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At least 1,585 records · Page 88

DISTURBED ZONE AND PISTON SHOCK AHEAD OF CORONAL MASS EJECTION

The 2010 June 13 coronal mass ejection (CME) propagating toward the position angle P.A. Almost-Equal-To 245 Degree-Sign (measured counterclockwise from the Sun's north pole) was studied from the SDO/AIA and SOHO/LASCO C2, C3 data. We show that ahead of the CME frontal structure, as a result of its interaction with the undisturbed solar wind, a disturbed region (with an increased and disturbed plasma density), whose size increases as the CME travels away from the Sun, emerges gradually. Discontinuity formation at the disturbed zone front is observed in the narrow P.A. Almost-Equal-To 245 Degree-Sign -250 Degree-Sign range. Its characteristics satisfy the properties of a piston collision shock. In the other directions relative to the CME motion axis (P.A. > 250 Degree-Sign and P.A. < 245 Degree-Sign ), there exists only the disturbed zone, whose density gradually decreases with distance. The discontinuity that was always observed at all distances where measurements were made is absent. The analysis of this CME and several other limb CMEs with different velocities from the MK4, LASCO C2, C3, and STEREO/COR2 data confirmed the previously established laws of piston shock formation ahead of a CME, which are as follows: (1) Shock formation ahead of a CME in a vicinity along its propagation axis may occur at various distances R = R{sub u} from the Sun's center. Its formation is determined by fulfilling a local inequality u(R) > V{sub A} (R), where u(R) is a CME velocity relative to the surrounding solar wind and V{sub A} (R) is a local Alfven velocity that is approximately equal to the velocity of fast magnetic sound in the solar corona. (2) At R < 6 R{sub Sun }, the shock front width {delta}{sub F} is on the order of the proton mean free path {lambda}{sub p}, and the mechanism for energy dissipation at the front is, apparently, collisional. (3) At R {approx}> 10-15 R{sub Sun }, one observes the formation of a new discontinuity {delta}{sup *}{sub F} << {lambda}{sub p} wide at the head of the collision front. Within limits of error, {delta}{sup *}{sub F} does not depend on R and is determined to be {delta}{sup *}{sub F} Almost-Equal-To 0.1-0.2 R{sub Sun} by the LASCO C3 spatial resolution and {delta}{sup *}{sub F} Almost-Equal-To 0.03 R{sub Sun} for COR2. This discontinuity is identified with a collisionless shock.

79 ASTRONOMY AND ASTROPHYSICS↗

PROBING SHOCK BREAKOUT AND PROGENITORS OF STRIPPED-ENVELOPE SUPERNOVAE THROUGH THEIR EARLY RADIO EMISSIONS

We study properties of early radio emission from stripped-envelope supernovae (SNe; those of Type IIb/Ib/Ic). We suggest there is a sub-class of stripped-envelope SNe based on their radio properties, including the optically well-studied Type Ic SNe (SNe Ic) 2002ap and 2007gr, showing a rapid rise to a radio peak within {approx}10 days and reaching a low luminosity (at least an order of magnitude fainter than a majority of SNe IIb/Ib/Ic). They show a decline after the peak that is shallower than that of other stripped-envelope SNe while their spectral index is similar. We show that all these properties are naturally explained if the circumstellar material (CSM) density is low and therefore the forward shock is expanding into the CSM without deceleration. Since the forward shock velocity in this situation, as estimated from the radio properties, still records the maximum velocity of the SN ejecta following the shock breakout, observing these SNe in radio wavelengths provides new diagnostics on the nature of both the breakout and the progenitor which otherwise require a quite rapid follow-up in other wavelengths. The inferred post-shock breakout velocities of SNe Ic 2002ap and 2007gr are sub-relativistic, {approx}0.3c. These are higher than that inferred for SN II 1987A, in line with suggested compact progenitors. However, these are lower than expected for a Wolf-Rayet (W-R) progenitor. It may reflect an as yet unresolved nature of the progenitors just before the explosion, and we suggest that the W-R progenitor envelopes might have been inflated which could quickly reduce the maximum ejecta velocity from the initial shock breakout velocity.

79 ASTRONOMY AND ASTROPHYSICS↗

MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

79 ASTRONOMY AND ASTROPHYSICS↗

DYNAMICS OF ASTROPHYSICAL BUBBLES AND BUBBLE-DRIVEN SHOCKS: BASIC THEORY, ANALYTICAL SOLUTIONS, AND OBSERVATIONAL SIGNATURES

Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amounts of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, the dynamics of which is markedly different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here, we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, L(t). In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling law, L{proportional_to}(t/t{sub s} ) {sup p} (with p and t{sub s} being constants) and the finite activity time case, L{proportional_to}(1 - t/t{sub s} ){sup -p}. The latter with p > 0 describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions.

79 ASTRONOMY AND ASTROPHYSICS↗

POLARIZATION STRUCTURE IN THE CORE OF 1803+784: A SIGNATURE OF RECOLLIMATION SHOCKS?

The extragalactic radio source 1803+784 is a BL Lac object that shows rapid variability and strong linear polarization. Very long baseline interferometry observations reveal that the core possesses a distinctive structure in polarized intensity with two maxima on axis and two minima symmetrically placed on either side. The approximately radial pattern of electric field polarization rods is reminiscent of the results obtained earlier by Cawthorne for conical shocks, but, individually, these do not reproduce the main features of the polarized intensity images. In numerical simulations and experiments, these shocks occur in pairs and help to stabilize jets as they adjust to changes in environment. Here, the polarization resulting from such structures is investigated using an approximate, analytical approach, by making some simple assumptions about the nature of the flow between two such shock waves. For fairly small viewing angles, it is found that a reasonable representation of the core polarization of 1803+784 can be obtained. The similarity between the observed and model polarizations supports the view that the core structure in 1803+784 represents a recollimation shock, and that such shock waves may be responsible for the first disturbance and hence brightening of the quiescent flow in astrophysical jets.

79 ASTRONOMY AND ASTROPHYSICS↗

THE INFLUENCE OF INELASTIC NEUTRINO REACTIONS WITH LIGHT NUCLEI ON THE STANDING ACCRETION SHOCK INSTABILITY IN CORE-COLLAPSE SUPERNOVAE

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light nuclei on the standing accretion shock instability (SASI). The time evolution of shock waves is calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions, and alpha particles are taken into account in the hydrodynamical simulations. In addition, the effects of ordinary charged-current interactions with nucleons is addressed in the simulations. Axial symmetry is assumed but no equatorial symmetry is imposed. We show that the heating rates of deuterons reach as high as {approx}10% of those of nucleons around the bottom of the gain region. On the other hand, alpha particles are heated near the shock wave, which is important when the shock wave expands and the density and temperature of matter become low. It is also found that the models with heating by light nuclei evolve differently in the non-linear phase of SASI than do models that lack heating by light nuclei. This result is because matter in the gain region has a varying density and temperature and therefore sub-regions appear that are locally rich in deuterons and alpha particles. Although the light nuclei are never dominant heating sources and they work favorably for shock revival in some cases and unfavorably in other cases, they are non-negligible and warrant further investigation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MAGNETOHYDRODYNAMIC SHOCK-CLUMP EVOLUTION WITH SELF-CONTAINED MAGNETIC FIELDS

We study the interaction of strong shock waves with magnetized clumps. Previous numerical work focused on a simplified scenario in which shocked clumps are immersed in a globally uniform magnetic field that extends through both the clump and the ambient medium. Here, we consider the complementary circumstance in which the field is completely self-contained within the clumps. This situation could arise naturally during clump formation via dynamical or thermal instabilities, for example, as a magnetic field pinches off from the ambient medium. Using our adaptive mesh refinement magnetohydrodynamics code AstroBEAR, we carry out a series of simulations with magnetized clumps that have different self-contained magnetic field configurations. We find that the clump and magnetic evolution are sensitive to the fraction of the magnetic field aligned with, or perpendicular to, the shock normal. The relative strength of magnetic pressure and tension in the different field configurations allows us to analytically understand the different cases of post-shock evolution. We also show how turbulence and the mixing it implies depends of the initial field configuration and suggest ways in which the observed shock-clump morphology may be used as a proxy for identifying internal field topologies a posteriori.

79 ASTRONOMY AND ASTROPHYSICS↗

STABILITY OF COSMIC-RAY MODIFIED SHOCKS: TWO-FLUID APPROACH

The stability of cosmic-ray modified shocks (CRMSs) is studied by means of numerical simulations. Owing to the nonlinear feedback of cosmic-ray (CR) acceleration, a downstream state of the modified shock can no longer be uniquely determined for given upstream parameters. It is known that up to three distinct solutions exist, which are characterized by CR production efficiency as the 'efficient', 'intermediate', and 'inefficient' branches. The stability of these solutions is investigated by performing direct time-dependent simulations of a two-fluid model. It is found that both the efficient and inefficient branches are stable even against a large-amplitude perturbation, while the intermediate one is always unstable and evolves into the inefficient state as a result of nonlinear time development. This bistable feature is robust in a wide range of parameters and does not depend on the injection model. Fully nonlinear time evolution of a hydrodynamic shock with injection results in the least efficient state in terms of CR production, consistent with the bistable feature. This suggests that the CR production efficiency in supernova remnant shocks may be lower than previously discussed in the framework of the nonlinear shock acceleration theory considering the efficient solution of the CRMS.

79 ASTRONOMY AND ASTROPHYSICS↗

Electron heating, magnetic field amplification, and cosmic-ray precursor length at supernova remnant shocks

We investigate the observability, by direct and indirect means, of a shock precursor arising from magnetic field amplification by cosmic rays. We estimate the depth of such a precursor under conditions of nonresonant amplification, which can provide magnetic field strengths comparable to those inferred for supernova remnants. Magnetic field generation occurs as the streaming cosmic rays induce a plasma return current, and it may be quenched by either nonresonant or resonant channels. In the case of nonresonant saturation, the cosmic rays become magnetized and amplification saturates at higher magnetic fields. The precursor can extend out to 10{sup 17}-10{sup 18} cm and is potentially detectable. If resonant saturation occurs, the cosmic rays are scattered by turbulence and the precursor length will likely be much smaller. The dependence of precursor length on shock velocity has implications for electron heating. In the case of resonant saturation, this dependence is similar to that in the more familiar resonantly generated shock precursor, which when expressed in terms of the cosmic-ray diffusion coefficient kappav and shock velocity v{sub s} is kappav/v{sub s} . In the nonresonantly saturated case, the precursor length declines less quickly with increasing v{sub s} . Where precursor length proportional to 1/v{sub s} gives constant electron heating, this increased precursor length could be expected to lead to higher electron temperatures for nonresonant amplification. This should be expected at faster supernova remnant shocks than studied by previous works. Existing results and new data analysis of SN 1006 and Cas A suggest some observational support for this idea.

79 ASTRONOMY AND ASTROPHYSICS↗

Simultaneous transverse oscillations of a prominence and a filament and longitudinal oscillation of another filament induced by a single shock wave

We present the first stereoscopic and Doppler observations of simultaneous transverse oscillations of a prominence and a filament and longitudinal oscillation of another filament launched by a single shock wave. Using Hα Doppler observations, we derive the three-dimensional oscillation velocities at different heights along the prominence axis. The results indicate that the prominence has a larger oscillation amplitude and damping time at higher altitude, but the periods at different heights are the same (i.e., 13.5 minutes). This suggests that the prominence oscillates like a linear vertical rigid body with one end anchored on the Sun. One of the filaments shows weak transverse oscillation after the passing of the shock, which is possibly due to the low altitude of the filament and the weakening (due to reflection) of the shock wave before the interaction. Large-amplitude longitudinal oscillation is observed in the other filament after the passing of the shock wave. The velocity amplitude and period are about 26.8 km s{sup –1} and 80.3 minutes, respectively. We propose that the orientation of a filament or prominence relative to the normal vector of the incoming shock should be an important factor for launching transverse or longitudinal filament oscillations. In addition, the restoring forces of the transverse prominence are most likely due to the coupling of gravity and magnetic tension of the supporting magnetic field, while that for the longitudinal filament oscillation is probably the resultant force of gravity and magnetic pressure.

79 ASTRONOMY AND ASTROPHYSICS↗

Numeric spectral radiation hydrodynamic calculations of supernova shock breakouts

We present here an efficient numerical scheme for solving the non-relativistic one-dimensional radiation-hydrodynamics equations including inelastic Compton scattering, which is not included in most codes and is crucial for solving problems such as shock breakout. The devised code is applied to the problems of a steady-state planar radiation mediated shock (RMS) and RMS breakout from a stellar envelope. The results are in agreement with those of a previous work on shock breakout, in which Compton equilibrium between matter and radiation was assumed and the 'effective photon' approximation was used to describe the radiation spectrum. In particular, we show that the luminosity and its temporal dependence, the peak temperature at breakout, and the universal shape of the spectral fluence derived in this earlier work are all accurate. Although there is a discrepancy between the spectral calculations and the effective photon approximation due to the inaccuracy of the effective photon approximation estimate of the effective photon production rate, which grows with lower densities and higher velocities, the difference in peak temperature reaches only 30% for the most discrepant cases of fast shocks in blue supergiants. The presented model is exemplified by calculations for supernova 1987A, showing the detailed evolution of the burst spectrum. The incompatibility of the stellar envelope shock breakout model results with observed properties of X-ray flashes (XRFs) and the discrepancy between the predicted and observed rates of XRFs remain unexplained.

79 ASTRONOMY AND ASTROPHYSICS↗

THE POSSIBLE ROLE OF CORONAL STREAMERS AS MAGNETICALLY CLOSED STRUCTURES IN SHOCK-INDUCED ENERGETIC ELECTRONS AND METRIC TYPE II RADIO BURSTS

Two solar type II radio bursts, separated by ∼24 hr in time, are examined together. Both events are associated with coronal mass ejections (CMEs) erupting from the same active region (NOAA 11176) beneath a well-observed helmet streamer. We find that the type II emissions in both events ended once the CME/shock fronts passed the white-light streamer tip, which is presumably the magnetic cusp of the streamer. This leads us to conjecture that the closed magnetic arcades of the streamer may play a role in electron acceleration and type II excitation at coronal shocks. To examine such a conjecture, we conduct a test-particle simulation for electron dynamics within a large-scale partially closed streamer magnetic configuration swept by a coronal shock. We find that the closed field lines play the role of an electron trap via which the electrons are sent back to the shock front multiple times and therefore accelerated to high energies by the shock. Electrons with an initial energy of 300 eV can be accelerated to tens of keV concentrating at the loop apex close to the shock front with a counter-streaming distribution at most locations. These electrons are energetic enough to excite Langmuir waves and radio bursts. Considering the fact that most solar eruptions originate from closed field regions, we suggest that the scenario may be important for the generation of more metric type IIs. This study also provides an explanation of the general ending frequencies of metric type IIs at or above 20-30 MHz and the disconnection issue between metric and interplanetary type IIs.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing the physics of narrow-line regions in active galaxies. iii. accretion and cocoon shocks in the liner NGC 1052

We present Wide Field Spectrograph integral field spectroscopy and Hubble Space Telescope Faint Object Spectrograph spectroscopy for the low-ionization nuclear emission line region (LINER) galaxy NGC 1052. We infer the presence of a turbulent accretion flow forming a small-scale accretion disk. We find a large-scale outflow and ionization cone along the minor axis of the galaxy. Part of this outflow region is photoionized by the active galactic nucleus and shares properties with the extended narrow-line region of Seyfert galaxies, but the inner (R≲1.0″) accretion disk and the region around the radio jet appear shock excited. The emission-line properties can be modeled by a “double-shock” model in which the accretion flow first passes through an accretion shock in the presence of a hard X-ray radiation, and the accretion disk is then processed through a cocoon shock driven by the overpressure of the radio jets. This model explains the observation of two distinct densities (∼10{sup 4} and ∼10{sup 6} cm{sup −3}) and provides a good fit to the observed emission-line spectrum. We derive estimates for the velocities of the two shock components and their mixing fractions, the black hole mass, and the accretion rate needed to sustain the LINER emission and derive an estimate for the jet power. Our emission-line model is remarkably robust against variation of input parameters and hence offers a generic explanation for the excitation of LINER galaxies, including those of spiral type such as NGC 3031 (M81).

79 ASTRONOMY AND ASTROPHYSICS↗

MAGNETOHYDRODYNAMIC SHOCKS IN AND ABOVE POST-FLARE LOOPS: TWO-DIMENSIONAL SIMULATION AND A SIMPLIFIED MODEL

Solar flares are an explosive phenomenon where super-sonic flows and shocks are expected in and above the post-flare loops. To understand the dynamics of post-flare loops, a two-dimensional magnetohydrodynamic (2D MHD) simulation of a solar flare has been carried out. We found new shock structures in and above the post-flare loops, which were not resolved in the previous work by Yokoyama and Shibata. To study the dynamics of flows along the reconnected magnetic field, the kinematics and energetics of the plasma are investigated along selected field lines. It is found that shocks are crucial to determine the thermal and flow structures in the post-flare loops. On the basis of the 2D MHD simulation, we developed a new post-flare loop model, which we defined as the pseudo-2D MHD model. The model is based on the one-dimensional (1D) MHD equations, where all variables depend on one space dimension, and all the three components of the magnetic and velocity fields are considered. Our pseudo-2D model includes many features of the multi-dimensional MHD processes related to magnetic reconnection (particularly MHD shocks), which the previous 1D hydrodynamic models are not able to include. We compared the shock formation and energetics of a specific field line in the 2D calculation with those in our pseudo-2D MHD model, and found that they give similar results. This model will allow us to study the evolution of the post-flare loops in a wide parameter space without expensive computational cost or neglecting important physics associated with magnetic reconnection.

79 ASTRONOMY AND ASTROPHYSICS↗

SHOCK STRENGTH IN SPACE AND ASTROPHYSICAL PLASMAS

The Rankine–Hugoniot (R–H) jump conditions are the most important and frequently used equations in studies of the properties of space and astrophysical plasmas during their passage through shock discontinuities. This paper revisits the R–H conditions for shocks, develops the formulation of the compression ratio, and examines its range of values and properties. The analysis expresses the downstream thermodynamic variables and the compression ratio as functions of the upstream thermodynamic variables, either for equal or different polytropic indices upstream and downstream of the shock. In the general case of space plasmas with an oblique magnetic field, the compression ratio is given by a quartic polynomial, which is reduced to a cubic trinomial when the upstream/downstream polytropic indices are equal. The special cases of magnetic fields that are perpendicular or parallel to the shock normal are also examined. In any case, the compression ratio polynomial has one degree larger order, when the upstream/downstream polytropic indices are different. Emphasis is placed on the maximum value of the compression ratio, which is known to be ∼4 for adiabatic polytropic index ∼5/3. However, the compression ratio can be much larger if the upstream/downstream polytropic indices are not equal to each other and less than one. Several other issues are investigated: (i) the entropic condition, showing that statistical mechanics and thermodynamics lead to the same relation of entropy variation; (ii) the effect of kappa distributions on jump conditions; and (iii) the upper limit of the upstream temperature for a shock to exist.

79 ASTRONOMY AND ASTROPHYSICS↗

SHOCK WAVE STRUCTURE IN ASTROPHYSICAL FLOWS WITH AN ACCOUNT OF PHOTON TRANSFER

For an accurate treatment of the shock wave propagation in high-energy astrophysical phenomena, such as supernova shock breakouts, gamma-ray bursts and accretion disks, knowledge of radiative transfer plays a crucial role. In this paper we consider one-dimensional (1D) special relativistic radiation hydrodynamics by solving the Boltzmann equation for radiative transfer. The structure of a radiative shock is calculated for a number of shock tube problems, including strong shock waves, and relativistic- and radiation-dominated cases. Calculations are performed using an iterative technique that consistently solves the equations of relativistic hydrodynamics and relativistic comoving radiative transfer. A comparison of radiative transfer solutions with the Eddington approximation and the M1 closure is made. A qualitative analysis of moment equations for radiation is performed and the conditions for the existence of jump discontinuity for non-relativistic cases are investigated numerically.

79 ASTRONOMY AND ASTROPHYSICS↗

Diffusive shock acceleration and reconnection acceleration processes

Shock waves, as shown by simulations and observations, can generate high levels of downstream vortical turbulence, including magnetic islands. We consider a combination of diffusive shock acceleration (DSA) and downstream magnetic-island-reconnection-related processes as an energization mechanism for charged particles. Observations of electron and ion distributions downstream of interplanetary shocks and the heliospheric termination shock (HTS) are frequently inconsistent with the predictions of classical DSA. We utilize a recently developed transport theory for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets. Particle energization associated with the anti-reconnection electric field, a consequence of magnetic island merging, and magnetic island contraction, are considered. For the former only, we find that (i) the spectrum is a hard power law in particle speed, and (ii) the downstream solution is constant. For downstream plasmoid contraction only, (i) the accelerated spectrum is a hard power law in particle speed; (ii) the particle intensity for a given energy peaks downstream of the shock, and the distance to the peak location increases with increasing particle energy, and (iii) the particle intensity amplification for a particular particle energy, f(x,c/c{sub 0})/f(0,c/c{sub 0}), is not 1, as predicted by DSA, but increases with increasing particle energy. The general solution combines both the reconnection-induced electric field and plasmoid contraction. The observed energetic particle intensity profile observed by Voyager 2 downstream of the HTS appears to support a particle acceleration mechanism that combines both DSA and magnetic-island-reconnection-related processes.

79 ASTRONOMY AND ASTROPHYSICS↗

Behaviour of rippled shocks from ablatively-driven Richtmyer-Meshkov in metals accounting for strength

While numerous continuum material strength and phase transformation models have been proposed to capture their complex dependences on intensive properties and deformation history, few experimental methods are available to validate these models particularly in the large pressure and strain rate regime typical of strong shock and ramp dynamic loading. In the experiments and simulations we present, a rippled shock is created by laser-ablation of a periodic surface perturbation on a metal target. The strength of the shock can be tuned to access phase transitions in metals such as iron or simply to study high-pressure strength in isomorphic materials such as copper. Simulations, with models calibrated and validated to the experiments, show that the evolution of the amplitude of imprinted perturbations on the back surface by the rippled shock is strongly affected by strength and phase transformation kinetics. Increased strength has a smoothing effect on the perturbed shock front profile resulting in smaller perturbations on the free surface. Lastly, in iron, faster phase transformations kinetics had a similar effect as increased strength, leading to smoother pressure contours inside the samples and smaller amplitudes of free surface perturbations in our simulations.

36 MATERIALS SCIENCE↗