Dimensionless similarity invariants and criteria of cylindrical Z-pinch compression regimes in a gas

A dimensionless equation containing two dimensionless complexes Z and d ₀ was derived from the consideration of the energy balance at the early stage of cylindrical Z-pinch development in a gas. The requirement of the equation invariance under the transformation of stretching (compression) of coordinates and time imply that the Ξ and d ₀ complexes are dimensionless similarity invariants of the indicated discharge. These invariants were shown to be quantitative criteria of realization of single, double, triple, etc. cylindrical Z-pinch plasma column compression regimes.     

MHD cylindrical shock wave in self-gravitating gas

Summary Similarity solutions of the propagation of cylindrical blast waves through a self-gravitating polytropic gas caused by an instantaneous release of finite energy are investigated theoretically including the influence of transverse magnetic field. A comparative study of the distributions of velocity, density, mass, pressure, temperature and magnetic field has been illustrated through figures. The authors of this paper have agreed to not receive the proofs for correction.     

Dynamics of shock waves caused by pulsed high-current electric discharges in gas. I. Toroidal (ring-shaped) shock wave

Dynamics of convergence and reflection of the toroidal (ring-shaped) shock wave (SW) in the torus plane and in the plane passing through its symmetry axis is experimentally studied. It is shown that such an SW is significantly amplified near the torus symmetry axis. The maximum amplification of the toroidal SW near its symmetry axis is estimated.     

理想气体球面强冲击波一般自模拟运动模型

应用理想气体一维不定常流自模拟运动基本微分方程，详细讨论了球面强冲击波波后气体自模拟特性，推导出具有自模拟运动特性的球面强冲击波传播公式的一般形式.分析结果表明：球面强冲击波自模拟运动模型不必从具有奇异性质的点源出发，冲击波初始速度和自模拟温度函数解一般不存在趋于无穷大的问题.Taylor点爆炸冲击波自模拟模型只是一般自模拟模型中假设自模拟运动总能量为定值条件下的特例. 关键词： 理想气体 球面强冲击波 自模拟运动     

Plane and cylindrical shock waves in magnetogasdynamics

Summary The Chisnell-Chester-Whitham method has been used to study the propagation of diverging plane and cylindrical shock waves through an ideal gas in the presence of a magnetic field having only constant axial and azimuthal components, simultaneously for both weak and strong cases. By assuming an initial density distribution ϱ₀ = ϱ′r ^−W , where ϱ′ is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density and the particle velocity immediately behind the shock have been derived for both the cases.

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Riassunto Il metodo di Chisnell-Chester-Whitham è stato usato per studiare la propagazione di onde d’urto divergenti cilindriche e piane attraverso un gas ideale in presenza di un campo magnetico che ha solo componenti costanti assiali e azimutali, contemporaneamente per casi deboli e forti. Assumendo una distribuzione di densità iniziale ϱ₀ = ϱ′r ^−W , dove ϱ′ è la densità al piano/asse di simmetria ew è una costante, si sono ottenute le espressioni analitiche per la velocità d’urto e la forza d’urto. Le espressioni per la pressione, la densità e la velocità delle particelle immediatamente dopo l’urto sono state determinate per entrambi i casi.

     

Magnetohydrodynamic shock waves in a gas mixture

The properties of the non-relativistic propagation of a plane shock wave in a gas mixture of charged particles in the presence of an external uniform magnetic field, oriented in a direction transverse to the direction of propagation, are studied. Expressions for the pressure, density and velocity ratios are obtained. It is shown that the presence of a transverse magnetic field narrows down the range of values of the density ratio.     

Converging spherical and cylindrical elastic–plastic waves of small amplitude

Converging spherical and cylindrical elastic–plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region.After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic–plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.     

Shock wave structure in a two-components gas mixture

Summary The nonlinear differential equations describing the problem of shock wave structure in a two-component gas mixture are reduced to a system of two coupled nonlinear differential equations. This system is solved numerically using the finite-difference method. It is found that the relative shock wave thickness of the mixture increases with the increase of the ratio between the viscosity coefficients when the ratio between the mass fractions is constant. It is also shown that the relative shock wave thickness of the mixture decreases with the increase of the ratio between the mass fractions when the ratio between the viscosity coefficients is constant.

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Riassunto Si riducono le equazioni differenziali non lineari che descrivono il problema della struttura dell’ onda d’urto in una miscela di gas a 2 componenti a un sistema di due equazioni differenziali accoppiate non lineari. Questo sistema si risolve numericamente usando il metodo delle differenze finite. Si trova che il relativo spessore dell’onda d’urto della miscela aumenta con l’aumento del rapporto tra i coefficienti di viscosità, quando il rapporto tra le frazioni di massa è costante. Si mostra anche che lo spessore relativo dell’onda d’urto della miscela diminuisce con l’aumento del rapporto tra le frazioni della massa, quando il rapporto tra i coefficienti di viscosità è costante.

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Резюме Нелинейные дифференциальные уравнения, описывающие проблему структуры ударной в двух-компоентной газовой смеси, сводятся к системе двух связанных нелинейыых дифференциальных уравнений. Получается, что относительная толщина ударной волны в смеси увеличвается с увеличением отношения между коэффиыентами вязкоти, когда отнощение между массовыми доями остается постоянным. Также показывается. что относительная толщина ударной волны уменьшается с увеличением отношения между массовыми долями. когда отношение между коэффициентами вязкости остается постоянным.

     

Orthogonality catastrophe and shock waves in a nonequilibrium Fermi gas

A semiclassical wave packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock-wave phenomenon. The nonlinear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the orthogonality catastrophe. We study a generalization of this phenomenon to the nonequilibrium regime and show how the orthogonality catastrophe cures the gradient catastrophe, by providing a dispersive regularization mechanism.     

Nonlinear effects and shock formation in the focusing of a spherical acoustic wave

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, nonlinear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of nonlinearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. In addition, the comparison between numerical and experimental results allows us to calibrate the vibration of the ceramic used to produce the wave, as a function of the applied voltage.Received: 11 July 2003, Published online: 24 October 2003PACS: 67.40.-w Boson degeneracy and superfluidity of 4He - 43.25. + y Nonlinear acoustics - 62.60. + v Acoustical properties of liquids     

Observation of shock waves in a strongly interacting Fermi gas

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.     

Distortion of a spherical gaseous interface accelerated by a plane shock wave

The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces.     

Study for particular solutions of cylindrical shock waves in magnetogasdynamics

In this research article, a problem of shock waves propagation in magnetogasdynamics is considered in ideal gas. The problem can be represented by hyperbolic non-linear system of partial differential equations (PDEs). It is solved by similarity method under invariant surface conditions. I reduced non-linear system of magnetogasdynamics into first order system of ordinary differential equations (ODEs) and it is non-linear. The ratio of heat capacity at constant pressure to heat capacity at constant volume is also known as the adiabatic constant and their values for monatomic, diatomic gasses are more than one in ideal gas. So, I have obtained exact solution of magnetogasdynamics system in ideal gas for particular value of adiabatic index$\gamma =2$. The effect of the ambient density exponent $\theta$ on flow quantities density, velocity, pressure, and magnetic field are determined before the shock.     

Measurement of scaling laws for shock waves in thermal nonlocal media

We are able to detect the details of spatial optical collisionless wave breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how nonlocality and nonlinearity affect the point of shock formation and compare results with numerical simulations.     

柱和球尘埃离子声孤波的绝热近似解

通过运用等价粒子理论，得到了尘埃声孤波中的KdV类型方程（包括KdV方程，柱KdV方程和球KdV方程）的绝热近似解。这种方法也可以运用到其它的非线性演化方程。     

二次曝光全息术在圆柱形冲击波会聚过程观测中的应用

本文对全息曝光技术进行了分析,设计了一种全息干涉仪,对圆柱形冲击波会聚过程的不稳定性进行了观察,并得出了几个有重要价值的结论。