Application of GdC1(sub 3) Thermometry Near the Liquid-Gas Critical Point of (sup 3)He
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paramagnetic salt thermometer SQUID measurementGer↗
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Kinetics of diffusional droplet growth in a liquid/liquid two-phase system
This report contains experimental results for the interdiffusion coefficient of the system, succinonitrile plus water, at a number of compositions and temperatures in the single phase region of the phase diagram. The concentration and temperature dependence of the measured diffusion coefficient has been analyzed in terms of Landau - Ginzburg theory, which assumes that the Gibb free energy is an analytic function of its variables, and can be expanded in a Taylor series about any point in the phase diagram. At most points in the single phase region this is adequate. Near the consolute point (critical point of solution), however, the free energy is non-analytic, and the Landau - Ginzburg theory fails. The solution to this problem dictates that the Landau - Ginzburg form of the free energy be replaced by Widom scaling functions with irrational values for the scaling exponents. As our measurements of the diffusion coefficient near the critical point reflect this non-analytic character, we are preparing for publication in a refereed journal a separate analysis of some of the data contained herein as well as some additional measurements we have just completed. When published, reprints of this article will be furnished to NASA.
Baird, James K.↗
THE DENSITIES OF SATURATED LIQUID HYDROGEN
This laboratory is engaged in a programme for the determination of thermostatic, thermodynamic, and transport properties of para-hydrogen, emphasizing high densities. Reported here are new data for the density of saturated liquid pura-hydrogen from boiling point to critical point. A review of hydrogen properties includes densities of normal hydrogen from triple to critical points and of pura-hydrogen up to the boiling point? More recent determinations of vapour pressures and critical constants have been made for both hydrogen modification.
LIQUID HYDROGEN↗
Thermodynamic properties of oxygen and nitrogen III
The final equation for nitrogen was determined. In the work on the equation of state for nitrogen, coefficients were determined by constraining the critical point to selected critical point parameters. Comparisons of this equation with all the P-density-T data were made, as well as comparisons to all other thermodynamic data reported in the literature. The extrapolation of the equation of state was studied for vapor to higher temperatures and lower temperatures, and for the liquid surface to the saturated liquid and the fusion lines. A new vapor pressure equation was also determined which was constrained to the same critical temperature, pressure, and slope (dP/dT) as the equation of state. Work on the equation of state for oxygen included studies for improving the equation at the critical point. Comparisons of velocity of sound data for oxygen were also made between values calculated with a preliminary equation of state and experimental data. Functions for the calculation of the derived thermodynamic properties using the equation of state are given, together with the derivative and integral functions for the calculation of the thermodynamic properties using the equations of state. Summary tables of the thermodynamic properties of nitrogen and oxygen are also included to serve as a check for those preparing computer programs using the equations of state.
Stewart, R. B.↗
Viscosity of Xenon Examined in Microgravity
Why does water flow faster than honey? The short answer, that honey has a greater viscosity, merely rephrases the question. The fundamental answer is that viscosity originates in the interactions between a fluid s molecules. These interactions are so complicated that, except for low-density gases, the viscosity of a fluid cannot be accurately predicted. Progress in understanding viscosity has been made by studying moderately dense gases and, more recently, fluids near the critical point. Modern theories predict a universal behavior for all pure fluids near the liquid-vapor critical point, and they relate the increase in viscosity to spontaneous fluctuations in density near this point. The Critical Viscosity of Xenon (CVX) experiment tested these theories with unprecedented precision when it flew aboard the Space Shuttle Discovery (STS-85) in August 1997. Near the critical point, xenon is a billion times more compressible than water, yet it has about the same density. Because the fluid is so "soft," it collapses under its own weight when exposed to the force of Earth s gravity - much like a very soft spring. Because the CVX experiment is conducted in microgravity, it achieves a very uniform fluid density even very close to the critical point. At the heart of the CVX experiment is a novel viscometer built around a small nickel screen. An oscillating electric field forces the screen to oscillate between pairs of electrodes. Viscosity, which dampens the oscillations, can be calculated by measuring the screen motion and the force applied to the screen. So that the fluid s delicate state near the critical point will not be disrupted, the screen oscillations are set to be both slow and small.
Zimmerli, Gregory A.↗
Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology
We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.
Gandhi, Amar↗
The G1 restriction point as critical regulator of neocortical neuronogenesis
Neuronogenesis in the pseudostratified ventricular epithelium is the initial process in a succession of histogenetic events which give rise to the laminate neocortex. Here we review experimental findings in mouse which support the thesis that the restriction point of the G1 phase of the cell cycle is the critical point of regulation of the overall neuronogenetic process. The neuronogenetic interval in mouse spans 6 days. In the course of these 6 days the founder population and its progeny execute 11 cell cycles. With each successive cycle there is an increase in the fraction of postmitotic cells which leaves the cycle (the Q fraction) and also an increase in the length of the cell cycle due to an increase in the length of the G1 phase of the cycle. Q corresponds to the probability that postmitotic cells will exit the cycle at the restriction point of the G1 phase of the cell cycle. Q increases non-linearly, but the rate of change of Q with cycle (i.e., the first derivative) over the course of the neuronogenetic interval is a constant, k, which appears to be set principally by cell internal mechanisms which are species specific. Q also seems to be modulated, but at low amplitude, by a balance of mitogenic and antimitogenic influences acting from without the cell. We suggest that intracellular signal transduction systems control a general advance of Q during development and thereby determine the general developmental plan (i.e., cell number and laminar composition) of the neocortex and that external mitogens and anti-mitogens modulate this advance regionally and temporally and thereby produce regional modifications of the general plan.
NASA Discipline Cell Biology↗
Autocorrelation function of scattered light for a binary fluid near the critical mixing point
A time-to-amplitude conversion technique was applied to measure the second-order autocorrelation function of light scattering by a binary fluid from concentration fluctuations of the fluid very close to the critical point. The experimental setup included two photomultipliers, a time-to-amplitude converter, and a pulse height analyzer.
Bendjaballah, C.↗
Stirring Up an Elastic Fluid: Critical Viscosity of Xenon-2 (CVX-2)
Whipped cream stays in place even when turned upside down. Yet it readily flows through the nozzle of a spray can to reach the dessert plate. This demonstrates the phenomenon of shear thinning that is important to many industrial and physical processes. Paints, film emulsions, and other complex solutions that are highly viscous under normal conditions but become thin and flow easily under shear forces. A simple fluid, such as water, does not exhibit shear thinning under normal conditions. Very close to the liquid-vapor critical point, where the distinction between liquid and vapor disappears, the fluid becomes more complex and is predicted to display shear thinning. At the critical point, xenon atoms interact over long distances in a classical model of cooperative phenomena. Physicists rely on this system to learn how long-range order arises. The Critical Viscosity of Xenon Experiment (CVX-2) will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Although it does not easily combine with other chemicals, its viscosity at the critical point can be used as a model for a range of fluids. Viscosity originates from the interactions of individual molecules. It is so complicated that, except for the simplest gas, it cannot be calculated accurately from theory. Tests with critical fluids can provide key data, but are limited on Earth because critical fluids are highly compressed by gravity. CVX-2 employs a tiny metal screen vibrating between two electrodes in a bath of critical xenon. The vibrations and how they dampen are used to measure viscosity. CVX flew on STS-85 (1997), where it revealed that, close to the critical point, the xenon is partly elastic: it can 'stretch' as well as flow. For STS-107, the hardware has been enhanced to determine if critical xenon is a shear-thinning fluid.
Berg, Robert F.↗
Choked flow of fluid nitrogen with emphasis on the thermodynamic critical region
A critical flow experiment was performed with fluid nitrogen in a converging-diverging nozzle at stagnation conditions from 87.5 to 234 K and pressures to 9.3 MN/sq m, with particular emphasis on the thermodynamic critical region. The nozzle throat conditions ranged from two-phase to near critical to gaseous. Proximity of the fluid in the nozzle to the critical point has a significant influence on the critical flow rate and pressure ratio curves. The flow rate exhibits an inflection and the pressure ratio shows a sharp peak when stagnation conditions are near the transposed critical point. The critical flow data are compared with equilibrium and nonequilibrium theories, and conditions are defined for which various methods of prediction remain valid.
Hendricks, R. C.↗
Multiple transonic solutions with a new class of shock transitions in steady isothermal solar and stellar winds
It is shown that a new class of shock transitions arises in the transonic solutions of the steady isothermal solar wind equations when momentum deposition and/or nonradial flow tube divergence give rise to multiple critical points in the flow. These shock transitions between critical solutions occur for a certain range of the parameters which characterize the momentum deposition function. The isothermal wind equations allow multiple transonic solutions in the presence of such shock transitions, yielding a continuous solution passing through an inner critical point and solutions involving a shock transition between critical solutions. It is determined that these multiple transonic solutions have the same flow speed at the base but different supersonic flow speeds at infinity. It is found that the nonradial flow tube divergence and momentum addition are equivalent, which gives rise to multiple critical points and hence to multiple transonic solutions with shock transitions. In addition, the physical relevance of these properties are examined for astrophysical systems such as the inner solar wind, flows in extragalactic jets, and accretion discs.
Habbal, S. R.↗
Analysis and representation of complex structures in separated flows
We discuss our recent work on extraction and visualization of topological information in separated fluid flow data sets. As with scene analysis, an abstract representation of a large data set can greatly facilitate the understanding of complex, high-level structures. When studying flow topology, such a representation can be produced by locating and characterizing critical points in the velocity field and generating the associated stream surfaces. In 3D flows, the surface topology serves as the starting point. The 2D tangential velocity field near the surface of the body is examined for critical points. The tangential velocity field is integrated out along the principal directions of certain classes of critical points to produce curves depicting the topology of the flow near the body. The points and curves are linked to form a skeleton representing the 2D vector field topology. This skeleton provides a basis for analyzing the 3D structures associated with the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations. Integration origins are successively refined to produce stream surfaces. The map of the global topology is completed by generating those stream surfaces associated with 3D critical points.
Helman, James↗
Specific heats of oxygen at coexistence.
Specific heats of oxygen at coexistence from triple point to critical point and corresponding values for liquid phase
Goodwin, R. D.↗
ASRDI oxygen technology survey. Volume 4: Low temperature measurement
Information is presented on temperature measurement between the triple point and critical point of liquid oxygen. The criterion selected is that all transducers which may reasonably be employed in the liquid oxygen (LO2) temperature range are considered. The temperature range for each transducer is the appropriate full range for the particular thermometer. The discussion of each thermometer or type of thermometer includes the following information: (1) useful temperature range, (2) general and particular methods of construction and the advantages of each type, (3) specifications (accuracy, reproducibility, response time, etc.), (4) associated instrumentation, (5) calibrations and procedures, and (6) analytical representations.
Sparks, L. L.↗
An approach to simultaneous system design. II - Nonswitching gain and dynamic feedback compensation by algebraic geometric methods
This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. Furthermore, the author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Various other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.
Ghosh, Bijoy K.↗
Efficient identification of critical stresses in structures subject to dynamic loads
Optimum structural design problems generally employ constraints which are parametric in terms of space and time variables. A parametric constraint may be replaced by equivalent critical point constraints at its local minima for optimization applications. In complex structures, accurate identification of such critical points is computationally expensive due to the cost of finite element analyses. Three techniques are described for efficiently and accurately identifying critical points for space- and time-dependent parametric constraints. An adaptive search technique and a spline interpolation technique are developed for exactly known response. A least squares spline approximation is suggested for noisy behavior. A helicopter tail-boom structure subjected to transient loading is used as an example to demonstrate the techniques described. All three techniques are shown to be computationally efficient for critical point identification and the least squares approximation also removes noise from the data. The case of multiple constraints per element is shown to be particularly suited to the use of spline techniques.
Haftka, R. T.↗
Surface representations of two- and three-dimensional fluid flow topology
We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.
Helman, James L.↗
Temporal evolution of the solar wind and the formation of a standing shock
The temporal evolution of the solar wind from one steady state to another is explored when momentum deposition produces multiple critical points in the flow. It is shown that the wind always evolves in time to a new steady state compatible with the solution of the steady state equation of motion. However, for the same initial state and identical asymptotic momentum deposition rate, the temporal evolution pattern of the wind depends on the detailed time history of momentum addition and is therefore not unique. This feature plays an important role in the particular case when multiple (three in this study) steady states exist for identical boundary conditions; each one of these solutions is thus shown to be physically accessible. The details of the temporal evolution pattern of the wind reveal the formation of a shock discontinuity whenever the flow becomes supersonic at a critical point upstream from the initial critical point. If the flow remains supersonic at that inner critical point, the shock can become a standing one, depending on the strength and the temporal history of momentum addition. The results of this study indicate that the time scale required for the solar wind to evolve between steady states is of the order of 30-60 hours. Furthermore, the results also reveal the interesting and novel phenomenon that a standing shock is likely to develop in the inner solar wind flow within this time frame, in particular, in coronal hole regions with rapidly diverging geometries.
Habbal, S. R.↗