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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.

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DOE OSTI2021

Joint ptycho-tomography with deep generative priors

Abstract Joint ptycho-tomography is a powerful computational imaging framework to recover the refractive properties of a 3D object while relaxing the requirements for probe overlap that is common in conventional phase retrieval. We use an augmented Lagrangian scheme for formulating the constrained optimization problem and employ an alternating direction method of multipliers (ADMM) for the joint solution. ADMM allows the problem to be split into smaller and computationally more efficient subproblems: ptychographic phase retrieval, tomographic reconstruction, and regularization of the solution. We extend our ADMM framework with plug-and-play (PnP) denoisers by replacing the regularization subproblem with a general denoising operator based on machine learning. While the PnP framework enables integrating such learned priors as denoising operators, tuning of the denoiser prior remains challenging. To overcome this challenge, we propose a denoiser parameter to control the effect of the denoiser and to accelerate the solution. In our simulations, we demonstrate that our proposed framework with parameter tuning and learned priors generates high-quality reconstructions under limited and noisy measurement data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543–1608, 2004), (Bull Inst Math Acad Sin 1:1–78, 2006), (Bull Inst Math Acad Sin 6:151–243, 2011) and Lee et al. (Commun Math Phys 269:17–37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

L{sup ∞} error bound of conservative compact difference scheme for the generalized symmetric regularized long-wave (GSRLW) equations

In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is O(τ{sup 2}+h{sup 4}) in the L{sup ∞}-norm for u and ρ. For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accurate Determination of the Values of Fundamental Physical Constants: The Basis of the New “Quantum” SI Units

The metric system appeared as the system of units designed for macroscopic (laboratory scale) measurements. The progress in accurate determination of the values of quantum constants (such as the Planck constant) in SI units shows that the capabilities in high-precision measurement of microscopic and macroscopic quantities in terms of the same units have increased substantially recently. At the same time, relative microscopic measurements (for example, the comparison of atomic transition frequencies or atomic masses) are often much more accurate than relative measurements of macroscopic quantities. This is the basis for the strategy to define units in microscopic phenomena and then use them on the laboratory scale, which plays a crucial role in practical methodological applications determined by everyday life and technologies. The international CODATA task group on fundamental constants regularly performs an overall analysis of the precision world data (the so-called Adjustment of the Fundamental Constants ) and publishes their recommended values. The most recent evaluation was based on the data published by the end of 2014; here, we review the corresponding data and results. The accuracy in determination of the Boltzmann constant has increased, the consistency of the data on determination of the Planck constant has improved; it is these two dimensional constants that will be used in near future as the basis for the new definition of the kelvin and kilogram, respectively. The contradictions in determination of the Rydberg constant and the proton charge radius remain. The accuracy of determination of the fine structure constant and relative atomic weight of the electron has improved. Overall, we give a detailed review of the state of the art in precision determination of the values of fundamental constants. The mathematical procedure of the Adjustment, the new data and results are considered in detail. The limitations due to macroscopic properties of material standards (such as the International prototype of the kilogram) and the isotopic composition of substances involved in precision studies in general (as standard measures for the triple point of water) and, in particular, in the determination of the fundamental constants are discussed. The perspectives of the introduction of the new quantum units, which will be free from the mentioned problems, are considered. Many physicists feel no sympathy for the International system of units (SI), believing that it does not properly reflect the character of physical laws. In fact, there are three parallel systems, namely the systems of quantities, system of their units and the related standards. The definition of the units, in particular, the SI units, above all, reflects our ability to perform precision measurements of physical values under certain conditions, in particular, to create appropriate standards. This requirement is not related to the beauty of fundamental laws of nature. More accurate determination of the fundamental constants is one of the areas where we accumulate such experience.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Binary Control Pulse Optimization for Quantum Systems

Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared L 2 -penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Solving the sample size problem for resource selection functions

Abstract Sample size sufficiency is a critical consideration for estimating resource selection functions (RSFs) from GPS‐based animal telemetry. Cited thresholds for sufficiency include a number of captured animals and as many relocations per animal N as possible. These thresholds render many RSF‐based studies misleading if large sample sizes were truly insufficient, or unpublishable if small sample sizes were sufficient but failed to meet reviewer expectations. We provide the first comprehensive solution for RSF sample size by deriving closed‐form mathematical expressions for the number of animals M and the number of relocations per animal N required for model outputs to a given degree of precision. The sample sizes needed depend on just 3 biologically meaningful quantities: habitat selection strength, variation in individual selection and a novel measure of landscape complexity, which we define rigorously. The mathematical expressions are calculable for any environmental dataset at any spatial scale and are applicable to any study involving resource selection (including sessile organisms). We validate our analytical solutions using globally relevant empirical data including 5,678,623 GPS locations from 511 animals from 10 species (omnivores, carnivores and herbivores living in boreal, temperate and tropical forests, montane woodlands, swamps and Arctic tundra). Our analytic expressions show that the required M and N must decline with increasing selection strength and increasing landscape complexity, and this decline is insensitive to the definition of availability used in the analysis. Our results demonstrate that the most biologically relevant effects on the utilization distribution (i.e. those landscape conditions with the greatest absolute magnitude of resource selection) can often be estimated with much fewer than animals. We identify several critical steps in implementing these equations, including (a) a priori selection of expected model coefficients and (b) regular sampling of background (pseudoabsence) data within a given definition of availability. We discuss possible methods to identify a priori expectations for habitat selection coefficients, effects of scale on RSF estimation and caveats for rare species applications. We argue that these equations should be a mandatory component for all future RSF studies.

Street, Garrett M.↗
DOE OSTI2021

Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

Schloegl's second model (also known as the quadratic contact process) on a lattice involves spontaneous particle annihilation at rate p and autocatalytic particle creation at empty sites with n ≥ 2 occupied neighbors. The particle creation rate for exactly n occupied neighbors is selected here as n(n - 1)/[z(z - 1)] for lattice coordination number z. We analyze this model on a Bethe lattice. Precise behavior for stochastic models on regular periodic infinite lattices is usually surmised from kinetic Monte Carlo simulation on a finite lattice with periodic boundary conditions. However, the persistence of boundary effects for a Bethe lattice complicates this process, e.g., by inducing spatially heterogenous states. This motivates the exploration of various boundary conditions and unconventional simulation ensembles on the Bethe lattice to predict behavior for infinite size. Here, we focus on z = 3, and predict a discontinuous transition to the vacuum state on the infinite lattice when p exceeds a threshold value of around 0.053.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order (p = 1) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, requiring specialized solvers to treat the anisotropy. We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and Bassi and Rebay (BR2) discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Finally, numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The impact of autonomous vehicles on commute ridesharing with uncertain work end time

The uncertainty in work end time can prevent ridesharing between two commuters with identical home and work locations. This effect can be alleviated by autonomous vehicles (AV): when two commuters share a ride from home to work, if the realized work end times result in a long wait between the two, an additional AV can be easily repositioned from home to work, whereas with regular human-driven vehicles one has to either bear the long wait or request expensive taxi service. This observation implies that AVs have great potential for increasing commute ridesharing. To study this effect, we develop evening commute bottleneck models with uncertain work end time and establish mode choice equilibrium for the round-trip commute. We find that, with regular vehicles, because of the expected waiting cost caused by work end time uncertainty, commuters typically do not share rides even though they have the same home and work locations. With AVs, commuters always share rides for the morning commute, and they also share rides for the evening commute if their work end times turn out to be close; otherwise, they reposition an additional AV to pick one of them up. Finally, our numerical examples show that AVs can encourage commute ridesharing and significantly reduce the expected round-trip travel costs for commuters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗
DOE OSTI2023

Pool-Based Tow System for Testing Tethered Hydrokinetic Devices Being Developed to Harvest Energy From Ocean Currents

Abstract The immense potential for ocean current energy harvesting is being actively explored as the push for renewable energy becomes more urgent. This paper demonstrates a tow testing platform built to examine and validate mathematical models related to the performance of tethered, underwater, hydrokinetic devices in development to harvest energy from ocean currents, and presents experimental results illustrating how such a system can be used. The platform has been modularly designed to allow for the testing of various tethered, underwater energy-generation systems, including kite-based systems, coaxial turbines, and duct sails. Previous research on tethered energy-generating systems has primarily been focused on airborne systems. Additionally, the limited experimental research on tethered, underwater energy-generation systems has relied on a rigid rod for mechanical and electrical connections between the test articles and instrumentation. The tow testing platform presented in this paper accomplishes the mechanical and electrical connection through a dual-function tether, featuring internal conductors and an external sheath to support towing loads. The goal of this platform was to enable the emulation of ocean currents, which are largely unidirectional, and to retrofit a regular pool into a cost-effective, adaptable, small-scale tow tank test bed. The capabilities of the system include two-way communication with tethered devices, multiple towing profiles in order to emulate different flow regimes, real-time control, and differential velocities via dual winch operation.

Engineering↗
DOE OSTI2018

H{sub ∞} memory feedback control for uncertain singular Markov jump systems with time-varying delay and input saturation

This paper concerns with the H{sub ∞} robust exponential stability and memory state feedback stabilization of singular Markov jump systems with time-delay and input saturation. Linear matrix inequality conditions are given to guarantee regularity, impulse-freeness and exponential stability for the singular Markov jump system. Moreover, sufficient conditions are presented to ensure the H{sub ∞} disturbance attenuation level, and the design method of memory feedback controller is developed by solving linear matrix inequalities optimization problem without any decompositions of system matrices and equivalent transformation. Furthermore, the function in the proof procedure belongs to multiple Lyapunov-like functions whose advantage lies in their flexibility. Finally, numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Phase I Closeout Report: Invoking Artificial Neural Networks to Measure Insider Threat Mitigation

Researchers from Sandia National Laboratories (Sandia) and the University of Texas at Austin (UT) conducted this study to explore the effectiveness of commercial artificial neural network (ANN) software to improve insider threat detection and mitigation (ITDM). This study hypothesized that ANNs could be "trainee to learn patterns of organizational behaviors, detect off-normal (or anomalous) deviations from these patterns, and alert when certain types, frequencies, or quantities of deviations emerge. The ReconaSense ANN system was installed at UT's Nuclear Engineering Teaching Laboratory (NETL) and collected 13,653 access control data points and 694 intrusion sensor data points over a three-month period. Preliminary analysis of this baseline data demonstrated regularized patterns of life in the facility, and that off-normal behaviors are detectable under certain situations -- even for a facility with anticipated highly non-routine, operational behaviors. Completion of this pilot study demonstrated how the ReconaSense ANN could be used to identify expected operational patterns and detect unexpected anomalous behaviors in support of a data-analytic approach to ITDM. While additional studies are needed to fully understand and characterize this system, the results of this initial study are overall very promising for demonstrating a new framework for ITDM utilizing ANNs and data analysis techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

BioXTAS RAW 2 : new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI ; updated automated Guinier fitting and D max finding algorithms; automated series ( e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares ( REGALS ); creation of electron-density reconstructions using electron density via solution scattering ( DENSS ); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

97 MATHEMATICS AND COMPUTING↗