Dynamics of density waves in a two dimensional funnel on an inclined plane

We report here experiments on two-dimensional funnel flow of diameter glass beads on an inclined plane. We have investigated the properties of the flow according to the outlet size D of the funnel and the gravity. We have identified three different regimes. For small funnel outlet sizes, there is no significant change in flow density: the flow is rather steady and homogeneous. For intermediate outlet sizes (), the flow is intermittent, consisting of spatially ordered density waves propagating upwards. At bigger outlet sizes, density waves do not exhibit any ordering and the flow dynamics becomes chaotic. In addition, we find that the flow dynamics is independent of the funnel opening angle except close to the channel flow configuration. Finally, it is stressed that the interactions between the beads and the inclined plane play a crucial role in the mechanism of formation of density waves. Received: 9 July 1998 / Received in final form and Accepted: 18 September 1998     

Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.     

超声速层流/湍流压缩拐角流动结构的实验研究

在Ma=3.0的超声速风洞中, 分别对上游边界层为超声速层流和湍流, 压缩角度为25°和28°的压缩拐角流动进行了实验研究. 采用纳米粒子示踪平面激光散射(NPLS)技术获得了流场整体和局部区域的精细结构, 边界层、剪切层、分离激波、回流区和再附激波等典型结构清晰可见, 测量了超声速层流压缩拐角壁面的压力系数. 从时间平均的流场结构中测量出分离激波、再附激波的角度和再附后重新发展的边界层的增长情况, 通过分析时间相关的流场NPLS图像, 可以发现流场结构随时间的演化特性. 实验结果表明: 在25°的压缩角度下, 超声速层流压缩拐角流动发生了典型的分离, 边界层迅速增长失稳转捩, 并引起一道诱导激波, 流场中出现了K-H涡、剪切层和微弱压缩波结构, 而超声速湍流压缩拐角流动没有出现分离, 湍流边界层始终表现为附着状态; 在28° 的压缩角度下, 超声速层流压缩拐角流动进一步分离, 回流区范围明显扩大, 诱导激波、分离激波向上游移动, 再附激波向下游移动, 分离区流动结构复杂, 相比之下, 超声速湍流压缩拐角流动的回流区范围明显较小, 边界层增长缓慢, 流场中没有出现诱导激波、K-H涡和压缩波, 流动分离区域的结构也相对简单, 但分离激波的强度则明显更强. 关键词： 压缩拐角 层流 湍流 流动结构     

Low frequency pressure waves in a vapor-liquid medium with a fixed layer of spherical particles

The features of the propagation of low-frequency pressure waves in a liquid-vapor flow through a layer of close-packed spherical solid particles have been studied. Principal measurements have been performed at two pressure values, mainly 0.2 and 0.6 MPa; in a cylindrical channel using lead balls sized 3 and 8 mm. The experimental results allowed defining the characteristic parameters and conditions providing that the wave’s propagation velocity coincides with the thermodynamic equilibrium’s acoustic speed in the vapor-liquid mixture. The results show the dispersive nature of the acoustic speed in the vapor-liquid medium.     

Characteristics and application of laser-generated acoustic shock waves in air

When a high-power laser beam is focused at a point, the air at the focal point is heated to temperatures of thousands of degrees within several nanoseconds and breaks down. This generates a spark that, in turn, is accompanied by an acoustic shock wave. The acoustic shock waves generated by focussing the beam from a pulsed laser with a 1064 nm wavelength and a power of 800 mJ per pulse have been measured using 1/4″ and 1/8″ B&K microphones. Nonlinear sound levels are observed up to 1.5 m from the laser-induced sparks. Beyond a certain region close to the source, levels are found to decrease in a manner consistent with spherical spreading plus nonlinear hydrodynamic losses. Analysis of the waveforms shows that the acoustic pulses associated with the laser-induced sparks are more repeatable and have higher intensity than those from an electrical spark source. Laser-generated acoustic shock waves are ideal for simulating a blast wave or a sonic boom in the laboratory and for studying the associated propagation effects. To illustrate this application, the propagation of the laser generated shock waves over a series of different hard, rough surfaces has been investigated. The results show the distinctive influences of ground roughness on the propagation of the shock wave.     

Microfabricated evanescent-light funnel with high-intensity cold atom flux

We process a silicon-on-insulator substrate into a funnel with a 25-μm-side square-shaped outlet by photolithography and anisotropic chemical etching. The funnel is utilized to form a cold atomic beam by means of reflection and cooling on repulsive evanescent light. Monte Carlo simulations show that the flux intensity of emitted cold Rb atoms reaches 10¹² cm⁻² s⁻¹. The mean horizontal velocity is estimated to be below 10 cm/s, while the mean vertical velocity decreases in proportion to the outlet side. The evanescent-light funnel can be developed to concentrate 80% of Rb atoms falling from a standard magneto-optical trap.     

Ion-acoustic shock waves with negative ions in presence of dust particulates

Dust acoustics shock waves have been investigated experimentally in a homogeneous unmagnetized dusty plasma device containing negative ions. When the negative ion density larger than a critical concentration ‘rc’ negative shock waves were observed instead of positive shock waves. Again when it is nearly equal to ‘rc’ both positive and negative shock waves propagate. The experimental findings are compared with modified KdV-Burgers equation. The velocity of the shock waves are also measured and compared with the numerical integration of modified KdV-Burgers equation.     

Quantum shock waves and domain walls in the real-time dynamics of a superfluid unitary Fermi gas

We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by π and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase jumps appear to collide elastically.     

Temperature overshoots for a 4-velocity unidimensional discrete Boltzmann model

We propose a 4-velocity unidimensional discrete Boltzmann model with two different speeds 2, 1 and two different masses 1, 2. With the three conservation laws of mass, momentum, and energy satisfied, we can introduce a nontrivial temperature. First, we determine the similarity shock waves satisfying physical properties: positivity, shock stability, inequalities of the subsonic and supersonic flows, increase or decrease of both mass and temperature across the shock. It results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive. We observe overshoots of the temperature, across the shock, with bumps higher and higher as the shock front speed increases. Second, we study the (1+1)-dimensional shock waves. They represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times.     

Solar energetic particles: is there time to hide?

In the large solar energetic particle (SEP) events that constitute a serious radiation hazard, particles are accelerated at shock waves driven out from the Sun by coronal mass ejections (CMEs). A self-regulating mechanism of wave formation by the streaming particles limits SEP intensities early in the event. Hazardous intensities do not occur until the arrival of the shock itself. This provides an opportunity to warn astronauts to take shelter after the onset of the event at the Sun and before arrival of the shock, a time of approximately 12 h or more. The actual time history of particle intensities depends strongly on the longitude of the event at the Sun, on the width the CME, and especially on the speed of the shock. Fortunately, hazardous events are relatively rare. Unfortunately, this gives us few events to study, so we are forced to extrapolate knowledge gained at lower energies in the frequent smaller events. It is essential that the spacecraft with our best instrumentation be positioned outside the Earth's magnetosphere where they can observe these rare large events when they do occur.     

Molecular dynamics simulations of microscopic structure of ultra strong shock waves in dense helium

Hydrodynamic properties and structure of strong shock waves in classical dense helium are simulated using non-equilibrium molecular dynamics methods. The shock speed in the simulation reaches 100 km/s and the Mach number is over 250, which are close to the parameters of shock waves in the implosion process of inertial confinement fusion. The simulations show that the high-Mach-number shock waves in dense media have notable differences from weak shock waves or those in dilute gases. These results will provide useful information on the implosion process, especially the structure of strong shock wave front, which remains an open question in hydrodynamic simulations.     

Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensatewith dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of ~/ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.     

Numerical investigation of supersonic flow breakdown at the inlet duct throttling

The work presents the results of investigating the process of supersonic flow deceleration in a duct of the two-dimensional inlet throttled by variation of the outlet cross-sectional area. An inlet with three external compression shock waves designed for the freestream Mach number M_d = 7 was considered as an example for the investigation. A one-dimensional analysis of the conditions for realization of the supersonic flow deceleration regimes in the inlet duct with two throats — in the inlet entrance and at the inlet duct outlet, has been carried out. The parametric numerical computations of two-dimensional inviscid or turbulent flows in the inlet were performed with the use of the Euler and Navier—Stokes codes of the program package FLUENT. The critical conditions for the nonuniform flow in the outlet throat bringing to choking the inlet duct were determined.     

Current discontinuities on superconducting cosmic strings

The propagation of current perturbations on superconducting cosmic strings is considered. The conditions for the existence of discontinuities similar to shock waves have been found. The formulas relating the string parameters and the discontinuity propagation speed are derived. The current growth law in a shock wave is deduced. The propagation speeds of shock waves with arbitrary amplitudes are calculated. The reason why there are no shock waves in the case of time-like currents (in the “electric” regime) is explained; this is attributable to the shock wave instability with respect to perturbations of the string world sheet.     

Nature of convection-stabilized DC arcs in dual-flow nozzlegeometry. I. The cold flow field and DC arc characteristics

An experimental investigation of the steady-state low current air arcs in a dual-flow nozzle system is presented. The cold flow field with no arc was determined for various nozzle geometries, i.e. two- and three-dimensional and orifice nozzles, and nozzle pressure ratios. Supersonic flow separation and oblique and detached shock waves were observed in the flow field. Using a finite-element computer program, the Mach number contours were determined in the flow field for various nozzle-gap spacings and pressure ratios. In addition, the DC arc voltage and current measurements were made for an electrode gap spacing of ≈5.5 cm and current levels of I≈25, 50, and 100 A for the three nozzle geometries. The arc voltage and arc power increased rapidly as the flow speed increased from zero to sonic velocity at the nozzle throat. The shock waves in the converging-diverging nozzles resulted in a decrease in the overall resistance by about 15%     

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Effect of positron density and temperature on the electron acoustic waves in a magnetized dissipative plasma

Zakharov–Kuznetsov–Burgers (ZKB) equation is derived for electron acoustic shock waves in magnetized e–p–i plasma. In the present model, magnetized plasma containing two electron population with kappa distributed positrons has been considered. The propagation characteristics of three dimensional electron acoustic (EA) shock waves have been studied under the influence of magnetic field. Our present plasma model supports the negative potential shocks. Combined action of dissipation (η), superthermality (κ), concentration of positrons (β), temperature ratio of cold electrons to positrons (σ), and magnetic field (ω_c) significantly modify the properties of EA shock waves. The width and amplitude of the shock structures are modified by various physical parameters. It is found that shock wave width decreases with increase in β, η₀, and ω_c whereas it becomes wider for κ and σ. Further, potential of the shock wave decreases as one departs away from superthermal distribution.     

Obliquely Propagating Electron Acoustic Shock Waves in Magnetized Plasma

Obliquely propagating electron acoustic shock waves in plasma with stationary ions, cold and superthermal hot electrons are investigated in magnetized plasma. Employing reductive perturbation method, Korteweg-de Vries-Burgers equation (KdVB) is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdVB equation show the variation of shock waves structure (amplitude, velocity, and width) with different plasma parameters. Particle density (α), superthermal parameter (κ), electron temperature ratio (??), kinetic viscosity (η₀), obliqueness (k_z), and strength of magnetic field (ω_c) significantly modify the properties of the shock waves structures. The present investigation is useful to understand dissipative structures observed in space or laboratory plasma where multielectrons population with superthermal electrons are prevalent.     

Myocardial effects of local shock wave therapy in a Langendorff model

Objective

Applying shock waves to the heart has been reported to stimulate the heart and alter cardiac function. We hypothesized that shock waves could be used to diagnose regional viability.

Method

We used a Langendorff model to investigate the acute effects of shock waves at different energy levels and times related to systole, cycle duration and myocardial function.

Results

We found only a small time window to use shock waves. Myocardial fibrillation or extrasystolic beats will occur if the shock wave is placed more than 15 ms before or 30 ms after the onset of systole. Increased contractility and augmented relaxation were observed after the second beat, and these effects decreased after prolonging the shock wave delay from 15 ms before to 30 ms after the onset of systole. An energy dependency could be found only after short delays (−15 ms). The involved processes might include post-extrasystolic potentiation and simultaneous pacing.

Conclusion

In summary, we found that low-energy shock waves can be a useful tool to stimulate the myocardium at a distance and influence function.     

Waves in interplanetary shocks: a wind/WAVES study

We describe results from the first statistical study of waveform capture data during 67 interplanetary (IP) shocks with Mach numbers ranging from approximately 1-6. Most of the waveform captures and nearly 100% of the large amplitude waves were in the ramp region. Although solitary waves, Langmuir waves, and ion acoustic waves (IAWs) are all observed in the ramp region of the IP shocks, large amplitude IAWs dominate. The wave amplitude is correlated with the fast mode Mach number and with the shock strength. The observed waves produced anomalous resistivities from approximately 1-856 Omega.m (approximately 10(7) times greater than classical estimates.) The results are consistent with theory suggesting IAWs provide the primary dissipation for low Mach number shocks.