Pre-white dwarf evolution, 3
Mathematical model to estimate changes introduced in cooling times of white dwarfs by ion lattice
Vila, S. C.↗
SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Phenomenology of SUGRA extensions of the Starobinsky model
We analyze BI-extended model in a complete form and compare the predictions with that of Starobinsky model. Under the parameter constraints in Planck 2018, we find that the dynamics of the whole inflation process described by BI-extended and Starobinsky models are nearly the same, even though there are some differences in the regions out of inflation. We also find the scales of parameters in BI-extended model and inflaton values at the first horizon crossing required to implement inflation. The changes of (n{sub s},r) fingerprints of BI-extended model and that of evolutions of inflaton field due to the variations of relevant parameters are also investigated.
79 ASTRONOMY AND ASTROPHYSICS↗
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.↗
Time-evolution methods for matrix-product states
Highlights: • Introductory review of time-evolution methods for matrix-product states. • Detailed description of five state-of-the-art algorithms. • Extended comparison of numerical examples. • Extended error analysis of each algorithm. • Pseudo-code examples towards an implementation where necessary. - Abstract: Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W{sup I,II} method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
Analytically Derived Piezoelectric Ejecta Data Transformations, with Implications for Claims of Experimentally Observed Self-Similarity
Building upon a previously documented analytic formalism, we derive a set of data transformations that relate piezoelectrically inferred time-dependent ejecta masses, dynamical ejecta cloud densities, and "radiographic" ejecta cloud density distributions. These transformation rules are derived rigorously, with careful attention to the assumption of instant ejecta production which is inherent in the piezoelectric mass inference procedure. Some of these relationships have not appeared previously in the literature, including solutions for the unique ejecta velocity distribution and radiographic ejecta cloud density distribution consistent with the instant-production assumption for a given piezoelectrically inferred mass dataset. In deriving the latter, we prove that—again subject to the ubiquitous instant-creation assumption—measurements at a single sensor are sufficient to determine properties of the ejecta cloud everywhere at all times. Other data transformation relationships have appeared in the literature without a rigorous derivation, or have been stated in forms that obscure the key mathematical relationships. We apply these results to arguments for self-similar ejecta cloud evolution, thereby deriving mathematical expressions by which claims of self-similarity may be examined. We prove that one analysis used in the literature to claim experimental evidence of a short ejecta production timescale—and consequently of self-similar cloud evolution—in fact places no constraint the ejecta production interval and therefore does not support the associated conclusion. We also provide a potentially useful uniqueness proof.
30 DIRECT ENERGY CONVERSION↗
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.↗
Magnetic field evolution and reconnection in low resistivity plasmas
The mathematics and physics of each of the three aspects of magnetic field evolution—topology, energy, and helicity—are remarkably simple and clear. When the resistivity η is small compared to an imposed evolution, a/v , timescale, which means $R$ m ≡ μ 0 va/η $\gg$ 1, magnetic field-line chaos dominates the evolution of field-line topology in three-dimensional systems. Chaos has no direct role in the dissipation of energy. A large current density, j η ≡ vB/η, is required for energy dissipation to be on a comparable timescale to the topological evolution. Nevertheless, chaos plus Alfvén wave damping explain why both timescales tend to be approximately an order of magnitude longer than the evolution timescale a/v. Magnetic helicity is injected onto tubes of field lines when boundary flows have vorticity. Chaos can spread but not destroy magnetic helicity. Resistivity has a negligible effect on helicity accumulation when $R$ m $\gg$ 1. Helicity accumulates within a tube of field lines until the tube erupts and moves far from its original location.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
An Analysis of the Impact of Particle Growth on Transport Losses in Polymer-Electrolyte Fuel Cells
Voltage cycling causes catalyst nanoparticles in polymer-electrolyte fuel cells to grow. The concomitant loss of interfacial area results in larger kinetic, transport, and possibly ohmic overpotentials. This paper uses recently published experimental data and mathematical models to investigate the evolutions of transport and ohmic resistances to platinum nanoparticles located on the surface and inside the micropores of carbon black supports. Resistance to oxygen transport rises as surface area declines primarily because the flux to each remaining larger platinum particle increases. The path lengths governing oxygen diffusion to surface and buried platinum sites also increase as nanoparticles grow. Platinum nanoparticles on the surface become relatively less favorable as voltage cycling proceeds because they grow faster than platinum in micropores. Because voltage cycling causes total interfacial area to decline, and the fraction located inside micropores to increase, nanoscale ohmic losses increase as a catalyst layer decays. The practical importance of this effect is difficult to discern because proton conductivity in carbon micropores is not well characterized.
07 ISOTOPE AND RADIATION SOURCES↗