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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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A Volterra series approach was applied to the identification of nonlinear systems which are described by a neural network model. A procedure is outlined by which a mathematical model can be developed from experimental data obtained from the network structure. Applications of the results to the control of robotic systems are discussed.
Some molecular clock estimates of divergence times of taxonomic groups undergoing evolutionary radiation are much older than the groups' first observed fossil record. Mathematical models of branching evolution are used to estimate the maximal rate of fossil preservation consistent with a postulated missing history, given the sum of species durations implied by early origins under a range of species origination and extinction rates. The plausibility of postulated divergence times depends on origination, extinction, and preservation rates estimated from the fossil record. For eutherian mammals, this approach suggests that it is unlikely that many modern orders arose much earlier than their oldest fossil records.
The Massachusetts Institute of Technology (MIT) Commission on Industrial Productivity, in their report Made in America, found that six recurring weaknesses were hampering American manufacturing industries. The two weaknesses most relevant to product development were 1) technological weakness in development and production, and 2) failures in cooperation. The remedies to these weaknesses are considered the essential twin pillars of CE: 1) improved development process, and 2) closer cooperation. In the MIT report, it is recognized that total cooperation among teams in a CE environment is rare in American industry, while the majority of the design research in mathematically modeling CE has assumed total cooperation. In this paper, we present mathematical constructs, based on game theoretic principles, to model degrees of collaboration characterized by approximate cooperation, sequential decision making and isolation. The design of a pressure vessel and a passenger aircraft are included as illustrative examples.
Development of mathematical models of heat and mass transfer in glass-melting furnaces began in the 1970s and progressed rapidly with advances in sophisticated experimental/numerical techniques and increasing computational power. Today, practically all newly built or rebuilt furnaces are optimized with these models to meet stringent quality requirements, reduce the unit costs of manufacturing, or control emissions. One remaining hurdle is to model the batch-to-glass conversion accurately enough to reliably assess the glass production rate. This article summarizes two key aspects of the batch-conversion modeling—the heat transfer and the kinetics of conversion—and reviews the current state-of-the-art approaches to simulating them. We critically examine the advantages of the commonly used heat transfer approach, but also explain that its predictive capabilities are significantly restricted by the dependence of batch thermal properties on the time-temperature history. We argue that kinetic approaches to the batch-conversion modeling would offer a significant improvement when coupled with the heat transfer approach. Finally, we summarize key areas requiring further research on the way toward a realistic model of the batch blanket.
We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis . The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis . The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.
Mathematical models for IBM 7094 computer program prediction of neutron induced activation
Mathematical model for frequency response of forced flow, hollow, single tube boiler inlet pressure to inlet flow
Mathematical models of wave propagation in three-fluid plasma and numerical solutions to dispersion and propagation properties
The critical thermal control problems and verification of thermal mathematical model results for the space shuttle concept are discussed. The use of a small scale thermal model of the space shuttle is proposed. It was determined that a one-third scale model of the space shuttle would serve as a useful tool throughout the entire thermal design and verification program. The major considerations in modeling the conduction-radiation-convection fields, the level of detail for modeling various systems, preliminary test requirements, and potential applications of the thermal scale model are summarized.
Reference describes standard formulas, techniques, and terminology used in constructing mathematical models.
Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).
A geochemical mathematical modeling study designed to investigate the well plugging problems encountered at the Auburn University experimental field tests is summarized. The results, primarily of qualitative interest, include: (1) loss of injectivity was probably due to a combination of native particulate plugging and clay swelling and dispersion; (2) fluid-fluid incompatibilities, hydrothermal reactions, and oxidation reactions were of insignificant magnitude or too slow to have contributed markedly to the plugging; and (3) the potential for and contributions from temperature-induced dissolved gas solubility reductions, capillary boundary layer viscosity increases, and microstructural deformation cannot be deconvolved from the available data.
MOVER uses experimental data to verify mathematical models of "mixed" dynamic systems. The term "mixed" refers to interactive mechanical, hydraulic, electrical, and other components. Program compares analytical transfer functions with experiment.
The role of the mathematical model is to relate the individual processes to environmental conditions and the behavior of the whole plant. Using the controlled-environment facilities of the phytotron at North Carolina State University for experimentation at the whole-plant level and methods for handling complex models, researchers developed a plant growth model to describe the relationships between hierarchial levels of the crop production system. The fundamental processes that are considered are: (1) interception of photosynthetically active radiation by leaves, (2) absorption of photosynthetically active radiation, (3) photosynthetic transformation of absorbed radiation into chemical energy of carbon bonding in solube carbohydrates in the leaves, (4) translocation between carbohydrate pools in leaves, stems, and roots, (5) flow of energy from carbohydrate pools for respiration, (6) flow from carbohydrate pools for growth, and (7) aging of tissues. These processes are described at the level of organ structure and of elementary function processes. The driving variables of incident photosynthetically active radiation and ambient temperature as inputs pertain to characterization at the whole-plant level. The output of the model is accumulated dry matter partitioned among leaves, stems, and roots; thus, the elementary processes clearly operate under the constraints of the plant structure which is itself the output of the model.
A mathematical model based on the Euler-Bernoulli beam theory is proposed for predicting the effective Young's moduli of piecewise isotropic composite laminates with local ply curvatures in the main load-carrying layers. Strains in corrugated layers, In-Phase layers, Out-of-Phase layers are predicted for various geometries and material configurations by assuming matrix layers as elastic foundations of different spring constants. The effective Young's moduli measured from corrugated aluminum specimens and aluminum/epoxy specimens with In-Phase and Out-of-Phase wavy patterns coincide very well with the model predictions. Moire fringe analysis of an In-Phase specimen and an Out-of-Phase specimen are also presented confirming the main assumption of the model related to the elastic constraint due to the matrix layers. The present model is also compared with the experimental results and other models, including the micro-buckling models, published in the literature. The results of the present study show that even a very small scale local ply curvature produces a noticeable effect on the mechanical constitutive behavior of a laminated composite.
A mathematical model of transient seas modulated by coherent swells is developed as a Rayleigh-Poisson random process subject to deterministic correlations of scattering sites, as they appear in a time window defined by a SAR's range-Doppler measurements of the surface coordinates. This model of SAR response to sea surface dynamics is discussed as a Fourier domain predictor/corrector of a dynamic motion blur.
This paper presents a mathematical model for the cooling of an active flow with two separate thermal components, one of which is a crust that cools by radiation and thickens with time and the other an inner core that is vertically isothermal and partially exposed at the top surface, where heat is lost by radiation. This model provides a more realistic description of active lava flows than the existing models that assume thermal homogeneity in each vertical cross section perpendicular to the direction of flow advance. The results of the model were found to compare favorably with existing field data. The effects of different crustal thickening rates, fractional areas of crust, and eruption temperatures on the cooling of the two thermal components were examined.
Report presents comparative review of four mathematical models of micromechanical behaviors of fiber/metal-matrix composite materials. Models differ in various details, all based on properties of fiber and matrix constituent materials, all involve square arrays of fibers continuous and parallel and all assume complete bonding between constituents. Computer programs implementing models used to predict properties and stress-vs.-strain behaviors of unidirectional- and cross-ply laminated composites made of boron fibers in aluminum matrices and silicon carbide fibers in titanium matrices. Stresses in fiber and matrix constituent materials also predicted.