking of probability density functions in a specific fixed domain of interest and this is especially effective for switched systems.

关键词： Stochastic Systems Uncertainty Analysis Switched Systems numerical algorithms Thesis

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