Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical physics methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Second Order System Study

During my education in mathematics, engineering and physics, I learned transform pairs and their usage mechanics but I never remember seeing the derivations of the solutions to second order ordinary differential equations (ODE) and difference equations. A solution to a question posed in a potential funder meeting put me on a path to solving second order systems using the five principal Fourier based methods: Fourier transform (FT), Z-transform (ZT), discrete time Fourier transform (DTFT), discrete Fourier transform (DFT) and Laplace transform (LT).

42 ENGINEERING↗
DOE OSTI2020

Advanced Methods for Immersed Domain Multi-physics Computations

This is the final report on the project, and describes the main accomplishments in the development of the Shifted Boundary Method (SBM), a new computational framework for embedded/immersed computational mechanics applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics

In this paper, we present a new intersection-distribution-based remapping method between arbitrary polygonal meshes for indirect staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. All cell-centered material quantities are conservatively remapped using intersections between the Lagrangian (old, source) mesh and the rezoned (new, target) mesh. The new nodal masses are obtained by conservative distribution of all material masses in each new cell to the cell's corners and then collecting those corner masses at new nodes. This distribution is done using a local constrained optimization approach for each cell in the new mesh. In order to remap nodal momentum we first define cell-centered momentum for each cell in the old mesh, conservatively remap this to the new mesh and then conservatively distribute the new zonal momentum to each cell's bounding nodes, again using local constrained optimization. Our method also conserves total energy by applying a new nodal kinetic energy correction that relies on a process similar to that used for remapping nodal mass and momentum. Cell-centered kinetic energy is computed, conservatively remapped and then distributed to nodes. The discrepancy between this conservatively remapped and actual nodal kinetic energy is then conservatively distributed to the internal energies of the materials in the cells surrounding each node. Unlike conventional cell-based corrections of this type, this new nodal kinetic energy correction has not been observed to drive material internal energy negative in any of our testing. Unlike flux based remapping, our new intersection-distribution method can be applied to remapping between source and target meshes that are arbitrarily different, which provides superior flexibility in the rezoning strategy. Our method is accurate, essentially conservative and essentially bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

Herein this paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A weighted state redistribution algorithm for embedded boundary grids

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. Notably, the stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bayesian Learning of Adatom Interactions from Atomically Resolved Imaging Data

Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. In this work, we develop a workflow based on a machine-learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Benchmark problems for the Mesoscale Multiphysics Phase Field Simulator (MEMPHIS)

This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported classical phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Evaluating Space Object Conjunction Probabilities Using Characteristic Function Inversion

This report discusses an approach to computing the probability of a conjunction between two space objects in the short-term encounter scenario. A conjunction is defined here as an event where the miss distance between the objects is less than some specified value. The scenario assumptions are that the motion of the objects is linear, their positions are Gaussian distributed, and their velocities are known and constant. Under these assumptions, the squared-miss distance is shown to have the generalized chi-square distribution. An established statistical technique called characteristic function inversion is employed to evaluate the distribution and obtain conjunction probabilities. The method is closely related to a recent approach based on moment generating function inversion, and a qualitative comparison of the approaches is provided. Last, the method is tested on several benchmark test cases where it agrees with numerical integration on the cases with conjunction probabilities above 10 –12 . However, the exact probability in these cases is usually not needed and this probability can be bounded above using an independent Gaussian approximation. Overall, the report shows how to compute conjunction probabilities using a standard statistical method, though numerical integration seems to perform equally well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

DUNE Data Management: Network Visualization Monitoring Software

Fermilab’s fagship Deep Underground Neutrino Experiment (DUNE) seeks to better understand the nature of neutrinos within the context of Leptogenesis, neutrino oscillations, multi-messenger Astronomy, and other scientifc phenomena. The experiment will send a beam of neutrinos from the Fermilab site in Illinois to the Sanford Underground Neutrino Facility (SURF) in South Dakota, generating petabytes of scientifc data. Given the high volume of data expected when measurements begin at the end of the decade, DUNE computing and the data management group must carefully monitor data transfers across the 15 remote storage sites and, more generally, the 36 global DUNE computing sites. This report will describe both the frontend and backend data monitoring software designed to analyze and visualize these data transfers. Specifc emphasis will be placed on the software’s setup, usage, and methods for future implementations. The full software code can be found under the DUNE/data-mgmt-testing GitHub repository.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Complex Langevin and other approaches to the sign problem in quantum many-body physics

In this work, we review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

SANS quantification of bound water in water-soluble polymers across multiple concentration regimes

Contrast-variation small-angle neutron scattering (CV-SANS) is a widely used technique for quantifying hydration water in soft matter systems, but it is predominantly applied in the dilute regime or for systems with a well-defined structure factor. Here, CV-SANS was used to quantify the number of hydration water molecules associating with three water-soluble polymers with different critical solution temperatures and types of water–solute interactions in dilute, semidilute, and concentrated solution through the exploration of novel methods of data fitting and analysis. Multiple SANS fitting workflows with varying levels of model assumptions were evaluated and compared to give insight into SANS model selection. These fitting pathways ranged from general, model-free algorithms to more standard form and structure factor fitting. In addition, Monte Carlo bootstrapping was evaluated as a method to estimate parameter uncertainty through simulation of technical replicates. The most robust fitting workflow for dilute solutions was found to be form factor fitting without CV-SANS ( i.e. polymer in 100% D 2 O). For semidilute and concentrated solutions, while the model-free approach can be mathematically defined for CV-SANS data, the addition of a structure factor imposes physical constraints on the optimization problem, suggesting that the optimal fitting pathway should include appropriate form and structure factor models. The measured hydration numbers were consistent with the number of tightly bound water molecules associated with each monomer unit, and the concentration dependence of the hydration number was largely governed by the chemistry-specific interactions between water and polymer. Polymers with weaker water–polymer interactions ( i.e. those with fewer hydration water molecules) were found to have more bound water at higher concentrations than those with stronger water–polymer interactions due to the increase in the number of forced water–polymer contacts in the concentrated system. This SANS-based method to count hydration water molecules can be applied to polymers in any concentration regime, which will lead to improved understanding of water–polymer interactions and their impact on materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An adaptive approach to machine learning for compact particle accelerators

Abstract Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spectral Denoising for Accelerated Analysis of Correlated Ionic Transport

Computation of correlated ionic transport properties from molecular dynamics in the Green-Kubo formalism is expensive, as one cannot rely on the affordable mean square displacement approach. We use spectral decomposition of the short-time ionic displacement covariance to learn a set of diffusion eigenmodes that encode the correlation structure and form a basis for analyzing the ionic trajectories. This allows systematic reduction of the uncertainty and accelerate computations of ionic conductivity in systems with a steady-state correlation structure. We provide mathematical and numerical proofs of the method’s robustness and demonstrate it on realistic electrolyte materials.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Inverse Volume Scaling of Finite-Size Error in Periodic Coupled Cluster Theory

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

CONGO²: Scalable Online Anomaly Detection and Localization in Power Electronics Networks

Rapid and accurate detection and localization of electronic disturbances simultaneously are important for preventing its potential damages and determining potential remedies. Existing anomaly detection methods are severely limited by the low accuracy, the expensive computational cost and the need for highly trained personnel. There is an urgent need for a scalable online algorithm for in-field analysis of large-scale power electronics networks. Here in this paper, we propose a fast and accurate algorithm for anomaly detection and localization of power electronics networks: stratified colored-node graph (CONGO2). This algorithm hierarchically models the change of correlated waveforms and then correlated sensors using the colored-node graph. By aggregating the change of each sensor with its neighbors’ inputs, we can spontaneously identify and localize the anomaly that cannot be detected by data collected from a single sensor. As our proposed method only focuses on the changes within a short time frame, it is highly computational efficient and only needs small data storage. Thus, our method is ideal for online and reliable anomaly detection and localization of large-scale power electronic networks. Compared to existing anomaly detection methods, our method is entirely data-driven without training data, highly accurate and reliable for wide-spectrum anomalies detection, and more importantly, capable of both detection and localization. Thus, it is ideal for infield deployment for large-scale power electronic networks. As illustrated by a distributed energy resources (DERs) power grid with 37-node, our method can effectively detect and localize various cyber and physical attacks.

42 ENGINEERING↗