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 1,513 records · Page 84

NRC Multiphysics Analysis Capability Deployment (FY2021--Part 1)

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” The tasks completed for this report are as follows: First, Task 1d: The net radiation transfer method was implemented into MOOSE for modeling reactor cavity cooling system geometries. RCCS models for two experiments were created: (1) Natural Convection Shutdown Heat Removal Test Facility (NSTF) experiment R022, and (2) HTTR VCS mockup. For validation, computed temperature distributions were compared to measured temperatures. Next, Task 4c: An algorithm for computing the pebble bed reactor equilibrium core isotopic com-position was developed and an initial version is implemented into the reactor multi-physics code Griffin. Initial results for a simplified axisymmetric pebble bed reactor are presented. Finally, Task 7: generation of a reference plant model for molten salt cooled pebble bed reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Decomposing causality into its synergistic, unique, and redundant components

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

applied mathematics↗

Relativistic approach to manipulating angular distribution of charged particles via kinetic equations

Deflection angles of charged particles interacting with materials play a critical role in various plasma applications. The development of a mathematically well-posed kinetic collision operator that accounts for deflection angles of strong Coulomb interactions remains a fundamental open problem. This paper presents a relativistic method for modifying the electromagnetic field in an anisotropic and adjustable manner to manipulate a system of charged particles, specifically by the transfer of angular momentum from a superluminal wave source to particles at specific times and locations. The method provides a mechanism to influence the scattering outcomes of strong interactions by manipulating the angular distribution of particles, and thus the deflection angles of their interactions with a solid surface, without requiring detailed knowledge of the kinetic collision operator. To this end, we demonstrate how a specific type of singularity, generated by Maxwell's equations for a superluminal wave source at the boundary of the plasma, can modify the electromagnetic field in a highly directional manner. The proposed method can lead to the development of novel approaches for controlling interactions of charged particles with a material in plasma systems. Published by the American Physical Society 2025

Moini, Nima (ORCID:0009000929568824)↗

Convective Melting of Particles in Flow Under Microgravity Conditions

Study of melting of dispersed or packed solid particles in a fluid under gravity and microgravity conditions provides benchmark information for many engineering applications such as material processing, environmental assessment and protection and space fire protection. During such processes, packed or dispersed solid particles are interacting with fluid flow at above-melting temperatures. By unmasking the buoyancy effects in coupled flow, phase change and heat transport phenomena, a better understanding of melting rate in non-thermal equilibrium, convective conditions can be studied. A series of flight experiments were conducted onboard the NASA KC-135 Microgravity Research Airplane. The Particle Melting in Plow (PMF) module was designed to allow flow through the initially packed ice particles at controlled temperature and velocity. To achieve this, a close-loop flow system was designed. Video images were taken to record the visualization of the melting process, from which a time variation of packed particle thickness distribution at different times can be obtained by the image analysis method. The fluid temperature distribution within the melting zone is measured by thermocouples. An infrared camera was mounted from the top of the test section to record the ice-water thermal images at a given location. The results from thermal images yield local temperature variation between melting solid and liquid and local Stephan number. Typical results for a number of cases are presented. The mathematical model, describing mass, energy, and momentum balance equations for the liquid and solid phases, is presented. It is found that melting rate is influenced mainly by the ratio of Reynolds number (based on the initial particle diameter) to the Froud number, and Stephan number. At the absence of gravity, Froud number approaches zero, Reynolds number and Stephan number become dominant factors governing the melting rate. The numerically determined results are compared with the experimental ones. It is found that the discrepancy between the predicted and measured melting rate is largely due to the inaccuracy in the constitutive equations for effective thermal physical properties, such as effective thermal conductivity and diffusivity, and transport properties, such as particle interaction coefficient, and local heat transfer coefficient of particles.

Stewart, C.↗

Spatially Patterned Architectures to Modulate CO 2 Reduction Cascade Catalysis Kinetics

Electrochemical CO 2 reduction using renewable sources of electrical energy holds promise for converting CO 2 into fuels and chemicals. The complex interactions among chemical/electrochemical reactions and mass transport make it difficult to analyze the effect of an individual process on electrode performance based only on experimental methods. Here, we developed a generalized steady-state simulation to describe an electrode surface in which sequential cascade catalysts are patterned in a periodic trench design. If appropriately constructed, this trench geometry is hypothesized to be able to yield a higher net current density for a CO 2 reduction (CO 2 R) cascade reaction. We have used realistic experimental reaction kinetics to investigate the role of trench geometry in mass transport, local microenvironments, and selectivity for a model CO 2 R cascade reaction. The model considers local concentration gradients of bicarbonate species at quasi-equilibrium and catalytic surface reactions based on concentration-dependent Butler–Volmer kinetics. Our results suggest that varying the spatial distribution of active sites plays a significant role in facilitating effective mass transport between active sites, modulating selectivity for the cascade reaction, and enhancing the yield of desirable cascade products. Moreover, we observe that this trench geometry significantly alters the cascade reaction rate by affecting the local pH, which can cause inadvertent depletion of available aqueous CO 2 to limit the CO 2 R cascade kinetics and modest suppression of the hydrogen evolution reaction (HER). The results highlight the trade-offs between mass transport, pH, and reaction kinetics that become apparent only when considering the coupled physics of all processes at the electrode surface. Here, this model can thus serve as a primary tool to build more selective and efficient patterned architectures for the CO 2 R cascade catalysis.

CO2 reduction↗

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Network Optimization of the Electrosynthesis of Chemicals from CO2

Carbon dioxide electroreduction (ECO2R) is gaining attention due to its capacity to mitigate CO2 emissions while using electricity that would otherwise be curtailed. Its foreseeable industrial implementation requires of holistic methods to assess the technological and economic performance of ECO2R processes and integrate them in current chemical supply chains and power systems. Here, we combine techno-economic assessment and mathematical programming to find the optimal paths to electroreduce CO2 into valuable chemicals under variable electricity prices. The proposed approach is tested with a case study addressing the CO2 capture from flue gas or direct air and its electricity-powered reduction into carbon monoxide, formic acid or multi-carbon compounds. The results obtained demonstrate the ability of the framework to build ECO2R networks and provide operation profiles that respond to fluctuating electricity prices.

carbon dioxide↗

Pynta-An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. Here, we present Pynta, a workflow software for automating the calculation of surface and gas–surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ARM-IRL: Adaptive Resilience Metric Quantification Using Inverse Reinforcement Learning

The resilience of safety-critical systems is gaining importance due to the rise in cyber and physical threats, especially within critical infrastructure. Traditional static resilience metrics may not capture dynamic system states, leading to inaccurate assessments and ineffective responses to cyber threats. This work aims to develop a data-driven, adaptive method for resilience metric learning. We propose a data-driven approach using inverse reinforcement learning (IRL) to learn a single, adaptive resilience metric. The method infers a reward function from expert control actions. Unlike previous approaches using static weights or fuzzy logic, this work applies adversarial inverse reinforcement learning (AIRL), training a generator and discriminator in parallel to learn the reward structure and derive an optimal policy. The proposed approach is evaluated on multiple scenarios: optimal communication network rerouting, power distribution network reconfiguration, and cyber–physical restoration of critical loads using the IEEE 123-bus system. The adaptive, learned resilience metric enables faster critical load restoration in comparison to conventional RL approaches.

97 MATHEMATICS AND COMPUTING↗

Compressive sensing optical design and simulation tool

A system or method for designing optical systems includes generating a mathematical model of an imaging system; tracing a plurality of light rays from a source through the model of the imaging system in a forward direction and a backward direction incident upon an arbitrarily defined detector location; calculating the total light rays incident upon the arbitrarily defined detector location in response to the plurality of light rays; tracing a series of calibration images first through the computational or compressive imager mathematical model; measuring an output set of parameters based on a plurality of detected rays calibration images at the defined detector location; storing the output set of parameters in software, and determining an estimated system transfer function.

42 ENGINEERING↗

Experimental measurements and mathematical modeling of cold plate for aviation thermal management

Herein, this study, which has been motivated by the recent applications of the cold plate device in aviation thermal management, reports on physics-based mathematical models derived from the conservation laws of mass, momentum, and energy, and empiricism-based models. One of the objectives of the present work is to report on an elaborate and successful experimental work carried out on an additively manufactured device for the purpose of rigorously validating the numerical predictions. The excellent agreement between the numerical predictions and measured performance provides much needed confidence in the implementation, in the software package, of the offset-strip fin passage correlations, as well as in the software implementation of user-defined wavy fin correlations for aerospace heat exchangers and cold plates operating with ram air at Reynolds numbers below 8000. The contributions of this work can also be found in the development of a new and accurate thermal-hydraulic analysis procedure, referred to in this paper as plate-fin analogy. Results from this procedure are compared with those from thermal resistance network. The comparative study in this paper of the bulk and discrete enthalpy flux method is also new, as is the relative assessment of four off-set strip fin thermal-hydraulic models.

42 ENGINEERING↗

Fourier method for 3-dimensional data fusion of X-ray Computed Tomography and ultrasound

X-ray Computed Tomography (CT) is essential for nondestructive inspection of many manufactured components but is susceptible to various forms of artifacts and noise. In particular, multi-detector row cone-beam CT systems can suffer from so called “cone-beam” artifacts and partial volume effects, particularly on planar edges at the periphery of the field of view in the cone angle dimension. Uni-directional ultrasonic testing methods generally have extremely accurate in-plane depth resolution but poorer lateral resolution due to physical and geometric constraints. This paper presents a novel technique called Computed Tomographic Fusion (CT-F) which uses three-dimensional Fourier filtering to combine x-ray cone-beam CT reconstructions and ultrasound data in the frequency space. The result is a single image with improved accuracy and quality. CT-F mitigates artifacts while allowing for rapid, accurate characterization of large three-dimensional CT volumes. Finally, using simulations and experiments, we demonstrate artifact reduction and edge contrast improvement in volumetric reconstructions.

42 ENGINEERING↗

Fast neural Poincaré maps for toroidal magnetic fields

Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. Furthermore, this structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

Here, we propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple “snapshots.” Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates “fake” sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks. We refer to this method as generative “ensemble-regression” (GER), in analogy to the classic “point-regression,” where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

97 MATHEMATICS AND COMPUTING↗

High-performance finite elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. Furthermore, this paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

97 MATHEMATICS AND COMPUTING↗

Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

97 MATHEMATICS AND COMPUTING↗

General formulas for adiabatic invariants in nearly periodic Hamiltonian systems

While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. Here, a less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Monolithic Multigrid Methods for Magnetohydrodynamics

The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Here, three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.

97 MATHEMATICS AND COMPUTING↗