Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas
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George Livadiotis↗
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Overall Traveling-Wave-Tube Efficiency Improved By Optimized Multistage Depressed Collector Design
Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.
Vaden, Karl R.↗
Physical concepts in the development of constitutive equations
Proposed viscoplastic material models include in their formulation observed material response but do not generally incorporate principles from thermodynamics, statistical mechanics, and quantum mechanics. Numerous hypotheses were made for material response based on first principles. Many of these hypotheses were tested experimentally. The proposed viscoplastic theories and the experimental basis of these hypotheses must be checked against the hypotheses. The physics of thermodynamics, statistical mechanics and quantum mechanics, and the effects of defects, are reviewed for their application to the development of constitutive laws.
Cassenti, B. N.↗
Proton production in relativistic heavy ion collisions; comparison with a thermodynamical model
Experimental results concerning proton production in nuclear collisions, obtained at Saturne with the Diogene 4 pi facility, are compared with the predictions of a thermodynamical model, using collective velocity distributions combined with a statistical thermodynamics in local rest frames. Experimental differential cross sections for alpha + nucleus and Neon + nucleus central collisions at incident energies between 200 and 800 MeV per nucleon are well reproduced by the model, for an angular range 30-110 degrees in the laboratory system. Extracted values of the temperatures are compared with those given by other authors.
NASA Program Biomedical Research↗
Model atmospheres, predicted spectra, and colors
Theoretical models of stellar atmospheres and the process of forming a spectrum are reviewed with particular reference to the spectra of B stars. In the case of classical models the stellar atmosphere is though to consist of plane parallel layers of gas in which radiative and hydrostatic equilibrium exists. No radiative energy is lost or gained in the model atmosphere, but the detailed shape of the spectrum is changed as a result of the interactions with the ionized gas. Predicted line spectra using statistical equilibrium local thermodynamic equilibrium (LTE), and non-LTE physics are compared and the determination of abundances is discussed. The limitations of classical modeling are examined. Models developed to demonstrate what motions in the upper atmosphere will do to the spectrum and to explore the effects of using geometries different from plane parallel layer are reviewed. In particular the problem of radiative transfer is addressed.
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Molecular Dynamics Calculations
The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two winning videos in a competition held at the meeting of the American Physical Society's Division of Fluid Dynamics, held in Atlanta, Georgia, in November 1994. Of great interest was the result that in every shock there were a few high-speed precursor particles racing ahead of the shock, carrying information about its impending arrival. Most recently, Dr. Woo has been applying molecular dynamics techniques to the problem of determining the drag produced by the space station truss structure as it flies through the thin residual atmosphere of low-Earth orbit. This problem is made difficult by the complex structure of the truss and by the extreme supersonic nature of the flow. A fully filled section of the truss has already been examined, and drag predictions have been made. Molecular dynamics techniques promise to make realistic drag calculations possible even for very complex partially filled truss segments flying at arbitrary angles.
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Lagrange thermodynamic potential and intrinsic variables for He-3 He-4 dilute solutions
For a two-fluid model of dilute solutions of He-3 in liquid He-4, a thermodynamic potential is constructed that provides a Lagrangian for deriving equations of motion by a variational procedure. This Lagrangian is defined for uniform velocity fields as a (negative) Legendre transform of total internal energy, and its primary independent variables, together with their thermodynamic conjugates, are identified. Here, similarities between relations in classical physics and quantum statistical mechanics serve as a guide for developing an alternate expression for this function that reveals its character as the difference between apparent kinetic energy and intrinsic internal energy. When the He-3 concentration in the mixtures tends to zero, this expression reduces to Zilsel's formula for the Lagrangian for pure liquid He-4. An investigation of properties of the intrinsic internal energy leads to the introduction of intrinsic chemical potentials along with other intrinsic variables for the mixtures. Explicit formulas for these variables are derived for a noninteracting elementary excitation model of the fluid. Using these formulas and others also derived from quantum statistical mechanics, another equivalent expression for the Lagrangian is generated.
Jackson, H. W.↗
Comments on "The Sensitivity Study of Radiative-Convective Equilibrium in the Tropics with a Convective Resolving Model"
In general, there are two broad scientific objectives when using cloud resolving models (CRMs or cloud ensemble models-CEMs) to study tropical convection. The first one is to use them as a physics resolving models to understand the dynamic and microphysical processes associated with the tropical water and energy cycles and their role in the climate system. The second approach is to use the CRMs to improve the representation of moist processes and their interaction with radiation in large-scale models. In order to improve the credibility of the CRMs and achieve the above goals, CRMs using identical initial conditions and large-scale influences need to produce very similar results. Two CRMs produced different statistical equilibrium (SE) states even though both used the same initial thermodynamic and wind conditions. Sensitivity tests to identify the major physical processes that determine the SE states for the different CRM simulations were performed. Their results indicated that atmospheric horizontal wind is treated quite differently in these two CRMs. The model that had stronger surface winds and consequently larger latent and sensible heat fluxes from the ocean produced a warmer and more humid modeled thermodynamic SE state. In addition, the domain mean thermodynamic state is more unstable for those experiments that produced a warmer and more humid SE state. Their simulated wet (warm and humid) SE states are thermally more stable in the lower troposphere (from the surface to 4-5 km in altitude). The large-scale horizontal advective effects on temperature and water vapor mixing ratio are needed when using CRMs to perform long-term integrations to study convective feedback under specified large-scale environments. In addition, it is suggested that the dry and cold SE state simulated was caused by enhanced precipitation but not enough surface evaporation. We find some problems with the interpretation of these three phenomena.
Tao, W.-K.↗
The X-43A Flight Research Program: Lessons Learned on the Road to Mach 10
During an aerospace engineer's undergraduate studies, he or she will attend classes in aerodynamics, thermodynamics, structures, stability and control, dynamics, design, propulsion, and computer science, along with the related courses in mathematics, physics, statistics, and chemistry required to understand the material. Upon graduation, the new engineer will have acquired a basic knowledge of how to build an aerospace vehicle. What only comes through experience, however, is the understanding of the inevitable imperfect process through which an aerospace vehicle is built. This is the adventure of turning a basic concept into functional hardware. Engineers working on a project must often deal with ambiguous situations. They are routinely asked by management to provide risk assessments of a project, yet even after careful analysis uncertainties remain. The project must be accomplished within finite limits of time and money. The question an engineer answers is whether the solution to potential problem is worth the cost and schedule delay, or if the solution might actually be worse than the problem it is meant to solve. Review protocols are established to ensure that an unknown has not been overlooked. But these cannot protect against an unknown unknown. Examples of these situations can be found in the history of the X-43A Hyper-X (Hypersonic Experiment) program. In this NASA project, a supersonic combustion ramjet (scramjet) engine was flight tested on a subscale vehicle. The X-43A Hyper-X Research Vehicle (HXRV) was launched from a B-52B mothership, then boosted to the test speed by a modified Pegasus rocket first stage, called the Hyper-X Launch Vehicle (HXLV). Once at the proper speed and altitude, the X-43A separated from the booster, stabilized itself, and then the engine test began. Although wind-tunnel scramjet engine tests had begun in the late 1950s, before the Hyper-X program there had never been an actual in-flight test of such an engine integrated with an appropriate airframe. Thus, while the scramjet had successfully operated in the artificial airflow of wind tunnels, the concept had yet to be proven in real air. These conditions meant changes in density and temperature, as well as changes in angle of attack and sideslip of a free-flying vehicle. A wind tunnel is limited in its ability to simulate these subtle factures, which have a major impact on almost any vehicle, but especially that of a scramjet's performance. The Hyper-X project was to provide a real-world benchmark of the ground test data. The full scale X-43A engine would be operated in the wind tunnel, and then flown, and the data from its operation would then be compared with projections. If these matched, the wind tunnel data would be considered a reliable design tool for future scramjet. If there were significant differences, the reasons for these would have to be identified. Until such information was available, scramjets would lack the technological maturity to be considered for future space launch or high-speed atmospheric flight vehicles.
Peebles, Curtis↗
Equilibrium Statistical Thermodynamics of a Many-Particle System Coupled to an External Scalar Field
The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.
Salvino, R. E.↗
Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean
One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.
Borovikov, Anna↗
Thermodynamic analysis of turbulent combustion in a spark ignition engine. Experimental evidence
A method independent of physical modeling assumptions is presented to analyze high speed flame photography and cylinder pressure measurements from a transparent piston spark ignition research engine. The method involves defining characteristic quantities of the phenomena of flame propagation and combustion, and estimating their values from the experimental information. Using only the pressure information, the mass fraction curves are examined. An empirical burning law is presented which simulates such curves. Statistical data for the characteristics delay and burning angles which show that cycle to cycle fractional variations are of the same order of magnitude for both angles are discussed. The enflamed and burnt mass fractions are compared as are the rates of entrainment and burning.
Beretta, G. P.↗
Spatial and Temporal Distribution of Clouds as Observed by MODIS Onboard the Terra and Aqua Satellites
The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4, 2002. It achieved its final orbit and began Earth observations on February 24,2000 for Terra and June 24,2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, and fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. Over the last year, extensive improvements and enhancements in the global cloud products have been implemented, and reprocessing of all MODIS data on Terra has commenced since first light in February 2000. In the cloud mask algorithm, the most extensive improvements were in distinguishing clouds at nighttime, including the challenging polar darkness regions of the world. Additional improvements have been made to properly distinguish sunglint from clouds in the tropical ocean regions, and to improve the identification of clouds from snow during daytime in Polar Regions. We will show global monthly mean cloud fraction for both Terra and Aqua, and show how similar the global daytime cloud fraction is from these morning and afternoon orbits, respectively. We will also show the zonal distribution of cloud fraction over land and ocean regions for both Terra and Aqua, and show the time series of global cloud fraction from July 2002 through June 2006.
King, Michael D.↗
Global Multispectral Cloud Retrievals from MODIS
The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4,2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua, and will show characteristics of cloud optical and microphysical properties as a function of latitude for land and ocean separately, and contrast the statistical properties of similar cloud types in various parts of the world.
King, Michael D.↗
Global Multispectral Cloud Retrievals from MODIS
The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4,2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua, and will show characteristics of cloud optical and microphysical properties as a function of latitude for land and ocean separately, and contrast the statistical properties of similar cloud types in various parts of the world.
King, Michael D.↗
Multi-Spectral Cloud Retrievals from Moderate Image Spectrometer (MODIS)
MODIS observations from the NASA EOS Terra spacecraft (1030 local time equatorial sun-synchronous crossing) launched in December 1999 have provided a unique set of Earth observation data. With the launch of the NASA EOS Aqua spacecraft (1330 local time crossing! in May 2002: two MODIS daytime (sunlit) and nighttime observations are now available in a 24-hour period allowing some measure of diurnal variability. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate modeling, climate change studies, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. An overview of the instrument and cloud algorithms will be presented along with various examples, including an initial analysis of several operational global gridded (Level-3) cloud products from the two platforms. Statistics of cloud optical and microphysical properties as a function of latitude for land and Ocean regions will be shown. Current algorithm research efforts will also be discussed.
Platnick, Steven↗
Spatial and Temporal Distribution of Tropospheric Clouds Observed by MODIS Onboard the Terra and Aqua Satellites
The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4, 2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua. These include the latitudinal distribution of cloud optical and radiative properties of both liquid water and ice clouds, as well as joint histograms of cloud optical thickness and effective radius for selected geographical locations around the world.
King, Michael D.↗
Spatial and Temporal Distribution of Tropospheric Clouds Observed by MODIS Onboard the Terra and Aqua Satellites
The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18, 1999 and Aqua spacecraft on May 4, 2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua. These include the latitudinal distribution of cloud optical and radiative properties of both liquid water and ice clouds, as well as joint histograms of cloud optical thickness and effective radius for selected geographical locations around the world.
King, Michael D.↗