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Results for “Mathematical Model”

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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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Preliminary development of a fundamental analysis model for crack growth in a fiber reinforced composite material

A mathematical model for the strength of fiber reinforced composites containing specific flaws is described. The approach is to embed a local heterogeneous region surrounding the crack tip in an anisotropic elastic continuum. By consideration of the individual failure events activated near the flaw tip, a strength prediction can be made from basic properties of the composite constituents. Computations for arbitrary flaw size and orientation have been performed for unidirectional composites with linear elastic-brittle constituent behavior. The mechanical properties were those of graphite epoxy. With the rupture properties arbitrarily varied to test the capability of the model to reflect real fracture modes in fiber composites, it is shown that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting all can occur during gradually increasing load prior to catastrophic fracture. Qualitative comparisons with experimental results on edge-notched unidirectional graphite epoxy specimens have also been made.

Kanninen, M. F.↗
NASA NTRS1979

Development of a model and computer code to describe solar grade silicon production processes

Mathematical models, and computer codes based on these models were developed which allow prediction of the product distribution in chemical reactors in which gaseous silicon compounds are converted to condensed phase silicon. The reactors to be modeled are flow reactors in which silane or one of the halogenated silanes is thermally decomposed or reacted with an alkali metal, H2 or H atoms. Because the product of interest is particulate silicon, processes which must be modeled, in addition to mixing and reaction of gas-phase reactants, include the nucleation and growth of condensed Si via coagulation, condensation, and heterogeneous reaction.

Srivastava, R.↗
NASA NTRS1979

Development of a Model and Computer Code to Describe Solar Grade Silicon Production Processes

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 were developed. The following tasks were accomplished: (1) formulation of a model for silicon vapor separation/collection from the developing turbulent flow stream within reactors of the Westinghouse (2) modification of an available general parabolic code to achieve solutions to the governing partial differential equations (boundary layer type) which describe migration of the vapor to the reactor walls, (3) a parametric study using the boundary layer code to optimize the performance characteristics of the Westinghouse reactor, (4) calculations relating to the collection efficiency of the new AeroChem reactor, and (5) final testing of the modified LAPP code for use as a method of predicting Si(1) droplet sizes in these reactors.

Srivastava, R.↗
NASA NTRS1977

A life cycle cost economics model for automation projects with uniformly varying operating costs

The described mathematical model calculates life-cycle costs for projects with operating costs increasing or decreasing linearly with time. The cost factors involved in the life-cycle cost are considered, and the errors resulting from the assumption of constant rather than uniformly varying operating costs are examined. Parameters in the study range from 2 to 30 years, for project life; 0 to 15% per year, for interest rate; and 5 to 90% of the initial operating cost, for the operating cost gradient. A numerical example is presented.

Remer, D. S.↗
NASA NTRS1989

Model Of Turbulent Gas Eddies Containing Drops

Report proposes development of mathematical model of turbulent eddy of gas containing drops of liquid fuel. Closely related to those described in "Turbulence and Evaporation in Clusters of Drops" (NPO-17323) and "Effects of Turbulence on Ignition" (NPO-17335). Goal to initiate development of theory of interactions of several eddies containing drops during evaporation, ignition, and combustion of liquid fuels injected into combustors. Numerical results of analysis given as plot of nondimensionalized evaporation time versus initial ratio of air mass to fuel mass.

Bellan, Josette↗
NASA NTRS1992

Simplified Modeling Of A Helicopter

Report discusses development of minimum-complexity mathematical model of helicopter for use in flight simulator. Development motivated by computational delays, costs, long development times, and inflexibility of sophisticated models now in use. New model overcomes these disadvantages and provides better engineering understanding of those features pertaining to handling qualities apparent to pilot who uses simulator.

Heffley, Robert K.↗
NASA NTRS1993

Model Of Neural Network With Creative Dynamics

Paper presents analysis of mathematical model of one-neuron/one-synapse neural network featuring coupled activation and learning dynamics and parametrical periodic excitation. Demonstrates self-programming, partly random behavior of suitable designed neural network; believed to be related to spontaneity and creativity of biological neural networks.

Zak, Michail↗
NASA NTRS1995

Finite-Element Modeling For Structural Analysis

Report presents study of finite-element mathematical modeling as used in analyzing stresses and strains at joints between thin, shell-like components (e.g., ducts) and thicker components (e.g., flanges or engine blocks). First approach uses global/local model to evaluate system. Provides correct total response and correct representation of stresses away from any discontinuities. Second approach involves development of special transition finite elements to model transitions between shells and thicker structural components.

Min, J. B.↗
NASA NTRS2010

Parachute Drag Model

DTV-SIM is a computer program that implements a mathematical model of the flight dynamics of a missile-shaped drop test vehicle (DTV) equipped with a multistage parachute system that includes two simultaneously deployed drogue parachutes and three main parachutes deployed subsequently and simultaneously by use of pilot parachutes. DTV-SIM was written to support air-drop tests of the DTV/parachute system, which serves a simplified prototype of a proposed crew capsule/parachute landing system.

Cuthbert, Peter↗
NASA NTRS2008

A Modification and Analysis of Lagrangian Trajectory Modeling and Granular Dynamics of Lunar Dust Particles

A previously developed mathematical model is amended to more accurately incorporate the effects of lift and drag on single dust particles in order to predict their behavior in the wake of high velocity gas flow. The model utilizes output from a CFD or DSMC simulation of exhaust from a rocket nozzle hot gas jet. An extension of the Saffman equation for lift based on the research of McLaughlin (1991) and Mei (1992) is used, while an equation for the Magnus force modeled after the work of Oesterle (1994) and Tsuji et al (1985) is applied. A relationship for drag utilizing a particle shape factor (phi = 0.8) is taken from the work of Haider and Levenspiel (1989) for application to non-spherical particle dynamics. The drag equation is further adjusted to account for rarefaction and compressibility effects in rarefied and high Mach number flows according to the work of Davies (1945) and Loth (2007) respectively. Simulations using a more accurate model with the correction factor (Epsilon = 0.8 in a 20% particle concentration gas flow) given by Richardson and Zaki (1954) and Rowe (1961) show that particles have lower ejection angles than those that were previously calculated. This is more prevalent in smaller particles, which are shown through velocity and trajectory comparison to be more influenced by the flow of the surrounding gas. It is shown that particles are more affected by minor changes to drag forces than larger adjustments to lift forces, demanding a closer analysis of the shape and behavior of lunar dust particles and the composition of the surrounding gas flow.

Long, Jason M.↗
DOE OSTI2018

Estimation of the HIV-1 infection rate and the basic reproductive ratio

This paper proposes and analyzes an alternative method to estimate important parameters of the HIV-1 infection: the infection rate and the basic reproductive ratio (in the presence and absence of the immune response). These parameters are of great relevance, impacting on the infection chronicity. The method consists in comparing clinical data in the chronic stage with predicted equilibrium points of a mathematical model which describes the dynamics of HIV-1 in the acute infection phase. The fact that the method uses only clinical data relating to the chronic stage is an important aspect since most patients are diagnosed at this stage, and thus only have data available for this stage. A comparison between the proposed method and other estimation methods, as well as between numerical simulations, is presented and the results are quite satisfactory. In addition, by applying the proposed method for data of 31 patients, we estimate the basic reproductive ratio in the presence of the immune response and the HIV-1 infection rate for which we obtained a median of 1.95 (IQR 0.55) and 1.96×10{sup −5} mm{sup 3} virions{sup −1} day{sup −1} (IQR 3.52×10{sup −5}), respectively.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Quantifying the basic reproduction number and underestimated fraction of Mpox cases worldwide at the onset of the outbreak

In 2022, there was a global resurgence of mpox, with different clinical-epidemiological features compared with previous outbreaks. Sexual contact was hypothesized as the primary transmission route, and the community of men having sex with men (MSM) was disproportionately affected. Because of the stigma associated with sexually transmitted infections, the real burden of mpox could be masked. We quantified the basic reproduction number (R 0 ) and the underestimated fraction of mpox cases in 16 countries, from the onset of the outbreak until early September 2022, using Bayesian inference and a compartmentalized, risk-structured (high-/low-risk populations) and two-route (sexual/non-sexual transmission) mathematical model. Machine learning (ML) was harnessed to identify underestimation determinants. Estimated R 0 ranged between 1.37 (Canada) and 3.68 (Germany). The underestimation rates for the high- and low-risk populations varied between 25–93% and 65–85%, respectively. The estimated total number of mpox cases, relative to the reported cases, is highest in Colombia (3.60) and lowest in Canada (1.08). In the ML analysis, two clusters of countries could be identified, differing in terms of attitudes towards the 2SLGBTQIAP+ community and the importance of religion. Given the substantial mpox underestimation, surveillance should be enhanced, and country-specific campaigns against the stigmatization of MSM should be organized, leveraging community-based interventions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Calculation of the Present Value of Separative Work for Uranium Isotopes

An economics-mathematical model for performing analytical calculations of the present value of separative work for uranium isotopes in a separation plant currently being designed using gas centrifuge technology is examined. Analytical expressions are obtained for the present value of the separative work, the internal rate of return, and the payback period of the separation plant as a function of its main engineering and economics parameters – productivity (capacity), capital investment, and operating expenses. Calculations of these criteria for investment efficiency are presented for a wide range of initial data. It is shown that the calculation of the present value of separative work must be performed in a complex with other investment efficiency criteria in order to determine their optimal combination.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Heteronuclear complexation in the system 1-hydroxyethylidenediphosphonic acid—manganese(II)—gadolinium(III) in aqueous solution

pH-Potentiometric method in combination with mathematical modeling was used to study the system manganese(II)—gadolinium(III)—1-hydroxyethylidenediphosphonic acid (HEDP, H{sub 4}L). When both cations simultaneously are present in the solution, the accumulation of heteronuclear forms with the ratio of Gd: Mn: HEDP equal to 1: 1: 1, 1: 1: 2, and 1: 1: 3 was observed already in the strongly acidic pH region, while from homonuclear forms only five complexes were detected in the solution, namely, MnL{sub 2}{sup 6–}, GdH{sub 4}L{sub 2}{sup –}, GdH{sub 2}L{sup +}, KGd{sub 2}HL{sub 2}↓, and K{sub 3}Gd{sub 2}L{sub 2}(OH)↓. It was concluded that heteronuclear complexes are much stronger and replace homonuclear forms in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Controlling circuitry underlies the growth optimization of Saccharomyces cerevisiae

Microbial growth emerges from coordinated synthesis of various cellular components from limited resources. In Saccharomyces cerevisiae, cyclic AMP (cAMP)-mediated signaling is shown to orchestrate cellular metabolism; however, it remains unclear quantitatively how the controlling circuit drives resource partition and subsequently shapes biomass growth. Here we combined experiment with mathematical modeling to dissect the signaling-mediated growth optimization of S. cerevisiae. We showed that, through cAMP-mediated control, the organism achieves maximal or nearly maximal steady-state growth during the utilization of multiple tested substrates as well as under perturbations impairing glucose uptake. However, the optimal cAMP concentration varies across cases, suggesting that different modes of resource allocation are adopted for varied conditions. Under settings with nutrient alterations, S. cerevisiae tunes its cAMP level to dynamically reprogram itself to realize rapid adaptation. Moreover, to achieve growth maximization, cells employ additional regulatory systems such as the GCN2-mediated amino acid control. This study establishes a systematic understanding of global resource allocation in S. cerevisiae, providing insights into quantitative yeast physiology as well as metabolic strain engineering for biotechnological applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Photonic generation of millimeter-wave ultra-wideband monocycle signal using up-conversion based on stimulated Brillouin scattering effect

We propose a novel scheme for photonic generation of millimeter-wave (MMW) ultra-wideband monocycle signal free of strong local oscillation (LO) and low-frequency component. A theory and a mathematical model are built to investigate the proposed scheme. Firstly, a differentiator is implemented using a dual-drive Mach–Zehnder modulator to attain monocycle pulses by differentiating a series of Gauss pulses. Subsequently, a dual-parallel Mach–Zehnder modulator and stimulated Brillouin scattering effect are employed to realize single-sideband modulation for up-converting the monocycle pulses to the MMW band. In the calculation, the generated signal is centered at 26 GHz with 10-dB bandwidth of 7 GHz and its power efficiency is about 50.08%. In addition, on–off keying modulation, amplitude modulation (PAM) and pulse position modulation monocycle pulses are generated. The spectrum of the generated signal meets with the FCC mask efficiently, so this technique has a potential application in MMW radar communication systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2008

Thermal Capacitance (Slug) Calorimeter Theory Including Heat Losses and Other Decaying Processes

A mathematical model, termed the Slug Loss Model, has been developed for describing thermal capacitance (slug) calorimeter behavior when heat losses and other decaying processes are not negligible. This model results in the temperature time slope taking the mathematical form of exponential decay. When data is found to fit well to this model, it allows a heat flux value to be calculated that corrects for the losses and may be a better estimate of the cold wall fully catalytic heat flux, as is desired in arc jet testing. The model was applied to the data from a copper slug calorimeter inserted during a particularly severe high heating rate arc jet run to illustrate its use. The Slug Loss Model gave a cold wall heat flux 15% higher than the value of 2,250 W/sq cm obtained from the conventional approach to processing the data (where no correction is made for losses). For comparison, a Finite Element Analysis (FEA) model was created and applied to the same data, where conduction heat losses from the slug were simulated. The heat flux determined by the FEA model was found to be in close agreement with the heat flux determined by the Slug Loss Model.

Hightower, T. Mark↗
DOE OSTI2016

Sci-Fri PM: Radiation Therapy, Planning, Imaging, and Special Techniques - 09: Impact of the distance of reflective markers from linac isocenter on the positional accuracy of an infrared tracking system

Purpose: The HexaPOD™ six degree of freedom couchtop is equipped with an optical tracking system, consisting of a stereoscopic camera and a reference frame (RF) carrying infrared reflective markers. The manufacturer recommends placing the RF within 50 cm from linac isocenter (ISO), which is a serious limitation since the RF does not fit around the shoulders of most brain patients. This study quantifies the impact of extended RF distances from ISO on positional accuracy. Methods: An in-house tool with an estimated resolution of 0.3 mm and 0.1° was used. It is a large cube and a mathematical model of HexaPOD motion to determine the intersection of room lasers with the ruled cube edges. Combinations of translations (±1 and ±3 cm) and rotations (±2.5°) were executed on two HexaPOD couchtops for multiple RF distances from ISO (35 to 77 cm). For each combination, ten laser readings were fed into a least squares algorithm to determine the executed translations and rotations while minimizing operator reading errors. Results: The usable tracking volume is up to an RF distance of 82 cm from ISO. Positional accuracy of the HexaPOD/iGuide system is 0.6 mm and 0.1° (95% confidence). Positional accuracy variations versus RF distance from ISO are statistically insignificant (p = 0.05). Our results generally confirm recent internal estimates by the manufacturer (for future release). Conclusions: RF distances up to 77 cm from ISO are clinically acceptable, provided performing a patient safety study with a verification scan.

60 APPLIED LIFE SCIENCES↗