Showing papers on "Rarefaction published in 1972"

Properties of the Rarefaction Diversity Measurement

Abstract: increase, unless the pertinent loci are otherwise selected. The second objection stems from the observation that too-weak balancing selection still leaves the population open to loss of variability by drift. But with the present model there is no need to postulate low selection intensity so, at least theoretically, drift becomes less of a problem. Loci, or linkage groups conforming in their demographic characteristics to the Charlesworth-Giesel model, will thus be maintained in a polymorphic state at little or no cost. In addition, any linkage (Franklin and Lewontin 1970) contributes to maintenance of heterozygosity of the rest of the genoiue. The result is perpetuation of population variability and adaptability.

Comments on the Moon's Magnetism

Abstract: Various lines of evidence indicate that permanent magnetization of lunar rocks, acquired during the early history of the Moon, is responsible for the weak (tens of gammas) and patchy magnetic field found at the surface of the Moon. It would be necessary to invoke a core dynamo (with all its important implications) in order to account for the inducing fieldB of not less than 103 γ in which lunar rocks acquired their stable permanent magnetization if no other source ofB can be found. In this connection we point out that the magnetic effects of high-velocity meteoroid impacts have not yet been ruled out. Indeed, according to rough calculations these effects might not be negligible and detailed studies would be worth carrying out. Shock waves followed by rarefaction waves would spread out into the body of the Moon from the area of impact, first demagnetizing any material shock-heated above the Curie temperature and then, as the material cools rapidly during the passage of the rarefaction wave, re-magnetizing the material to an intensity determined by the background fieldB. The main source ofB would be the pulse of electric current generated by magneto-hydrodynamic interaction between the electrically-conducting ejecta from the explosion and the weak ambient interplanetary magnetic field. This ‘impact dynamo’ hypothesis also has possible implications concerning the magnetism of meteorites.

Magnetohydrodynamic theory for the interaction of an interplanetary double-shock ensemble with the Earth's bow shock

Abstract: The interactions between interplanetary shocks and the earth's bow shock are formulated first on a gas-dynamic basis. The problem is repeated on a magnetohydrodynamic (MHD) basis for the special case of perpendicular shocks. In particular, an interplanetary double-shock ensemble (composed of forward and reverse shocks) is allowed to interact with the earth's bow shock. It is found that the collision of a forward shock with the bow shock creates two shocks and a contact surface; the symbolism S→S← → S←CS→ is used to represent this particular interaction. The collision of a reverse shock with the bow shock, hitherto not discussed, yields a shock, contact surface, and rarefaction wave: S←S← → S←CR→. The results of the interactions are discussed on the basis of several representative computations. An order-of-magnitude increase of thermal pressure is the major consequence of the ‘shock-on-shock’ interaction. The effect of the magnetic field is minor; for example, the bow-shock velocity after impact of a forward shock is only ∼10% less than the velocity computed on the basis of ordinary gas dynamics. Interaction dynamics are applied, in the case of the geomagnetic storm's sudden commencement, to the characteristic time and energy of the instantaneous compression. Several magnetic-storm sudden-commencement events (including the March 8, 1970, event) are discussed on the basis of spacecraft plasma observations and magnetogram records on the earth. Comparison of available diagnostics with the theory suggests the physical plausibility of the present fluid-dynamic study.

Auditory discrimination between compressions and rarefactions by goldfish.

Abstract: 1. Goldfish were taught to discriminate between a given click and the same click inverted, that is, with the compression and rarefaction phases reversed. 2. The responses were true auditory responses involving the sacculus but not the lateral line. 3. The responses were independent of both waveform (frequency) and intensity and could be elicited with single clicks. Phase was the relevant parameter. 4. Tail flips were found to send a rarefaction wave (rarefaction is the first deflexion) forward from the fish and a compression wave backward. 5. It is proposed that phase analysis of tail-flip sounds is used to tell whether a swimming fish is approaching or receding.

Discharges Guided by Laser‐Induced Rarefaction Channels

Abstract: Preliminary experiments demonstrating the channeling and guidance of an electrical breakdown streamer via a laser‐induced rarefaction channel are reported. The ability of this phenomenon to extend the range of a given spark is also demonstrated.

A Shock Tube Study on Condensation Kinetics

Abstract: Refrigerant vapors were filled in the high pressure side of a shock tube, and measurements were made as the vapors condensed spontane usly through adiabatic expansion in the rarefaction wave. The experimental observations were analyzed on the basis of the classical nucleation theory, and for each of the test vapors, the surface energy density (or the surface tension) of critical-sized droplets, which corresponds to the activation energy in chemical reactions, was evaluated utilizing the condensation point locus on the P-T plane. It turned out that the estimated surface tension was consistently smaller than the macroscopic value for three kinds of refrigerants studied. In the case of methyl alcohol vapor, for which the expansion rate was varied over a wide range, the condensation locus was found to shift accordingly in agreement with the theoretical prediction. It was also shown that the droplet growth history could be inferred from the temporal change of the light transmission.

Phenomenal rarefaction and visual acuity under 'illusory' conditions.

Abstract: Given a striped pattern, there are two ways of obtaining a phenomenal rarefaction of it: (a) by reducing the area of the pattern, leaving the distance between the stripes unchanged, or (b) by placing the pattern within one of Delboeuf's illusion contexts. With (a) phenomenal rarefaction is coupled with an increment of visual acuity, since the stripes are distinctly seen at a greater distance. With (b) the phenomenal rarefaction is the same as with (a), but is not associated with any increase of visual acuity. The role of ‘actual’ and ‘illusory’ conditions on visual perception is discussed.

Propagation of an Ion Rarefaction Wave from a Growing Sheath

Abstract: The structure of an ion rarefaction wave propagating from a sheath growing into a nonuniform plasma column is determined using the method of characteristics. Ionization and collisions both tend to damp out the wave. The interaction between two identical ion rarefaction waves from opposite sides of a plasma column produces a secondary ion rarefaction wave which spreads outward from the center of the column. The density profile in the column relaxes toward a new equilibrium profile, corresponding to that for the new (i.e., contracted) column width.

Numerical Analysis on Source Expansion Flow into Vacuum

Abstract: A numerical analysis of the source expansion flow into a vacuum is presented. Applying the BGK kinetic equation described in spherical coordinates to the problem, it is solved by combining a proposed computational technique with a discrete ordinate method. The actual computation is carried out for a large variety of rarefaction conditions, covering a wide extent from an equilibrium region near the sonic radius up to one sufficiently far downstream. Calculated results for the radial and perpendicular temperatures are compared with results obtained by existing methods.

Rarefaction Effects in High-Altitude Rocket Plumes

Abstract: A theoretical assessment of rarefaction effects in high-altitude rocket plumes is presented. The plume size and rarefaction conditions are written as a function of the rocket thrust, altitude, and Mach number. Five distinct flow regimes are predicted: Inviscid, merged, transition, first collision and free molecular. The range of thrust and altitude applicable to each of these regimes is estimated and models applicable to each regime are discussed.

17‐Moment Theory of Sound Propagation in Polyatomic Gases

Abstract: The problem of combined translational and internal relaxation of sound waves in polyatomic gases is studied using the 17‐moment approximation. When applied to the sound problem, the moment equations, which are valid for any number of internal degrees of freedom, yield a generalized complex matrix eigenvalue equation which is solved numerically for the absorption coefficient and propagation speed as a function of the rarefaction parameter (the approximate ratio of collision frequency to sound frequency). The physical parameters in the equations are the self‐diffusion coefficient (assumed the same for each internal mode), the internal relaxation times, and the internal specific heats. Our solutions for the combined absorption for the case of a single internal mode are compared to those obtained assuming the total absorption is the sum of that due to the translational and internal effects separately, and to that obtained by using the combination rule of Greenspan. Comparison is also made between the combined dispersion calculated by the 17‐moment method and the Greenspan rule. In addition, absorption curves are calculated for the case of two internal degrees of freedom for various combinations of internal collision numbers. When applied to rotational relaxation in N2 our theory yields, for a rotational collision number of 5.26, good agreement with experiment over the range of values of the rarefaction parameter for which a continuum theory is expected to be valid.The problem of combined translational and internal relaxation of sound waves in polyatomic gases is studied using the 17‐moment approximation. When applied to the sound problem, the moment equations, which are valid for any number of internal degrees of freedom, yield a generalized complex matrix eigenvalue equation which is solved numerically for the absorption coefficient and propagation speed as a function of the rarefaction parameter (the approximate ratio of collision frequency to sound frequency). The physical parameters in the equations are the self‐diffusion coefficient (assumed the same for each internal mode), the internal relaxation times, and the internal specific heats. Our solutions for the combined absorption for the case of a single internal mode are compared to those obtained assuming the total absorption is the sum of that due to the translational and internal effects separately, and to that obtained by using the combination rule of Greenspan. Comparison is also made between the combined...

Relaxation of overdriven detonation waves with finite reaction rate

Abstract: A numerical study is made of the interaction of a detonation wave having finite reaction velocity with a rarefaction wave of different intensity which approaches it from the rear, for the Zeldovich-Neumann-Doring (ZND) model with a single irreversible reaction A → B. It is found that, for a fixed value of the parameter characterizing the initial supercompression (depending on the activation energy and the heating value of the mixture), the considered interaction leads either to a gradual relaxation of the detonation wave and its transition to the Chapman-Jouguet (CJ) regime, or to the development of undamped oscillations.

Solution of variational problems of gasdynamics of supersonic nonequilibrium flows

Abstract: The problem of the optimization of the supersonic portion of a nozzle for gas flow in the case of certain nonequilibrium processes was solved in [1, 2]. The authors examined the flow scheme in which the closing Mach line of the first family arrives at the initial rarefaction wave fan. At the same time, in [3] in the solution of the analogous problem for the case of gas flow with foreign particles it was shown that it is advisable to consider also a different scheme, in which the closing characteristic arrives at the axis of symmetry outside the initial rarefaction wave fan. In the following we present results of a study of such a scheme for gas flow with nonequilibrium processes taking place. The necessary conditions which define the optimum contour are obtained and, in particular, the conditions which define the coordinate x and the magnitude of the angle at the corner points.

Heat transfer to linear bodies in two-dimensional hypersonic low density flow

Abstract: The heat transfer from a two-dimensional hypersonic low density stream to wedges and sharp flat plates at expansion angles of attack has been studied; the range of surface inclinations was extended from 6° expansion to 14° compression angles; the heat transfer rates were measured using the thin skin transient technique. The study was carried out in the Princeton University Hypersonic Nitrogen Tunnel N-3; the free stream conditions were approximately: Mach number 25; Reynolds number per inch 9000, rarefaction parameter V¯∞; from 0.12 to 0.5. As the plate angles become more negative, larger deviations from the predictions of the strong interaction theory for the heat transfer are found; analogous behaviour is shown by the surface pressure data; comparisons with the strong interaction theory and with other measurements have been made. The results strongly support the idea that the “merged” region length increases continuously for decreasing compression and increasing expansion angles of attack.

Derivation of a linear theory for nonequilibrium and equilibrium flows

Abstract: Conventional linear theory of nonequilibrium and equilibrium gas flows yields correct results only for very small deviations of the stream parameters from the unperturbed values. Moreover, if in linearization we take the coordinates in planar flow as independent variables, then the flow past concave and convex corners is described in exactly the same fashion. In this case the characteristic emanating from the corner is (depending on the type of corner) a compression or rarefaction shock. In the case of a break in the wall of an axisymmetric channel the shock intensity approaches infinity with approach to the centerline, which indicates a deficiency of this type of linear theory. In the following we use a modification which eliminates the deficiencies noted above. This involves conversion to new independent and dependent variables such that the coefficients of the exact equations being linearized become weakly varying functions of the unknown parameters, the linearized boundary conditions coincide with the exact conditions at all or part of the boundaries, and the rarefaction shocks become rarefaction wave bundles of finite width. The last condition is achieved as a result of the fact that, in accordance with the Lighthill method of deformable coordinates [1], we take as one of the independent variables a quantity which maintains a constant value on each characteristic of the bundle of characteristics emanating from the break point [for equilibrium flows the semicharacteristic (or characteristic) independent variables were used in deriving the linear theory, for example, in [2–4]]. The study was based on the example of two-dimensional stationary nonequilibrium flow of an inviscid and nonheatconducting gas. In this case we find that boththelinear equations at a finite distance from the walls and the boundary conditions for determining the potential and nonequilibrium parameters outside the rarefaction wave bundles coincide with the equations and the conditions of conventional linear theory [5], while the relations associating the values of the parameters on the closing characteristics of each bundle (outside the bundles the same value of the characteristic variable corresponds to these characteristics) at some distance from the axis or from some reflecting surface are identical to the conditions on the rarefaction shocks. This fact makes it possible to use several results of conventional linear theory.