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At least 1,027 records · Page 57

Computing virtual dark-field X-ray microscopy images of complex discrete dislocation structures from large-scale molecular dynamics simulations

Dark-field X-ray microscopy (DFXM) is a novel diffraction-based imaging technique that non-destructively maps the local deformation from crystalline defects in bulk materials. While studies have demonstrated that DFXM can spatially map 3D defect geometries, it is still challenging to interpret DFXM images of the high-dislocation-density systems relevant to macroscopic crystal plasticity. This work develops a scalable forward model to calculate virtual DFXM images for complex discrete dislocation structure(s) (DDS) obtained from atomistic simulations. Our new DDS-DFXM model integrates a non-singular formulation for calculating the local strain from the DDS and an efficient geometrical optics algorithm for computing the DFXM image from the strain field. We apply the model to complex DDS obtained from a large-scale mol­ecular dynamics simulation of compressive loading on single-crystal silicon. Simulated DFXM images exhibit prominent contrast for dislocation features between the multiple slip systems, demonstrating the potential of DFXM to resolve features from dislocation multiplication. In conclusion, the integrated DDS-DFXM model provides a toolbox for DFXM experimental design and image interpretation in the context of bulk crystal plasticity for a range of measurements across shock plasticity and the broader materials science community.

X-ray imaging↗

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗

A multiresolution spatial parametrization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization. The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10 computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.

Ray, Jaideep↗

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

An automated technique for stellar magnitude, color index, and position measurements of astronomical photographs

Computer programs have been developed for use in collecting and processing data from a PDS scanning microdensitometer. The goal is to obtain fast and simple algorithms for handling an entire astronomical photograph with one-pass digitization. This capability is realized by a real-time detection scheme that provides a data compression of a factor of 100, and a processing program that produces a catalog of magnitudes, color indices, and positions for up to 90,000 multicolor stellar images.

Green, R. F.↗

Shock modelling in transonic and supersonic flow

Numerical simulation studies of problems in transonic flow are conducted in connection with the design of aircraft flying near the speed of sound, while recently there has also been a great deal of interest in supersonic and hypersonic flow calculations. Three important models for inviscid compressible gasdynamics are utilized in the study of these flow problems, taking into account the transonic small disturbance equation (TSD), the transonic full potential equation (FP), and the full Euler equations for compressible gasdynamics (EU). The present paper has the objective to provide a description of shock capturing methods recently developed for each model. The design principles behind the algorithms are also examined, giving attention to consistency, conservative form, monotone and sharp discrete shocks, and a bound on the variation, which prevents spurious oscillations.

Osher, S.↗

Computational fluid dynamics - A personal view

This paper provides a personal view of computational fluid dynamics. The main theme is divided into two categories - one dealing with algorithms and engineering applications and the other with scientific investigations. The former category may be termed computational aerodynamics, with the objective of providing reliable aerodynamic or engineering predictions. The latter category is essentially basic research, where the algorithmic tools are used to unravel and elucidate fluid-dynamic phenomena hard to obtain in a laboratory. A critique of the numerical solution techniques for both compressible and incompressible flows is included. The discussion on scientific investigations deals in particular with transition and turbulence.

Hussaini, M. Y.↗

A study of the compressible flow through a diffusing S-duct

Benchmark aerodynamic data are presented for compressible flow through a representative S-duct configuration. A numerical prediction of the S-duct flow field, obtained from a subsonic parabolized Navier-Stokes algorithm, is also shown. The experimental and numerical results are compared. Measurements of the three-dimensional velocity field, total pressures, and static pressures were obtained at five cross-sectional planes. Aerodynamic data were gathered with calibrated pneumatic probes. Surface static pressure and surface flow visualization data were also acquired. All reported tests were conducted with an inlet centerline Mach number of 0.6. The Reynolds number, based on the inlet centerline velocity and duct inlet diameter, was 2.6 x 10(exp 6). Thin inlet turbulent boundary layers existed. The collected data should be beneficial to aircraft inlet designers and the measurements are suitable for the validation of computational codes. The results show that a region of streamwise flow separation occurred within the duct. Details about the separated flow region, including mechanisms which drive this complicated flow phenomenon, are discussed. Results also indicate that the duct curvature induces strong pressure driven secondary flows. The cross flows evolve into counter-rotating vortices. These vortices convect low momentum fluid of the boundary layer toward the center of the duct, degrading both the uniformity and magnitude of the total pressure profile.

Wellborn, Steven R.↗

A new re-redistribution scheme for weighted state redistribution with adaptive mesh refinement

State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow problems. When used in conjunction with adaptive mesh refinement (AMR), additional steps are needed to preserve the accuracy and conservation properties of the solution if the embedded boundary is not restricted to a single level of the mesh hierarchy. In this work, we extend the weighted state redistribution algorithm to cases where cut cells live at or near a coarse-fine interface within the domain. Here, we present numerical results that demonstrate that the algorithm is conservative when the coarse-fine interface intersects the embedded boundary. Additionally we compare the numerical solution of the Sod shock tube problem in an inclined cylinder with the analytic solution, and we compare the simulation of a shock hitting a cylindrical obstacle with experimental data. Finally we demonstrate the methodology for simulation of the multicomponent compressible Navier-Stokes equations in a piston-bowl geometry, and discuss the computational efficiency gained by not requiring the entire embedded boundary to be defined at the finest level.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

The measurement matrix employed in compressive sensing typically cannot be known precisely a priori and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. A collaborative maximum likelihood algorithm and alternating proximal gradient algorithm are proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve flexibility and generality. Connections between the maximum likelihood methods and the Bayesian model are developed, and example results are presented for a real compressive X-ray imaging system.

Bayesian compressive sensing↗

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗

Coherent control of plasma dynamics by feedback-optimized wavefront manipulation

Plasmas generated by an intense laser pulse can support coherent structures such as large amplitude wakefield that can affect the outcome of an experiment. We investigate the coherent control of plasma dynamics by feedback-optimized wavefront manipulation using a deformable mirror. The experimental outcome is directly used as feedback in an evolutionary algorithm for optimization of the phase front of the driving laser pulse. In this paper, we applied this method to two different experiments: (i) acceleration of electrons in laser driven plasma waves and (ii) self-compression of optical pulses induced by ionization nonlinearity. The manipulation of the laser wavefront leads to orders of magnitude improvement to electron beam properties such as the peak charge, beam divergence, and transverse emittance. The demonstration of coherent control for plasmas opens new possibilities for future laser-based accelerators and their applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗

MO-DE-207A-06: ECG-Gated CT Reconstruction for a C-Arm Inverse Geometry X-Ray System

Purpose: To obtain ECG-gated CT images from truncated projection data acquired with a C-arm based inverse geometry fluoroscopy system, for the purpose of cardiac chamber mapping in interventional procedures. Methods: Scanning-beam digital x-ray (SBDX) is an inverse geometry fluoroscopy system with a scanned multisource x-ray tube and a photon-counting detector mounted to a C-arm. In the proposed method, SBDX short-scan rotational acquisition is performed followed by inverse geometry CT (IGCT) reconstruction and segmentation of contrast-enhanced objects. The prior image constrained compressed sensing (PICCS) framework was adapted for IGCT reconstruction to mitigate artifacts arising from data truncation and angular undersampling due to cardiac gating. The performance of the reconstruction algorithm was evaluated in numerical simulations of truncated and non-truncated thorax phantoms containing a dynamic ellipsoid to represent a moving cardiac chamber. The eccentricity of the ellipsoid was varied at frequencies from 1–1.5 Hz. Projection data were retrospectively sorted into 13 cardiac phases. Each phase was reconstructed using IGCT-PICCS, with a nongated gridded FBP (gFBP) prior image. Surface accuracy was determined using Dice similarity coefficient and a histogram of the point distances between the segmented surface and ground truth surface. Results: The gated IGCT-PICCS algorithm improved surface accuracy and reduced streaking and truncation artifacts when compared to nongated gFBP. For the non-truncated thorax with 1.25 Hz motion, 99% of segmented surface points were within 0.3 mm of the 15 mm diameter ground truth ellipse, versus 1.0 mm for gFBP. For the truncated thorax phantom with a 40 mm diameter ellipse, IGCT-PICCS surface accuracy measured 0.3 mm versus 7.8 mm for gFBP. Dice similarity coefficient was 0.99–1.00 (IGCT-PICCS) versus 0.63–0.75 (gFBP) for intensity-based segmentation thresholds ranging from 25–75% maximum contrast. Conclusions: The PICCS algorithm was successfully applied to reconstruct truncated IGCT projection data with angular undersampling resulting from simulated cardiac gating. Research supported by the National Heart, Lung, and Blood Institute of the NIH under award number R01HL084022. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

60 APPLIED LIFE SCIENCES↗

Understanding plasticity in irradiated alloys through TEM in situ compression pillar tests

Depth-sensing transmission electron microscopic (TEM) in situ mechanical testing has become widely utilized for understanding deformation in irradiated materials. Until now, compression pillars have primarily been used to study the elastic properties and yield of irradiated materials. In this study, we utilize TEM in situ compression pillars to investigate plastic deformation in two ion-irradiated alloys: Fe–9% Cr oxide dispersion strengthened (ODS) alloy and nanocrystalline Cu–24% Ta. We develop an algorithm to automate the extraction of instantaneous pillar dimensions from TEM videos, which we use to calculate true stress–strain curves and strain hardening exponents. True stress–strain curves reveal intermitted plastic flow in all specimen conditions. In the Fe–9% Cr ODS, intermitted plastic flow is linked to strain bursts observed in TEM videos. Low strain hardening or strain softening is observed in all specimen conditions. TEM videos link the strain softening in irradiated Fe–9% Cr ODS to dislocation cross-slip, and in Cu–24% Ta to grain boundary sliding.

36 MATERIALS SCIENCE↗

A Nonlocal Peridynamic Plasticity Model for the Dynamic Flow and Fracture of Concrete.

A nonlocal, ordinary peridynamic constitutive model is formulated to numerically simulate the pressure-dependent flow and fracture of heterogeneous, quasi-brittle ma- terials, such as concrete. Classical mechanics and traditional computational modeling methods do not accurately model the distributed fracture observed within this family of materials. The peridynamic horizon, or range of influence, provides a characteristic length to the continuum and limits localization of fracture. Scaling laws are derived to relate the parameters of peridynamic constitutive model to the parameters of the classical Drucker-Prager plasticity model. Thermodynamic analysis of associated and non-associated plastic flow is performed. An implicit integration algorithm is formu- lated to calculate the accumulated plastic bond extension and force state. The gov- erning equations are linearized and the simulation of the quasi-static compression of a cylinder is compared to the classical theory. A dissipation-based peridynamic bond failure criteria is implemented to model fracture and the splitting of a concrete cylinder is numerically simulated. Finally, calculation of the impact and spallation of a con- crete structure is performed to assess the suitability of the material and failure models for simulating concrete during dynamic loadings. The peridynamic model is found to accurately simulate the inelastic deformation and fracture behavior of concrete during compression, splitting, and dynamically induced spall. The work expands the types of materials that can be modeled using peridynamics. A multi-scale methodology for simulating concrete to be used in conjunction with the plasticity model is presented. The work was funded by LDRD 158806.

Vogler, Tracy↗