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NASA NTRS1979

A possible closure relation for heat transport in the solar wind

The objective of the present paper is to search for an empirical closure relation for solar wind heat transport that applies to a microscopic scale. This task is approached by using the quasi-linear wave-particle formalism proposed by Perkins (1973) as a guide to derive an equation relating the relative drift speed between core-electron and proton populations to local bulk flow conditions. The resulting relationship, containing one free parameter, is found to provide a good characterization of Los Alamos Imp electron data measuring during the period from March 1971 through August 1974. An empirical closure relation is implied by this result because of the observed proportionality between heat flux and relative drift speed.

Feldman, W. C.↗

NASA NTRS2019

Closure Relations of Gamma-Ray Bursts in High Energy Emission

The synchrotron external shock model predicts the evolution of the spectral (β) and temporal (α) indices during the gamma-ray burst (GRB) afterglow for different environmental density profiles, electron spectral indices, electron cooling regimes, and regions of the spectrum. We study the relationship between α and β, the so-called “closure relations” with GRBs detected by Fermi Large Area Telescope (Fermi-LAT) from 2008 August to 2018 August. The spectral and temporal indices for the >100 MeV emission from the Fermi-LAT as determined in the Second Fermi-LAT Gamma-Ray Burst Catalog (2FLGC) are used in this work. We select GRBs whose spectral and temporal indices are well constrained (58 long-duration GRBs and 1 short-duration GRBs) and classify each GRB into the best-matched relation. As a result, we found that a number of GRBs require a very small fraction of the total energy density contained in the magnetic field (òB <~10−7). The estimated mean and standard deviation of electron spectral index p are 2.40 and 0.44, respectively. The GRBs satisfying a closure relation of the slow cooling tend to have a softer p value compared to those of the fast cooling. Moreover, the Kolmogorov–Smirnov test of the two p distributions from the fast and slow coolings rejects a hypothesis that the two distributions are drawn from the single reference distribution with a significance of 3.2σ. Lastly, the uniform density medium is preferred over the medium that decreases like the inverse of distance squared for long-duration GRBs.

Gamma-ray bursts↗

NASA NTRS1988

The turbulent heat flux in low Mach number flows with large density variations

A transport equation has been derived which is the difference between the volume- and mass-averaged velocities and is simply related to the turbulent heat flux phi sup h. Using this equation and an assumption analogous to the drift flux approximation of two-phase flow modeling, an algebraic closure relation for phi sup h that exibits fluxes due to directed transport proportional to -del anti p and due to gradient transport proportional to -del tau has been obtained.

Orourke, Peter J.↗

NASA NTRS2010

Parametric Analysis of Life Support Systems for Future Space Exploration Missions

Having adopted a flexible path approach to space exploration, the National Aeronautics and Space Administration is in a process of evaluating future targets for space exploration. In order to maintain the welfare of a crew during future missions, a suite of life support technology is responsible for oxygen and water generation, carbon dioxide control, the removal of trace concentrations of organic contaminants, processing and recovery of water, and the storage and reclamation of solid waste. For each particular life support subsystem, a variety competing technologies either exist or are under aggressive development efforts. Each individual technology has strengths and weaknesses with regard to launch mass, power and cooling requirements, volume of hardware and consumables, and crew time requirements for operation. However, from a system level perspective, the favorability of each life support architecture is better assessed when the sub-system technologies are analyzed in aggregate. In order to evaluate each specific life support system architecture, the measure of equivalent system mass (ESM) was employed to benchmark system favorability. Moreover, the results discussed herein will be from the context of loop-closure with respect to the air, water, and waste sub-systems. Specifically, closure relates to the amount of consumables mass that crosses the boundary of the vehicle over the lifetime of a mission. As will be demonstrated in this manuscript, the optimal level of loop closure is heavily dependent upon mission requirements such as duration and the level of extra- vehicular activity (EVA) performed. Sub-system level trades were also considered as a function of mission duration to assess when increased loop closure is practical. Although many additional factors will likely merit consideration in designing life support systems for future missions, the ESM results described herein provide a context for future architecture design decisions toward a flexible path program.

Swickrath, Michael J.↗

NASA NTRS2011

Parametric Analysis of Life Support Systems for Future Space Exploration Missions

The National Aeronautics and Space Administration is in a process of evaluating future targets for space exploration. In order to maintain the welfare of a crew during future missions, a suite of life support technology is responsible for oxygen and water generation, carbon dioxide control, the removal of trace concentrations of organic contaminants, processing and recovery of water, and the storage and reclamation of solid waste. For each particular life support subsystem, a variety competing technologies either exist or are under aggressive development efforts. Each individual technology has strengths and weaknesses with regard to launch mass, power and cooling requirements, volume of hardware and consumables, and crew time requirements for operation. However, from a system level perspective, the favorability of each life support architecture is better assessed when the sub-system technologies are analyzed in aggregate. In order to evaluate each specific life support system architecture, the measure of equivalent system mass (ESM) was employed to benchmark system favorability. Moreover, the results discussed herein will be from the context of loop-closure with respect to the air, water, and waste sub-systems. Specifically, closure relates to the amount of consumables mass that crosses the boundary of the vehicle over the lifetime of a mission. As will be demonstrated in this manuscript, the optimal level of loop closure is heavily dependent upon mission requirements such as duration and the level of extra-vehicular activity (EVA) performed. Sub-system level trades were also considered as a function of mission duration to assess when increased loop closure is practical. Although many additional factors will likely merit consideration in designing life support systems for future missions, the ESM results described herein provide a context for future architecture design decisions toward a flexible path program.

Swickrath, Michael J.↗

NASA NTRS2006

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

The objective of this paper is to define empirical parameters (or closwre models) for an initial thermai non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two CFD codes currently being used at Glenn Research Center (GRC) for Stirling engine modeling are Fluent and CFD-ACE. The porous-media models available in each of these codes are equilibrium models, which assmne that the solid matrix and the fluid are in thermal equilibrium at each spatial location within the porous medium. This is believed to be a poor assumption for the oscillating-flow environment within Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, we non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location end time during the cycle. A NASA regenerator research grant has been providing experimental and computational results to support definition of various empirical coefficients needed in defining a noa-equilibrium, macroscopic, porous-media model (i.e., to define "closure" relations). The grant effort is being led by Cleveland State University, with subcontractor assistance from the University of Minnesota, Gedeon Associates, and Sunpower, Inc. Friction-factor and heat-transfer correlations based on data taken with the NASAlSunpower oscillating-flow test rig also provide experimentally based correlations that are useful in defining parameters for the porous-media model; these correlations are documented in Gedeon Associates' Sage Stirling-Code Manuals. These sources of experimentally based information were used to define the following terms and parameters needed in the non-equilibrium porous-media model: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity (including themal dispersion and estimate of tortuosity effects}, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity (including the effect of tortuosity) was also estimated. Determination of the porous-media model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Convertor (TDC), which uses a random-fiber regenerator matrix. The non-equilibrium porous-media model presented is considered to be an initial, or "draft," model for possible incorporation in commercial CFD codes, with the expectation that the empirical parameters will likely need to be updated once resulting Stirling CFD model regenerator and engine results have been analyzed. The emphasis of the paper is on use of available data to define empirical parameters (and closure models) needed in a thermal non-equilibrium porous-media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates. However, it is anticipated that a thermal non-equilibrium model such as that presented here, when iacorporated in the CFD codes, will improve our ability to accurately model Stirling regenerators with CFD relative to current thermal-equilibrium porous-media models.

Tew, Roy↗

NASA NTRS1994

The whistler heat flux instability: Threshold conditions in the solar wind

Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropics and relative average speeds of these components correspond to a heat flux that has the potential to excite several different electromagetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasco dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma paramaters, and a global model based on average electron properties observed during the in-eliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of helisopheric radius that scales in the same way as the average heat flux observed form Ulysses and that provides an approximate upper bound for that same quantity. This theoretical scaling is combined with the observational results to yield a semi-empirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU.

Gary, S. Peter↗

NASA NTRS1979

Z1/3/ contribution to the energy loss of heavy charged particles

The Z1(3) contribution of distant collisions to the average energy loss of heavy charged particles is obtained by extending Bethe's quantum-mechanical calculation to the next highest order in Z1. The second-order Born approximation for the inelastic-collision cross section is simplified by using two major approximations. The infinite summation over terms arising from the coupling to intermediate states of the target atom is approximated with the aid of a parameter and the closure relation. This parameter is proportional to the average excitation energy of the intermediate states as described in the literature. The atomic form factors are simplified through a dipole expansion. Results are obtained in terms of an average excitation energy of the medium. Exemplary results for stopping in Al are presented for estimated values of the average excitation energy of the intermediate states. These results approach the classical and experimental values as the velocity of the penetrating particle increases, agreeing within 20% at beta = 0.3.

Morgan, S. H., Jr.↗

NASA NTRS1994

The proton cyclotron instability and the anisotropy/B inverse correlation

Spacecraft observations in the strongly compressed subsolar magnetosheath show an inverse correlation between the proton temperature anistrophy (T(sub perpendicular to p)/T(sub parallel to p) greater than 1 where perpendicular to and parallel to denote directions perpendicular and parallel to the background magnetic field) and the parallel proton beta (beta(sub parallel to p). This manuscript uses one-dimensional hybrid simulations of the proton cyclotron anisotropy instability in homogeneous electron-proton plasmas to study this correlation which may represent a limited closure relation for fluid theories of anisotropic space plasmas. The emphasis is on driven simulation which increase the temperature anisotropy by periodically reducing the magnetic-field-aligned velocities of the protons. The late-time states from ensembles of both initial value and driven simulations yield very similar expressions for the proton anisotropy/beta(sub parallel to P) inverse correlation, and provide a basis for explaining differences between sheath observations from different spacecraft. The driven simulations also yield expressions for the maximum instability growth rate and the fluctuating field energy as functions of beta (sub parallel to p) and a parameter characterizing the anisotropy driver.

Gary, S. Peter↗

NASA NTRS1995

Optically thick winds: How is the mass flux determined?

Expanding envelopes of compact objects that possess a buring region at the base of the envelope are commonly observed and modeled. In many cases, such as the late stages of classical nova, the expanding envelope develops into a stationary, optically thick wind of matter escaping from the star. In the usual theoretical formalism there is one more unknown than equations, with closure being obtained by the requirement that the solution pass through the singularity at the sonic point. It is shown analytically that the mass flux, which is one of the unknowns, is almost completely determined by the physical conditions near the base of the envelope just above the burning zone. The sonic point closure relation determines whether the expanding solution can develop into a wind solution. For a given core mass the range of possible wind solutions is an outcome of the great sensitivity of the mass flux to the inner luminosity. Solutions determined through numerical integrations are shown to lie entirely within the narrow analytic boundaries.

Glasner, S. Ami↗

NASA NTRS2018

Bloom Modeling and Prediction of the Harmful Algae Alexandrium in Bellingham Bay, WA

Bellingham, Washington is located near the American-Canadian border in the northwestern part of Washington state, and is bordered on its west side by the Lummi reservation. Between Lummi and Bellingham lies Bellingham bay, which has a history of harmful algae related closures dating back to 1978. The subject of this work is a genus of dinoflagellates: Alexandrium, within which many species have the capacity to produce a suite of toxins known as saxitoxin. These toxins bioaccumulate in bivalves, which in turn cause paralytic shellfish poisoning in marine consumers (mammals, birds, and fish), including humans. Symptoms in humans can range from tingling and numbness to difficulty or inability to breathe, resulting in death. Because of the longstanding history of shellfish gathering among Salish tribes and the fact that Washington is the leading U.S. producer of farmed bivalves, harmful algae blooms impact both native and non-native peoples living in the Salish Sea area negatively. The objective of this work is to identify factors which influence Alexandrium blooms in Bellingham Bay, as well as predict Alexandrium blooms in the future. The method of doing so involves two processes: an initial statistical modeling phase to find in situ and remote sensing observations correlated to bloom density (including, but not limited to: water temperature, chlorophyll-a, salinity, color dissolved organic matter, and discharge rate of local rivers), followed by use of that data as a training set for a recursive neural network. This predictive capacity may inform future closures, help ensure the safety of shellfish consumers, and act as a baseline for future modeling efforts in the region.

Harmful↗

NASA NTRS1993

Fast parallel algorithms that compute transitive closure of a fuzzy relation

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. The original algorithm proposed by L. Zadeh (1971) requires the computation time O(n(sup 4)), where n is the number of elements in the relation. In 1974, J. C. Dunn proposed a O(n(sup 2)) algorithm. Since we must compute n(n-1)/2 different values s(a, b) (a not equal to b) that represent the fuzzy relation, and we need at least one computational step to compute each of these values, we cannot compute all of them in less than O(n(sup 2)) steps. So, Dunn's algorithm is in this sense optimal. For small n, it is ok. However, for big n (e.g., for big databases), it is still a lot, so it would be desirable to decrease the computation time (this problem was formulated by J. Bezdek). Since this decrease cannot be done on a sequential computer, the only way to do it is to use a computer with several processors working in parallel. We show that on a parallel computer, transitive closure can be computed in time O((log(sub 2)(n))2).

Kreinovich, Vladik YA.↗

NASA NTRS2020

Aerosol-Ice Formation Closure Pilot Study (AEROICESTUDY) Field Campaign Report

The aerosol-ice formation closure pilot study (AEROICESTUDY) was a field campaign conducted at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility at the Southern Great Plains (SGP) observatory from October 7 to 28, 2019. The purpose of this campaign was to test a field observational approach for conducting an aerosol-ice formation closure study. In other words, the goal was to predict the number of ice nucleating particles (INPs) from the measurements of physical and chemical aerosol properties and compare those to measured INP number concentrations. This project was motivated by the fact that the aerosol community has widely conducted aerosol radiative closure, aerosol-cloud condensation nuclei (CCN), and CCN-droplet closure studies to test the physical models and parameterizations that cloud-resolving and climate models rely on to perform reliable simulations of the Earth system and energy budget. However, very few closure studies related to INPs have been conducted, and to our knowledge, none using robust, size-resolved, ambient aerosol composition measurements as model inputs

AEROICESTUDY↗

NASA NTRS1974

The structure of radio sources 3C 273B and 3C 84 deduced from the 'closure' phases and visibility amplitudes observed with three-element interferometers

The derived 'closure' phase relation for a three-element interferometer is used in a presented analysis of data obtained from observations at 7.8 GHz of the radio sources 3C 273B and 3C 84 by antennas in Massachusetts, California, Alaska, and Sweden (the first two antennas were used in combination with each of the last two separately to form two three-element interferometers). The brightness distribution is found for each source by expansion of both the fringe amplitude and the fringe phase in separate Fourier series.

Rogers, A. E. E.↗

NASA NTRS2020

Aerosol-Ice Formation Closure Pilot Study (AEROICSTUDY) Field Campaign Report

aerosol-ice formation↗

NASA NTRS1994

National facilities study. Volume 4: Space operations facilities task group

The principal objectives of the National Facilities Study (NFS) were to: (1) determine where U.S. facilities do not meet national aerospace needs; (2) define new facilities required to make U.S. capabilities 'world class' where such improvements are in the national interest; (3) define where consolidation and phase-out of existing facilities is appropriate; and (4) develop a long-term national plan for world-class facility acquisition and shared usage. The Space Operations Facilities Task Group defined discrete tasks to accomplish the above objectives within the scope of the study. An assessment of national space operations facilities was conducted to determine the nation's capability to meet the requirements of space operations during the next 30 years. The mission model used in the study to define facility requirements is described in Volume 3. Based on this model, the major focus of the Task Group was to identify any substantive overlap or underutilization of space operations facilities and to identify any facility shortfalls that would necessitate facility upgrades or new facilities. The focus of this initial study was directed toward facility recommendations related to consolidations, closures, enhancements, and upgrades considered necessary to efficiently and effectively support the baseline requirements model. Activities related to identifying facility needs or recommendations for enhancing U.S. international competitiveness and achieving world-class capability, where appropriate, were deferred to a subsequent study phase.

Source record↗

NASA NTRS1983

Measurement and analysis of critical crack tip processes associated with variable amplitude fatigue crack growth

Crack growth retardation following overloads can result in overly conservative life predictions in structures subjected to variable amplitude fatigue loading when linear damage accumulation procedures are employed. Crack closure is believed to control the crack growth retardation, although the specific closure mechanism is debatable. Information on the relative contributions to crack closure from: (1) plasticity left in the wake of the advancing crack and (2) crack tip residual stresses is provided. The delay period and corresponding crack growth rate transients following overloads are systematically measured as a function of load ratio (R) and overload magnitude. These responses are correlated in terms of the local 'driving force' for crack growth as measured by crack tip opening loads and delta K sub eff. The latter measurements are obtained using a scanning electron microscope equipped with a cyclic loading stage; measurements are quantified using a relatively new stereoimaging technique. Combining experimental results with analytical predictions suggests that both plastic wake and residual stress mechanism are operative, the latter becoming predominate as R increases.

Hudak, S. J., Jr.↗

NASA NTRS1992

Strongly transitive fuzzy relations: A more adequate way to describe similarity

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on fuzzifying only the positive side of transitivity: if R(a,b) and R(b,c), then R(a,c); but transitivity also includes a negative side: if R(a,b) and not R(a,c), then not R(b,c). In classical logic, this negative statement follows from the standard 'positive' definition of transitivity. In fuzzy logic, this negative part of the transitivity has to be formulated as an additional demand. A strongly transitive fuzzy relation as the one that satisfies both the positive and the negative transitivity demands is defined, the existence of strongly transitive closure is proven, and the relationship between strongly transitive similarity and clustering are found.

Kreinovich, Vladik YA.↗