Rigid disks and spheres at high densities - Bounds on the partition function.
Upper and lower bounds on partition functions for finite systems of rigid disks and spheres for high density limit
FACE CENTERED CUBIC /FCC/ CRYSTAL↗
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Results for “finite density”
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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The correlation function for density perturbations in an expanding universe. I - Linear theory
The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.
Mcclelland, J.↗
The structure of Saturn's rings - Implications from the Voyager stellar occultation
A 100-m resolution has been obtained in the radial direction, across the entire Saturn ring system, in Voyager 2 photopolarimeter observations of Delta Scorpii as it was occulted by the rings. An automatic search with finite Fourier transforms located 13 density waves excited by resonances with Saturn's satellites. Although strong density waves can be easily located, no waves have been identified which have predicted torques/surface mass density values lower than 4 x 10 to the 16th cu cm/sec-squared. This suggests a limit of less than 100 waves to be found in the Saturn rings. Total ring mass is estimated as 5 x 10 to the -8th of the mass of Saturn. The power spectrum for the rings shows no dominant individual wavelengths. The majority of ring structures and most variance in ring optical depth are not explainable by currently entertained physical mechanisms.
Esposito, L. W.↗
Aerothermodynamic heating and performance analysis of a high-lift aeromaneuvering AOTV concept
The thermal-control requirements for design-optimized aeromaneuvering performance are determined for space-based applications and low-earth orbit sorties involving large, multiple plane-inclination changes. The leading-edge heating analysis is the most advanced developed for hypersonic-rarefied flow over lifting surfaces at incidence. The effects of leading-edge bluntness, low-density viscous phenomena, and finite-rate flow-field chemistry and surface catalysis are accounted for. The predicted aerothermodynamic heating characteristics are correlated with thermal-control and flight-performance capabilities. The mission payload capability for delivery, retrieval, and combined operations is determined for round-trip sorties extending to polar orbits. Recommendations are given for future design refinements. The results help to identify technology issues required to develop prototype operational systems.
Menees, G. P.↗
Design and performance analysis of an aero-maneuvering orbital-transfer vehicle concept
Systems requirements for design-optimized, lateral-turn performance were determined for reusable, space-based applications and low-Earth orbits involving large multiple plane-inclination changes. The aerothermodynamic analysis is the most advanced available for rarefield-hypersonic flow over lifting surfaces at incidence. The effects of leading-edge bluntness, low-density viscous phenomena, and finite-rate flow-field chemistry and surface catalysis are accounted for. The predicted aerothermal heating characteristics are correlated with thermal-control and flight-performance capabilities. The mission payload capacity for delivery, retrieval, and combined operations was determined for round-trip sorties extending to polar orbits. Recommendations are given for future design refinements. The results help to identify technology issues required to develop prototype operational vehicles.
Menees, G. P.↗
Design and performance analysis of an aeromaneuvering orbital-transfer vehicle concept
Systems requirements for design-optimized, lateral-turn performance were determined for reusable, space-based applications and low-earth orbits involving large multiple plane-inclination changes. The aerothermodynamic analysis is the most advanced available for rarefied-hypersonic flow over lifting surfaces at incidence. The effects of leading-edge bluntness, low-density viscous phenomena, and finite-rate flow-field chemistry and surface catalysis are accounted for. The predicted aerothermal heating characteristics are correlated with thermal-control and flight-performance capabilities. The mission payload capacity for delivery, retrieval, and combined operations was determined for round-trip sorties extending to polar orbits. Recommendations are given for future design refinements. The results help to identify technology issues required to develop prototype operational vehicles.
Menees, G. P.↗
NASA Glenn Research Center Program in High Power Density Motors for Aeropropulsion
Electric drive of transport-sized aircraft propulsors, with electric power generated by fuel cells or turbo-generators, will require electric motors with much higher power density than conventional room-temperature machines. Cryogenic cooling of the motor windings by the liquid hydrogen fuel offers a possible solution, enabling motors with higher power density than turbine engines. Some context on weights of various systems, which is required to assess the problem, is presented. This context includes a survey of turbine engine weights over a considerable size range, a correlation of gear box weights and some examples of conventional and advanced electric motor weights. The NASA Glenn Research Center program for high power density motors is outlined and some technical results to date are presented. These results include current densities of 5,000 A per square centimeter current density achieved in cryogenic coils, finite element predictions compared to measurements of torque production in a switched reluctance motor, and initial tests of a cryogenic switched reluctance motor.
Brown, Gerald V.↗
Intensity Conserving Spectral Fitting
The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.
Klimchuk, J. A.↗
A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field
Fluid structural interaction problems that estimate panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. Even when the analyst elects to use a fitted function for the spatial correlation an error may be introduced if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Both qualitative and quantitative illustrations evaluating the adequacy of different patch density assumptions to approximate the fitted spatial correlation function are provided. The actual response of a typical vehicle panel system is then evaluated in a convergence study where the patch density assumptions are varied over the same finite element model. The convergence study results are presented illustrating the impact resulting from a poor choice of patch density. The fitted correlation function used in this study represents a Diffuse Acoustic Field (DAF) excitation of the panel to produce vibration response.
Smith, Andrew↗
Optimal estimation for the satellite attitude using star tracker measurements
An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.
Lo, J. T.-H.↗
Resonance absorption of propagating fast waves in a cold plasma
Absorption of propagating waves impinging on a surface in which the plasma and magnetic field may change is investigated by examining in depth the problem of a combination of cold plasma, uniform magnetic field and a surface density which varies linearly from zero at the left end to some finite value at the right end, beyond which the density is constant. Two cases are considered: one in which the plasma is a vacuum everywhere to the left of the surface (which may correspond to coronal conditions) and one in which the plasma density jumps to a very large value to the left of the surface (which may mimic the magnetosphere with the dense region at the left corresponding to the plasmasphere). A complete discussion of the resonance absorption of propagating fast waves for the case considered by Kiveloson and Southwood (1986) is presented, emphasizing approximate analytical results whenever possible; these results are then compared with exact numerical solutions.
Hollweg, Joseph V.↗
v-representability and density functional theory
It is shown that if n(r) is the discrete density on a lattice (enclosed in a finite box) associated with a nondegenerate ground state in an external potential v(r) (i.e., is 'v-representable'), then the density n(r) + mu(r), with m(r) arbitrary (apart from trivial constraints) and mu small enough, is also associated with a nondegenerate ground state in an external potential v'(r) near v(r); i.e., n(r) + m(r) is also v-representable. Implications for the Hohenberg-Kohn variational principle and the Kohn-Sham equations are discussed.
Kohn, W.↗
Generalization of the Manley-Rowe relations for non-periodic signals constrained in bandwidth with finite energy
General relations for the energy spectral densities of nonperiodic signals constrained in bandwidth in nonlinear reactances are derived. It is assumed that the charge-voltage characteristics of the reactances are polynomials. In addition certain conditions for the frequency bands of the signals must be met. By contrast with the Manley-Rowe relations integrals with respect to frequency appear instead of the ratios power over frequency. The integrands are energy spectral densities divided by frequency. For parametric devices inequalities can be derived for the ratios of the energy levels in the different circuits and the limiting frequencies of the energy spectral densities. With these inequalities it is possible to determine limits for the energy levels.
Proksch, P.↗
Thermal Transport Model for Heat Sink Design
A document discusses the development of a finite element model for describing thermal transport through microcalorimeter arrays in order to assist in heat-sinking design. A fabricated multi-absorber transition edge sensor (PoST) was designed in order to reduce device wiring density by a factor of four. The finite element model consists of breaking the microcalorimeter array into separate elements, including the transition edge sensor (TES) and the silicon substrate on which the sensor is deposited. Each element is then broken up into subelements, whose surface area subtends 10 10 microns. The heat capacity per unit temperature, thermal conductance, and thermal diffusivity of each subelement are the model inputs, as are the temperatures of each subelement. Numerical integration using the Finite in Time Centered in Space algorithm of the thermal diffusion equation is then performed in order to obtain a temporal evolution of the subelement temperature. Thermal transport across interfaces is modeled using a thermal boundary resistance obtained using the acoustic mismatch model. The document concludes with a discussion of the PoST fabrication. PoSTs are novel because they enable incident x-ray position sensitivity with good energy resolution and low wiring density.
Chervenak, James A.↗
Hot ion plasma heating experiments in SUMMA
Initial empirical results are presented for the hot-ion plasma heating experiments conducted in the new SUMMA (Superconducting Magnetic Mirror Apparatus) at NASA Lewis Research Center. A discharge was formed by applying a radially inward dc electric field near the mirror throats. Data were obtained at midplane magnetic flux densities from 1.0 to 3.5 tesla. Charge-exchange neutral particle energy analyzer data were reduced to ion temperatures using a plasma model that included a Maxwellian energy distribution superimposed on an azimuthal drift, finite ion orbits, and radial variations in density and electric field. Using this plasma model, the highest ion temperatures computed were 5 keV, 1.2 keV, and 1 keV for He(+), H2(+), and H(+), respectively. These were obtained at a midplane magnetic flux density of 1.6 T.-
Reinmann, J. J.↗
Consistent Initial Conditions for the DNS of Compressible Turbulence
Relationships between diverse thermodynamic quantities appropriate to weakly compressible turbulence are derived. It is shown that for turbulence of a finite turbulent Mach number there is a finite element of compressibility. A methodology for generating initial conditions for the fluctuating pressure, density and dilatational velocity is given which is consistent with finite Mach number effects. Use of these initial conditions gives rise to a smooth development of the flow, in contrast to cases in which these fields are specified arbitrarily or set to zero. Comparisons of the effect of different types of initial conditions are made using direct numerical simulation of decaying isotropic turbulence.
Ristorcelli, J. R.↗
Evanescent pressure gradient response in the upper ocean to subinertial wind stress forcing of finite wavelength
A schematic model is used to interpret field observations related to the mixed layer response to wind stress at subinertial frequencies. It is shown that subinertial density and pressure fluctuations can arise locally from the finite wavelength character of the wind stress forcing as a fundamental part of the upper ocean transient, wind-driven response on time scales of 2-10 pendulum days. Evanescent vertical motions arise which alter the density field of the pycnocline, and hence the pressure field over the entire upper ocean. It is thus found that in the real ocean driven by wind stress, a transient geostrophic response exists which can be as large or larger than the transient Eckman response.
White, Warren B.↗
The effect of energetically produced O2/+/ on the ion temperatures of the Martian thermosphere
The heating rates and ion temperatures of the Martian thermosphere resulting from the thermalization of the energetic O2(+) ions produced by the reactions of the solar ionization products CO2(+) and O(+) with neutral particles are calculated and the effects of small magnetic fields on the ion thermal balance are investigated. The energy transfer and transport of energetic ions is modelled by solving the continuity equation for the ions over a series of finite energy cells yielding the equilibrium densities as a function of energy and altitude. Particles which are able to proceed upwards without collisions are dealt with separately from the continuity equation. It is shown that the thermalization of the energetic O2(+) ions can greatly increase ion temperatures above 200 km compared to those calculated for only ambient electron heating. Current solar wind interaction models predict that small horizontal magnetic fields act to restrict the ion thermal conductivity and to increase upper altitude ion temperatures. The combined effects of these processes provide a partial agreement with measurements made by Viking 1.
Rohrbaugh, R. P.↗