Hugoniot States and Mie–Grüneisen Equation of State of Iron Estimated Using Molecular Dynamics

The objective of this study was to develop a micromechanical approach for determining the Mie–Grüneisen EOS parameters of iron under the Hugoniot states. The multiscale shock technique (MSST) coupled with molecular dynamics (MD) simulations was employed to describe the shocked Hugoniot relation of single-crystal (SC) and nanocrystalline (NC) iron under high pressures. The Mie–Grüneisen equation of state (EOS) parameters, the cold pressure (Pc), the cold energy (Ec), the Grüneisen coefficient (γ), and the melting temperature (Tm) are discussed. The error between SC and NC iron results was found to be less than 1.5%. Interestingly, the differences in Hugoniot state (PH) and the internal energy between SC and NC iron were insignificant, which shows that the effect of grain size (GS) under high pressures was not significant. The Pc and Ec of SC and NC iron calculated based on the Morse potential were almost the same with those calculated based on the Born–Mayer potential; however, those calculated based on the Born–Mayer potential were a little larger at high pressures. In addition, several empirical and theoretical models were compared for the calculation of γ and Tm. The Mie–Grüneisen EOSs were shown on the 3D contour space; the pressure obtained with the Hugoniot curves as the reference was larger than that obtained with the cold curves as the reference.

MHD-shock structures of astrospheres: λ Cephei -like astrospheres

ABSTRACT The interpretation of recent observations of bow shocks around O-stars and the creation of corresponding models require a detailed understanding of the associated (magneto-)hydrodynamic structures. We base our study on 3D numerical (magneto-)hydrodynamical models, which are analysed using the dynamically relevant parameters, in particular, the (magneto)sonic Mach numbers. The analytic Rankine–Hugoniot relation for HD and MHD are compared with those obtained by the numerical model. In that context, we also show that the only distance which can be approximately determined is that of the termination shock, if it is an HD shock. For MHD shocks, the stagnation point does not, in general, lie on the inflow line, which is the line parallel to the inflow vector and passing through the star. Thus an estimate via the Bernoulli equation as in the HD case is, in general, not possible. We also show that in O-star astrospheres, distinct regions exist in which the fast, slow, Alfvénic, and sonic Mach numbers become lower than one, implying subslow magnetosonic as well as subfast and subsonic flows. Nevertheless, the analytic MHD Rankine–Hugoniot relations can be used for further studies of turbulence and cosmic ray modulation.

Rapid distortion theory analysis on the interaction between homogeneous turbulence and a planar shock wave

The interactions between homogeneous turbulence and a planar shock wave are analytically investigated using rapid distortion theory (RDT). Analytical solutions in the solenoidal modes are obtained. Qualitative answers to unsolved questions in a report by Andreopoulos et al. (Annu. Rev. Fluid Mech., vol. 524, 2000, pp. 309–345) are provided within the linear theoretical framework. The results show that the turbulence kinetic energy (TKE) is increased after interaction with a shock wave and that the contributions to the amplification can be interpreted primarily as the combined effect of shock-induced compression, which is a direct consequence of the Rankine–Hugoniot relation, and the nonlinear effect, which is an indirect consequence of the Rankine–Hugoniot relation via the perturbation manner. For initial homogeneous axisymmetric turbulence, the amplification of the TKE depends on the initial degree of anisotropy. Furthermore, the increase in energy at high wavenumbers is confirmed by the one-dimensional spectra. The enstrophy is also increased; its increase is more significant than that of the TKE because of the significant increase in enstrophy at high wavenumbers. The vorticity components perpendicular to the shock-induced compressed direction are amplified more than the parallel vorticity component. These results strongly suggest that a high resolution is needed to obtain accurate results for the turbulence–shock-wave interaction. The integral length scales ($L$) and the Taylor microscales ($\unicode[STIX]{x1D706}$) are decreased for most cases after the interaction. However, $L_{22,3}(=\,L_{33,2})$ and $\unicode[STIX]{x1D706}_{22,3}(=\,\unicode[STIX]{x1D706}_{33,2})$ are amplified. Here, the subscripts 2 and 3 indicate the perpendicular components relative to the shock-induced compressed direction. The dissipation length and TKE dissipation rate are amplified.

Delta Shock Wave for the Suliciu Relaxation System

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that model viscoelastic fluids. An important issue is that the considered3×3system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data inL∞. We also study the Riemann problem for this system. Under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta-shock type solutions are established.

SHOCK HUGONIOT RELATION OF UNREACTED HETEROGENEOUS EXPLOSIVES

There is a continuing interest in determining the characteristics of unreacted plastic bonded explosives (PBXs). In this work, a Particle Velocity Comparing Method to determine the unreacted Hugoniot of heterogeneous explosive using magnetic particle velocity gauge is described. The Hugoniot for the PBXs has been measured using flyer driven by planar wave lens. A superposition principle considering unreacted explosives as composite and porous materials is presented, the unreacted Hugoniot of explosives is calculated, and the results of calculation are compared with the experiment results.