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Exploring shock-shock interactions has been limited by experimental constraints, particularly in laser-induced shock experiments due to specialized equipment requirements. Herein, we introduce a tabletop approach to systematically investigate the excitation and superposition of dual laser-induced shock waves in water. Utilizing two laser pulses, spatio-temporally separated and focused into a confined water layer, we identify the optimal superposition leading to the highest combined shock pressure. Our results demonstrate that combining two shock waves each of $\sim$0.6~GPa pressure yields an overall shock pressure of $\sim$3~GPa. Our findings, suggesting an inherent nonlinear summation from the laser excitation process itself and highlights a new pathway for energy-efficient laser shock wave excitation.
The evolution of a deformed subcritical fast magnetosonic shock front is compared between two two-dimensional PIC simulations with different orientations of the magnetic field relative to the simulation box. All other initial and simulation conditions are kept identical. Shock boundary oscillations are observed in the simulation where the magnetic field direction is resolved. This oscillation is caused by the reformation of the shock front. One part of the front acts as a shock, while the other functions as a magnetic piston, with both halves changing their states in antiphase. The oscillation period corresponds to the time required for one shock wave to grow as the other collapses. In contrast, the corrugated fast magnetosonic shock does not oscillate in the second simulation, where the magnetic field is oriented out of the simulation plane. This dependence on magnetic field orientation suggests that the shock oscillation is induced by magnetic tension, which is only effective in the first simulation. In both simulations, the shock perturbation does not grow over time, indicating that the shocks are stable. The potential relevance of these findings for the Alfvénic oscillations of
Cosmic rays are charged particles that are accelerated to relativistic speeds by astrophysical shocks. Numerical models have been successful in confirming the acceleration process for (quasi-)parallel shocks, which have the magnetic field aligned with the direction of the shock motion. However, the process is less clear when it comes to (quasi-)perpendicular shocks, where the field makes a large angle with the shock-normal. For such shocks, the angle between the magnetic field and flow ensures that only highly energetic particles can travel upstream at all, reducing the upstream current. This process is further inhibited for relativistic shocks, since the shock can become superluminal when the required particle velocity exceeds the speed of light, effectively inhibiting any upstream particle flow. In order to determine whether such shocks can accelerate particles, we use the particle-in-cell (PIC) method to determine what fraction of particles gets reflected initially at the shock. We then use this as input for a new simulation that combines the PIC method with grid-based magnetohydrodynamics to follow the acceleration (if any) of the particles over a larger time-period in a two-di
Sedimentary rocks often form the upper layers or the entire target rocks in impact events. Thermodynamic properties of sedimentary rocks related to porosity and water saturation affect the process of impact crater formation. The heterogeneous distribution of sedimentary facies can complicate the development and distribution of shock effects, especially in numerical modeling. This work focuses on the shock thermodynamic properties of carbonate rocks with differing porosity textures (e.g., isolated pores, interstitial porosity, elongated pores) and water saturation levels. Using mesoscale numerical modeling, we found that water saturation reduces shock temperatures compared to those in dry, porous carbonate rocks. The orientation of elongated pores and porosity lineations influences the shock temperature distribution and rock deformation at angles of 50-90° to the shock front. Additionally, due to complex shock wave interactions, interstitial porosity is key in creating temperature zonations around larger grains.
Meso-scale simulations of energy localization at hotspots provide closure models for multiscale frameworks of shock-to-detonation transition (SDT). Validation of such meso-scale calculations is challenging as direct comparison with experiments is constrained both by limitations of data acquisition in the experiments (e.g., of temperature fields) and modeling over-simplifications in the simulations. To address the latter problem and bring modeling closer to experiments, we advance a high-fidelity meso-scale computational framework for interface-resolved reactive calculations of shock initiation in plastic-bonded explosives (PBXs). Accurate resolution of shock and interfacial dynamics is achieved through higher-order (5th-order WENO) schemes, and sharp interface treatments are implemented for physically accurate material-material interactions. Recently obtained atomistics-consistent material models are used for HMX, with the grid resolution taken down to atomistic scale (O(nm)). The crystal geometries are obtained directly from experiments via nano-CT imaging. The impacting flyer plate, energetic crystal and binder are tracked as distinct phases, and flyer-binder impact and separatio
We propose a method to learn the nonlinear impulse responses to structural shocks using neural networks, and apply it to uncover the effects of US financial shocks. The results reveal substantial asymmetries with respect to the sign of the shock. Adverse financial shocks have powerful effects on the US economy, while benign shocks trigger much smaller reactions. Instead, with respect to the size of the shocks, we find no discernible asymmetries.
The intracluster medium (ICM) is expected to experience on average about three passages of weak shocks with low sonic Mach numbers, $M\lesssim 3$, during the formation of galaxy clusters. Both protons and electrons could be accelerated to become high energy cosmic rays (CRs) at such ICM shocks via diffusive shock acceleration (DSA). We examine the effects of DSA by multiple shocks on the spectrum of accelerated CRs by including {\it in situ} injection/acceleration at each shock, followed by repeated re-acceleration at successive shocks in the test-particle regime. For simplicity, the accelerated particles are assumed to undergo adiabatic decompression without energy loss and escape from the system, before they encounter subsequent shocks. We show that in general the CR spectrum is flattened by multiple shock passages, compared to a single episode of DSA, and that the acceleration efficiency increases with successive shock passages. However, the decompression due to the expansion of shocks into the cluster outskirts may reduce the amplification and flattening of the CR spectrum by multiple shock passages. The final CR spectrum behind the last shock is determined by the accumulated e
The transmission lines we consider are constructed from the nonlinear inductors and the nonlinear capacitors. In the first part of the paper we additionally include linear ohmic resistors. Thus, the dissipation being taken into account leads to the existence of \mbox{shocks -- the} travelling waves with different asymptotically constant values of the voltage (the capacitor charge) and the current before and after the front of the wave. For the particular values of ohmic resistances (corresponding to strong dissipation) we obtain the analytic solution for the profile of a shock wave. Both the charge on a capacitor and current through the inductor are obtained as the functions of the time and space coordinate. In the case of weak dissipation, we obtain the stationary dispersive shock waves. In the second part of the paper we consider the nonlinear lossless transmission line. We formulate a simple wave approximation for such transmission line, which decouples left/right-going waves. The approximation can also be used for the lossy transmission line, which is considered in the first part of the paper, to describe the formation of the shock wave (but, of course, not the shock wave itsel
We derive the shock strength area rule for a Noble-Abel stiffened gas (NASG) equation of a state required in Whitham's geometrical shock dynamics approach to determine shock wave dynamics in dense gases, liquids and solids. An exact formulation requiring the solution of an ordinary differential equation is provided. Closed form solutions of various levels of approximations are also obtained as an expansion in shock wave strength. The leading order approximation recovers the geometrical acoustic limit, while higher order approximations account for the medium's compressibility. The exact shock strength area relation and the various order approximations are illustrated for shocks in liquid water. The simple closed form of the first order solution predicts the shock strength area rule up to shock pressures of approximately twice the stiffening pressure in water, i.e., approximately 1-2 GPa.
Nanopowder consolidation under high strain rate shock compression is a potential method for synthesizing and processing bulk nanomaterials. A thorough investigation of the shock deformation of powder materials is of great engineering significance. Here we combine nonequilibrium molecular dynamics (NEMD) simulations and X-ray diffraction (XRD) simulation methods to investigate the deformation twinning and pore compaction in shock-compressed np-Mg. Significant anisotropy and strong dependence on crystallographic orientation are presented during shock-induced deformation twinning. During the shock stage, three typical types of twins were firstly induced, namely {11-21} twin (T1), {11-22} twin (T2) and {10-12} twin (T3). Most of them were generated in grains with a larger angle between the impact direction and the c-axis of the lattice. With the increase in strain rate, the types and quantities of twins continued to enrich, but they did not occur when the strain rate was too high. We also discussed the deformation mechanisms of the three types of twins and found that the coupling of slip and shuffle dominated twin deformation. In addition, void filling occurred due to the interaction o
The origin of radio afterglows or delayed radio flares in tidal disruption events (TDEs) is not fully understood. They could be generated either by a forward shock (FS) propagating into diffuse circumnuclear medium (CNM), or a bow shock (BS) around a dense cloud, each of which is fundamentally different. To elucidate the distinctions between these two scenarios, we conducted two-fluid simulations incorporating relativistic electrons to investigate the spatial evolution of these electrons after being accelerated by shock. Based on their spatial distribution, we performed radiative transfer calculations to obtain the synchrotron spectra. In Paper I (Mou 2025), we reported the results for the FS scenario; in this article, we focus on the BS scenario. Compared to that from the FS, the radio emission from the BS exhibits a higher peak frequency, and its flux shows a much steeper rise and a more rapid decline. The radio flux from the BS also responds to fluctuations in the outflow. The combined effects of the BS and FS substantially alter radio spectra, causing significant deviations from the single-zone emission model, and in some cases producing double-peaked or flat-top features in sp
Fewer gas giants have been caught in their accretion phase than mature ones are known. Extremely Large Telescope (ELT) instruments will have a higher sensitivity and a smaller inner working angle than tools up to now, which should increase search yields. We examine what METIS, the first-generation ELT spectrograph with R=1e5, can reveal about accreting gas giants. We focus on the accessible hydrogen recombination lines, mainly Brackett alpha and Pfund-series lines. Our approach is general but we take PDS70b as a fiducial case. It is similar to WISPIT2b. To calculate high-resolution line profiles, we combine a semianalytical multi-D description of the flow onto an accreting planet and its circumplanetary disc (CPD) with local non-LTE shock-emission models. We assume the limiting scenario of no extinction, appropriate for gas giants in gaps, and negligible contribution from magnetospheric accretion. We use simulated detector sensitivities to compute needed observing times. Both the planet- and the CPD-surface shocks contribute to the line, which has a Gaussian core but wider, asymmetrical wings. The line is much narrower than the free-fall velocity, and in fact has a nearly constant
Zero viscosity limits are central to the study of classical shock waves. By identifying the correct physical (Lax admissible) shocks, they are a cornerstone in the design of analytical and numerical schemes. For relativistic fluid flow, however, the underlying dissipation mechanism, based on the Euclidean Laplace operator (so-called ``artificial viscosity''), violates Lorentz invariance, the fundamental principle of Special Relativity ensuring the speed of light bound. In this paper we show that replacing the Laplacian on conserved quantities by the wave operator on the fluid four-velocity alone, (not involving the density), provides a simplest Lorentz invariant description of dissipative relativistic fluid flow. We prove the resulting equations are causal and well-posed in one spatial dimension, and we establish their dissipativity by proving decay of Fourier Laplace modes near steady states. Moreover, we prove shock waves have profiles (a unique viscous travelling wave approximation in $L^2$) if and only if the shock wave is Lax admissible, and we prove that entropy production of travelling wave solutions is positive if and only if they obey the speed of light bound. This establi
We experimentally demonstrate laser-induced vortex shock waves formed by carbon nanotubes drilling optical fibers for the first time. Three samples of standard single-mode optical fibers (SMF) are sequentially inserted in a syringe loaded with a 1 mL solution of single-walled carbon nanotubes (CNT) and methanol, and a high-power laser is injected into the fibers for 5 (SMF 1), 10 (SMF 2), and 20 (SMF 3) minutes. The CNT solution thermally expands and generates vortex acoustic flows, which are confined in the syringe cavity, significantly increasing the velocity and impact of nanotubes at the fiber tip. The resulting shock waves achieve estimated hypersonic velocities (5742 m/s) and high pressures (6.7 GPa), overcoming the silica tensile strength and ablating structured vortices in the fibers. The material, geometry, and depth profile of the vortices are characterized, providing details of mixing carbon and silica layers, increasing radially from the fiber core center and in thickness to the cladding for longer laser periods (850 nm to 10 micron thickness). The cross-sections of the measured vortices are compared to analytical simulations, revealing unprecedented Fibonacci helices d
A common defect of the Roe scheme is the production of non-physical expansion shock and shock instability. An improved method with several advantages was presented to suppress the shock instability. However, this method cannot prevent expansion shock and is incompatible with the traditional curing method for expansion shock. Therefore, the traditional curing mechanism is analyzed. The discussion explains the effectiveness of the traditional curing method and identifies several defects, one of which leads to incompatibility between curing the shock instability and expansion shock. Consequently, a new improved Roe scheme is proposed in this study. This scheme is concise, easy to implement, low computational cost, and robust. More importantly, the scheme can simultaneously cure the shock instability and expansion shock without additional costs.
In recent years many models of chondrule formation have been proposed. One of those models is the processing of dust in shock waves in protoplanetary disks. In this model, the dust and the chondrule precursors are overrun by shock waves, which heat them up by frictional heating and thermal exchange with the gas. In this paper we reanalyze the nebular shock model of chondrule formation and focus on the downstream boundary condition. We show that for large-scale plane-parallel chondrule-melting shocks the postshock equilibrium temperature is too high to avoid volatile loss. Even if we include radiative cooling in lateral directions out of the disk plane into our model (thereby breaking strict plane-parallel geometry) we find that for a realistic vertical extent of the solar nebula disk the temperature decline is not fast enough. On the other hand, if we assume that the shock is entirely optically thin so that particles can radiate freely, the cooling rates are too high to produce the observed chondrules textures. Global nebular shocks are therefore problematic as the primary sources of chondrules.
We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1ns. The later times are calculated with the CRASH code. This code solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The produced synthetic radiographs can be used for comparison with future nozzle experiments at high-energy-density laser facil
The current literature is rather vague regarding how to calculate the exact numerical value of the resonant ion scattering cross-section that should be used for a specific bandpass of finite width. Such a value was needed in order to calculate the ion and mass densities in the shock fronts of hot, close binary star systems. This was done based on a modeling of ultraviolet wind-line profiles, using IUE spectra. Therefore, a numerical integration has been carried out, in wavelength-space, of the exact expression for the cross-section over two band-passes of astrophysical interest. The exact expression employed was that derived from a solution of the Abraham-Lorentz equation. The numerical results depend on the resonant wavelength, which is taken to be at the center of the bandpass. Most texts on the subject derive an expression for the scattering cross-section in frequency-space, based on the assumption that the radiation reaction term in the Abraham-Lorentz equation may be approximated by a resistive term. The integral of this cross-section over the entire spectrum is independent of the resonant frequency, except for the transition probability. This has limited practical use when de
Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources remain strong and interesting candidate sites for the generation of ultra-high energy cosmic rays. In this paper, key predictions of DSA at relativistic shocks that are salient to the issue of cosmic ray ion and electron production are outlined. Results from a Monte Carlo simulation of such diffusive acceleration in test-particle, relativistic, oblique, MHD shocks are presented. Simulation output is described for both large angle and small angle scattering scenarios, and a variety of shock obliquities including superluminal regimes when the de Hoffman-Teller frame does not exist. The distribution function power-law indices compare favorably with results from other techniques. They are found to depend sensitively on the mean magnetic field orientation in the shock, and the nature of MHD turbulence that propagates along fields in shock environs. An interesting regime of flat spectrum generation is addressed, providing evidence for its origin being
Wall-resolved large eddy simulations are employed to investigate the shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade. An analysis of the suction side separation bubbles forming due to the SBLIs is presented for adiabatic and isothermal (cooled) walls. Flow snapshots indicate that the separation bubble contracts and expands in a similar fashion for both thermal boundary conditions. However, the skin-friction coefficient distributions reveal a downstream displacement of the separation region when cooling is applied. The separation bubble is also smaller for this setup compared to the adiabatic one. A steeper pressure rise is observed for the isothermal wall downstream of the incident oblique shock, and this occurs because the incident shock wave gets closer to the blade surface when cooling is applied. The Reynolds stresses are computed to investigate the effects of wall temperature on the turbulence activity. While the levels of the tangential stresses are similar for the cases analyzed, those for the wall-normal component are higher for the cooled wall.