A model of the physiological systems of vegetation
Mathematical models for explaining working of physiological systems in plants
Viswanathan, M. M.↗
SEARCH · Engineering Papers
Results for “mathematical modelling”
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 thermal model for analysis of infrared images
A mathematical model derived from the equation of heat conduction was developed to assist in interpreting thermal infrared images acquired from aircraft and spacecraft. The model assumes steady state boundary conditions. It contains parameters of rock and soil properties, atmospheric effects, site location, and season. The results predicted provide an explanation for the thermal differences among granite, limestone, and dolomite recorded in the December 1968 daytime and predawn flights over the Mill Creek, Oklahoma test site, during which representative thermal inertia and albedo values were used. A second test of the model made use of data acquired during the June 1970 predawn overflight of Mill Creek. A simple model of transient heating of the ground was constructed as an extension of the overall model, in order to examine the effects of atmospheric perturbations. The results obtained are consistent with those of ground observations made at the time of the overflight.
Watson, K.↗
Multipath signal model development
The development and use of mathematical models of signals received through the multipath environmental of a TDRS-to-user spacecraft link and vice versa are discussed. The TDRS (tracking and data relay satellite) will be in synchronous orbit. The user spacecraft will be in a low altitude orbit between 200 and 4000 km.
Ghais, A. F.↗
Galactic gamma rays: Models involving variable cosmic-ray density
Mathematical models were developed to determine variable cosmic ray flux around the galactic plane. Data indicate point sources, molecular hydrogen concentration, increased cosmic ray density toward the galactic center, and neutral pion production combine to cause radiation density variables in the galactic plane.
Strong, A. W.↗
A vortex entrainment model applied to slender delta wings
A mathematical model of the vortex flow over a slender sharp-edged delta wing is proposed, and is shown to provide good agreement with the experiment. Although the technique requires experimental data in the form of the vortex core locations, it does account for the previously ignored mass entrainment of the vortex core.
Coe, P. L., Jr.↗
Simple intuitive models of programming
It is hypothesized that mathematical models of the programming process can be formulated to gauge the sensitivities of that process to various given parameters, and that such models can be calibrated on an empirical basis and used as guides toward maximizing productivity, documentation quality, and programming reliability. Three oversimplified models are presented as illustrations.
Tausworthe, R. C.↗
Modeling of turbine blade tip contact
A mathematical model is developed to evaluate a number of physical effects in turbomachine blade tip contact on the basis of a broad brush approach to provide insights without undue complexity. The analysis is restricted to the case of a shoe encountering a moving blade row and pressing against it with a fixed time-average force. Relative displacement components in the contact region are identified and determined. Two key equations are derived, where it is shown that wear rate plays a strong role in determining the traversal speed of the contact patch. The formula for estimating the size of the contact patch shows that the higher the traversal speed is, the wider is the contact patch.
Burton, R. A.↗
Combustion response modeling for composite solid propellants
A computerized mathematical model of the combustion response function of composite solid propellants was developed with particular attention to the contributions of the solid phase heterogeneity. The one-dimensional model treats the solid phase as alternating layers of ammonium perchlorate and binder, with an exothermic melt layer at the surface. Solution of the Fourier heat equation in the solid provides temperature and heat flux distributions with space and time. The problem is solved by conserving the heat flux at the surface from that produced by a suitable model of the gas phase. An approximation of the BDP flame model is utilized to represent the gas phase. By the use of several reasonable assumptions, it is found that a significant portion of the problem can be solved in closed form. A method is presented by which the model can be applied to tetramodal particle size distributions. A computerized steady-state version of the model was completed, which served to validate the various approximations and lay a foundation for the combustion response modeling. The combustion response modeling was completed in a form which does not require an iterative solution, and some preliminary results were acquired.
Source record↗
The dynamic modelling of a slotted test section
A mathematical model of the wind tunnel dynamics was developed. The modelling techniques were restricted to the use of one dimensional unsteady flow. The dynamic characteristics of slotted test section incorporated into the model are presented.
Gumas, G.↗
Wind Field and Trajectory Models for Tornado-Propelled Objects
A mathematical model to predict the trajectory of tornado born objects postulated to be in the vicinity of nuclear power plants is developed. An improved tornado wind field model satisfied the no slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Subscale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12 inch pipe and automobile. The original six degree of freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three degree of freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12 inch diameter pipe are examined.
Redmann, G. H.↗
Further observational support for the lossy radial diffusion model of the inner Jovian magnetosphere
A mathematical model describing radial diffusion, with violation of the third adiabatic invariant and with local losses, is applied to the Pioneer 10 and 11 observations of omnidirectional integral intensities of electrons with energy exceeding 21 MeV. Local losses outside L = 3 are much stronger than synchrotron losses but weaker than the losses one would expect for strong pitch angle diffusion. If radial diffusion is driven by ionospheric winds, as was suggested by Brice and McDonough (1973), it is found that the theoretical solution which best fits the data requires that the radial diffusion coefficient equals 3 x 10 to the -9th L-cubed/s and the lifetime against local losses is approximately a few million seconds.
Goertz, C. K.↗
Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part B
A mathematical model was developed and computerized simulations were obtained for a brushless dc motor. Experimentally obtained oscillograms of the machine phase currents are presented and the corresponding current and voltage waveforms for various modes of operation of the motor are presented and discussed.
Demerdash, N. A. O.↗
Multilevel modeling of the space construction base
A mathematical model representing a flexible space vehicle in terms of interconnected discrete masses is recast into hierarchical form to facilitate the application of multilevel control techniques. The model's state equations are temporarily decoupled by utilization of a set of coordination equations. A hierarchical form of the model is constructed with the set of coordination equations at the top of the hierarchy and the set of decoupled scalar state equations in the bottom level.
Chichester, F. D.↗
A Markov chain model for reliability growth and decay
A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.
Siegrist, K.↗
Forward and reverse transfer function model synthesis
A process for synthesizing a mathematical model for a linear mechanical system using the forward and reverse Fourier transform functions is described. The differential equation for a system model is given. The Bode conversion of the differential equation, and the frequency and time-domain optimization matching of the model to the forward and reverse transform functions using the geometric simplex method of Nelder and Mead (1965) are examined. The effect of the window function on the linear mechanical system is analyzed. The model is applied to two examples; in one the signal damps down before the end of the time window and in the second the signal has significant energy at the end of the time window.
Houghton, J. R.↗
Improved Statistical Model Of 10.7-cm Solar Radiation
Improved mathematical model simulates short-term fluctuations of flux of 10.7-cm-wavelength solar radiation during 91-day averaging period. Called "F10.7 flux", important as measure of solar activity and because it is highly correlated with ultraviolet radiation causing fluctuations in heating and density of upper atmosphere. F10.7 flux easily measureable at surface of Earth.
Vedder, John D.↗
Multiaxial Temperature- and Time-Dependent Failure Model
A temperature- and time-dependent mathematical model predicts the conditions for failure of a material subjected to multiaxial stress. The model was initially applied to a filled epoxy below its glass-transition temperature, and is expected to be applicable to other materials, at least below their glass-transition temperatures. The model is justified simply by the fact that it closely approximates the experimentally observed failure behavior of this material: The multiaxiality of the model has been confirmed (see figure) and the model has been shown to be applicable at temperatures from -20 to 115 F (-29 to 46 C) and to predict tensile failures of constant-load and constant-load-rate specimens with failure times ranging from minutes to months..
Richardson, David↗
Adopting Code Verification Methodology Based on Model Form
Code verification is an essential part of credibility analysis for computational models. It assesses whether the mathematical model is implemented correctly into the code and whether the numerical methods behave consistently, and is done before solution verification and validation. Robust guidance for code verification exists in the literature. However, there is no known, concise guide for selecting the approach based on the model form that also presents an overview of the common elements. This document was written to address this gap as an accessible reference for beginning a code-verification effort.
97 MATHEMATICS AND COMPUTING↗