Collision Of Shock Waves Research Articles

Colliding Shock Waves and Hydrodynamics in Small Systems.

Using numerical holography, we study the collision of a planar sheet of energy with a bounded localized distribution of energy. The collision, which mimics proton-nucleus collisions, produces a localized lump of debris with transverse size R∼1/T_{eff} with T_{eff} the effective temperature, and has large gradients and large transverse flow. Nevertheless, the postcollision evolution is well described by viscous hydrodynamics. Our results bolster the notion that debris produced in proton-nucleus collisions may be modeled using hydrodynamics.

Universal hydrodynamic flow in holographic planar shock collisions

We study the collision of planar shock waves in AdS$_5$ as a function of shock profile. In the dual field theory the shock waves describe planar sheets of energy whose collision results in the formation of a plasma which behaves hydrodynamically at late times. We find that the post-collision stress tensor near the light cone exhibits transient non-universal behavior which depends on both the shock width and the precise functional form of the shock profile. However, over a large range of shock widths, including those which yield qualitative different behavior near the future light cone, and for different shock profiles, we find universal behavior in the subsequent hydrodynamic evolution. Additionally, we compute the rapidity distribution of produced particles and find it to be well described by a Gaussian.

Holography and off-center collisions of localized shock waves

Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description, we solve 5D Einstein equations with no dimensionality reducing symmetry restrictions to find the asymptotically anti-de Sitter spacetime geometry. Implications of our results on the understanding of early stages of heavy ion collisions, including the development of transverse radial flow, are discussed.

Formation time of quark–gluon plasma in heavy-ion collisions in the holographic shock wave model

We estimate the thermalization time in two colliding shock waves holographic model of heavy-ion collisions. For this purpose we model the process by the Vaidya metric with a horizon defined by the trapped surface location. We consider two bottom-up AdS/QCD models that give, within the colliding shock waves approach, the dependence of multiplicity on the energy compatible with RHIC and LHC results. One model is a bottom-up AdS/QCD confining model and the other is related to an anisotropic thermalization. We estimate the thermalization time and show that increasing the confining potential decreases the thermalization time as well as an anisotropy accelerates the thermalization.

Asymmetrical interference of counter oblique shock waves

Subject of Study. The paper deals with data on the interference of shock waves with different intensity and slope angles to the flow of them. This problem is related to the problem of designing air intakes to the internal compression and detonation combustion engines in stationary overdriven detonation wave. A regular form of interference and irregular Mach one are considered. Intensity calculations of reflected shock waves for both cases are given. As shown below, there is a possibility of a very large difference in the intensity of the reflected shocks. Main Results. We describe transition criteria from regular to irregular reflection of counter shocks: von Neumann criterion and a stationary Mach configuration criterion. Intensity dependences of the reflected intensity shocks from the interaction of colliding shock waves are presented both for the case of regular interaction, and irregular interference. We demonstrate intensity dependence of a reflected shock wave on the intensity of the two interacting shock waves, as in the transition from regular to irregular reflection, in accordance with von Neumann detaching criterion, and in accordance with a stationary Mach configuration criterion. In the first case, the transition is accompanied by an abrupt change in the intensity of the reflected shock; in the second case, the intensity varies in a continuous manner. Practical Relevance. The results supplement interference theory of stationary gas-dynamic discontinuities and are usable in the design of advanced air intakes of internal compression supersonic and hypersonic aircrafts.

No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families.

We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C0,1 to C1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C1,1, cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein-Euler equations remains open.

Head on collision of shock and breaking waves in degenerate hadronic plasmas

Astronomical compact objects, like neutron stars, are made of Fermi-Dirac distributed hadronic matter which has a wide range of densities. In this work, non-relativistic dynamics of high density hadronic plasmas with shear and bulk viscosities are studied. The propagation of localized waves in media with hadronic gas equation of state is investigated. Initially, localized lumps are propagated as breaking and shock waves in inviscid media. It is shown that in the viscous case, the localized waves can travel longer distances before changing into shock or breaking profiles.

Shock waves in Lifshitz-like spacetimes

We construct shock waves for Lifshitz-like geometries in four- and fivedimensional effective theories as well as in D3-D7 and D4-D6 brane systems. The solutions to the domain wall profile equations are found. Further, the study makes a connection with the implications for the quark-gluon plasma formation in heavy-ion collisions. According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions. We calculate the areas of trapped surfaces in the geometry of two colliding Lifshitz domain walls. Our estimates show that for five-dimensional cases with certain values of the critical exponent the dependence of multiplicity on the energy of colliding ions is rather close to the experimental data $$ \mathrm{\mathcal{M}} $$ ∼ s 0.15 observed at RHIC and LHC.

Holographic thermalization in a quark confining background

We study holographic thermalization of a strongly coupled theory inspired by two colliding shock waves in a vacuum confining background. Holographic thermalization means a black hole formation, in fact a trapped surface formation. As a vacuum confining background we considered a well know bottom-up AdS/QCD model that provides the Cornell potential as well as reproduces QCD beta-function. We perturb vacuum background by colliding domain shock waves, that are assumed to be holographically dual to heavy ions collisions. Our main physical assumption is that we can make a restriction on the time of a trapped surface production that makes a natural limitation on the size of the domain where the trapped surface is produced. This limits the intermediate domain where the main part of the entropy is produced. In this domain one can use an intermediate vacuum background as an approximation to the full confining background. In this intermediate background a dependence of the produced entropy on colliding energy is very similar to the experimental dependence of particles multiplicities on colliding ions energy obtained from RHIC and LHC. This permits us to conclude that the entropy produced in collisions of domain shock waves during a short time models rather well the experimental data.

Numerical investigations on the interaction of shock waves with spherical SF6 bubbles

Based on the simulation of large eddy current, combined with the high-precision computational scheme, the study of planar shock wave and reflected shock waves at different reflected distances, which interact with spherical SF6 bubbles, is carried out numerically in 3D. Our numerical results show clearly the deformation of spherical interface that is induced by the Richtmyer-Meshkov instability due to the collision of shock wave. Jets induced by incident shock wave and reflected shock waves are revealed, and the flow field of the interactions between the reflected shock waves at different reflected distances and the SF6 bubbles is also discussed in detail.

Radiation from a D-dimensional collision of shock waves: proof of first order formula and angular factorisation at all orders

In two previous papers we have computed the inelasticity $\epsilon$ in a head-on collision of two $D$-dimensional Aichelburg-Sexl shock waves, using perturbation theory to calculate the geometry in the future light-cone of the collision. The first order result, obtained as an accurate numerical fit, yielded the remarkably simple formula $\epsilon_{\rm 1st\, order} = 1/2 - 1/D$. Here we show, analytically, that this result is exact in first order perturbation theory. Moreover, we clarify the relation between perturbation theory and an angular series of the inelasticity's angular power around the symmetry axis of the collision $(\theta = 0,\pi)$. To establish these results, firstly, we show that at null infinity the angular dependence factorises order by order in perturbation theory, as a result of a hidden symmetry. Secondly, we show that a consistent truncation of the angular series in powers of $\sin^2 \theta$ at some order $O(n)$ requires knowledge of the metric perturbations up to $O(n+1)$. In particular, this justifies the isotropy assumption used in first order perturbation theory. We then compute, analytically, all terms that contribute to the inelasticity and depend linearly on the initial conditions (surface terms), including second order contributions.

Emergent cosmological constant from colliding electromagnetic waves

In this study we advocate the view that the cosmological constant is of electromagnetic (em) origin, which can be generated from the collision of em shock waves coupled with gravitational shock waves. The wave profiles that participate in the collision have different amplitudes. It is shown that, circular polarization with equal amplitude waves does not generate cosmological constant. We also prove that the generation of the cosmological constant is related to the linear polarization. The addition of cross polarization generates no cosmological constant. Depending on the value of the wave amplitudes, the generated cosmological constant can be positive or negative. We show additionally that, the collision of nonlinear em waves in a particular class of Born-Infeld theory also yields a cosmological constant.

Head-on collision of dust-acoustic shock waves in strongly coupled dusty plasmas

A theoretical investigation is carried out to study the propagation and the head-on collision of dust-acoustic (DA) shock waves in a strongly coupled dusty plasma consisting of negative dust fluid, Maxwellian distributed electrons and ions. Applying the extended Poincaré–Lighthill–Kuo method, a couple of Korteweg–deVries–Burgers equations for describing DA shock waves are derived. This study is a first attempt to deduce the analytical phase shifts of DA shock waves after collision. The impacts of physical parameters such as the kinematic viscosity, the unperturbed electron-to-dust density ratio, parameter determining the effect of polarization force, the ion-to-electron temperature ratio, and the effective dust temperature-to-ion temperature ratio on the structure and the collision of DA shock waves are examined. In addition, the results reveal the increase of the strength and the steepness of DA shock waves as the above mentioned parameters increase, which in turn leads to the increase of the phase shifts of DA shock waves after collision. The present model may be useful to describe the structure and the collision of DA shock waves in space and laboratory dusty plasmas.

Blast-induced dynamic rock fracture in the surfaces of tunnels

Hanging roofs or high hang-ups, a common problem in sublevel caving mining, usually result in a large ore loss and undermine mining safety. This paper analyzed the formation of a hanging roof and showed that increased confining pressure and reduced free surface were its main characteristics. In order to break down a hanging roof, a new method based on shock wave collision and stress superposition was developed. In this method, two blastholes containing multi-primer at different positions are simultaneously initiated at first. By doing this, a new free surface and a swell room can be created. After these holes are fired, a long delay time is given to the next blasthole so that the fragments from the first two-hole blasting have enough time to fall down. This new method was applied to three hanging roofs in one production area, and all of them were successfully broken down. Field inspection indicated that almost no damage was caused in the nearby drifts/tunnels due to the new method. In addition, the far field vibrations were found to be smaller than the maximum vibrations induced by some other blasts.

Effect of double-primer placement on rock fracture and ore recovery

The double-primer placement is based on the principle of shock wave collision. When two shock waves meet each other, the final pressure is greater than the sum of the initial two pressures. Stress analysis indicates that this should be favorable to rock fracture and fragmentation in blasting. This double-primer placement was tested in Malmberget mine by using electronic detonators, aiming to improve rock fragmentation. At the same time, another method, named DRB (Dividing Ring Blasting), was tested, too. Two production drifts in an ore body were taken as test drifts. In each test drift both methods were tried. For comparison, two nearest production drifts to the test drifts were taken as reference drifts. The results showed that on average the double-primer placement recovered more iron ore than either the DRB method or the ordinary method used in the reference drifts. In addition, fragmentation looked much finer and the eyebrow break became much less for the double-primer rings, compared with the reference rings.

Initiation and suppression of explosive processes in hydrogen-containing mixtures by means of permeable barriers

Experimental data on the interaction of detonation and shock waves with permeable barriers in cylindrical channels in hydrogen—air mixtures are presented. The method of soot tracks on semi-cylindrical smoked inserts made it possible to elucidate the mechanisms of initiation of the detonation downstream of the barriers. The possibility of initiating explosive processes, including detonation wave decay, is demonstrated. The numerical simulation of the detonation initiation behind the permeable barrier represented by a perforated screen is performed. Analysis of the experimental and calculation results demonstrated that in the near zone behind the barrier, detonation is initiated upon collision (focusing) of hemispherical shock waves emerging from separate holes. In the far zone, the initiation mechanism is similar to that observed on deflagration-to-detonation transition.

Lax pair, conservation laws, and multi-shock wave solutions of the DJKM equation with Bell polynomials and symbolic computation

The integrability and multi-shock wave solutions of the DJKM equation are studied by means of Bell polynomials scheme, Hirota bilinear method, and symbolic computation. A more generalized bilinear system of the DJKM equation is constructed via Bell polynomials scheme. Moreover, Lax pair and infinite conservation laws of this equation are first obtained via its corresponding Bell-polynomials-type Backlund transformation. Furthermore, the multi-shock wave solutions are also obtained by applying standard Hirota bilinear method, and the propagation and collision of shock waves are graphically demonstrated by graphs.

Longitudinal coherence in a holographic model of asymmetric collisions.

As a model of the longitudinal structure in heavy ion collisions, we simulate gravitational shock wave collisions in anti-de Sitter space in which each shock is composed of multiple constituents. We find that all constituents act coherently, and their separation leaves no imprint on the resulting plasma, when this separation is ≲0.26/T_{hyd}, with T_{hyd} the temperature of the plasma at the time when hydrodynamics first becomes applicable. In particular, the center-of-mass of the plasma coincides with the center-of-mass of all the constituents participating in the collision, as opposed to the center-of-mass of the individual collisions. We discuss the implications for nucleus-nucleus and proton-nucleus collisions.

Stationary strong magnetohydrodynamic discontinuities and pressure balanced structures in the solar wind stream

Strong disturbances of magnetic clouds in the solar wind stream are considered when solar MHD shock waves from the surrounding plasma collide with these inhomogeneities. The boundaries of the considered plasma inhomogeneities are presented as stationary tangential discontinuities. The collision of solar fast shock waves with the back and front boundaries is studied as a decomposition of an arbitrary discontinuity. It is asserted that secondary waves of rarefaction and reverse shock waves arise depending on the initial conditions. It is pointed out that a change occurs in the configuration of the plasma inhomogeneity under study, which is caused by the incoming perturbation repeatedly observed by spacecrafts.

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.