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At least 235 records · Page 13

Nonlinear Convection in Mushy Layers

When alloys solidify in a gravitational field there are complex interactions between solidification and natural, buoyancy-driven convection that can alter the composition and impair the structure of the solid product. The particular focus of this project has been the compositional convection within mushy layers that occurs in situations where the lighter component of the alloy is rejected into the melt during solidification by cooling from below. The linear stability of such a situation was previously described and has been further elucidated in a number of published articles. Here we describe some recent developments in the study of nonlinear evolution of convection in mushy layers.

Worster, M. Grae↗

Intelligent Partitioning based Fully Parallel AC Security-Constrained Optimal Power Flow

Today’s power grid is becoming more diverse and integrated with high-level distributed energy resources and smart control technologies that is creating a new set of grid management challenges in terms of large-scale, nonlinear, and non-convex problem modeling, complex and time-consuming computation, as well as difficult uncertainty handling. This project focused on solving a challenging multi-period security-constrained generation scheduling problem, which is of great importance for maximizing the social welfare of real-time dispatch, day-ahead market, as well as weekly planning of power systems. Our developed software explored parallel optimization algorithms for complex and realistic power system models, and develop fast, efficient, and robust grid optimization solutions on the high-performance computing platform that will enable increased grid economics, flexibility, resilience, as well as energy security in the United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A method for linearizing a nonlinear system with six state variables and three control variables

A nonlinear system governed by x = f(x,u) with six state variables and three control variables is considered in this project. A set of transformations from (x,u) - space to (z,v) - space is defined such that the linear tangent model is independent of the operating point in the z-space. Therefore, it is possible to design a control law satisfying all operating points in the transformed space. An algorithm to construct the above transformations and to obtain the associated linearized system is described in this report. This method is applied to a rigid body using pole placement for the control law. Results are verified by numerical simulation. Closed loop poles in x-space using traditional local linearization are compared with those pole placements in the z-space.

Hsia, W. S.↗

Diode pumped solid-state laser oscillators for spectroscopic applications

The rapid improvement in diode laser pump sources has led to the recent progress in diode laser pumped solid state lasers. To date, electrical efficiencies of greater than 10 percent were demonstrated. As diode laser costs decrease with increased production volume, diode laser and diode laser array pumped solid state lasers will replace the traditional flashlamp pumped Nd:YAG laser sources. The use of laser diode array pumping of slab geometry lasers will allow efficient, high peak and average power solid state laser sources to be developed. Perhaps the greatest impact of diode laser pumped solid state lasers will be in spectroscopic applications of miniature, monolithic devices. Single-stripe diode-pumped operation of a continuous-wave 946 nm Nd:YAG laser with less than 10 m/w threshold was demonstrated. A slope efficiency of 16 percent near threshold was shown with a projected slope efficiency well above a threshold of 34 percent based on results under Rhodamine 6G dye-laser pumping. Nonlinear crystals for second-harmonic generation of this source were evaluated. The KNbO3 and periodically poled LiNbO3 appear to be the most promising.

Byer, R. L.↗

Continuous-wave operation of a room-temperature, diode-laser-pumped, 946-nm Nd:YAG laser

Single-stripe diode-laser-pumped operation of a continuous-wave 946-nm Nd:YAG laser with less than 10-mW threshold has been demonstrated. A slope efficiency of 16 percent near threshold was shown with a projected slope efficiency well above a threshold of 34 percent based on results under Rhodamine 6G dye-laser pumping. Nonlinear crystals for second-harmonic generation of this source were evaluated. KNbO3 and periodically poled LiNbO3 appear to be the most promising.

Fan, T. Y.↗

Dynamic rain fade compensation techniques for the advanced communications technology satellite

The dynamic and composite nature of propagation impairments that are incurred on earth-space communications links at frequencies in and above the 30/20 GHz Ka band necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) project by the implementation of optimal processing schemes derived through the use of the ACTS Rain Attenuation Prediction Model and nonlinear Markov filtering theory. The ACTS Rain Attenuation Prediction Model discerns climatological variations on the order of 0.5 deg in latitude and longitude in the continental U.S. The time-dependent portion of the model gives precise availability predictions for the 'spot beam' links of ACTS. However, the structure of the dynamic portion of the model, which yields performance parameters such as fade duration probabilities, is isomorphic to the state-variable approach of stochastic control theory and is amenable to the design of such statistical fade processing schemes which can be made specific to the particular climatological location at which they are employed.

Manning, Robert M.↗

Physics of the thermal quench in MST tokamak plasmas (Final Technical Report)

This project at the University of Wisconsin-Madison targeted measurements in tokamak plasmas in the Madison Symmetric Torus (MST) to help elucidate the physics of the tokamak disruption. We intended to focus on the thermal quench, during which energy is lost from the plasma in a very short time. Understanding and ultimately mitigating the thermal quench are among the highest priority research thrusts for ITER, a large international fusion experiment presently under construction. The measurements in MST exploited an advanced set of diagnostics for internal measurements with high time resolution, targeting linear and nonlinear magnetohydrodynamic (MHD) activity as well as the electron temperature and density profiles. We also exploited other features of the MST device, including very flexible power supplies for the toroidal magnetic field and toroidal plasma current that are capable of producing almost arbitrary waveforms. While the work funded by this project was purely experimental, we continued and expanded an existing collaboration with UW-Madison experts in nonlinear MHD computational modeling of tokamak plasmas. That modeling incorporated realistic, experimentally measured parameters. The results of the modeling were anticipated to deepen considerably our understanding of the experimental measurements, and in turn, the experimental measurements were anticipated to help validate the modeling results. The science of transients such as disruptions is one of the highest priority research areas in the U.S. and international fusion programs. The work carried out in this project was targeted to help advance the science of tokamak disruptions which will in turn contribute to the success of ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

OC6 Phase Ib: Validation of the CFD predictions of difference-frequency wave excitation on a FOWT semisubmersible

During the previous OC5 11 project, state-of-the-art mid-fidelity engineering tools for floating wind systems were found to consistently underpredict the nonlinear, low-frequency responses of semisubmersible offshore wind platforms, leading to substantial errors in the structural loads because of low-frequency surge and pitch resonance. To examine this underprediction, a coordinated investigation with computational fluid dynamics (CFD) simulations and model-basin experiments was carried out. Both investigations involved a fixed and simplified OC5-DeepCwind semisubmersible in bichromatic waves. The wave excitations - especially the nonlinear, difference-frequency excitation - on the structure from the CFD simulations were compared to the experimental measurements for validation, with uncertainty analyses for both the experimental and the CFD results. Furthermore, the wave excitations on each column of the semisubmersible were measured separately in the experiment, allowing the validation of the CFD results to be done on a per-column basis. Overall, the CFD predictions of the difference-frequency excitations agree with the experimental measurements, suggesting the CFD solutions can be used as a reference for tuning and improving the engineering-level tools and can provide a means to better understand the underprediction at low frequencies.

16 TIDAL AND WAVE POWER↗

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗

Tracking system study

A digital computer program was generated which mathematically describes an optimal estimator-controller technique as applied to the control of antenna tracking systems used by NASA. Simulation studies utilizing this program were conducted using the IBM 360/91 computer. The basic ideas of applying optimal estimator-controller techniques to antenna tracking systems are discussed. A survey of existing tracking methods is given along with shortcomings and inherent errors. It is explained how these errors can be considerably reduced if optimal estimation and control are used. The modified programs generated in this project are described and the simulation results are summarized. The new algorithms for direct synthesis and stabilization of the systems including nonlinearities, are presented.

Dennis, A. R.↗

Determining Wheel-Soil Interaction Loads Using a Meshfree Finite Element Approach Assisting Future Missions with Rover Wheel Design

A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.

Contreras, Michael T.↗

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗

Investigation of Nonlinear Difference-Frequency Wave Excitation on a Semisubmersible Offshore-Wind Platform with Bichromatic-Wave CFD Simulations: Preprint

The natural surge and pitch frequencies of semisubmersible offshore wind platforms are typically designed to be below the wave frequencies to avoid direct excitation. However, surge or pitch resonance can be excited by the nonlinear low-frequency loads generated by irregular incident waves. Second-order potential-flow models with added Morison drag have been found to underpredict this low-frequency excitation and response. As part of the OC6 project, Computational Fluid Dynamics (CFD) simulations were performed to enable a better understanding of the low-frequency loads and the limitations of lower-fidelity models. The focus of the current paper is to set up a computationally cost-effective CFD simulation of a fixed semisubmersible platform to investigate nonlinear difference-frequency loads and establish the corresponding uncertainty in the results. Due to the high computing cost, CFD simulations of irregular waves can be challenging. Instead, simulations were performed with bichromatic waves having a shorter repeat period. A preliminary comparison with Quadratic Transfer Functions from second-order potential-flow theory shows that CFD models consistently predict higher nonlinear wave loads at the difference frequency, likely due to flow separation and viscous drag not accounted for in potential-flow theory.

2nd order↗

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term experiments

Climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (<10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.

54 ENVIRONMENTAL SCIENCES↗

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term manipulations: Alaskan Benchmark Data and Model runs

This submission aimed to assess differences in short-term step warming manipulations and long-term chronic response to climate change in Alaskan ecosystems. Briefly, climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (< 10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.The model used in the current study is available publicly (https://github.com/jinyun1tang/ECOSYS), and the current submission contains the python/ matlab codes for analyzing output from the model (includng a readme file to explain the codes). The benchmark data, also enclosed, was collected from a range of published and publicly available sources (extracted using GRABIT: https://www.mathworks.com/matlabcentral/fileexchange/7173-grabit). These sources describe warming induced changes in tundra/ boreal ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Sparse and Random Sampling Techniques for High-Resolution, Full-Field, BSS-Based Structural Dynamics Identification from Video

Video-based techniques for identification of structural dynamics have the advantage that they are very inexpensive to deploy compared to conventional accelerometer or strain gauge techniques. When structural dynamics from video is accomplished using full-field, high-resolution analysis techniques utilizing algorithms on the pixel time series such as principal components analysis and solutions to blind source separation the added benefit of high-resolution, full-field modal identification is achieved. An important property of video of vibrating structures is that it is particularly sparse. Typically video of vibrating structures has a dimensionality consisting of many thousands or even millions of pixels and hundreds to thousands of frames. However the motion of the vibrating structure can be described using only a few mode shapes and their associated time series. As a result, emerging techniques for sparse and random sampling such as compressive sensing should be applicable to performing modal identification on video. This work presents how full-field, high-resolution, structural dynamics identification frameworks can be coupled with compressive sampling. The techniques described in this work are demonstrated to be able to recover mode shapes from experimental video of vibrating structures when 70% to 90% of the frames from a video captured in the conventional manner are removed.

47 OTHER INSTRUMENTATION↗