Concept# Shock wave

Summary

In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium.
For the purpose of comparison, in supersonic flows, additional increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The sonic boom associated with the passage of a supersonic aircraft is a type of sound wave produced by constructive interference.
Unlike solitons (another kind of nonlinear wave), the energy and speed of a shock wave alone dissipates relatively quickly with distance.
When a shock wave passes through matter,

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This article is part of the project to model the kinetics of high-temperature combustions, occurring behind shock waves and in detonation waves. The "conventional" semi-empirical correlations of ignition delays have been reformulated, by keeping the Arrhenius equation form. It is shown how it polynomial with 3(N) Coefficients (where N is an element of [1, 4] is the number of adjustable kinetic parameters, likely to be simultaneously chosen among the temperature T, the pressure P, the inert fraction X-Ar, and the equivalence ratio Phi) can reproduce the delays predicted by the Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz. C.K. Westbrook, Combust. Flame 129 (2002) 253-280] detailed mechanism (565 species and 22538 reactions), over it wide range of conditions (comparable with the validity domain). The deviations between the simulated times and their fits (typically 1%) are definitely lower than the Uncertainties related to the mechanism (at least 25%). In addition. using, this new formalism to evaluate these durations is about 10(6) times faster than simulating them With SENKIN (CHEMKIN III package) and only 10 times slower than using the classical correlations. The adaptation of the traditional method for predicting delays is interesting, for modeling. because those performances are difficult to obtain simultaneously with Other reduction methods (either purely mathematical, chemical, or even mixed). After a physical and mathematical justification of the proposed formalism, some of its potentialities for n-heptane combustion are presented. In particular, the trends of simulated delays and activation energies are shown for T is an element of [1500 K, 1900 K], P is an element of [10 kPa, 1 MPa] X-Ar is an element of [0, 0, 7], and Phi is an element of [0.25, 4.0]. (C) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

2008We study the evolution of a system composed of N non-interacting particles of mass m distributed in a cylinder of length L. The cylinder is separated into two parts by an adiabatic piston of a mass M ≫ m. The length of the cylinder is a fix parameter and can be finite or infinite (in this case N is infinite). For the infinite case we carry out a perturbative analysis using Boltzmann's equation based on a development of the velocity distribution of the piston in function of a small dimensionless parameter ε = √(m/M). The non-stationary case is solved up to the order ε ;; our analysis shows that the system tends exponentially fast towards a stationary state where the piston has an average velocity V. The characteristic time scale for this relaxation is proportional to the mass of the piston (τ0 = M/A where A is the cross-section of the piston). We show that for equal pressures the collisions of the particles induce asymmetric fluctuations of the velocity of the piston which leads to a macroscopic movement of the piston in the direction of the higher temperature. In the case of the finite model a perturbative approach based on Liouville's equation (using the parameter α = 2m/(M + m)) shows that the evolution towards thermal equilibrium happens on two well separated time scales. The first relaxation step is a fast, deterministic and adiabatic evolution towards a state of mechanical equilibrium with approximately equal pressures but different temperatures. The movement of the piston is more or less damped. This damping qualitatively depends on whether the ratio R = Mgas/M between the total mass of the gas and the mass of the piston is small (R < 2) or large (R > 4). The second part of the evolution is much slower ; the typical time scales are proportional to the mass of the piston. There is a stochastic evolution including heat transfer leading to thermal equilibrium. A microscopic analysis yields the relation XM(t) = L(1/2 - ξ(at)) where the function ξ is independent of M. Using the hypothesis of homogeneity (i.e. the values of the densities, pressures and temperatures at the surface of the piston can be replaced by their respective average values) introduced in the previous analysis the observed damping does not show up. This can be explained by shock waves propagating between the piston and the walls at the extremities of the cylinder. In order to study the behaviour of the system there is hence a need to adequately describe the non-equilibrium fluids around the piston. We carry out an analysis of the infinite case, based on the perturbative approach introduced earlier. In this case the initial conditions are chosen in such a manner that the piston on average stays at the origin. It is shown that it is possible to describe the evolution of the fluids in such a way that it is coherent with the two laws of thermodynamics and the phenomenological relationships. Finally we study the case of a constant velocity of the piston in a finite cylinder. Such a condition and elastic collisions allow us to derive an explicit expression for the distribution of the fluids and hence for the hydrodynamics fields. This expression reveals the presence of shock waves between the piston and the extremities of the cylinder.

High-pressure studies in silica are of great interest to earth and planetary sciences. Highpressure phases are rarely found in nature as a result of shock events like meteorite impacts orvolcanic events in nature. Recreating these phases remains a challenging task in lab conditions and can synthesize only very limited volume using static loading techniques like diamondanvil cell. In this thesis, we aim at recreating high pressure phases in silica using shock waves generated from a femtosecond laser. We put forth three different approaches for the high pressure generation in the bulk of the silica matrix. The frst method being a double beam exposure method; it potentially offers a means to create arbitrary patterns of laser-induced high-pressure impacted zones by scanning the two beams across the specimen volume. Tightly focused femtosecond laser-beam in the non-ablative regime can induce a shockwave suffciently intense to reach local pressures in the giga-Pascal range or more. In a single beam confguration, the locationof the highest-pressure zone is nested within the laser-focus area, making it diffcult to differentiate the effect of the shockwave pressure from photo-induced and plasma relaxation effects.To circumvent this diffculty, we consider two spatially separated focused beams individually acting as quasi-simultaneous pressure-wave emitters. The zone in between the two laserbeams where both shockwaves superpose forms a region of extreme pressure range, physically separated from the regions where the plasma formed. Here, we present a detailed materialinvestigation of pressured-induced densifcation in fused silica between the foci of two laser beams.Further, we investigated the effect of ultrashort-pulsed laser (50 fs) on material transformation by the shockwave emitted by the pulses and the repeated hammering effect of cumulativepulse exposure. This was done by characterizing the ablated particles after oblique writing on a fused silica substrate. Finally, we used a simultaneous spatial temporal focusing technique(SSTF) to achieve higher energy confnement inside a limited volume within the substrate, thereby inducing high pressure in the material. All materials were characterized using a Ramanspectroscope to evaluate the phase transformation introduced by the dynamic laser shock loading. Although this study focused on fused silica due to its relevance for both geophysicaland engineering investigations, the methodology used is generic and can be implemented in a variety of other transparent substrates for high-pressure physics studies.