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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 OSTI2022

GenASiS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations (version 2)

We report GenASiS Mathematics provides modern Fortran classes furnishing extensible object-oriented functionality for the solution of fields governed by selected partial differential equations. The initial release included extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon. This revision - Version 2 of Mathematics - includes significant reorganization and streamlining of these classes, higher-order reconstruction by a different method, a Poisson solver, coarsening to avoid Courant time step limitations near coordinate singularities, and the offloading of computational kernels to GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

A mathematical model of the passage of an asteroid-comet body through the Earth’s atmosphere

In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth’s atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Mathematical modeling of deformation of a porous medium, considering its strengthening due to pore collapse

Based on the generalized rheological method, the mathematical model describing small deformations of a single-phase porous medium without regard to the effects of a fluid or gas in pores is constructed. The change in resistance of a material to the external mechanical impacts at the moment of pore collapse is taken into account by means of the von Mises–Schleicher strength condition. In order to consider irreversible deformations, alongside with the classical yield conditions by von Mises and Tresca– Saint-Venant, the special condition modeling the plastic loss of stability of a porous skeleton is used. The random nature of the pore size distribution is taken into account. It is shown that the proposed mathematical model satisfies the principles of thermodynamics of irreversible processes. Phenomenological parameters of the model are determined on the basis of the approximate calculation of the problem on quasi-static loading of a cubic periodicity cell with spherical voids. In the framework of the obtained model, the process of propagation of plane longitudinal waves of the compression in a homogenous porous medium, accompanied by the plastic deformation of a skeleton and the collapse of pores, is analyzed.

42 ENGINEERING↗

DOE OSTI2023

Improving Mathematical Exposition of an Industrial-Scale Linear Program

Industrial-scale models require considerable setup time; hence, once built, they are used in myriad ways to consider closely related cases. In practice, the code for these models frequently evolves without appropriate notational choices, largely as a result of the lengthy development time of, and the number of individuals contributing to, their formulation. This leads to inefficiencies and obfuscates model structures that might be leveraged to expedite solutions. In this paper, we advocate for an emerging literature on model formulation “best practices” and present the reformulation of a widely used industrial-scale linear program. The efficient mathematical expression of this linear program, used to plan capacity expansion in the energy sector, allows for greater transparency of model structures and enhanced ability to identify computational performance improvements, as well as a lucid interpretation of its solutions. This type of formulation is employed in several mathematical programming courses at our university as an example of the advantages of best practices; the model more broadly is used widely to inform policy in the U.S. energy sector.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performing a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

Evaluation of the Validity of Bio-Mathematical Models in Predicting Fatigue in an Operational Environment

During long-duration spaceflight missions, crewmembers and ground-support staff experience irregular sleep schedules, erratic natural light patterns, and high workload due to mission demands. Such conditions can cause circadian misalignment and sleep loss, which in turn cause deficits in cognitive performance. While bio-mathematical models have been implemented within workplace settings to predict fatigue profiles, the accuracy of sleep-wake models under conditions of non-traditional shiftwork is little known. Thus, the present study aims to evaluate the validity of four sleep-wake models (e.g., SAFTE-FAST, the Unified Model of Performance, the Adenosine-Circadian Model, and the State-Space Model) designed to predict human performance and fatigue levels against objective measures of performance in a spaceflight analog. To accomplish this aim, we will collect Psychomotor Vigilance Task (PVT) data from four crews (n=16) in the Human Exploration Research Analog (HERA) over 45 days. HERA is a closed, 3-story habitat at Johnson Space Center where inhabitants are exposed to extreme space exploration scenarios under varying sleep-wake conditions. The PVT is a simple reaction time test that involves minimal learning, making it sensitive to the effects of sleep loss and circadian misalignment. Findings from this study will help inform work scheduling and implementation of effective countermeasures (e.g., caffeine, lighting) to improve work efficiency and combat fatigue, as well as offer valuable insight into the applicability of bio-mathematical fatigue models in future space exploration missions.

fatigue↗

DOE OSTI2024

Recent developments in mathematical aspects of relativistic fluids

Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

Disconzi, Marcelo (ORCID:0000000234497778)↗

DOE OSTI2021

Solving the puzzle of Fe homeostasis by integrating molecular, mathematical, and societal models

To ensure optimal utilization and bioavailability, iron uptake, transport, subcellular localization, and assimilation are tightly regulated in plants. In this work, we examine recent advances in our understanding of cellular responses to Fe deficiency. We then use intracellular mechanisms of Fe homeostasis to discuss how formalizing cell biology knowledge via a mathematical model can advance discovery even when quantitative data is limited. Using simulation-based inference to identify plausible systems mechanisms that conform to known emergent phenotypes can yield novel, testable hypotheses to guide targeted experiments. However, this approach relies on the accurate encoding of domain-expert knowledge in exploratory mathematical models. We argue that this would be facilitated by fostering more “systems thinking” life scientists and that diversifying your research team may be a practical path to achieve that goal.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Understanding the Connection between Nanoparticle Uptake and Cancer Treatment Efficacy using Mathematical Modeling

Nanoparticles have shown great promise in improving cancer treatment efficacy while reducing toxicity and treatment side effects. Predicting the treatment outcome for nanoparticle systems by measuring nanoparticle biodistribution has been challenging due to the commonly unmatched, heterogeneous distribution of nanoparticles relative to free drug distribution. We here present a proof-of-concept study that uses mathematical modeling together with experimentation to address this challenge. Individual mice with 4T1 breast cancer were treated with either nanoparticle-delivered or free doxorubicin, with results demonstrating improved cancer kill efficacy of doxorubicin loaded nanoparticles in comparison to free doxorubicin. We then developed a mathematical theory to render model predictions from measured nanoparticle biodistribution, as determined using graphite furnace atomic absorption. Model analysis finds that treatment efficacy increased exponentially with increased nanoparticle accumulation within the tumor, emphasizing the significance of developing new ways to optimize the delivery efficiency of nanoparticles to the tumor microenvironment.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties

Abstract We present a state‐of‐the‐art report on time‐dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time‐independent to time‐dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time‐dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.

Bujack, Roxana↗

DOE OSTI2022

Characteristics and mathematical modeling of apple slice drying in an electrohydrodynamic system with a needle‐plate electrode

Abstract The drying of apple slices in an electrohydrodynamic (EHD) system with a needle‐plate electrode was characterized and mathematically modeled at voltages of 30, 40, and 50 kV and with distances between needles of 5, 6, and 7 cm. The results showed that the drying rate, effective water diffusion coefficient, and rehydration ratio of the apple slices, and specific energy consumption of drying, all increased with increasing voltage. Initially, there was a period when the drying rate was approximately constant in the low‐voltage EHD, but not in the high voltage conditions. At the same voltage, the drying rate was highest when the distance between needles was 6 cm. The voltage and distance between needles had a significant ( p < .05) interactive effect on the effective water diffusion coefficient and specific energy consumption, but not on the rehydration ratio. General mathematical models for drying can be used to represent the drying behavior of apple slices. The Midilli and Kucuk model and the Logarithmic model had the best fits, with correlation coefficients of 0.998803 and 0.998267, respectively. Predictive functions for the moisture ratio of apple slices based on voltage and distance between needles were established and verified. The results indicated that the Logarithmic model could more accurately predict the moisture ratio of apple slices dried using the EHD method. Practical Applications As a new drying technology, electrohydrodynamic (EHD) drying has unequaled advantages. According to the results, using the appropriate voltage and distance between needles improves not only drying efficiency, but also the rehydration ratio of apple slices, which reflects the quality of dried products. The Logarithmic model can accurately predict the EHD drying behavior of apple slices, which is of great significance in optimizing actual production.

Li, Bowen↗

DOE OSTI2022

Applied Mathematics Challenge: Simulation of Power Electronics in Future Power Grid

There has been a buzz around increased grid modernization for more than a decade. Grid modernization includes, but is not limited to, upgrades to the grid to enhance reliability, resilience, security, and access to clean energy sources. One significant change that has been happening in this context is the increased penetration of computing power and controlled devices like power electronics in the power grid. As this change happens, the operation and characteristics of the power grid are set to undergo a significant change. The power grid moves from an older electric machine dominated grid that used analog electronics for controls to a power electronics dominated grid that uses digital computing for controls. As this transition happens, there are significant problems of applied mathematics that will need to be resolved in power electronics and power grid. The problems include the ability to simulate in different timescales, while also leveraging the significantly improved computing capabilities available today. In this paper, the challenges related to simulation of power electronics are discussed and the challenge problems laid down that applied mathematics may help resolve in future.

Debnath, Suman↗

DOE OSTI2023

Mathematical Framework Underlying the In Situ Electrochemical Diagnosis of Adsorbed Intermediates Formed during Redox Reactions at Electrode Surfaces

Previously, we have presented an electrochemical technique wherein an electroactive tracer species is employed to probe the rate-limiting factors governing redox reactions at an electrode surface. In this technique, the electrode is first held potentiostatically to facilitate a redox process (step 1), and then the potential is released to open circuit conditions (step 2) so as to monitor the time-dependent re-equilibration of the electrode potential in the presence of the tracer. The time-dependent potential response in step 2 has been shown to contain information about diffusion—limited or desorption—limited steps, enabling in situ probing of the electrochemistry at the electrode surface during step 1. In the present contribution, a theoretical model governing the transient response in step 2 is developed for two limiting cases: diffusion—limited and desorption—limited recovery of the electrode potential. Mathematical modeling shows that, during re-equilibration, the step 2 potential transient corresponding to a case where step 1 involves surface adsorbed species which undergo desorption in step 2 exhibits a much longer time constant than that when re-equilibration occurs under diffusion limitations. The mathematical framework presented herein provides a sound fundamental basis for applying the aforementioned technique to studying adsorption-desorption processes during electrochemistry. Also, technique limitations are presented in light of the modeling findings.

25 ENERGY STORAGE↗

DOE OSTI2026

Mathematical Modeling of the Potential and Time Dependence of Ir Dissolution from Hydrous Ir Oxide Oxygen Evolution Catalysts

One of the main degradation mechanisms of hydrous iridium oxide acidic oxygen evolution reaction (OER) catalysts is dissolution and loss into the acidic membrane. While degradation models have been proposed, there is a gap in understanding the potential and time dependence of the iridium dissolution reaction and its mechanistic underpinnings. In this work, Ir dissolution rates measured as a function of time and potential via time-resolved inductively-coupled plasma mass spectrometry (ICP-MS) in aqueous acidic electrolyte are used to establish a mathematical model for Ir dissolution. The mathematical model is generated using proposed formation and dissolution reactions for Ir species. Through comparison with the ICP-MS data and existing information on the potential-dependent Ir phase, we find that the potential and time-dependence of dissolution can be modeled as dissolution of an oxide phase, here represented as IrO 2 , with potential dependent kinetics and formation of a passivating species, a process with a rate-limiting step that is not potential dependent. This understanding of the potential dependence of dissolution and passivation kinetics using aqueous electrolyte half-cell measurements can be used to predict the degradation of Ir oxide in operating energy conversion devices relying on the OER, such as proton-exchange membrane water electrolyzers.

Kariuki, Nancy N. [Argonne National Laboratory (AN↗

DOE OSTI2024

Machine learning mathematical models for incidence estimation during pandemics

Accurate estimates of the incidence of infectious diseases are key for the control of epidemics. However, healthcare systems are often unable to test the population exhaustively, especially when asymptomatic and paucisymptomatic cases are widespread; this leads to significant and systematic under-reporting of the real incidence. Here, we propose a machine learning approach to estimate the incidence of a pandemic in real-time, using reported cases and the overall test rate. In particular, we use Bayesian symbolic regression to automatically learn the closed-form mathematical models that most parsimoniously describe incidence. We develop and validate our models using COVID-19 incidence values for nine different countries, confirming their ability to accurately predict daily incidence. Remarkably, despite the differences in epidemic trajectories and dynamics across countries, we find that a single model for all countries offers a more parsimonious description and is more predictive of actual incidence compared to separate models for each country. Our results show the potential to accurately model incidence in real-time using closed-form mathematical models, providing a valuable tool for public health decision-makers.

Fajardo-Fontiveros, Oscar (ORCID:0000000207058972)↗

DOE OSTI2021

AmeriFlux US-MWU Battle Creek Area Mathematics and Science Center

This is the AmeriFlux version of the carbon flux data for the site US-MWU Battle Creek Area Mathematics and Science Center. Site Description - Urban site located above the roof of the Battle Creek Area Mathematics and Science Center, a regional STEM magnet school. Site was chosen to represent urban areas within the Kalamazoo River watershed.

Chen, Jiquan↗

DOE OSTI2025

Mathematical Morphological Filtering with a Self-Adaptive Reconstruction Technique and Application to Local Seismic Data

Recorded seismic data are generally contaminated by noise from different sources, which masks the signals of interest. In the seismology community, frequency filtering (FF) is the standard method for noise suppression. However, when the signal of interest and noise share the same frequency band, the latter cannot be filtered out without infringing on the former. We implemented a noise suppression approach based on the mathematical morphology theorem. The method involves compound operations of dilation and erosion using structuring elements of varying lengths and decomposes an input noisy waveform into several time functions with differing characteristics. Further, the filtered waveform is constructed from the time functions using a self-adaptive reconstruction technique. Application to a data set of >4700 local waveforms suggests that the implemented mathematical morphological filtering (MMF) approach is efficient for data with low signal-to-noise ratio (SNR) and significantly outperforms FF in that SNR range. For most of the dataset, FF, machine learning (ML) denoising, and continuous wavelet transform (CWT) thresholding result in higher SNR values compared with the MMF method. However, for ~42% of the waveforms, MMF outperforms FF, and the SNR gain achieved with MMF is as large as ~23 dB. Compared to ML denoising and CWT thresholding, this proportion drops to only ~10%–14%. Our results suggests that in an operational setting, MMF cannot replace the other noise suppression methods; however, signal detection can be improved if MMF is used to supplement them in some scenarios. MMF could help detect signals in problematic low-SNR data, which are currently being missed particularly when using FF alone.

58 GEOSCIENCES↗