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Showing papers on "Rarefaction published in 1982"


Journal ArticleDOI
TL;DR: In this paper, a continuous family of axisymmetric disturbances that preserve their form as they move through a Bose condensate are obtained numerically by the solution of the appropriate nonlinear Schrodinger equation.
Abstract: Axisymmetric disturbances that preserve their form as they move through a Bose condensate are obtained numerically by the solution of the appropriate nonlinear Schrodinger equation. A continuous family is obtained that, in the momentum (p)-energy (E) plane, consists of two branches meeting at a cusp of minimum momentum around 0.140 PK~/C' and minimum energy about 0.145 p~~/c, where p is density, c is the speed of sound and K is the quantum of circulation. For all larger p, there are two possible energy states. One (the lower branch) is (for large enough p) a vortex ring of circulation K; as p+m its radius G-(~/TK)"* becomes infinite and its forward velocity tends to zero. The other (the upper branch) lacks vorticity and is a rarefaction sound pulse that becomes increasingly one dimensional as p +a; its velocity approaches c for large p. The velocity of any member of the family is shown, both numerically and analytically, to be aE/ap, the derivative being taken along the family. At great distances, the disturbance in the condensate is pseudo-dipolar (dipolar in a stretched coordinate system); the strength of the pseudo-dipole moment is obtained numerically. Analogous calculations are presen- ted for the corresponding two-dimensional problem. Again, a continuous sequence of solitary waves is obtained, but the momentum per unit length p and energy per unit length E have no minima. For small forward velocities, the wave consists of two widely separated parallel, oppositely directed line vortices. As the forward velocity increases the wave loses its vorticity and becomes a rarefaction pulse of ever increasing spatial extent but ever decreasing amplitude. As its velocity approaches c, both p and E tend to zero, and Elp + c.

248 citations


Journal ArticleDOI
TL;DR: In this article, an optical technique to determine rarefaction wave velocities is described, which utilizes the property that many transparent materials emit copious radiation when shocked to high pressures.
Abstract: An optical technique to determine rarefaction wave velocities is described. The technique utilizes the property that many transparent materials emit copious radiation when shocked to high pressures. The usual method of producing a rarefaction wave by impacting a target plate with a thinner rapidly moving driver plate is employed. The target plate is made in the form of a step wedge which is covered by the transparent material (or analyzer). When the shock reaches the analyzer it radiates steadily until the rarefaction from the backside of the driver plate overtakes the shock front causing the radiation to decrease. The time between these events is a decreasing linear function of the target thickness and when extrapolated to zero determines the thickness where the rarefaction would have overtaken the shock wave at the surface of the target. Light pipes are used to transmit the radiation to photomultipliers whose response is measured by high‐speed oscilloscopes.

130 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the wave reflexion at the contact surface separating pure gas from the dusty-gas layer in terms of the properties of the gas and the dusty gas, and the time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator splitting technique.
Abstract: The flow resulting from the passage of a shock wave through a dusty-gas layer is studied theoretically. On the basis of an idealized equilibrium-gas approximation, the criteria for the wave reflexion at the contact surface separating the pure gas from the dusty-gas layer are obtained in terms of the properties of the gas and the dusty gas. For the cases treated here, a shock wave is reflected at the first contact surface and a shock wave stronger than the incident one is transmitted into the dusty-air layer. Subsequently, a rarefaction wave is reflected at the second contact surface and the shock wave transmitted into the free air is weakened by this nonlinear interaction. The induced rarefaction wave reflects later at the first contact surface as a compression wave, which runs through the layer to overtake the transmitted shock wave in air. The final emergent shock wave from the dusty air has almost the same strength as the original shock wave entering the layer. The time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator-splitting technique.

118 citations



Journal ArticleDOI
TL;DR: In this article, a small volume of an initially uniform plasma is heated with a CO2 laser focused to an intensity of 1.3*1011 W cm-2, and the evolving thermal and rarefaction wave is measured by Thomson scattering.
Abstract: A small volume of an initially uniform plasma is heated with a CO2 laser focused to an intensity of 1.3*1011 W cm-2. The evolving thermal and rarefaction wave is measured by Thomson scattering. Comparison of these measurements with a one-dimensional simulation shows that the heat flux reaches 15% of the free-streaming limit.

5 citations


Journal ArticleDOI
01 May 1982
TL;DR: In this paper, a flow model with uniform distribution of mineral grains is considered, and an equation of motion for a one-dimensional flow is derived for the energy balance, the rarefaction flow, the throttling process, and for flows when gas and grain particles have some velocity.
Abstract: This study of the nonstabilized flow of a mixture of ideal gas deals particularly with a disturbance of equilibrium and expansion of pore gas into a flow caused by a reduction or elimination of the plunger pressure. The nature of this flow depends upon porosity, the ''A ratio'', and the mutual disposition of the mineral grains. A flow model with uniform distribution of mineral grains is considered here. The elementary volume is cut with an arbitrarily oriented plane. The tablet with a unit area located at the intersection of the medium and plane, and the part of j-th grain, is considered. An equation of motion for a one-dimensional flow is derived. It is defined that free flow occurs when forces at grain contacts are nonexistent or negligible as compared with gas dissociative forces. Equations are derived for the energy balance, the rarefaction flow, the throttling process, a solid-gas mixture with partly strengthened structure, and for flows when gas and grain particles have some velocity. The wave generated by the sudden elimination of the plunger is studied. The process of pore expansion is treated. Part III deals with shock waves passing over mineral grains in mixture with gas.

4 citations


01 Jan 1982
TL;DR: In this article, the authors studied the wave reflexion at the contact surface separating pure gas from the dusty-gas layer in terms of the properties of the gas and the dusty gas, and the time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator splitting technique.
Abstract: The flow resulting from the passage of a shock wave through a dusty-gas layer is studied theoretically. On the basis of an idealized equilibrium-gas approximation, the criteria for the wave reflexion at the contact surface separating the pure gas from the dusty-gas layer are obtained in terms of the properties of the gas and the dusty gas. For the cases treated here, a shock wave is reflected at the first contact surface and a shock wave stronger than the incident one is transmitted into the dusty-air layer. Subsequently, a rarefaction wave is reflected at the second contact surface and the shock wave transmitted into the free air is weakened by this nonlinear interaction. The induced rarefaction wave reflects later at the first contact surface as a compression wave, which runs through the layer to overtake the transmitted shock wave in air. The final emergent shock wave from the dusty air has almost the same strength as the original shock wave entering the layer. The time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator-splitting technique.

4 citations


Journal ArticleDOI
TL;DR: In this paper, the steady flow in relativistic gasdynamics is studied and two possible regimes of flow: (1) a uniform flow and (2) the rarefaction wave.
Abstract: The steady flow in relativistic gasdynamics is studied. There are two possible regimes of flow: (1) a uniform flow and (2) the rarefaction wave. The rarefaction wave is similar to one studied in the Newtonian limit and is confined to a sectorial region. The maximum angle of this sector is smaller and the pressure drop is greater than in the Newtonian case. For the ultra‐relativistic fluid the results are described with simple formulae.

4 citations


Journal ArticleDOI
TL;DR: In this paper, a study of the form of the shock polars for two-parameter media with arbitrary equation of state was made, these satisfying the conditions of Cemplen's theorem.
Abstract: Special curves, called shock polars, are frequently used to determine the state of the gas behind an oblique shock wave from known parameters of the oncoming flow. For a perfect gas, these curves have been constructed and investigated in detail [1]. However, for the solution of problems associated with gas flow at high velocities and high temperatures it is necessary to use models of gases with complicated equations of state. It is therefore of interest to study the properties of oblique shocks in such media. In the present paper, a study is made of the form of the shock polars for two-parameter media with arbitrary equation of state, these satisfying the conditions of Cemplen's theorem. Some properties of oblique shocks in such media that are new compared with a perfect gas are established. On the basis of the obtained results, the existence of triple configurations in steady supersonic flows obtained by the decay of plane shock waves is considered. It is shown that D'yakov-unstable discontinuities decompose into an oblique shock and a centered rarefaction wave, while spontaneously radiating discontinuities decompose into two shocks or into a shock and a rarefaction wave.

3 citations



Journal ArticleDOI
TL;DR: In this paper, an experimental investigation of the behavior of a plane centered rarefaction wave which has a perturbation of the front shape at the time of origination was conducted in a shock tube and the flow pattern was recorded by a high speed camera.
Abstract: Results of an experimental investigation of the behavior of a plane centered rarefaction wave which has a perturbation of the front shape at the time of origination, are described in the paper. The experiments were conducted in a shock tube and the flow pattern was recorded by a high speed camera. Evolution of the wave front shape with time should proceed in conformity with the Huygens principle: each succeeding position of the front is the envelope of spherical waves issuing from the points of the preceding, as is confirmed by photochronograms. The characteristic feature of such evolution is the formation of a singularity at which the wave front undergoes a break. The flow perturbation in the domain between the reflected rarefaction wave and the passed shock results in the appearance of zones of reduced and elevated pressure relative to the mean level. The influence of the film separating the gases should be felt at the stage of the flow when the shock passes through the film. The investigation shows that points at which the front undergoes a break are formed during the evolution, and the wave front hence dissociates into series of divergent and intersecting waves. The appearance of secondarymore » compression and rarefaction waves is observed behind the perturbed wave front.« less

Proceedings ArticleDOI
01 Jun 1982
TL;DR: In this article, a single detonation of explosives in longcone, short-cone, straight, and firing-plug nozzles to provide propulsion in a simulated Jupiter atmosphere, as well as the ambient gases N, CO2 and He.
Abstract: Test data are presented for the use of a single detonation of explosives in long-cone, short-cone, straight, and firing-plug nozzles to provide propulsion in a simulated Jupiter atmosphere, as well as the ambient gases N, CO2 and He. The long-cone nozzle yielded a progressive increase with ambient pressure for the higher molecular weight gases CO2 and N, while the lower molecular weight He and simulated Jupiter atmosphere showed a specific pulse decrease with increasing ambient pressure. The short-plug nozzle yielded a small specific impulse reduction with increasing ambient pressure, and its results were found to be nearly independent of ambient gas molecular weight. All data gathered are analyzed by using first principles, approximate blast wave theory predictions, and two-dimensional numerical calculations. Rarefaction and oscillatory wave phenomena are found to significantly influence specific impulse.


Journal ArticleDOI
TL;DR: In this article, Batchelor et al. investigated the rheological behavior of a dilute suspension of spherical particles of condensed phase dispersed in its own slightly rarefied vapour gas.
Abstract: The rheological behaviour of a dilute suspension of spherical particles of condensed phase dispersed in its own slightly rarefied vapour gas is investigated on the basis of suspension theory (Batchelor 1970) and generalized slip-flow theory for a two-phase system of a gas and its condensed phase derived from the Boltzmann equation. The rarefaction of the gas and the phase-change process at the interfaces of the particles have the effect of reducing the Einstein coefficient of ϕ, volume fraction, in the expression for the effective viscosity in the suspension. In the case in which the pure rarefaction effect alone enters the problem, the coefficient is $\frac{5}{2}(1-2.702\,K)$ , where K is the Knudsen number, a rarefaction parameter defined by K = l / L , l and L being respectively the mean free path of gas molecules and the radius of a spherical particle. When both the rarefaction and the phase-change process are taken into account, this becomes $\frac{5}{2} (1-3.533\,K)$ . These modifications are not small, even at ordinary pressures, when the size of the particles is of the order of microns.

Dissertation
01 Jan 1982
TL;DR: In this article, an experimental and theoretical study of the response of a quiescent argon plasma to the motion of the positive space-charge sheath which bounds it is presented.
Abstract: This thesis contains an experimental and theoretical study of the response of a plasma to the motion of the positive space-charge sheath which bounds it. It is known theoretically that, if a sheath edge is moved at a speed less than the speed of ion acoustic waves, a region of ion rarefaction propagates into the plasma at the ion acoustic speed. In the past, difficulty has been encountered with the theory of ion acoustic wave generation from moving sheath edges, where compressions are necessary in addition to rarefactions. The initial conditions of many previous calculations omit the formation of a steady-state presheath where ions are accelerated to form the sheath. Some calculations are described which include the effects of an initial presheath by constructing a one-dimensional plasma solution where a production term balances the losses of ions to the walls. The plasma response to the motion of one boundary is found using the method of characteristics with appropriate boundary conditions. Ion rarefaction waves are associated with expanding sheaths while ion 'enhancement' waves (compressive features) are formed on sheath collapse. In each case the wave front moves at the local ion acoustic speed which includes the effects of ion drift. The presence of the presheath is essential to the generation of enhancements. The constructional details of a multidipole device are discussed, and the results of Langmuir probe and ion acoustic wave experiments are used to determine the parameters of a quiescent argon plasma. Some experiments on moving sheaths in such a plasma are then considered. Negative voltage ramps are applied to a plate and the plasma response is measured using sampled probe techniques. As the plate-plasma voltage increases, the ion-rich sheath expands at a speed which depends on the applied voltage waveform. For sheath edge speeds less than the ion acoustic speed, an ion rarefaction wave is formed. As the voltage decreases, the sheath collapses and an ion enhancement wave propagates into the plasma. Both wavefronts are observed to move at the local ion acoustic speed which increases with distance from the plate in agreement with theory.