Pre-white dwarf evolution, 3
Mathematical model to estimate changes introduced in cooling times of white dwarfs by ion lattice
Vila, S. C.↗
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Results for “MATHEMATICAL EVOLUTION”
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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Applicability of mathematical modeling to problems of environmental physiology
The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.
White, Ronald J.↗
NACA/NASA research related to evolution of U.S. gust design criteria
This paper traces the evolution of gust design criteria in the U.S. particularly from the standpoint of research that was used in the substantiation for the various versions in the evolution. The mathematical models of airplanes and of atmospheric turbulence and their rationale are described. Emphasis is given to the revisions and refinements made starting in the 1920's up to the present time. The major steps, beginning with the sharp edged gust formula, are traced through the modified formula specifying ramp-platform gusts and later to one-minus-cosine gusts and finally to criteria for continuous gust analyses. The influence of aircraft design developments on design criteria development needs is also addressed. A brief summary of military criteria is included. Significant discussion is devoted to measurements that have been made, including onboard recordings, to provide an extensive data base of (1) atmospheric turbulence experienced in routine flight operations, (2) specially-instrumented research aircraft measurements to provide atmospheric characterization for various flight and meteorological conditions, and (3) comparisons of measured and calculated aircraft responses in turbulence. Some features of the instrumentation used will be depicted.
Murrow, Harold N.↗
Stellar Evolution - a Survey with Analytic Models
Mathematical models of stellar structure for understanding of stellar evolution
GALACTIC EVOLUTION↗
Tidal evolution in close binary systems.
Mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum. Following a general outline of the problem the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure are established, and the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for a given amount of total momentum are investigated. These results are compared with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known from evidence furnished by the observed rates of apsidal advance. The results show that all such systems whether of detached or semidetached type - disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than 1% of the total -a situation characteristic of a state close to the minimum energy for given total momentum.
Kopal, Z.↗
A mathematical model of the structure and evolution of small scale discrete auroral arcs
A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.
Seyler, C. E.↗
A mathematical model of the structure and evolution of small-scale discrete auroral arcs
A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.
Seyler, Charles E.↗
Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue
Models of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232-246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.
Evaluation Studies↗
Progress in Modeling Nonlinear Dendritic Evolution in Two and Three Dimensions, and Its Mathematical Justification
We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.
Tanveer, S.↗
Evolutionary and preservational constraints on origins of biologic groups: divergence times of eutherian mammals
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.
Non-NASA Center↗
Systems analysis of the vestibulo-ocular system
The vestibulo-ocular system is examined from the standpoint of system theory. The evolution of a mathematical model of the vestibulo-ocular system in an attempt to match more and more experimental data is followed step by step. The final model explains many characteristics of the eye movement in vestibularly induced nystagmus. The analysis of the dynamic behavior of the model at the different stages of its development is illustrated in time domain, mainly in a qualitative way.
Schmid, R. M.↗
Microwave Brightness Of Land Surfaces From Outer Space
Mathematical model approximates microwave radiation emitted by land surfaces traveling to microwave radiometer in outer space. Applied to measurements made by Scanning Multichannel Microwave Radiometer (SMMR). Developed for interpretation of microwave imagery of Earth to obtain distributions of various chemical, physical, and biological characteristics across its surface. Intended primarily for use in mapping moisture content of soil and fraction of Earth covered by vegetation. Advanced Very-High-Resolution Radiometer (AVHRR), provides additional information on vegetative cover, thereby making possible retrieval of soil-moisture values from SMMR measurements. Possible to monitor changes of land surface during intervals of 5 to 10 years, providing significant data for mathematical models of evolution of climate.
Kerr, Yann H.↗
A one-dimensional model describing aerosol formation and evolution in the stratosphere. I - Physical processes and mathematical analogs. II - Sensitivity studies and comparison with observations
A new time-dependent one-dimensional model of the stratospheric sulfate aerosol layer is developed. The model treats atmospheric photochemistry and aerosol physics in detail and includes the interaction between gases and particles explicitly. It is shown that the numerical algorithms used in the model are quite precise. Sensitivity studies and comparison with observations are made. The simulated aerosol physics generates a particle layer with most of the observed properties. The sensitivity of the calculated properties to changes in a large number of aeronomic aerosol parameters is discussed in some detail. The sensitivity analysis reveals areas where the aerosol model is most uncertain. New observations are suggested that might help resolve important questions about the origin of the stratospheric aerosol layer.
Turco, R. P.↗
An axiomatic explanation of complete self- reproduction.
Axiomatic explanation of complete self reproduction, noting logical mathematical biological reasoning and evolution theories
Loefgren, L.↗
Nucleation and growth control in protein crystallization
The five topics summarized in this final report are as follows: (1) a technique for the expedient, semi-automated determination of protein solubilities as a function of temperature and application of this technique to proteins other than lysozyme; (2) a small solution cell with adjustable temperature gradients for the growth of proteins at a predetermined location through temperature programming; (3) a microscopy system with image storage and processing capability for high resolution optical studies of temperature controlled protein growth and etching kinetics; (4) growth experiments with lysozyme in thermosyphon flow ; and (5) a mathematical model for the evolution of evaporation/diffusion induced concentration gradients in the hanging drop protein crystallization technique.
Rosenberger, Franz↗
On-Line, Real-Time Diagnostics of a Single Fluid Atomization System
A drop tube-Impulse Atomization technique was used to produce copper droplets. In this method, energy is transferred to a liquid by plunger movement resulting in spherical droplets emanating from orifices. A mathematical model of the evolution of droplet velocity and temperature at various heights for different sized droplets was developed. A two-color pyrometer, DPV-2000, and a shadowgraph were used to measure droplets radiant energy, diameter and velocity. The temperature values from the model were used to assess the two color pyrometer assumption over the temperature range of measurement. The DVP 2000 measurements were found to be dependent of droplet size wavelength and position of droplets below the atomizing nozzle. By calibrating the instrument for effective emissivity over the range of measurements, the thermal history of droplets may be recorded using a single color pyrometer approach.
DelshadKhatibi, P.↗
Evolution of heuristics by human operators in control systems.
Decision making mathematical model for control system operation modes, generating human operators heuristics evolution
Thomas, R. E.↗
Low order dynamical models for mixing layers
The goal of this project was to investigate the feasibility of developing useful low order dynamical systems to allow one to determine cheaply the effect of various initial conditions on the evolution of mixing layers. A mathematically rigorous approach for a time evolving base flow as found in a mixing layer seems to be the singular value decomposition of the linear operator transforming some initial perturbations into the solution at a given later time. Unfortunately, this is very costly, if at all feasible, and only deals with the linear evolution of a disturbance. A different approach based on weakly nonlinear analysis was attempted, but numerous difficulties were encountered. Several formulations were proposed which may be ill-posed. The reasons for this possible failure of the attempted approach is related to the fundamental limitations of weakly nonlinear analysis. The clarification of these issues is attempted in this report.
Riahi, D. N.↗