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Shock wave

About: Shock wave is a research topic. Over the lifetime, 36184 publications have been published within this topic receiving 635848 citations. The topic is also known as: Shock waves & shockwave.


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TL;DR: In this paper, the authors study the evolution of a supernova core from the beginning of the gravitational collapse of a 15 M☉ star up to 1 s after core bounce and compare two sets of EOS, namely, those by Lattimer and Swesty (LS-EOS) and by Shen et al. (SH-Eos).
Abstract: We study the evolution of a supernova core from the beginning of the gravitational collapse of a 15 M☉ star up to 1 s after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic ν-radiation hydrodynamics in the implicit time differencing. We aim to explore the evolution of shock waves in the long term and investigate the formation of proto-neutron stars together with supernova neutrino signatures. These studies are done to examine the influence of the equation of state (EOS) on the postbounce evolution of shock waves in the late phase and the resulting thermal evolution of proto-neutron stars. We compare two sets of EOSs, namely, those by Lattimer and Swesty (LS-EOS) and by Shen et al. (SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 ms after bounce. A revival of the shock wave does not occur even after a long period in either case. However, the recession of the shock wave appears different beyond 200 ms after bounce, having different thermal evolution of the central core. A more compact proto-neutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. The resulting spectra of supernova neutrinos are different to an extent that may be detectable by terrestrial neutrino detectors.

296 citations

Journal ArticleDOI
TL;DR: In this article, an extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems is given. But the boundary conditions are exactly the same as those for steady supersonic potential flow past an obstacle, with a special choice of the density-speed relation.
Abstract: This paper gives the extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems. The basic equations are derived in §1, using the original assumption of a functional relation between the strength of the shock wave at any point and the area of the ray tube. An analogy with steady supersonic flow is found. For the diffraction of a plane shock wave by an obstacle, the equations and boundary conditions are exactly the same as those for steady supersonic potential flow past that obstacle, with a special choice of the density-speed relation. The successive positions of the shock wave are the equipotential surfaces of the supersonic flow. The 'shock-shocks’ introduced in Part 1, i.e. discontinuities in the slope and Mach number of the shock wave, correspond to the steady oblique shock waves in the supersonic flow problem. They arise when Mach reflexion occurs.In §2 the theory is applied in detail to the diffraction of a plane shock wave by a cone. Then, in §3, a small perturbation theory is applied to the two typical problems of (i) diffraction by a slender axi-symmetrical body of general shape, and (ii) the stability of a plane shock. Many further applications would be possible and some brief comments on these are made in §4.

295 citations

Journal ArticleDOI
TL;DR: The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit, and the zero-order effect of gas diffusion on bubble response is included.
Abstract: The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit The shock wave consists of a zero rise time positive spike that falls to 0 at 1 μs followed by a negative pressure component 6 μs long with amplitudes scaled to +1000 and −160 bars, P+ and P−, respectively This pressure wave drives the Gilmore–Akulichev formulation for bubble dynamics; the zero‐order effect of gas diffusion on bubble response is included The negative pressure component of a 1000‐bar shock wave will cause a preexisting bubble in the 1‐ to 10‐μm range to expand to over 100 times its initial size, R0, for 250 μs, with a peak radius of ∼1400 μm, then collapse very violently, emitting far UV or soft x‐ray photons (black body) Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature Diffusion also increases the bubble radius fro

295 citations

Journal ArticleDOI
TL;DR: In this paper, a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations was developed. But their formalism is applicable both to ordinary non-relativistic thermal gas, and to plasmas composed of relativistic cosmic rays (CRs) and thermal gas.
Abstract: We develop a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations. Shocks play a decisive role not only for the thermalization of gas in virializing structures but also for the acceleration of relativistic cosmic rays (CRs) through diffusive shock acceleration. Our formalism is applicable both to ordinary non-relativistic thermal gas, and to plasmas composed of CRs and thermal gas. To this end, we derive an analytic solution to the one-dimensional Riemann shock tube problem for a composite plasma of CRs and thermal gas. We apply our methods to study the properties of structure formation shocks in high-resolution hydrodynamic simulations of the Lambda cold dark matter (� CDM) model. We find that most of the energy is dissipated in weak internal shocks with Mach numbers M ∼ 2 which are predominantly central flow shocks or merger shock waves traversing halo centres. Collapsed cosmological structures are surrounded by external shocks with much higher Mach numbers up to M ∼ 1000, but they play only a minor role in the energy balance of thermalization. This is because of the higher pre-shock gas densities within non-linear structures, and the significant increase of the mean shock speed as the characteristic halo mass grows with cosmic time. We show that after the epoch of cosmic reionization the Mach number distribution is significantly modified by an efficient suppression of strong external shock waves due to the associated increase of the sound speed of the diffuse gas. Invoking a model for CR acceleration in shock waves, we find that the average strength of shock waves responsible for CR energy injection is higher than that for shocks that dominate the thermalization of the gas. This implies that the dynamical importance of shock-injected CRs is comparatively large in the low-density, peripheral halo infalling regions, but is less important for the weaker flow shocks occurring in central highdensity regions of haloes. When combined with radiative dissipation and star formation, our formalism can also be used to study CR injection by supernova shocks, or to construct models for shock-induced star formation in the interstellar medium.

294 citations

Journal ArticleDOI
H.-Th. Janka1
TL;DR: In this paper, a toy model is developed for discussing the neutrino heating phase analytically, which is useful to illuminate the conditions that can lead to delayed explosions and in this sense supplements detailed numerical simulations.
Abstract: Energy deposition by neutrinos can rejuvenate the stalled bounce shock and can provide the energy for the supernova explosion of a massive star. This neutrino-heating mechanism, though investigated by numerical simulations and analytic studies, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that different groups have obtained seemingly discrepant results, and the complexity of the hydrodynamic models often hampers a clear and simple interpretation of the results. This demands a deeper theoretical understanding of the requirements of a successful shock revival. A toy model is developed here for discussing the neutrino heating phase analytically. The neutron star atmosphere between the neutrinosphere and the supernova shock can well be considered to be in hydrostatic equilibrium, with a layer of net neutrino cooling below the gain radius and a layer of net neutrino heating above. Since the mass infall rate to the shock is in general different from the rate at which gas is advected into the neutron star, the mass in the gain layer varies with time. Moreover, the gain layer receives additional energy input by neutrinos emitted from the neutrinosphere and the cooling layer. Therefore the determination of the shock evolution requires a time-dependent treatment. To this end the hydrodynamical equations of continuity and energy are integrated over the volume of the gain layer to obtain conservation laws for the total mass and energy in this layer. The radius and velocity of the supernova shock can then be calculated from global properties of the gain layer as solutions of an initial value problem, which expresses the fact that the behavior of the shock is controlled by the cumulative effects of neutrino heating and mass accumulation in the gain layer. The described toy model produces steady-state accretion and mass outflow from the nascent neutron star as special cases. The approach is useful to illuminate the conditions that can lead to delayed explosions and in this sense supplements detailed numerical simulations. On grounds of the model developed here, a criterion is derived for the requirements of shock revival. It confirms the existence of a minimum neutrino luminosity that is needed for shock expansion, but also demonstrates the importance of a sufficiently large mass infall rate to the shock. If the neutrinospheric luminosity or accretion rate by the shock are too low, the shock is weakened because the gain layer loses more mass than is resupplied by inflow. On the other hand, very high infall rates damp the shock expansion and above some threshold, the development of positive total energy in the neutrino-heating layer is prevented. Time-dependent solutions for the evolution of the gain layer show that the total specific energy transferred to nucleons by neutrinos is limited by about 1052 erg (~5 MeV per nucleon). This excludes the possibility of very energetic explosions by the neutrino-heating mechanism, because the typical mass in the gain layer is about 0.1 and does not exceed a few tenths of a solar mass. The toy model also allows for a crude discussion of the global effects of convective energy transport in the neutrino-heating layer. Transfer of energy from the region of maximum heating to radii closer behind the shock mainly reduces the loss of energy by the inward flow of neutrino-heated matter through the gain radius.

293 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023754
20221,519
2021986
2020989
20191,091
20181,064