A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows
Not Available
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Sethian, James A.
Publications and source records attributed to Sethian, James A..
Insights from high-fidelity modeling of industrial rotary bell atomization
The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.
97 MATHEMATICS AND COMPUTING↗
Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.
97 MATHEMATICS AND COMPUTING↗
Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients
Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.
97 MATHEMATICS AND COMPUTING↗
Autonomous Discovery in Science and Engineering
The Center for Advanced Mathematics for Energy Research Applications (CAMERA) is an integrated, cross-disciplinary center aimed at inventing, developing, and delivering the fundamental new mathematics required to capitalize on experimental investigations at scientific facilities. Jointly funded by the Office of Advanced Scientific Computing Research (ASCR) and the Office of Basic Energy Sciences (BES) within the US Department of Energy’s Office of Science, CAMERA identifies areas in experimental science that can be aided by new mathematical insights, develops the needed algorithmic tools, and delivers them as user-friendly software to the experimental community.
97 MATHEMATICS AND COMPUTING↗
Gaussian processes for autonomous data acquisition at large-scale synchrotron and neutron facilities
The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets.
36 MATERIALS SCIENCE↗
A Kriging-Based Approach to Autonomous Experimentation with Applications to X-Ray Scattering
Abstract Modern scientific instruments are acquiring data at ever-increasing rates, leading to an exponential increase in the size of data sets. Taking full advantage of these acquisition rates will require corresponding advancements in the speed and efficiency of data analytics and experimental control. A significant step forward would come from automatic decision-making methods that enable scientific instruments to autonomously explore scientific problems—that is, to intelligently explore parameter spaces without human intervention, selecting high-value measurements to perform based on the continually growing experimental data set. Here, we develop such an autonomous decision-making algorithm that is physics-agnostic, generalizable, and operates in an abstract multi-dimensional parameter space. Our approach relies on constructing a surrogate model that fits and interpolates the available experimental data, and is continuously refined as more data is gathered. The distribution and correlation of the data is used to generate a corresponding uncertainty across the surrogate model. By suggesting follow-up measurements in regions of greatest uncertainty, the algorithm maximally increases knowledge with each added measurement. This procedure is applied repeatedly, with the algorithm iteratively reducing model error and thus efficiently sampling the parameter space with each new measurement that it requests. We validate the method using synthetic data, demonstrating that it converges to faithful replica of test functions more rapidly than competing methods, and demonstrate the viability of the approach in an experimental context by using it to direct autonomous small-angle (SAXS) and grazing-incidence small-angle (GISAXS) x-ray scattering experiments.
36 MATERIALS SCIENCE↗
An Efficient Algorithm for Automatic Structure Optimization in X-ray Standing-Wave Experiments
We present that x-ray standing-wave photoemission experiments involving multilayered samples are emerging as unique probes of the buried interfaces that are ubiquitous in current device and materials research. Such data require for their analysis a structure optimization process comparing experiment to theory that is not straightforward. In this work, we present a new computer program for optimizing the analysis of standing-wave data, called SWOPT, that automates this trial-and-error optimization process. The program includes an algorithm that has been developed for computationally expensive problems: so-called black-box simulation optimizations. It also includes a more efficient version of the Yang X-ray Optics Program (YXRO) [Yang, S.-H., Gray, A.X., Kaiser, A.M., Mun, B.S., Sell, B.C., Kortright, J.B., Fadley, C.S., J. Appl. Phys. 113, 1 (2013)] which is about an order of magnitude faster than the original version. Human interaction is not required during optimization. We tested our optimization algorithm on real and hypothetical problems and show that it finds better solutions significantly faster than a random search approach. The total optimization time ranges, depending on the sample structure, from minutes to a few hours on a modern laptop computer, and can be up to 100x faster than a corresponding manual optimization. Finally, these speeds make the SWOPT program a valuable tool for realtime analyses of data during synchrotron experiments.
36 MATERIALS SCIENCE↗
Xi-cam : a versatile interface for data visualization and analysis
Xi-cam is an extensible platform for data management, analysis and visualization. Xi-cam aims to provide a flexible and extensible approach to synchrotron data treatment as a solution to rising demands for high-volume/high-throughput processing pipelines. The core of Xi-cam is an extensible plugin-based graphical user interface platform which provides users with an interactive interface to processing algorithms. Plugins are available for SAXS/WAXS/GISAXS/GIWAXS, tomography and NEXAFS data. With Xi-cam 's `advanced' mode, data processing steps are designed as a graph-based workflow, which can be executed live, locally or remotely. Remote execution utilizes high-performance computing or de-localized resources, allowing for the effective reduction of high-throughput data. Xi-cam 's plugin-based architecture targets cross-facility and cross-technique collaborative development, in support of multi-modal analysis. Xi-cam is open-source and cross-platform, and available for download on GitHub.
Pandolfi, Ronald J. (ORCID:0000000308248548)↗
A mixed-scale dense convolutional neural network for image analysis
Significance Popular neural networks for image-processing problems often contain many different operations, multiple layers of connections, and a large number of trainable parameters, often exceeding several million. They are typically tailored to specific applications, making it difficult to apply a network that is successful in one application to different applications. Here, we introduce a neural network architecture that is less complex than existing networks, is easy to train, and achieves accurate results with relatively few trainable parameters. The network automatically adapts to a specific problem, allowing the same network to be applied to a wide variety of different problems.
97 MATHEMATICS AND COMPUTING↗
Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase
Significance Single-particle diffraction is an emerging technique in which diffraction images are collected from individual particles, and is used to study molecular structure from multiple conformational states that may be inaccessible through other methods. However, determining structure from these experiments is challenging, since orientations and states of imaged particles are unknown and images are highly contaminated with noise. Furthermore, the number of useful images is often limited by achievable single-particle hit rates, currently around 0.1%. We introduce an iterative projection framework to simultaneously determine orientations, states, and molecular structure from limited single-particle data by leveraging structural constraints throughout the reconstruction. This framework offers a potential pathway to increasing the amount of information that can be extracted from single-particle diffraction.
97 MATHEMATICS AND COMPUTING↗
Nanosurveyor: a framework for real-time data processing
Not Available
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
SHARP: a distributed GPU-based ptychographic solver
Ever brighter light sources, fast parallel detectors and advances in phase retrieval methods have made ptychography a practical and popular imaging technique. Compared to previous techniques, ptychography provides superior robustness and resolution at the expense of more advanced and time-consuming data analysis. Therefore, by taking advantage of massively parallel architectures, high-throughput processing can expedite this analysis and provide microscopists with immediate feedback. These advances allow real-time imaging at wavelength-limited resolution, coupled with a large field of view. This article describes a set of algorithmic and computational methodologies used at the Advanced Light Source and US Department of Energy light sources. These are packaged as a CUDA-based software environment named SHARP, aimed at providing state-of-the-art high-throughput ptychography reconstructions for the coming era of diffraction-limited light sources.
47 OTHER INSTRUMENTATION↗
Making Advanced Scientific Algorithms and Big Scientific Data Management More Accessible
Synchrotrons such as the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory are known as user facilities. They are sources of extremely bright X-ray beams, and scientists come from all over the world to perform experiments that require these beams. As the complexity of experiments has increased, and the size and rates of data sets has exploded, managing, analyzing and presenting the data collected at synchrotrons has been an increasing challenge. The ALS has partnered with high performance computing, fast networking, and applied mathematics groups to create a"super-facility", giving users simultaneous access to the experimental, computational, and algorithmic resources to overcome this challenge. This combination forms an efficient closed loop, where data despite its high rate and volume is transferred and processed, in many cases immediately and automatically, on appropriate compute resources, and results are extracted, visualized, and presented to users or to the experimental control system, both to provide immediate insight and to guide decisions about subsequent experiments during beam-time. In this paper, We will present work done on advanced tomographic reconstruction algorithms to support users of the 3D micron-scale imaging instrument (Beamline 8.3.2, hard X-ray micro-tomography).
97 MATHEMATICS AND COMPUTING↗
Multicellular Architecture of Malignant Breast Epithelia Influences Mechanics
Cell-matrix and cell-cell mechanosensing are important in many cellular processes, particularly for epithelial cells. A crucial question, which remains unexplored, is how the mechanical microenvironment is altered as a result of changes to multicellular tissue structure during cancer progression. In this study, we investigated the influence of the multicellular tissue architecture on mechanical properties of the epithelial component of the mammary acinus. Using creep compression tests on multicellular breast epithelial structures, we found that pre-malignant acini with no lumen (MCF10AT) were significantly stiffer than normal hollow acini (MCF10A) by 60%. This difference depended on structural changes in the premalignant acini, as neither single cells nor normal multicellular acini tested before lumen formation exhibited these differences. To understand these differences, we simulated the deformation of the acini with different multicellular architectures and calculated their mechanical properties; our results suggest that lumen filling alone can explain the experimentally observed stiffness increase. We also simulated a single contracting cell in different multicellular architectures and found that lumen filling led to a 20% increase in the "perceived stiffness" of a single contracting cell independent of any changes to matrix mechanics. Our results suggest that lumen filling in carcinogenesis alters the mechanical microenvironment in multicellular epithelial structures, a phenotype that may cause downstream disruptions to mechanosensing.
59 BASIC BIOLOGICAL SCIENCES↗
Augmented Topological Descriptors of Pore Networks for Material Science
One potential solution to reduce the concentration of carbon dioxide in the atmosphere is the geologic storage of captured CO 2 in underground rock formations, also known as carbon sequestration. There is ongoing research to guarantee that this process is both efficient and safe. We describe tools that provide measurements of media porosity, and permeability estimates, including visualization of pore structures. Existing standard algorithms make limited use of geometric information in calculating permeability of complex microstructures. This quantity is important for the analysis of biomineralization, a subsurface process that can affect physical properties of porous media. This paper introduces geometric and topological descriptors that enhance the estimation of material permeability. Our analysis framework includes the processing of experimental data, segmentation, and feature extraction and making novel use of multiscale topological analysis to quantify maximum flow through porous networks. We illustrate our results using synchrotron-based X-ray computed microtomography of glass beads during biomineralization. As a result, we also benchmark the proposed algorithms using simulated data sets modeling jammed packed bead beds of a monodispersive material.
36 MATERIALS SCIENCE↗
Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains
Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.
Barth, Timothy J.↗
Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains
Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.
Barth, Timothy J.↗