Classification of shock wave reflections from a wedge. Part 2: Experimental and numerical simulations of different types of Mach reflections

Classification of various types of the reflections of a shock wave over straight wedge is supposed. The idea about entire reflection phenomenon as a result of interaction of two processes—the shock wave refection process and the flow deflection process—serves as a basis for the classification. To recognize the types of reflection, changes in the shapes of the reflected wave, Mach stem and contact surface are taken into account. The boundaries and domains of existence for various types of reflection are reported. New names for some types of reflection are proposed.     

Wavelet Analysis of Fractal Boundaries. Part 1: Local Exponents

Let be a domain of . In Part 1 of this paper, we introduce new tools in order to analyse the local behavior of the boundary of . Classifications based on geometric accessibility conditions are introduced and compared; they are related to analytic criteria based either on local L^p regularity of the characteristic function or on its wavelet coefficients. Part 2 deals with the global analysis of the boundary of . We develop methods for determining the dimensions of the sets where the local behaviors previously introduced occur. These methods are based on analogies with the thermodynamic formalism in statistical physics and lead to new classification tools for fractal domains.The first author is supported by the Institut Universitaire de France.This work was performed while the second author was at the Laboratoire d’Analyse et de Mathématiques Appliquées (University Paris XII, France) and at the Istituto di Matematica Applicata e Tecnologie Informatiche (Pavia, Italy) and partially supported by the Société de Secours des amis des Sciences and the TMR Research Network “Breaking Complexity”.     

Study on the Mach and regular reflections of shock wave

Journal of Visualization - While a moving incident shock wave moves through a sharp compression ramp with the fixed angle, θr, the incident shock wave is reflected by the ramp surface and the...     

Diffraction of a plane wave from a wedge in a chiral medium

In a rigorous electrodynamic formulation, we have investigated diffraction of a plane wave in a chiral medium from a wedge with ideally conducting faces. The boundary-value problem is reduced to a system of functional equations which are transformed to Fredholm integral equations and singular integral equations. We have carried out an asymptotic analysis of the diffraction fields. The scattered field contains plane waves reflected by the faces and cylindrical waves due to the edges, having two opposite types of circular polarization, and also two refraction waves whose polarization corresponds to polarization of the slower characteristic wave in the chiral medium.This paper is dedicated to the memory of Professor M. S. Bobrovnikov.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 108–116, October, 1993.     

Influence of the adiabatic index on switching between different types of shock wave reflection in a steady supersonic gas flow

A comprehensive pattern of different types of shock wave reflection in a steady supersonic gas flow is analytically constructed with regard to a new wave configuration found by the authors-negative-angle irregular reflection. A double Mach reflection with a negative reflection angle in a steady supersonic gas flow is numerically obtained for the first time.     

The reflection of a finite amplitude wave from a curvilinear unsteady shock wave

The reflection of a wave of finite amplitude from a curvilinear unsteady shock wave has been analyzed. A formula connecting reflected wave parameters with that of the incident wave, curvature and shock wave intensity has been obtained in closed form.     

The structure of a shock electromagnetic wave synchronous with several waves propagating in coupled transmission lines with different types of dispersion

A shock electromagnetic wave is studied numerically in the case when its structure is equally defined by two or more synchronous waves. The analysis relies on the previously suggested electrodynamic system of two coupled transmission lines one of which is normally dispersive (coaxial line) and the other is anomalously dispersive (ladder-type bar slow-wave structure).     

Wavelet Analysis of Fractal Boundaries. Part 2: Multifractal Analysis

This second part deals with the global analysis of the boundary of domains . We develop methods for determining the dimensions of the sets where the local behaviors introduced in Part 1 occur. These methods are based on analogies with the thermodynamic formalism in statistical physics and lead to new classification tools for fractal domains.The first author is supported by the Institut Universitaire de France.This work was performed while the second author was at the Laboratoire d’Analyse et de Mathématiques Appliquées (University Paris XII) and at the Istituto di Matematica Applicata e Tecnologie Informatiche (Pavia, Italy) and partially supported by the Société de Secours des amis des Sciences and the TMR Research Network “Breaking Complexity”.     

强激光驱动爆炸与冲击效应

随着高功率密度激光技术的快速发展,强激光驱动的爆炸与冲击效应逐渐引起国内外学者的广泛关注。对强激光诱导爆炸与冲击效应研究进展进行了综述,包括强激光诱导爆炸载荷特征与相似律,强激光对材料表面冲击强化处理,强激光冲击诱导材料相变动力学行为,以及利用强激光驱动微弹道冲击等方面的研究进展,并指出了强激光诱导爆炸与冲击效应研究的发展趋势和未来需要解决的关键科学问题。     

Modified shock waves for extracorporeal shock wave lithotripsy: a simulation based on the Gilmore formulation

Extracorporeal shock wave lithotripsy (SWL) is a reliable therapy for the treatment of urolithiasis. Nevertheless, improvements to enhance stone fragmentation and reduce tissue damage are still needed. During SWL, cavitation is one of the most important stone fragmentation mechanisms. Bubbles with a diameter between about 7 and 55 μm have been reported to expand and collapse after shock wave passage, forming liquid microjets at velocities of up to 400 m/s that contribute to the pulverization of renal calculi. Several authors have reported that the fragmentation efficiency may be improved by using tandem shock waves. Tandem SWL is based on the fact that the collapse of a bubble can be intensified if a second shock wave arrives tenths or even a few hundredths of microseconds before its collapse. The object of this study is to determine if tandem pulses consisting of a conventional shock wave (estimated rise time between 1 and 20 ns), followed by a slower second pressure profile (0.8 μs rise time), have advantages over conventional tandem SWL. The Gilmore equation was used to simulate the influence of the modified pressure field on the dynamics of a single bubble immersed in water and compare the results with the behavior of the same bubble subjected to tandem shock waves. The influence of the delay between pulses on the dynamics of the collapsing bubble was also studied for both conventional and modified tandem waves. For a bubble of 0.07 mm, our results indicate that the modified pressure profile enhances cavitation compared to conventional tandem waves at a wide range of delays (10-280 μs). According to this, the proposed pressure profile could be more efficient for SWL than conventional tandem shock waves. Similar results were obtained for a ten times smaller bubble.     

Energy of a shock wave generated in different metals under irradiation by a high-power laser pulse

The energies of a shock wave generated in different metals under irradiation by a high-power laser beam were determined experimentally. The experiments were performed with the use of targets prepared from a number of metals, such as aluminum, copper, silver and lead (which belong to different periods of the periodic table) under irradiation by pulses of the first and third harmonics of the PALS iodine laser at a radiation intensity of approximately 10¹⁴ W/cm². It was found that, for heavy metals, like for light solid materials, the fraction of laser radiation energy converted into the energy of a shock wave under irradiation by a laser pulse of the third harmonic considerably (by a factor of 2–3) exceeds the fraction of laser radiation energy converted under irradiation by a laser pulse of the first harmonic. The influence of radiation processes on the efficiency of conversion of the laser energy into the energy of the shock wave was analyzed.     

Determination of shock wave velocity from photographs obtained using a polarization interferometer

A polarization shear interferometer is described in which one of the two images of the flow being studied is produced outside the interference field and serves as a shadow pattern. This image is recorded again using an additional light source — a pulsed laser. In this way one can determine the shock wave velocity and establish, on the basis of gas-dynamic relationships, the proper numeration of the interference fringes on the interferogram.     

Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wave packet

The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.     

Reciprocity in the wave reflection and transmission problem: Part 1. Symmetry of the matrices of reflection coefficients

The reciprocity theorem in Lyamshev’s formulation is used to derive a general symmetry relationship for the matrices of reflection coefficients in homogeneous media and one-dimensional waveguides. This relationship is shown to be equivalent to the normalization of the amplitudes by the cross power flux of the forward and backward waves. The relationship is valid for both propagating and evanescent waves, and all the symmetry relationships known from the literature represent its particular cases.     

Criterion for existence of shock waves in relativistic magnetohydrodynamics with a general equation of state

Relativistic stationary shock waves in an ideal conducting fluid are studied for the general equation of state. We use small viscosity arguments to obtain a criterion that selects physically admissible shock transitions without any supposition about convexity of the Poisson adiabats. The relations between the magnetosound speeds and the speed of the shock obtained as a consequence of this criterion reveal specific differences between relativistic considerations versus classical ones.     

A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains

A grid-free high-resolution spatially-adaptive vortex method for two-dimensional incompressible flow in bounded domains is presented. The computational algorithm is based on operator splitting in which convection and diffusion are handled separately every time step. In the convection step, computational elements are convected with velocities obtained by fast approximations of the Biot–Savart superposition with second-order Runge–Kutta time integration scheme. Diffusion is performed using the smooth redistribution method that employs a Gaussian basis function for vorticity in the interior. Near solid walls, the core functions are modified to conserve circulation. The no-slip boundary condition is enforced by creating of a vortex sheet that is redistributed to neighboring elements using the redistribution method. The proposed method enables accurate and smooth recovery of the vorticity and does not require explicit use of vortex images or occasional re-meshing. Algorithms for reduction in computational cost by accurately removing elements in overcrowded regions and for spatial adaptivity that allows for variable core sizes and variable element spacing are presented. Computations of flow around an impulsively started cylinder for Reynolds number values of 1000, 3000, and 9500 are preformed to investigate various aspects of the proposed method.     

Microimplosions: cavitation collapse and shock wave emission on a nanosecond time scale

A streak camera with high spatial and temporal resolution was used for imaging the dynamics of the violent collapse in single-bubble sonoluminescence. The high pressure in the last phase of the bubble collapse leads to the emission of a shock wave, which is launched with a shock velocity of almost 4000 m/s. The shock amplitude decays much faster than approximately 1/r. From the strongly nonlinear propagation the pressure in the vicinity of the bubble can be calculated to be in the range of 40-60 kbar.     

楔块中脉冲声场及相控阵成像自检研究

相控阵横波检测必须在换能器前方加上楔块,对于楔块中的声场进行研究具有重要意义。本文通过数值计算和物理实验研究了超声相控阵楔块中的脉冲声场,分析并解释了超声相控阵系统自检成像过程中各种波形的产生机理和转换过程。首先从固体中超声传播理论出发,采用时域有限差分方法对相控阵楔块中各阵元独立发射条件下的脉冲声场进行仿真计算,给出了超声脉冲在楔块中的传播过程;然后开展了对应边界条件下相控阵楔块的B模式成像实验。数值模拟和物理实验的结果基本一致。本文的研究初步展示了楔块中的脉冲声场,其结果可为超声相控阵系统自检和楔块设计提供参考。     

Optical study of parameters of the passage of a shock wave from air to water

A study is made of the penetration of shock waves from air into water. The shock wave in air is generated as a result of dielectric breakdown induced by pulsed CO₂-laser radiation. A combination of the double-exposure shadow method and holographic interferometry is used to measure the shock-wave parameters. Density and pressure profiles behind the wave front are obtained at different times after onset of breakdown. It is shown experimentally that as the wave passes through the interface from the air to the water, there is a fourfold amplification of the pressure in the shock wave front. Estimates of the width of the shock wave front formed in the water are given in the context of studies of large-scale explosion processes. It is shown that simple empirical dependences, established in the course of studies of large-scale explosions, are also valid with certain corrections for microscopic laboratory experiments. Zh. Tekh. Fiz. 68, 39–43 (August 1998)     

Numerical study of shock wave entry and propagation in a microchannel

The entry of a shock wave with the Mach number M_is = 2.03 into a microchannel and its further propagation is numerically studied with the use of kinetic and continuum approaches. Numerical simulations on the basis of the Navier ?? Stokes equations and the Direct Simulation Monte Carlo method are performed for different Knudsen numbers Kn = 8·10^?3 and 8·10^?2 based on the microchannel half-height. At the Knudsen number Kn = 8·10^?3, amplification of the shock wave after its entry into the microchannel is observed. Further downstream, the shock wave is attenuated, which is in qualitative agreement with experimental data. It is demonstrated that results predicted by a quasi-one-dimensional model (which ignores viscosity and heat conduction) of shock wave propagation over a channel with an abrupt change in the area agrees with results of numerical simulations on the basis of the Euler equations. In both cases, shock wave acceleration (amplification) after its entry into the microchannel is observed. At the Knudsen number Kn = 8·10^?2, the influence of the entrance shape on shock wave propagation over the microchannel is examined. Intense attenuation of the shock wave is observed in three cases: channel with sudden contraction, junction of two channels with an additional thin separating plate, and rounded junction in the form of a sector with an angle of 90° (quarter of a circumference). It is shown that the microchannel entrance shape can affect further propagation of the shock wave. The wave has the highest velocity in the case with a rounded entrance.