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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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Anisotropic materials ductile fracture involving crack initation and propagation, using Dugdale mathematical model
A mathematical model of an ecosystem is developed. Secondary productivity is evaluated in terms of man related and controllable factors. Information from an existing physical parameters model is used as well as pertinent biological measurements. Predictive information of value to estuarine management is presented. Biological, chemical, and physical parameters measured in order to develop models of ecosystems are identified.
A parameter-estimation method is described for verifying the mathematical model of mixed (combined interactive components from various engineering fields) dynamic systems against pertinent experimental data. The model verification problem is divided into two separate parts: defining a proper model and evaluating the parameters of that model. The main idea is to use differences between measured and predicted behavior (response) to adjust automatically the key parameters of a model so as to minimize response differences. To achieve the goal of modeling flexibility, the method combines the convenience of automated matrix generation with the generality of direct matrix input. The equations of motion are treated in first-order form, allowing for nonsymmetric matrices, modeling of general networks, and complex-mode analysis. The effectiveness of the method is demonstrated for an example problem involving a complex hydraulic-mechanical system.
The program aims at developing mathematical models and computer codes based on these models, which allow prediction of the product distribution in chemical reactors for converting gaseous silicon compounds to condensed-phase silicon. The major interest is in collecting silicon as a liquid on the reactor walls and other collection surfaces. Two reactor systems are of major interest, a SiCl4/Na reactor in which Si(l) is collected on the flow tube reactor walls and a reactor in which Si(l) droplets formed by the SiCl4/Na reaction are collected by a jet impingement method. During this quarter the following tasks were accomplished: (1) particle deposition routines were added to the boundary layer code; and (2) Si droplet sizes in SiCl4/Na reactors at temperatures below the dew point of Si are being calculated.
An approach and a technique for effectively obtaining reduced order mathematical models of a given large order model for the purposes of synthesis, analysis and implementation of control systems is developed. This approach involves the use of an error criterion which is the H-infinity norm of a frequency weighted error between the full and reduced order models. The weightings are chosen to take into account the purpose for which the reduced order model is intended. A previously unknown error bound in the H-infinity norm for reduced order models obtained from internally balanced realizations was obtained. This motivated further development of the balancing technique to include the frequency dependent weightings. This resulted in the frequency weighted balanced realization and a new model reduction technique. Two approaches to designing reduced order controllers were developed. The first involves reducing the order of a high order controller with an appropriate weighting. The second involves linear quadratic Gaussian synthesis based on a reduced order model obtained with an appropriate weighting.
In this study a mathematical model and a computer code based on this model was developed to allow prediction of the product distribution in chemical reactors for converting gaseous silicon compounds to condensed-phase silicon. Specifically, the model formulated describes the silicon vapor separation/collection from the developing turbulent flow stream within reactors of the Westinghouse type. Migration of the silicon vapor to the reactor walls was described by the parametric solutions presented here, in order to reduce the experimentation necessary in the design of such reactors. Calculations relating to the collection efficiencies of such reactors are presented as a function of the reactor throughflow and distance along its length.
This paper proposes a mathematical model to simulate the cool-down behavior of a warm transfer line using liquid helium (including He II) in a microgravity environment. The thermal-hydraulic characteristics of different possible flow regimes which may occur during the cool-down process are discussed. Correlations for predicting the heat and momentum transfer rates in each flow regime are presented.
Three discrete-state-variable representations derived. Paper discusses mathematical modeling of digital control systems for plants in which outputs include combinations of instantaneous and moving-average-prefiltered measurements.
In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. Although this model predicted many general features of the response of the human circadian pacemaker to light exposure, additional data now available enable us to refine the original model. We first refined the original model by incorporating the results of a dose response curve to light into the model's predicted relationship between light intensity and the strength of the drive onto the pacemaker. Data from three bright light phase resetting experiments were then used to refine the amplitude recovery characteristics of the model. Finally, the model was tested and further refined using data from an extensive phase resetting experiment in which a 3-cycle bright light stimulus was presented against a background of dim light. In order to describe the results of the four resetting experiments, the following major refinements to the original model were necessary: (i) the relationship between light intensity (I) and drive onto the pacemaker was reduced from I1/3 to I0.23 for light levels between 150 and 10,000 lux; (ii) the van der Pol oscillator from the original model was replaced with a higher-order limit cycle oscillator so that amplitude recovery is slower near the singularity and faster near the limit cycle; (iii) a direct effect of light on circadian period (tau x) was incorporated into the model such that as I increases, tau x decreases, which is in accordance with "Aschoff's rule". This refined model generates the following testable predictions: it should be difficult to enhance normal circadian amplitude via bright light; near the critical point of a type 0 phase response curve (PRC) the slope should be steeper than it is in a type 1 PRC; and circadian period measured during forced desynchrony should be directly affected by ambient light intensity.
The capability of current remote sensing tools and mathematical models to study the Great Lakes ice conditions is reported.
Additive manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas for its ability to rapidly produce, prototype, and customize designs. Recently, a hybrid AM technique was successfully developed at Idaho National Laboratory (INL) to manufacture nuclear fuels [1]. Despite the advantages, this AM technique needs optimization due to defects from a highly complex melting and sintering process. The complex metallurgical phenomena during AM processes are strongly related to parameters such as applied laser power, traveling speed, and scan style, which could lead to differences in density, residual stress, crystallographic texture, and mechanical properties. In addition, stochastic variations in laser energy interaction and associated multiscale/multiphysics phenomena cause variations in microstructure evolution and mechanical properties. Currently, researchers at INL are focusing on developing a comprehensive modeling framework, leveraging INL’s simulation tools MOOSE/MARMOT/BISON/RAVEN [2-4] to describe all steps of this AM process across multiple length scales. Although this advanced framework plays a critical role in enabling enhancements to traditional trial and error approaches for design and optimization of nuclear fuel materials, it remains computationally intense, limiting its use in sensitivity and optimization analysis. In this case, an accurate and inexpensive surrogate becomes an effective tool for providing a tractable approximation of the underlying underline physics. Surrogate models generally not based on the physics of a system are purely mathematical models used to capture the relationships between specific system inputs and outputs. Popular approaches, including neural networks [5], response surfaces [6], and subspace-based reduced order models [7], have been applied to a wide range of disciplines, such as nuclear reactor design, aerospace design and automotive design. In this summary, we employ advanced time-dependent surrogate models such as high-dimensional model representation (HDMR) [8] and physics-informed deep neural network (PINNs) [9] to accelerate the design and optimization of AM process.
Supply chain operations and scheduling are well-studied problems in the literature. Although these problems are related, they are often solved sequentially. This uncoordinated approach usually leads to sub-optimal solutions. Here this paper proposes a methodology for integrating scheduling operations into the supply chain network, motivated by the available enterprise data, and feasibility analysis. Existing literature on integrated models for addressing the supply chain is reviewed and classified. Then the mathematical model formulation for each level is discussed, after which the proposed data-driven integrated framework is described. The methodology is tested on two different case studies of varying dimensions. For each case study, the solution solves a multi-objective problem with the overall aim of an optimal solution that is robust towards achieving optimal cost while keeping customer satisfaction in mind.
Two series of free-flight tests have been conducted for combat aircraft configuration research models in order to investigate flight behavior near departure conditions as well as to obtain response data from which aerodynamic characteristics can be derived. The structure of the mathematical model and values for the mathematical derivatives have been obtained through an analysis of the first series, using stepwise regression. The results thus obtained are the bases of the design of active control laws. Flight test results for a novel configuration are compared with predicted responses.
We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.
Physical and mathematical models to simulate effects of ground winds on erected launch vehicles
Physical and mathematical models for studying erected launch vehicle response to ground winds
Mathematical models for planetary landing configuration energy absorption, including payload penetration effect into crushable casing
Design of a discrete optimal regulator requires the a priori knowledge of a mathematical model for the system of interest. Because a second-order model with transport lag is very amenable to control computations and because this type of model has been used previously to represent certain high order single input-single output processes, an adaptive controller was designed based upon adjustment of controls computed for such a model. An extended Kalman filter was utilized for tracking the model parameters which were subsequently used to update a set of optimal control gains. Favorable results were obtained in applying this procedure to the control of several examples including a ninth order nonlinear process.