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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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Investigating categorization and formulation of stress and strength factors for semiconductor diodes to provide improved failure rate prediction from mathematical models
In an investigation of metal oxide semiconductor field effect transistor (MOFSET) devices, a one-dimensional mathematical model of device dynamics was prepared, from which an accurate and computationally efficient drain current expression could be derived for subsequent parameter extraction. While a critical review revealed weaknesses in existing 1-D models (Pao-Sah, Pierret-Shields, Brews, and Van de Wiele), this new model in contrast was found to allow all the charge distributions to be continuous, to retain the inversion layer structure, and to include the contribution of current from the pinched-off part of the device. The model allows the source and drain to operate in different regimes. Numerical algorithms used for the evaluation of surface potentials in the various models are presented.
Secondary electrons control a spacecraft's response to a plasma environment. To accurately simulate spacecraft charging, the NASA Charging Analyzer Program (NASCAP) has mathematical models of the generation, emission and transport of secondary electrons. The importance of each of the processes and the physical basis for each of the NASCAP models are discussed. Calculations are presented which show that the NASCAP formulations are in good agreement with both laboratory and space experiments.
In this report, Millstone 1- Develop Facility Energy System Models is documented, including an introduction of the energy facility in military microgrids through a set of mathematical models of the energy facility using electricity, natural gas, and heat as energy resources.
The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements.
The possibility of creating a plasma from fission fragments, and to utilize the energy of the particles to create population inversion that would lead to laser action is investigated. An investigation was made of various laser materials which could be used for nuclear-pumped lasing. The most likely candidate for a fissioning material in the gaseous form is uranium hexafluoride - UF6, and experiments were performed to investigate materials that would be compatible with it. One of the central problems in understanding a fission-induced plasma is to obtain a model of the electron behavior, and some preliminary calculations are presented. In particular, the rates of various processes are discussed. A simple intuitive model of the electron energy distribution function is also shown. The results were useful for considering a mathematical model of a nuclear-pumped laser. Next a theoretical model of a (3)He-Ar nuclear-pumped laser is presented. The theory showed good qualitative agreement with the experimental results.
Two mathematical models help in optimizing design of spiral bevel gears. In essence, replace actual generated tooth surface with mathematical conjugate approximation. Tooth surfaces of spiral bevel gears replaced (or approximated) by conjugate tooth surfaces. Surfaces generated by two conical surface's rigidly connected with each other and in linear tangency along common generatrix of tool cones and by conical surface and surface of revolution in linear tangency along circle. Gears have widespread applications in transmission systems of helicopters, airplanes, trucks, automobiles, tanks, and many other machines.
A semiempirical model to predict the unsteady loads on an airfoil that is experiencing dynamic stall, is investigated. The mathematical model is described from an engineering point of view, demonstrates the procedure for obtaining various empirical parameters, and compares the loads predicted by the model with those obtained in the experiment. It is found that the procedure is straightforward, and the final calculations are in qualitative agreement with the experimental results. Comparisons between calculations and measurements also indicate that a decrease in accuracy results when the values of both the reduced frequency and the amplitude of oscillation are large. Potential quantitative improvements in the accuracy of the calculations are discussed for accounting of both the hysteresis in the static data and the effects of stall delay in the governing equations.
The usefulness of wire rope in shock and vibration isolation is briefly reviewed and its modeling for the purpose of vibration analysis is addressed. A model of a nominally straight segment of wire rope is described in which the rope structure is represented by a maiden, or central, strand of wire with one (or more) strand(s) wrapped around it in a helix (helices). The individual strands are modeled using finite elements and MSC NASTRAN. Small linear segments of each wire are modeled mathematically by dividing them lengthwise into triangular prisms representing each prism by a solid NASTRAN element. To model pretensioning and allow for extraction of internal force information from the NASTRAN model, the wound strands are connected to the maiden strand and each other using spring (scalar elastic) elements. Mode shapes for a length of wire rope with one and fixed to a moving base and the other attached to a point mass, are presented. The use of the NASTRAN derived mode shapes to approximate internal normal forces in equations of motion for vibration analyses is considered.
SSE computer program provides simulation environment for modeling manufacturing systems containing relatively small numbers of stations and operators. Designed to simulate manufacturing of apparel, also used in other manufacturing domains. Excellent for small or medium-size firms including those lacking expertise to develop detailed models or have only minimal knowledge in describing manufacturing systems and in analyzing results of simulations on mathematical models. User does not need to know simulation language to use SSE. Used to design new modules and to evaluate existing modules. Originally written in Turbo C v2.0 for IBM PC-compatible computers running MS-DOS and successfully implemented by use of Turbo C++ v3.0.
Results of a previous metric analysis and an electronic simulation of acceleratory nystagmus are given. On this basis, a tentative mathematical model for describing acceleratory nystagmus is reported. The essential content of the model is Lorente de No's neuron circuit, to which the two-factor theory of excitation has been applied.
Recent developments in formula manipulation compilers and the design of several symbol manipulation languages, enable computers to be used for symbolic mathematical computation. A computer system and language that can be used to perform symbolic manipulations in an interactive mode are used to formulate a mathematical model of an aeronautical system. The example demonstrates that once the procedure is established, the formulation and modification of models for simulation studies can be reduced to a series of routine computer operations.
This paper attempts to review the steps involved in the development of mathematical models that can be used to simulate the in-orbit dynamics of large flexible systems. The use of graph theoretic techniques can often be used to reduce the computational effort involved for calculating the eigenvalues of large ordered systems. Computer generated graphical techniques may provide additional insight into the understanding of elastic modal shape functions of complex systems. Finally the numerical techniques commonly used to develop shape and attitude control laws will be briefly reviewed.
For presentation at the AIChE Annual Meeting, Orlando, FL, November 5-10, 2023.
This paper aims to first quantify the impact of various diffusion models (Maxwell-Stefan, Wilke, Dusty-Gas) on the predictions of a multi-scale membrane reactor/separator mathematical model, and to then demonstrate this model's use for the design and process intensification of membrane reactor/separator systems for hydrogen production. This multi-scale model captures velocity, temperature and species' concentration profiles along the catalyst pellet's radial direction, and along the reactor's axial direction, by solving the momentum, energy, and species transport equations, accounting for convection, conduction, reaction, and diffusion mechanisms. In the first part of work, the effect of pellet-scale design parameters (mean pore diameter, volumetric porosity, tortuosity factor, etc.) and various species' flux models on the model predictions is studied. In the second part, the study focuses on the comparison, in terms of their process intensification characteristics, of various hydrogen production processes. These include a conventional high-temperature shift reactor (HTSR)/low-temperature shift reactor (LTSR) sequence, a novel HTSR/membrane separator (MS)/LTSR/MS sequence, and a process that involves low-temperature shift membrane reactors-LTSMR in a series.
Efflux pumps that transport antibacterial drugs out of bacterial cells have broad specificity, commonly leading to broad spectrum resistance and limiting treatment strategies for infections. It remains unclear how efflux pumps can maintain this broad spectrum specificity to diverse drug molecules while limiting the efflux of other cytoplasmic content. We have investigated the origins of this broad specificity using theoretical models informed by the experimentally determined structural and kinetic properties of efflux pumps. We developed a set of mathematical models describing operation of efflux pumps as a discrete cyclic stochastic process across a network of states characterizing pump conformations and the presence/absence of bound ligands and protons. These include a minimal three-state model that lends itself to clear analytic calculations as well as a five-state model that relaxes some of the simpler model’s most strict assumptions. We found that the pump specificity is determined not solely by the drug affinity to the pump–as is commonly assumed–but it is also directly affected by the periplasmic pH and the transmembrane potential. Therefore, changes to the proton concentration gradient and voltage drop across the membrane can influence how effective the pump is at extruding a particular drug molecule. Furthermore, we found that while both the proton concentration gradient across the membrane and the transmembrane potential contribute to the thermodynamic force driving the pump, their effects on the efflux enter not strictly in a combined proton motive force. Rather, they have two distinguishable effects on the overall throughput. These results highlight the unexpected effects of thermodynamic driving forces out of equilibrium and illustrate how efflux pump structure and function are conducive to the emergence of multidrug resistance.
Mathematical models expressed in the form of discretized equations play an important role inmany scientific disciplines. In our experience, few domain scientists have sufficient backgroundin numerical computing (or the time required to acquire such a background) to use manyflexible and powerful but complex open source packages, such as FEniCS (Alnæs et al., 2015)and OpenFOAM (The OpenFOAM Foundation Ltd, n.d.). Many user-friendly open sourcepackages, such as FiPy (J. E. Guyer & Warren, 2009), and many commercial packages, suchas COMSOL Multiphysics (COMSOL AB, n.d.) and Simcenter STAR-CCM+ (Siemens DigitalIndustries Software, n.d.), provide limited flexibility in the equations that users can express.Additionally, the use of commercial packages, which by nature do not perform calculationstransparently, can hinder reproducibility, which is vital to the scientific process. PyGDH(“pigged”) is a Python 2 / Python 3 (Python Software Foundation, 1991–2020) package thatis meant to be accessible to scientists who might not be specialists in scientific computing,while approaching the level of flexibility associated with writing dedicated programs tailoredto solving specific problems. The PyGDH User’s Guide provides detailed instructions forcreating numerical models, including a brief introduction to necessary command line andPython (Python Software Foundation, 1991–2020) skills, and discussions of discretization andvalidation. Note that PyGDH emphasizes flexibility and simplicity over performance, and wasnot designed for high-performance applications or models describing complex spatial domains.
Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and anisotropic media, the mathematical models related to this phenomenon are not analytically tractable. Numerical simulations often provide a viable route to predict chemical mixing accurately. However, contemporary modeling approaches for mixing cannot utilize available spatial-temporal data to improve the accuracy of the future prediction and can be compute-intensive, especially when the spatial domain is large and for long-term temporal predictions. To address this knowledge gap, in this work we will present in this paper a deep learning (DL) modeling framework applied to predict the progress of chemical mixing under fast bimolecular reactions. This framework uses convolutional neural networks (CNN) for capturing spatial patterns and long short-term memory (LSTM) networks for forecasting temporal variations in mixing. By careful design of the framework—placement of non-negative constraint on the weights of the CNN and the selection of activation function, the framework ensures non-negativity of the chemical species at all spatial points and for all times. Our DL-based framework is fast, accurate, and requires minimal data for training. The time needed to obtain a forecast using the model is a fraction (≈ O(-6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinity norm) for capturing local-scale mixing features such as interfacial mixing, only 24% to 32% of the sequence data for model training is required. To achieve the same level of accuracy for capturing global-scale mixing features, the sequence data required for model training is 64% to 70% of the total spatial-temporal data. Hence, the proposed approach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modeling reactive-transport in a wide range of applications.