Superposition in a class of nonlinear systems
Nonlinear systems satisfying generalized principle of superposition, noting application to feedback control
NONLINEAR SYSTEM↗
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Superposition in a class of nonlinear systems.
Nonlinear systems satisfying generalized principle of superposition, noting application to feedback control
SIGNAL TRANSMISSION↗
Superposition of nonlinear plasma waves
We report results showing that spatially periodic Bernstein-Greene-Kruskal (BGK) waves, which are exact nonlinear traveling wave solutions of the Vlasov-Maxwell equations for collisionless plasmas, satisfy a nonlinear principle of superposition in the small amplitude limit. The analysis explicates the notion of superimposed BGK waves which, as recent numerical calculations suggest, is crucial in the proper description of the time-asymptotic state of a plasma when a large amplitude electrostatic wave undergoes nonlinear Landau damping.
Buchanan, Mark↗
Method for Rapid Modeling of Distortion in Laser Powder Bed Fusion Metal Additive Manufacturing Parts
The simulation and modeling of part-level distortion and residual stress in diverse metal additive manufacturing (AM) geometries has great potential to enable the rapid adoption of this technology in engineering design. Moreover, the use of additive manufacturing component libraries (CLs) offer a computationally efficient means of quantifying these part-level defects resultant from AM processing. We report on how the individual simulations of simple shapes, potential entries in a CL, can be superimposed to provide an indication of distortion and residual stresses in complex geometries. Laser powder bed fusion AM was used to construct test geometries of varied shapes and their combinations in the form of CLs in an effort to characterize location-dependent and feature-dependent distortion distributions. Blue light scanning was used to experimentally measure 3D distortions in order to investigate the interaction between the component shapes and local boundary conditions. Overall, part-level distortions were highly dependent on test component geometry, local boundary conditions, and shape combination. Commercial finite element software was used to verify experimental trends and to make predictions of distortion. The use of CLs resulted in over 20 times savings in computational cost while reproducing overall trends in distortion for test geometry assemblies. Therefore, it is anticipated that the use of CLs for L-PBF AM geometries has demonstrated potential to facilitate efficient simulations of full component AM assemblies, thereby reducing the need for costly trial-and-error-type experimental analysis.
36 MATERIALS SCIENCE↗
Efficient and Flexible Sensitivity Matrix Computation for Adaptive Electrical Capacitance Volume Tomography
Electrical capacitance tomography is a widely used sensor modality for flow imaging in many industrial settings. Adaptive Electrical Capacitance Volume Tomography (AECVT) extends the capabilities of traditional ECT by enabling direct volumetric imaging and an improved resolution. Construction of the sensitivity matrix is a necessary step to obtain flow images. This step requires computation of the electric field inside the sensing domain, which is done via a typical field solver such as the finite element method. In this work, we present an efficient and flexible method to construct the sensitivity matrix for Adaptive Electrical Capacitance Volume Tomography (AECVT) based on individual electrode segment excitations and their judicious combination to form desired matrix elements. We illustrate how the proposed method yields the same sensitivity matrix as the traditional method but at a much lower computational cost. Once all segment contributions are obtained, we also indicate how the proposed method, unlike the traditional approach, can generate the sensitivity matrix on demand for an arbitrary combination of synthetic electrodes and obviating the need for any additional field computations. Finally, we present image reconstruction results for two different experimental scenarios where the mutual capacitance data and the corresponding sensitivity vectors are obtained through the proposed measurement combination scheme.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Development of Time Lapse VSP Integration Workflow: A Case Study at Farnsworth CO2-EOR Project
Abstract This study aims to develop a 4D Vertical Seismic Profile (VSP) integration workflow to improve the prediction of subsurface stress changes. The selected study site is a 5-spot pattern within the ongoing CO2-EOR operations at the Farnsworth Field Unit FWU in Ochiltree County, Texas. The specific pattern has undergone extensive geological and geomechanical characterization through the acquisition of 3D seismic data, geophysical well logs, and core. This workflow constrains a numerical hydromechanical model by applying a penalty function formed between "modeled" versus "observed" time-lapse compressional and shear seismic velocity changes. Analyses of geophysical logs and ultra-sonic measurements on core exhibit measurable sensitivities to changes in both fluid saturation and mean effective stress. These data are used to develop a site-specific rock physics model and stress-velocity relationship, which inform the numerical models used to generate the "modeled" portion of the penalty function. The "observed" portion of the penalty function is provided by a novel elastic full-waveform inversion of the available 3D baseline and three monitor surveys to produce high-quality estimates of time-lapse compressional and shear seismic velocity changes. The modeling workflow accounts sequentially for fluid substitution and stress impacts. Hydrodynamic and geomechanical properties of the 3D coupled numerical model are estimated through geostatistical integration of well log and core data with 3D seismic inversion products. Changes in seismic velocities due to fluid substitution are computed using the Biot-Gassmann workflow and site-specific rock physics. Stress impacts on time-lapse seismic velocity changes are modeled from the effective stress output of the hydromechanical model and are initially based on the velocity versus effective stress relationship extracted from core mechanical testing. Based on the principle of superposition of seismic wavefields, seismic velocity changes attributed to fluid substitution and that due to changes in mean effective stress are treated as linearly additive. The modeled results are upscaled using Backus averaging to reconcile scale discrepancies between the modeled and measured datasets to formulate the penalty function. This manuscript presents the forward modeling process and concludes that for the base case, the seismic velocity changes due to mean effective stress dominates over the seismic velocity changes attributed to fluid substitution because of the extensive range of the pressure perturbations. Successful minimization of this penalty function calibrates the coupled hydrodynamic geomechanical numerical model and affirms the suitability of acoustic time-lapse measurements such as 4D-VSP for geomechanical calibration.
02 PETROLEUM↗
Experimentally Validated Computational Modeling of Creep and Creep-Cracking for Nuclear Concrete Structures
In a Nuclear Power Plant, one of the most important components is the concrete nuclear reactor cavity, which serves both a structural and protective function as the biological radiation shield. Given that creep has been identified as a major knowledge gap in the assessment of nuclear structures (NUREG/CR-7153), this work helps to further the understanding of creep behavior of massive concrete containment structures for decades to enable safe and long-term operation of these facilities. This project has developed a robust, experimentally validated model to predict creep in nuclear concrete structures for up 60 years using short-term creep data thereby enabling a longer service life of critical facilities and early detection of structural failure. The work presented in this report is a pairing of computational and experimental methods. For the first time, the time temperature superposition (TTS) principle was successfully used to generate a uniaxial creep compliance master curve to predict mortar creep response for up to 22,500 days (nearly 60 years) at a reference temperature of 20°C. These data were used as input into finite element analysis (FEA) codes that use highly realistic random, 3D concrete microstructures from reconstructed coarse limestone aggregates. Finite element analysis performed provides the ability to quickly upscale mortar viscoelastic behavior to long-term concrete creep/relaxation data. A master creep compliance curve, constructed from the TTS principle, spanning 27 years, was used to validate two and a half decades of simulated concrete creep. Concurrently, three different simulated wall specimens were designed to mimic the behavior of post-tensioned concrete nuclear containment facility vessel walls over time as a result of concrete creep. The specimens were designed with different thicknesses, transverse and longitudinal reinforcement ratios, and level of post-tensioning stress. Each specimen contained various instrumentation to measure internal concrete temperature, concrete strain, and post-tensioning strain hourly for over 3 years. The concrete creep model developed in this project, based on the FEA concrete simulations, was applied to simulate the structural-scale experiments of prestressed concrete walls conducted in this project using the Grizzly code. These models can represent the effects of reinforcing and prestressing. Although there are some discrepancies with the experimental data, the model can predict the overall trends of the creep response in these experiments. One of these experimental models was also applied to an extended time to demonstrate how the findings from this study can be used to predict the behavior of actual structures of interest that have been in service for extended periods of time.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Data Summarization and Inference at Scale
This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.
97 MATHEMATICS AND COMPUTING↗
Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions
The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time–concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.
42 ENGINEERING↗
The shear-stress intensity factor for a centrally cracked stiff-flanged shear web
By use of the principle of superposition the stiff-flanged shear web is modeled mathematically by an infinite elastic strip with fixed longitudinal edges. The shear-stress intensity factor for a central longitudinal crack is calculated for various values of the ratio of strip width to crack length, h/a, in the range 0.1-10. The interaction of the crack with the boundaries is illustrated by boundary shear-stress distributions for three values of h/a. Some implications of the results for the design of damage-tolerant shear webs are discussed briefly.
Fichter, W. B.↗
Hydroelastic vibration analysis of partially liquid-filled shells using a series representation of the liquid
A series representation of the oscillatory behavior of incompressible nonviscous liquids contained in partially filled elastic tanks is presented. Each term is selected on the basis of hydroelastic vibrations in circular cylindrical tanks. Using a complementary energy principle, the superposition of terms is made to approximately satisfy the liquid-tank interface compatibility. This analysis is applied to the gravity sloshing and hydroelastic vibrations of liquids in hemispherical tanks and in a typical elastic aerospace propellant tank. With only a few series terms retained, the results correlate very well with existing analytical results, NASTRAN-generated analytical results, and experimental test results. Hence, although each term is based on a cylindrical tank geometry, the superposition can be successfully applied to noncylindrical tanks.
Housner, J. M.↗
Full-coverage film cooling
Transpiration cooling is treated and then full coverage discrete hole injection for three injection orientations. Spacings with pitch to diameter ratios of 5 and 10 are discussed. The array is staggered, with the transverse pitch and the streamwise pitch the same. Results are presented in terms of the Stanton number using the heat transfer coefficient defined in terms of the difference between the wall temperature and the free stream temperature. Two values of Stanton number are provided for each situation: one with the injectant at wall temperature, and the other with the injectant at free stream temperature. These two values are equivalent to knowing the heat transfer coefficient and the adiabatic effectiveness. The heat transfer coefficient thus defined is used with the actual wall temperature to and the actual gas temperature to calculate the heat load. The principle of superposition thus invoked is valid exactly when the governing equations are linear.
Moffat, R. J.↗
Amplitude calibration of synthetic aperture radars - The effects of nonlinearities
Nonlinearities within a synthetic aperture radar (SAR) present significant obstacles to the calibration of the output imagery. The problem of calibrating a SAR is considerably more involved than that of calibrating a real aperture radar (RAR) or scatterometer, since the SAR relies heavily on the principle of superposition, which fails in nonlinear systems. It is shown in this paper that non-linearities can distort SAR imagery to such an extent that two areas of equal backscatter on the ground can be imaged to have significantly different intensities in the image.
Held, D. N.↗
An ideal clamping analysis for a cross-ply laminate
Different elementary clamping models are discussed for a three layer crossply laminate to study the sensitivity of clamping to the definition of cross-sectional rotation. All of these models leave a considerable residual warping at the edges. Using a complimentary energy principle and principle of superposition, an analysis is conducted to reduce this residual warping. This led to the identification of exact interior solution corresponding to the ideal clamping. This study also suggests a presence of stress singularities at the corners and between different layers near the fixed edge.
Valisetty, R. R.↗
Magellan stereo images and Venusian geology
Areas of Venus imaged by Magellan radar with multiple viewing conditions provide unique data that will contribute to the solution of venusian geologic problems and provide a basis for quantitative comparison of venusian landforms with those on other planetary bodies. Three sets of images with different viewing conditions have been acquired: (1) left-looking with variable incidence angles (cycle 1 profile), (2) right-looking with nearly constant incidence angles (cycle 2 profile), and (3) left-looking with variable incidence angles that are almost always smaller than those in (1) (cycle 3 profiles). The unique data provided by paired images of the same scene with different incidence angles arises from image displacements caused by the relief of individual landforms at scales comparable to the ground-range and azimuth resolutions of the images. There are two aspects of the data: (1) Stereopsis achieved by simultaneous viewing of paired left-looking images of the same scene permits three-dimensional perception and interpretation of the morphologies of landforms at resolutions much finer than the altimetry footprints. (2) Measurements of differences of image displacements (parallax) on paired images with known imaging geometries provide quantitative estimates of the relief and shapes of landforms. The potential scientific contributions of the data can be grouped into two interrelated classes: (A) geologic mapping, analysis, and interpretation and (B) topical studies that involve topographic measurements. Stereopsis, without quantitative measurements, enhances geologic mapping, analysis, and interpretation of the rock units of Venus to a degree that cannot be overestimated. In geologic mapping, assemblages of landforms, assessments of backscatter and variations in backscatter, and fine-scale topography are used to define and characterize geologic map units that represent laterally continuous deposits or rock units. Stereopsis adds the important dimension of local relief for characterization of geologic units at a scale that is not possible with Magellan altimetry or products derived from the altimetry. Relative ages of the geologic units are determined using the well-known principles of superposition and intersection. Here, the perception of relief is invaluable because superposition relations among the geological units are more readily and clearly established. The recognition of folds, faults, and fault systems, regardless of their orientations, is facilitated with stereopsis so that sequences of deformation of the geologic units can be determined and structural analyses vastly improved. Shapes of landforms are readily perceived so that they can be properly interpreted. The end result of the mapping, analyses, and interpretations is a geologic history of Venus that includes the sequences of formation and deformation of various geologic units. Measurements of relief at the finest scale possible are necessary for numerous topical studies. Standard altimetry will provide the necessary information on the relief of most large landforms, but it tends to underestimate the relief of small landforms and distorts their shapes. Although special processing of the altimeter echoes improves the estimates of the relief and shapes of some landforms, there are uncertainties in the interpretations of the echoes. Examples of topical studies requiring measurements of relief are given.
Moore, H. J.↗
Time-Temperature Dependent Response of Filament Wound Composites for Flywheel Rotors
Flywheel energy storage offers an attractive alternative to battery systems used in space applications such as the International Space Station. Rotor designs capable of high specific energies benefit from the load carrying capacity of hoop wound carbon fibers but their long-term durability may be limited by time-temperature dependent radial deformations. This was investigated for the carbon/epoxy rotor material, IM7/8552. Coupon specimens were sectioned from filament wound panels. These were tested in compression and tension at room temperature (RT), 95 and 135 C for strain rates from 5x10(exp -6) per second to 5x10(exp -3) per second. Time, temperature and load sign dependent effects were significant transverse to the fiber. At -0.5 percent strain for 72 hr, compressive stresses relaxed 16.4 percent at 135 C and 13 percent at 95 C. Tensile stresses relaxed only 7 percent in 72 hr at 135 C for 0.5 percent strain. Using linear hereditary material response and Boltzmann s principle of superposition to describe this behavior is problematic if not intractable. Micromechanics analysis including the effects of processing residual stresses is needed to resolve the paradoxes. Uniaxial compressive stress relaxation data may be used to bound the loss of radial pre-load stresses in flywheel rotors.
Thesken, John C.↗
Aerodynamic Analysis of the Truss-Braced Wing Aircraft Using Vortex-Lattice Superposition Approach
The SUGAR Truss-BracedWing (TBW) aircraft concept is a Boeing-developed N+3 aircraft configuration funded by NASA ARMD FixedWing Project. This future generation transport aircraft concept is designed to be aerodynamically efficient by employing a high aspect ratio wing design. The aspect ratio of the TBW is on the order of 14 which is significantly greater than those of current generation transport aircraft. This paper presents a recent aerodynamic analysis of the TBW aircraft using a conceptual vortex-lattice aerodynamic tool VORLAX and an aerodynamic superposition approach. Based on the underlying linear potential flow theory, the principle of aerodynamic superposition is leveraged to deal with the complex aerodynamic configuration of the TBW. By decomposing the full configuration of the TBW into individual aerodynamic lifting components, the total aerodynamic characteristics of the full configuration can be estimated from the contributions of the individual components. The aerodynamic superposition approach shows excellent agreement with CFD results computed by FUN3D, USM3D, and STAR-CCM+.
vortex lattice method↗
Viscoelastic characterization of thin-film polymers exposed to low Earth orbit
The materials made available through the Long Duration Exposure Facility (LDEF) satellite provide a set of specimens that can be well characterized and have a known exposure history with reference to atomic oxygen and ultraviolet radiation exposure. Mechanical characteristics measured from control samples and exposed samples provide a data base for predicting the behavior of polymers in low earth orbit. Samples of 1.0 mil thick low density polyethylene were exposed to the low earth orbit environment for a period of six years. These materials were not directly exposed to ram atomic oxygen and offer a unique opportunity for measuring the effect of atomic oxygen and UV radiation on mechanical properties with little concern to the effect of erosion. The viscoelastic characteristics of these materials were measured and compared to the viscoelastic characteristics of control samples. To aid in differentiating the effects of changes in crystallinity resulting from thermal cycling, from the effects of changes in chemical structure resulting from atomic oxygen/UV attack to the polymer, a second set of control specimens, annealed to increase crystallinity, were measured as well. The resulting characterization of these materials will offer insight into the impact of atomic oxygen/UV on the mechanical properties of polymeric materials. The viscoelastic properties measured for the control, annealed, and exposed specimens were the storage and loss modulus as a function of frequency and temperature. From these datum is calculated the viscoelastic master curve derived using the principle of time/temperature superposition. Using the master curve, the relaxation modulus is calculated using the method of Ninomiya and Ferry. The viscoelastic master curve and the stress relaxation modulus provide a direct measure of the changes in the chemical or morphological structure. In addition, the effect of these changes on long-term and short-term mechanical properties is known directly. It should be noted that the dependence on directionality for the polymer films was considered since these films were manufactured by a blown-film process.
Letton, Alan↗