Modeling Modulated Tool Path Machining Using Coupled Smoothed Particle Hydrodynamics and Finite Element Method
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Engineering, Materials science↗
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A Hybrid Finite Volume-Smoothed Particle Hydrodynamics Approach for Shock Capturing
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Myers, Conner↗
Machine learning for event detection in non-smooth initial value problems
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Saunders, Brian Evan↗
Measurement of shock roughness due to phase plate speckle imprinting relevant for x-ray diffraction experiments on 3rd and 4th generation light sources
Laser-shock compression experiments at 3rd and 4th generation light sources generally employ phase plates, which are inserted into the beamline to achieve a repeatable intensity distribution at the focal plane. Here, the laser intensity profile is characterized by a high-contrast, high-frequency laser speckle. Without sufficient smoothing, these laser non-uniformities can translate to a significant pressure distribution within the sample layer and can affect data interpretation in x-ray diffraction experiments. Here, we use a combination of one- and two-dimensional velocity interferometry to directly measure the extent to which spatial frequencies within the laser focal spot intensity pattern are smoothed out during propagation within the laser plasma and a polyimide ablator. We find that the use of thicker polyimide layers results in spatially smoother shock fronts, with the greatest degree of smoothing associated with the highest spatial frequencies. Focal spots with the smallest initial speckle separation produce the most rapid smoothing. Laser systems that employ smoothing by spectral dispersion techniques to rapidly modulate the focal plane intensity distribution are shown to be the most effective ones in producing a spatially smooth shock front. We show that a simple transport model combined with the known polyimide Hugoniot adequately describes the extent of shock smoothness as a function of polyimide thickness. Finally, our results provide a description of spatial structure smoothing across a shock front, which can be used to design targets on x-ray free electron laser facilities.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers
We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .
97 MATHEMATICS AND COMPUTING↗
Illuminating dark matter halo density profiles without subhaloes
Cold dark matter haloes consist of a relatively smooth dark matter component as well as a system of bound subhaloes. It is the prevailing practice to include all mass, including mass in subhaloes, in studies of halo density profiles in simulations. However, often in observational studies satellites are treated as having their own distinct dark matter density profiles in addition to the profile of the host. This difference can make comparisons between theoretical and observed results difficult. In this work, we investigate density profiles of the smooth components of host haloes by excluding mass contained within subhaloes. We find that the density profiles of the smooth halo component (without subhaloes) differ substantially from the conventional halo density profile, declining more rapidly at large radii. We also find that concentrations derived from smooth density profiles exhibit less scatter at fixed mass and a weaker mass dependence than standard concentrations. Both smooth and standard halo profiles can be described by a generalized Einasto profile, an Einasto profile with a modified central slope, with smaller residuals than either a Navarro–Frenk–White or Einasto profile. Furthermore, these results hold for both Milky Way-mass and cluster-mass haloes. This new characterization of smooth halo profiles can be useful for many analyses, such as lensing and dark matter annihilation, in which the smooth and clumpy components of a halo should be accounted for separately.
79 ASTRONOMY AND ASTROPHYSICS↗
Protection Against Graph-Based False Data Injection Attacks on Power Systems
Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.
Morgenstern, Gal↗
Improved Data Interpretation through Identification of Time Series Periodicity Changes
Analysis and interpretation of time series data is easiest when the data values occur at uniform intervals in time, but actual data may have differing data sampling frequencies, such as monthly and daily readings. Applying data analysis techniques, such as smoothing, to such a data set may not give a representative result between time segments. The ability to automatically distinguish time segments of differing data frequency would provide a means for applying data analysis independently to each segment, though a suitable blending at segment boundaries would be required. A method for detecting frequency changes was developed and applied to Gaussian and median smoothing of hydraulic head data from groundwater wells at the U.S. Department of Energy Hanford Site in southeastern Washington state. The process identifies time segments of high-frequency (daily) or low-frequency (greater than daily) data using adjusted-bandwidth Gaussian kernel density estimation and a threshold value, which are further refined to address small blocks of low-frequency data within larger blocks of high-frequency data. User-selectable levels of smoothing are then applied independently to the time segments prior to combining the segment results for a single smoothed data set. This time segment identification approach provides effective low- and high-frequency data separation, which provides a method to apply data analysis independently to each time segment.
97 MATHEMATICS AND COMPUTING↗
On the influence of over-parameterization in manifold based surrogates and deep neural operators
Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.
97 MATHEMATICS AND COMPUTING↗
Integrability, normal forms, and magnetic axis coordinates
Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation entirely consisting of invariant submanifolds. A compact regular leaf (a flux surface) of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact smooth normal forms in which the field lines are straight. However, these normal forms break down near singular leaves, including elliptic and hyperbolic magnetic axes. In this work, the existence of exact smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes is established. In the elliptic case, smooth near-axis Hamada and Boozer coordinates are defined and constructed. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydrodynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields: they are presymplectic systems.
97 MATHEMATICS AND COMPUTING↗
Non-parametric Lagrangian biasing from the insights of neural nets
We present a Lagrangian model of galaxy clustering bias in which we train a neural net using the local properties of the smoothed initial density field to predict the late-time mass-weighted halo field.By fitting the mass-weighted halo field in the AbacusSummit simulations at z = 0.5, we find that including three coarsely spaced smoothing scales gives the best recovery of the halo power spectrum. Adding more smoothing scales may lead to 2–5% underestimation of the large-scale power and can cause the neural net to overfit.We find that the fitted halo-to-mass ratio can be well described by two directions in the original high-dimension feature space.Projecting the original features into these two principal components and re-training the neural net either reproduces the original training result, or outperforms it with a better match of the halo power spectrum. The elements of the principal components are unlikely to be assigned physical meanings, partly owing to the features being highly correlated between different smoothing scales.Our work illustrates a potential need to include multiple smoothing scales when studying galaxy bias, and this can be done easily with machine-learning methods that can take in high dimensional input feature space.
79 ASTRONOMY AND ASTROPHYSICS↗
Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation
Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A Sparse and Low Rank Penalized Signal Decomposition Model with Constraints: Anomaly Detection in PV Systems
Recently, robust PCA has seen its wide application in various industries for its ability to perform the task of anomaly detection. The essence of robust PCA approach is to break down the signal into a low rank component and sparse component. In many applications, a simple breakdown of the signal without accounting for the signs of low rank components and sparse components would violate the physical constraints of the decomposed signal. In addition, often times, the signals in the real world collected for a long duration has smooth changes within a day and between days. As an example, the power signals collected in a photovoltaic (PV) system are cyclostationary, exhibiting these characteristics. Neglecting the smoothness of signals would result in miss detection of anomalous signals which are smooth within a day but non-smooth between days and vice versa. In this paper, we developed a signal decomposition approach for the purpose of anomaly detection based on the idea of low rank and sparse decomposition taking into consideration the signs of the decomposed low rank and sparse components and the within-day and between-day smooth changes in the original signals. The proposed unsupervised approach for fault detection eliminates the need for faulty samples required by other machine learning methods. It does not require the full I-V characteristics to work. Furthermore, there is no need for complex modelling of PV systems as in the case of power loss analysis. Using Monte Carlo simulations, we demonstrate the ability of our proposed approach for detecting anomalies of different duration and severity in PV systems.
14 SOLAR ENERGY↗
Bayesian Approach to Estimation of Water Table Elevations Using Historical Rasters as Prior Information 2019 - 20430
In cases of complex but only partially known geology and a lack of spatial control in observation well locations, water table elevation estimation is very challenging. In some cases, auxiliary information, such as observations of the movement of tracers, operation of injection and extraction wells, and calibration of groundwater models against the historical elevation data, can be combined with expert judgement to estimate flow directions in areas of sparse data and to aid in the production of more reliable contour maps (and associated rasters) than could be produced by relying on sparse well elevation data alone. Given a historical sequence of these raster maps, the question arises how to automate, to the extent possible, the process of producing new raster maps to reflect data from previous times, the current data and the operation of expert judgement. One solution is to adopt a Bayesian point of view and to regard the historical well elevation data, auxiliary information and historical raster maps as prior information. The well elevations for water table wells, as well as those for injection/extraction wells and the data associated with other relevant variables, can be viewed as predictors for the raster surface. From this prior information, we can, conditional on the values of these predictors for a new time period, compute an expected value map and a standard deviation map for the new raster. These then can be taken to specify a prior predictive distribution for the pixels in the new raster map. Then we condition the pixels, corresponding to water level observation wells within the raster, on the observed values in those wells (which in general will differ from the regression estimate) for the new time period. Given the smoothness of the water table surface, we then smooth the surface of deviations from the mean surface, based on the variograms of the historical rasters, and add this smoothed surface to the regression mean surface. The error structure of the produced raster map is defined by the regression error structure and the error due to smoothing based on the estimated variograms. This methodology has been developed and is being further refined for groundwater monitoring and remediation at LANL. It is a very flexible method that can also be applied with a variety of other predictors applied to model the water level wells in the area of interest over the historical record. The smoothness of the spatial process and its possible evolution over time can then be estimated from the residuals from this regression. This can be augmented by expert hydrogeological opinion based on site topography and hydrogeology. (authors)
54 ENVIRONMENTAL SCIENCES↗
Heat Transfer Coefficients of Additively Manufactured Tubes with Internal Pin Fins for Supercritical Carbon Dioxide Cycle Recuperators
This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO 2 flowing in additively manufactured tubes with internal pin fins at the US DOE’s National Energy Technology Laboratory in Morgantown, WV. The measurement procedures were validated by conducting benchmark tests with smooth stainless-steel tube and comparing the results with published correlations for Nusselt number (Nu) and friction factor. Over Reynolds numbers (ReD) ranging from 5 × 10 4 to 2.5 × 10 5 , measured Nu was within 5% of the Dittus-Boelter correlation and measured friction factors were within 5% of the McAdams correlation for smooth tube flow. The candidate pin fin patterned pipes were additively manufactured (AM) at the Oak Ridge National Laboratory. The pins were circular or elliptical in cross-section and were printed at a 30⁰ angle relative to the inner wall (to meet AM constraints). The pin arrangement was helical to promote enhanced heat transfer due to swirl flow. Pin length to diameter aspect ratio was 1.33, 2, and 8, while the pin diameter to tube diameter ratio was 0.188, 0.125, and 0.063. Tests were performed for ReD varying from 6.9 × 10 4 to 2.2 × 10 5 and at conditions equivalent to the low pressure (LP) outlet (8.69 MPa, 361 K) and the high pressure (HP) inlet (20.7 MPa, 350 K) of the low temperature recuperator (LTR) in an indirect sCO 2 cycle. The Wilson plot technique was utilized to measure the bulk heat transfer coefficients. For the best performing design (tube A, pin length to tube diameter ratio: 1.33, pin diameter to tube diameter ratio: 0.19), the local heat transfer coefficient increased by 136% relative to the Dittus-Boelter correlation at the LTR low pressure outlet and 194% at the LTR high pressure inlet. These correspond to a 282% and a 271% increase in the product of the heat transfer coefficient and surface area (adjusted for fin efficiency) product, respectively. Large pressure drops across the test articles were observed. For Tube Design A, the average friction factor, across the range of ReD considered, was significantly larger than the McAdams correlation at both the LTR LP outlet and the LTR HP inlet. A thermal performance factor was utilized to express the ratio of material required to build a finned heat exchanger relative to a finless heat exchanger with the same heat duty and pumping power. Tube Design A was estimated to decrease the required heat exchanger material by 13%.
Searle, Matthew↗
Simulation of Microcapsule Transport in Fractured Media Using Coupled CFD‐DEM
Geothermal energy is sustainable and gaining momentum as a solution to energy crises and environmental issues. However, challenges like production temperature and thermal breakthrough can impact geothermal project efficiency. One innovative solution to alleviate the thermal breakthrough is to inject polymer-based materials that are encapsulated in microcapsules into fractures to modify fracture permeability and prevent preferential flow. In our study, we utilized a coupled computational fluid dynamics and discrete element method to simulate the transport of microcapsules under various scenarios controlled by microcapsule size, microcapsule concentration, and fracture roughness. For a smooth fracture, the results indicate that small microcapsules can travel through a smooth fracture regardless of their concentrations. Large microcapsules can transport through a smooth fracture when present in lower concentrations. However, medium and mixed-size microcapsules tend to cause the sealing of a smooth fracture, irrespective of their concentrations. For a rough fracture, the transport of microcapsules is complicated by their interactions with the rough fracture walls. The presence of two sealing positions in a rough fracture adds further complexity to this transport phenomenon. The size and concentration of microcapsules control one sealing location, while the rough fracture walls determine the other sealing location. The rough walls substantially affect microcapsule transport, rendering the role of microcapsule size and concentration less significant. The simulation results suggest that complex fracture surfaces significantly elevate the occurrence of sealing behavior. To mitigate sealing behavior within more complex fractures, it would be beneficial to use smaller and lower concentrations of microcapsules.
15 GEOTHERMAL ENERGY↗
Velocity-dependent annihilation radiation from dark matter subhalos in cosmological simulations
Here, we use the suite of Milky Way-like galaxies in the Auriga simulations to determine the contribution to annihilation radiation from dark matter subhalos in three velocity-dependent dark matter annihilation models: Sommerfeld, p-wave, and d-wave models. We compare these to the corresponding distribution in the velocity-independent s-wave annihilation model. For both the hydrodynamical and dark-matter-only simulations, only in the case of the Sommerfeld-enhanced annihilation does the total annihilation flux from subhalos exceed the total annihilation flux from the smooth halo component within the virial radius of the halo. Progressing from Sommerfeld to the s, p, and d-wave models, the contribution from the smooth component of the halo becomes more dominant, implying that for the p-wave and d-wave models the smooth component is by far the dominant contribution to the radiation. Comparing to the Galactic center excess observed by Fermi-LAT, for all simulated halos the emission is dominated by the smooth halo contribution. However, it is possible that for Sommerfeld models, extrapolation down to mass scales below the current resolution limit of the simulation would imply a non-negligible contribution to the gamma-ray emission from the Galactic Center region.
79 ASTRONOMY AND ASTROPHYSICS↗
Molecular-gas-dynamics simulations of turbulent Couette flow over a mean-free-path-scale permeable substrate
Here we report flow statistics and visualizations from molecular-gas-dynamics simulations using the direct simulation Monte Carlo (DSMC) method for turbulent Couette flow in a minimal domain where the lower wall is replaced by an idealized permeable fibrous substrate representative of thermal-protection-system materials for which the Knudsen number is O(10 -1 ). Comparisons are made with smooth-wall DSMC simulations and smooth-wall direct numerical simulations (DNS) of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed. In the range of Reynolds numbers considered herein, the scalings of the skin friction on the permeable substrate and of the mean flow within the substrate suggest that they are dominated by viscous effects. While the regenerative cycle characteristic of smooth-wall turbulence remains intact for all cases considered, we observe that the near-wall velocity fluctuations are modulated by the permeable substrate with a wavelength equal to the pore spacing. Additionally, the flow within the substrate shows significant rarefaction effects, resulting in an apparent permeability that is 13% larger than the intrinsic permeability. In contrast, the smooth-wall DSMC and DNS simulations exhibit remarkably good agreement for the statistics examined, despite the Knudsen number based on the viscous length scale being as large as O(10 -1 ). This latter result is at variance with classical estimates for the breakdown of the continuum assumption and calls for further investigations into the interaction of noncontinuum effects and turbulence.
42 ENGINEERING↗