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At least 1,207 records · Page 67

Variational approach to probabilistic finite elements

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemical and Structural Alterations in the Amorphous Structure of Obsidian due to Nanolites

Obsidian is volcanic glass that results from the rapid cooling of silica-rich melt. Nanoscale crystallites precipitate out of the melt prior to solidification and remain embedded in the amorphous matrix. These crystallites provide information on the flow kinetics and composition of the melt. Due to the sparsity and size of nanolites, studies often focus on supramicron crystallites. This research takes advantage of the conchoidal fracture of obsidian by knapping samples with nanometer-thin edges for transmission electron microscopy characterization. Nanolites in the amorphous matrix are studied using energy-dispersive spectroscopy (EDS) and electron diffraction. Certain alkali and alkaline-earth cations exhibit patterns of depletion near Fe-oxide nanolites. EDS is used to identify nanolites and variations in the composition of the matrix. Parallel beam diffraction and radial distribution function analysis of nearest-neighbor distances determine average bond lengths in the matrix near nanolites, showing that nanolites influence the nearby short-range ordering and atomic character of the matrix. Analysis reveals decreased mean nearest-neighbor distances in the matrix adjacent to nanolites compared to the bulk. Our methods exhibit the required sensitivity to detect variations in the composition and structure near nanolites, and our findings indicate that obsidian nanolites contribute to quantifiable localized changes in the amorphous structure.

36 MATERIALS SCIENCE↗

Small-scale experiments in STOVL ground effects

A series of tests was completed in which suckdown and fountain forces and pressures were measured on circular plates and twin-tandem-jet generic STOVL (short takeoff and vertical landing) configurations. The tests were conducted using a small-scale hover rig, for jet pressure ratios up to 6 and jet temperatures up to 700 F. The measured suckdown force on a circular plate with a central jet was greater than that found with a commonly used empirical prediction method. The present data showed better agreement with other sets of data. The tests of the generic STOVL configurations were conducted to provide force and pressure data with a parametric variation of parameters so that an empirical prediction method could be developed. The effects of jet pressure ratio and temperature were found to be small. Lift improvement devices were shown to substantially reduce the net suckdown forces.

Corsiglia, Victor R.↗

Small-scale experiments in STOVL ground effects

A series of tests has been completed in which suckdown and fountain forces and pressures were measured on circular plates and twin-tandem-jet generic STOVL (short takeoff and vertical landing) configurations. The tests were conducted using a small-scale hover rig, for jet pressure ratios up to 6 and jet temperatures up to 700 F. The measured suckdown force on a circular plate with a central jet was greater than that found with a commonly used empirical prediction method. The present data showed better agreement with other sets of data. The tests of the generic STOVL configurations were conducted to provide force and pressure data with a parametric variation of parameters so that an empirical prediction method cold be developed. The effects of jet pressure ratio and temperature were found to be small. Lift improvement devices were shown to substantially reduce the net suckdown forces.

Corsiglia, Victor R.↗

Geophysical interpretation of the magnetic anomalies of the Earth derived from MAGSAT data

The ambiguities about geophysical implications based on the correlation of scalar magnetic anomalies and geological features were investigated. A method was developed to convert scalar magnetic anomalies into a map of the lateral variations of magnetic susceptibility of the lithosphere. This map is directly correlated with the causative sources. The method is based on spherical harmonic analysis of lateral variations seen on the scalar magnetic anomaly map and those of the lithospheric magnetic susceptibility. The harmonic coefficients are related through the fundamental causality relationship governing a magnetized body and its associated scalar magnetic anomaly. The main features of the resulting magnetic susceptibility anomalies are outlined.

Arkani-Hamed, J.↗

Correlation approach for quality assurance of additive manufactured parts based on optical metrology

Surface topography and surface finish are two significant factors for evaluating the quality of products in additive manufacturing (AM). AM parts are fabricated layer by layer, which is quite different from traditional formative or subtractive methods. Despite rapid progress in additive manufacturing and associated optical metrology for quality control and in-situ monitoring, limited research has been conducted to investigate the reliability of 3D surface measurement data. The surface topologies scanned by multiple optical systems demonstrated significant differences due to varying sampling mechanisms, resolutions, system noises, etc. The 3D datasets should be trustworthy in order to extract parameters for quality assurance or feedback control from 3D surface measurements. In this paper, we set up new standards to evaluate the reliability of 3D surface measurement data and analyze the variation in the topographical profile. In this study, two non-contact optical methods based on Focus Variation Microscopy (FVM) and Structured Light System (SLS) were adopted to measure the surface topography of the target components. The two optical metrology systems generated two entirely different point cloud datasets. Statistical methods were applied to test the difference between the data obtained from the two systems. By using a data analytics approach for comparison, it was found that the surface roughness estimated from the point cloud data sets of FVM and SLS has no significant difference, though the point cloud data sets were completely different. This paper provides standard validation approach to evaluate the plausibility of metrology data from in-situ real-time surface analysis for process planning of AM.

36 MATERIALS SCIENCE↗

Autonomous design of new chemical reactions using a variational autoencoder

Artificial intelligence based chemistry models are a promising method of exploring chemical reaction design spaces. However, training datasets based on experimental synthesis are typically reported only for the optimal synthesis reactions. This leads to an inherited bias in the model predictions. Therefore, robust datasets that span the entirety of the solution space are necessary to remove inherited bias and permit complete training of the space. In this study, an artificial intelligence model based on a Variational AutoEncoder (VAE) has been developed and investigated to synthetically generate continuous datasets. The approach involves sampling the latent space to generate new chemical reactions. This developed technique is demonstrated by generating over 7,000,000 new reactions from a training dataset containing only 7,000 reactions. The generated reactions include molecular species that are larger and more diverse than the training set.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.

low↗

Solar tri-diurnal variation of cosmic rays in a wide range of rigidity

Solar tri-diurnal variations of cosmic rays have been analyzed in a wide range of rigidity, using data from neutron monitors, and the surface and underground muon telescopes for the period 1978-1983. The rigidity spectrum of the anisotropy in space is assumed to be of power-exponential type as (P/gamma P sub o) to the gamma exp (gamma-P/P sub o). By means of the best-fit method between the observed and the expected variations, it is obtained that the spectrum has a peak at P (=gamma P sub o) approx = 90 GV, where gamma=approx 3.0 and P sub o approx. 30 GV. The phase in space of the tri-diurnal variation is also obtained as 7.0 hr (15 hr and 23 hr LT), which is quite different from that of approx. 1 hr. arising from the axisymmetric distribution of cosmic rays with respect to the IMF.

Mori, S.↗

Buckling of cylindrical shells with random imperfections

Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.

Fersht, R. S.↗

Analysis of Narrow Bipolar Events Using Mode Decomposition Methods

Multi-resolution analysis methods can reveal the underlying physical dynamics of nonstationary signals, such as those from lightning. In this paper we demonstrate the application of two multi-resolution analysis methods: Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) in a comparative way in the analysis of electric field change waveforms from lightning. EEMD and VMD decompose signals into a set of Intrinsic Mode Functions (IMFs). The IMFs can be combined using distance and divergence metrics to obtain noise reduction or to obtain new waveforms that isolate the physical processes of interest while removing irrelevant components of the original signal. We apply the EEMD and VMD methods to the observations of three close Narrow Bipolar Events (NBEs) that were reported by Rison et al. The ΔE observations reveal the occurrence of complex oscillatory processes after the main NBE sferic. We show that both EEMD and VMD are able to isolate the oscillations from the main NBE, with VMD being more effective of the two methods since it requires the least user supervision. The oscillations are found to begin at the end of the NBEs' downward fast positive breakdown and appear to be produced by a half-wavelength standing wave within a weakly-conducting resonant ionization cavity left behind in the wake of the streamer-based NBE event. In conclusion, additional analysis shows that one of the NBEs was likely initiated by an energetic cosmic ray shower, and also corrects a misinterpretation in the literature that fast breakdown is an artifact of NBE-like events in interferometer observations.

54 ENVIRONMENTAL SCIENCES↗

Thickness-Independent Ultrasonic Imaging Applied to Abrasive Cut-Off Wheels: An Advanced Aerospace Materials Characterization Method for the Abrasives Industry. A NASA Lewis Research Center Technology Transfer Case History

Abrasive cut-off wheels are at times unintentionally manufactured with nonuniformity that is difficult to identify and sufficiently characterize without time-consuming, destructive examination. One particular nonuniformity is a density variation condition occurring around the wheel circumference or along the radius, or both. This density variation, depending on its severity, can cause wheel warpage and wheel vibration resulting in unacceptable performance and perhaps premature failure of the wheel. Conventional nondestructive evaluation methods such as ultrasonic c-scan imaging and film radiography are inaccurate in their attempts at characterizing the density variation because a superimposing thickness variation exists as well in the wheel. In this article, the single transducer thickness-independent ultrasonic imaging method, developed specifically to allow more accurate characterization of aerospace components, is shown to precisely characterize the extent of the density variation in a cut-off wheel having a superimposing thickness variation. The method thereby has potential as an effective quality control tool in the abrasives industry for the wheel manufacturer.

Roth, Don J.↗

Quantum-Compatible Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

Wildfire occurrences have been increasing for the past decade, leaving devastating traces across the world. In the recent efforts, remote sensing and airborne missions have been utilized to better understand and manage wildfires. This has resulted in an exponential increase in volume of remote sensing data, which has pushed the need for intelligent automation of data extraction for wildfire studies. Machine learning offers accurate automation in detecting such natural anomalies and enable decision-makers to take actions in a timely manner. Recent advances in machine learning algorithms, namely probabilistic generative methods, allow researchers and decisionmakers to step beyond detection and study “what-if” scenarios for wildfire occurrences. Additionally, they offer better imitations to the stochastic behavior of nature, and wildfire events. However, optimizing the performance of these probabilistic generative models is a computationally expensive process, specially using digital computers. On the other hand, quantum computers have recently shown a promise to reduce computationally costly training of such models and provide performance improvements. There is a body of research investigating the potential for improved machine learning methods in which key operations are performed on a quantum computer. In this study, we propose a probabilistic image-toimage segmentation approach combining a very well-known segmentation method, U-NET, with a Conditional Variational Auto-Encoder (CVAE) to not only detect wildfires but also describe the stochasticity of the phenomenon and be capable of running “what-if” scenarios. Our proposed model is compatible with training on quantum computers, which results in a quantum-assisted image-to-image segmentation approach and can be used to benchmark the potential benefit of quantum computing over the classical one.

quantum↗

Symmetry dilemmas in quantum computing for chemistry: A comprehensive analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits; gate-efficient universal operator pools generally break symmetries; and gate-efficient, fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analyses provide a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessment of Ice Shape Roughness Using a Self-Orgainizing Map Approach

Self-organizing maps are neural-network techniques for representing noisy, multidimensional data aligned along a lower-dimensional and nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. Prior investigations of ice shapes have focused on using self-organizing maps to characterize mean ice forms. The Icing Research Branch has recently acquired a high resolution three dimensional scanner system capable of resolving ice shape surface roughness. A method is presented for the evaluation of surface roughness variations using high-resolution surface scans based on a self-organizing map representation of the mean ice shape. The new method is demonstrated for 1) an 18-in. NACA 23012 airfoil 2 AOA just after the initial ice coverage of the leading 5 of the suction surface of the airfoil, 2) a 21-in. NACA 0012 at 0AOA following coverage of the leading 10 of the airfoil surface, and 3) a cold-soaked 21-in.NACA 0012 airfoil without ice. The SOM method resulted in descriptions of the statistical coverage limits and a quantitative representation of early stages of ice roughness formation on the airfoils. Limitations of the SOM method are explored, and the uncertainty limits of the method are investigated using the non-iced NACA 0012 airfoil measurements.

Icing↗

Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning nonlinear state space models from observations. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.

97 MATHEMATICS AND COMPUTING↗

An Inductor Current Estimation Approach for DC/DC Converters Based on Bisection Method

The trends toward higher power density and efficiency for the DC/DC converters has posed more strict requirements for inductors. The inductor current in turn affect the operating characteristics of the converters significantly and thus needs to be accurately estimated. In this paper, a new bisection-method-based inductor current estimation approach considering the variation of inductance is proposed. The proposed approach can be adapted and applied for various DC/DC converters, including the widely used buck and boost converters and etc. Comparing to the conventional estimation method using constant inductance, the proposed method can obtain more precise estimations of both the inductor current waveform and the power loss. Experimental results on a buck converter with a ferrite-core inductor are presented to validate the effectiveness of the proposed approach.

Zhao, Zhe↗