Journal articles: 'Hugoniot states'

1

Wang, Yuntian, Xiangguo Zeng, Huayan Chen, Xin Yang, Fang Wang, and Jun Ding. "Hugoniot States and Mie–Grüneisen Equation of State of Iron Estimated Using Molecular Dynamics." Crystals 11, no. 6 (June 10, 2021): 664. http://dx.doi.org/10.3390/cryst11060664.

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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.

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Yang, Xin, Xiangguo Zeng, Chuanjin Pu, Wenjun Chen, Huayan Chen, and Fang Wang. "Molecular dynamics modeling of the Hugoniot states of aluminum." AIP Advances 8, no. 10 (October 2018): 105212. http://dx.doi.org/10.1063/1.5050426.

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Kalita, Pat, Marcus D. Knudson, Tom Ao, Caroline Blada, Jerry Jackson, Jeffry Gluth, Heath Hanshaw, and Ed Scoglietti. "Shock compression of poly(methyl methacrylate) PMMA in the 1000 GPa regime: Z machine experiments." Journal of Applied Physics 133, no. 3 (January 21, 2023): 035902. http://dx.doi.org/10.1063/5.0128681.

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Hydrocarbon polymers are used in a wide variety of practical applications. In the field of dynamic compression at extreme pressures, these polymers are used at several high energy density (HED) experimental facilities. One of the most common polymers is poly(methyl methacrylate) or PMMA, also called Plexiglass® or Lucite®. Here, we present high-fidelity, hundreds of GPa range experimental shock compression data measured on Sandia’s Z machine. We extend the principal shock Hugoniot for PMMA to more than threefold compression up to 650 GPa and re-shock Hugoniot states up to 1020 GPa in an off-Hugoniot regime, where experimental data are even sparser. These data can be used to put additional constraints on tabular equation of state (EOS) models. The present results provide clear evidence for the need to re-examine the existing tabular EOS models for PMMA above ∼120 GPa as well as perhaps revisit EOSs of similar hydrocarbon polymers commonly used in HED experiments investigating dynamic compression, hydrodynamics, or inertial confinement fusion.

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Taylor, DeCarlos E. "Molecular dynamics simulation of the Hugoniot states of boron suboxide." Materials Letters 188 (February 2017): 331–33. http://dx.doi.org/10.1016/j.matlet.2016.11.118.

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BRENNAN, JOHN K., and BETSY M. RICE. "Efficient determination of Hugoniot states using classical molecular simulation techniques." Molecular Physics 101, no. 22 (November 20, 2003): 3309–22. http://dx.doi.org/10.1080/00268970310001636404.

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6

EHRT, JULIA, and JÖRG HÄRTERICH. "ASYMPTOTIC BEHAVIOR OF SPATIALLY INHOMOGENEOUS BALANCE LAWS." Journal of Hyperbolic Differential Equations 02, no. 03 (September 2005): 645–72. http://dx.doi.org/10.1142/s0219891605000579.

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We study the longtime behavior of spatially inhomogeneous scalar balance laws with periodic initial data and a convex flux. Our main result states that for a large class of initial data the entropy solution will either converge uniformly to some steady state or to a discontinuous time-periodic solution. This extends results of Lyberopoulos, Sinestrari and Fan and Hale obtained in the spatially homogeneous case. The proof is based on the method of generalized characteristics together with ideas from dynamical systems theory. A major difficulty consists of finding the periodic solutions which determine the asymptotic behavior. To this end we introduce a new tool, the Rankine–Hugoniot vector field, which describes the motion of a (hypothetical) shock with certain prescribed left and right states. We then show the existence of periodic solutions of the Rankine–Hugoniot vector field and prove that the actual shock curves converge to these periodic solutions.

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7

Fu, Zhijian, Xianming Zhang, Rui Wang, Huayang Sun, Yangshun Lan, Jihong Xia, Zhiguo Li, and Jing Song. "Ab Initio Study of Structure and Transport Properties of Warm Dense Nitric Oxide." Inorganics 10, no. 8 (August 18, 2022): 120. http://dx.doi.org/10.3390/inorganics10080120.

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The structure, equation of state and transport properties of warm dense nitric oxide (NO) were investigated in wide density and temperature ranges by ab initio molecular dynamics simulations. Both the Perdew–Burke–Ernzerhof (PBE) and the strongly constrained and appropriately normed functional with revised Vydrov–van Voorhis nonlocal correlation (SCAN−rVV10) functionals were used in the simulations, and the pressures predicted by the SCAN−rVV10 functional were found to be systematically lower than those predicted using PBE and experimental data along the shock Hugoniot curve. Along the Hugoniot curve, as density increased, we found that the system transformed towards a mixture of atomic nitrogen and oxygen liquids with molecular NO that remained present up to the highest densities explored. The electrical conductivity along Hugoniot indicated that nonmetal to metal transition had taken place. We also calculated the electrical and thermal conductivities of nitric oxide in the warm dense matter regime, and used them to compute the Lorentz number. In addition, we also report the electronic density of states.

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GODWAL, B. K., R. S. RAO, A. K. VERMA, M. SHUKLA, H. C. PANT, and S. K. SIKKA. "Equation of state of condensed matter in laser-induced high-pressure regime." Laser and Particle Beams 21, no. 4 (October 2003): 523–28. http://dx.doi.org/10.1017/s0263034603214075.

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We have simulated the shock Hugoniot of copper and uranium based on the results of first principles electronic structure calculations. The room temperature isotherm has been obtained by evaluating the accurate ground state total energies at various compressions, and the thermal and electronic excitation contributions were obtained by adopting isotropic models using the results obtained by the band structure calculations. Our calculations ensure smooth consideration of pressure ionization effects as the relevant core states are treated in the semi-core form at the ambient pressure. The pressure variation of the electronic Grüneisen parameter was estimated for copper using the band structure results, which leads to good agreement of the simulated shock Hugoniot with the measured shock data. The simulation results obtained for U are also compared with the experimental data available in literature and with our own data.

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9

LIU, GAOMIN, FUPING ZHANG, JINMEI DU, HUA TAN, and HONGLIANG HE. "PHASE TRANSITION AND CURRENT PROPERTIES OF PZT 95/5-2NB FERROELECTRIC CERAMIC UNDER DYNAMIC LOADING." International Journal of Modern Physics B 22, no. 09n11 (April 30, 2008): 1171–76. http://dx.doi.org/10.1142/s0217979208046499.

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The high density ferroelectric ceramic with composition near Pb 0.99( Zr 0.95 Ti 0.05)0.98 Nb 0.02 O 3 ( PZT 95/5-2 Nb ) has been studied under dynamic loading. To characterize its ferroelectric-to-antiferroelectric(FE/AFE) phase transition under shock wave compression, reverse-impact experiments were conducted to determine the Hugoniot states of poled and unpoled PZT 95/5-2 Nb , and the shock-induced depoling currents were examined in an external circuit under short-circuit conditions for the poled PZT 95/5-2 Nb . The Hugoniot data and current results identify that the phase transition of FE/AFE has occured in the stress range of 0.4 GPa~1.8 GPa. In the phase transition stress range, the measured short-circuit currents show the increasing of rise time and the decreasing of final levels with the increase of shock stress.

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10

GAVRILYUK, S. L., and R. SAUREL. "Rankine–Hugoniot relations for shocks in heterogeneous mixtures." Journal of Fluid Mechanics 575 (March 2007): 495–507. http://dx.doi.org/10.1017/s0022112006004496.

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The conservation of mass, momentum and energy are not sufficient to close a system of jump relations for shocks propagating in a heterogeneous mixture of compressible fluids. We propose here a closed set of relations corresponding to a two-stage structure of shock fronts. At the first stage, microkinetic energy due to the relative motion of mixture components is produced at the shock front. At the second stage, this microkinetic energy disappears inducing strong variations in the thermodynamical states that reach mechanical equilibrium. The microkinetic energy produced at the shock front is estimated by using an idea developed earlier for turbulent shocks in compressible fluids. The relaxation zone between the shocked state and the equilibrium state is integrated over a thermodynamic path a justification of which is provided. Comparisons with experiments on shock propagation in a mixture of condensed materials confirm the proposed theory.

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11

Liu, Tai-Ping. "Shock waves in Euler equations for compressible medium." Journal of Hyperbolic Differential Equations 18, no. 03 (September 2021): 761–87. http://dx.doi.org/10.1142/s0219891621500235.

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Shock waves of arbitrary strength in the Euler equations for compressible media are studied. The admissibility condition for a shock wave is shown to be equivalent to its formation according to the entropy production criterion. The Riemann problem with large data has a unique admissible solutions. These quantitative results are based on the exact global expressions for the basic physical variables as the states move along the Hugoniot and wave curves.

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12

Wang, Aiju, Wangxun Yu, and Yanyan Zhang. "The Interaction of Waves in the Zero-Pressure Euler Equations with a Coulomb-Like Friction Term." Mathematical Problems in Engineering 2022 (February 28, 2022): 1–6. http://dx.doi.org/10.1155/2022/4837968.

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In this study, the interaction of waves in the zero-pressure Euler equations with a Coulomb-like friction term is considered, which is equivalent to the Riemann problem with three constant initial states for the zero-pressure Euler equations. By solving generalized Rankine–Hugoniot relations under suitable entropy conditions, four different structures of explicit solutions are obtained uniquely, in which the interactions among contact discontinuity, vacuum, and delta shock are presented.

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13

Zaretsky, E., and G. Ben-Dor. "Thermodynamic Law of Corresponding Shock States in Flexible Polymeric Foams." Journal of Engineering Materials and Technology 118, no. 4 (October 1, 1996): 493–502. http://dx.doi.org/10.1115/1.2805947.

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Based on thermodynamic considerations and experimental data on isothermal compression of elastomeric foams, a simple equation of state of flexible polymeric foams was developed. The developed equation of state is, in fact, a simple universal function relating the thermodynamic properties of the material of which the skeleton of the foam is made and the foam porosity. It was shown that the Hugoniot adiabat of foams, whose porosity is less than 0.3 and which are exposed to moderate shocks, could be expressed in a form similar to that of bulk solids, i.e., D = Co + Su, where D is the shock front velocity, Co is the speed of sound, u is the particle velocity and S is the maximum material compressibility.

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14

Gedalin, Michael, Michal Golan, Nikolai V. Pogorelov, and Vadim Roytershteyn. "Change of Rankine–Hugoniot Relations during Postshock Relaxation of Anisotropic Distributions." Astrophysical Journal 940, no. 1 (November 1, 2022): 21. http://dx.doi.org/10.3847/1538-4357/ac958d.

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Abstract Collisionless shocks channel the energy of the directed plasma flow into the heating of the plasma species and magnetic field enhancement. The kinetic processes at the shock transition cause the ion distributions just behind the shock to be nongyrotropic. Gyrotropization and subsequent isotropization occur at different spatial scales. Accordingly, for a given upstream plasma and magnetic field state, there would be different downstream states corresponding to the anisotropic and isotropic regions. Thus, at least two sets of Rankine–Hugoniot relations are needed, in general, to describe the connection of the downstream measurable parameters to the upstream ones. We establish the relation between the two sets.

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15

Renganathan, P., T. S. Duffy, and Y. M. Gupta. "Hugoniot states and optical response of soda lime glass shock compressed to 120 GPa." Journal of Applied Physics 127, no. 20 (May 29, 2020): 205901. http://dx.doi.org/10.1063/5.0010396.

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16

Knudson, M. D., J. R. Asay, and C. Deeney. "Adiabatic release measurements in aluminum from 240-to500-GPa states on the principal Hugoniot." Journal of Applied Physics 97, no. 7 (April 2005): 073514. http://dx.doi.org/10.1063/1.1863421.

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17

Zhang, Wei, Jin Song Bai, and De Jun Sun. "A Multi-State HLL Approximate Riemann Solver for Solid/Vacuum Riemann Problem." Applied Mechanics and Materials 872 (October 2017): 393–98. http://dx.doi.org/10.4028/www.scientific.net/amm.872.393.

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A new multi-state HLLD (‘‘D’’ stands for Discontinuities.) approximate Riemann solver for Riemann problem of nonlinear elastic solid is developed based on the assumption that a wave configuration for the solution that consists of five waves (two slow waves, two fast waves and a contact discontinuity) separating six constant states. Since the intermediate states satisfied with the Rankine-Hugoniot relations in this approximate Riemann system are analytically obtained, the HLLD Riemann solver can be constructed straightforwardly. The Piecewise Parabolic Method (PPM) is used directly to construct high-order finite-volume schemes. Numerical tests demonstrate that the scheme PPM coupled with HLLD is robust and efficient. It indicates that the scheme PPM+ HLLD can be useful in practical applications for the non-linear elasticity.

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18

Bhatt, Nisarg K., A. B. Patel, A. Y. Vahora, P. R. Vyas, B. Y. Thakore, and Ashvin R. Jani. "Structural and Vibrational Properties of FeO Using First-Principles." Advanced Materials Research 665 (February 2013): 49–52. http://dx.doi.org/10.4028/www.scientific.net/amr.665.49.

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We have studied the equation of states and vibrational properties of FeO using DFT based plane-wave pseudopotential (PW-DFT) within the generalized gradient approximation. The calculated cohesive properties at ambient condition, namely, lattice constant (a0), bulk modulus (B0) and its first pressure derivative (), are reported for B1-phase of FeO, in agreement with previous experimental and other theoretical results. A linear-response approach to the density functional theory was used to derive the phonon frequencies and phonon density of state (p-dos). Further, in order to calculate both static and dynamic equations of states, nearest-neighbour second-moment tight-binding energy model (TB-SMA) was used. Parameters of the present TB-SMA model were determined by the presentab initiopseudopotential calculations. It is found that the present simple TB-SMA scheme is able to mimic shock Hugoniot for such oxides correctly.

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19

Min, Sa Hoon, and Max L. Berkowitz. "A comparative computational study of coarse-grained and all-atom water models in shock Hugoniot states." Journal of Chemical Physics 148, no. 14 (April 14, 2018): 144504. http://dx.doi.org/10.1063/1.5011968.

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20

Setchell, Robert E. "Shock wave compression of the ferroelectric ceramic Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3: Hugoniot states and constitutive mechanical properties." Journal of Applied Physics 94, no. 1 (July 2003): 573–88. http://dx.doi.org/10.1063/1.1578526.

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21

Wu, Kailiang, Zhicheng Yang, and Huazhong Tang. "A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics." East Asian Journal on Applied Mathematics 4, no. 2 (May 2014): 95–131. http://dx.doi.org/10.4208/eajam.101013.100314a.

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AbstractA third-order accurate direct Eulerian generalised Riemann problem (GRP) scheme is derived for the one-dimensional special relativistic hydrodynamical equations. In our GRP scheme, the higher-order WENO initial reconstruction is employed, and the local GRPs in the Eulerian formulation are directly and analytically resolved to third-order accuracy via the Riemann invariants and Rankine-Hugoniot jump conditions, to get the approximate states in numerical fluxes. Unlike a previous second-order accurate GRP scheme, for the non-sonic case the limiting values of the second-order time derivatives of the fluid variables at the singular point are also needed for the calculation of the approximate states; while for the sonic case, special attention is paid because the calculation of the second-order time derivatives at the sonic point is difficult. Several numerical examples are given to demonstrate the accuracy and effectiveness of our GRP scheme.

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22

Henis, Zohar, Shalom Eliezer, and Erez Raicher. "Collisional shock waves induced by laser radiation pressure." Laser and Particle Beams 37, no. 03 (July 11, 2019): 268–75. http://dx.doi.org/10.1017/s0263034619000478.

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AbstractThe formation of a collisional shock wave by the light pressure of a short-laser pulse at intensities in the range of 1018–1023 W/cm2 is considered. In this regime the thermodynamic parameters of the equilibrium states, before and after the shock transition, are related to the relativistic Rankine–Hugoniot equations. The electron and ion temperatures associated with these shock waves are calculated. It is shown that if the time scale of energy dissipation is shorter than the laser pulse duration a collisional shock is formed. The electrons and the ions in the shock-heated layer may have equal or different temperatures, depending on the laser pulse duration, the material density and the laser intensity. This shock wave may serve as a heating mechanism in a fast ignition scheme.

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23

Lemke, R. W., D. H. Dolan, D. G. Dalton, J. L. Brown, K. Tomlinson, G. R. Robertson, M. D. Knudson, et al. "Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions." Journal of Applied Physics 119, no. 1 (January 7, 2016): 015904. http://dx.doi.org/10.1063/1.4939675.

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24

Gedalin, M. "Combining Rankine–Hugoniot relations, ion dynamics in the shock front, and the cross-shock potential." Physics of Plasmas 29, no. 11 (November 2022): 112904. http://dx.doi.org/10.1063/5.0120578.

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Rankine–Hugoniot relations (RH) connect the upstream and downstream plasma states. They allow us to determine the magnetic compression, the density compression, and the plasma heating as functions of the Mach number, shock angle, and upstream temperature. RH are based on the conservation laws in the hydrodynamical form. In collisionless shocks, the ion distributions behind the shock transition are determined by ion dynamics in the macroscopic fields of the shock front. The ion parameters upon crossing the shock are directly related to the magnetic compression and the cross-shock potential. For given upstream parameters, RH provide the magnetic compression. If there is no substantial overshoot, an analytical estimate provides the cross-shock potential as a function of the magnetic compression and the Mach number. Numerical tracing of ions across a shock profile with the derived parameters provides the ion pressure, which is in good agreement with the combination of the two theoretical approaches.

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25

Gojani, A. B., K. Ohtani, K. Takayama, and S. H. R. Hosseini. "Shock Hugoniot and equations of states of water, castor oil, and aqueous solutions of sodium chloride, sucrose and gelatin." Shock Waves 26, no. 1 (April 8, 2009): 63–68. http://dx.doi.org/10.1007/s00193-009-0195-9.

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26

Wu, Jizhou, Felipe González-Cataldo, François Soubiran, and Burkhard Militzer. "The phase diagrams of beryllium and magnesium oxide at megabar pressures." Journal of Physics: Condensed Matter 34, no. 14 (February 1, 2022): 144003. http://dx.doi.org/10.1088/1361-648x/ac4b2a.

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Abstract We perform ab initio simulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wu et al 2021 Phys. Rev. B 104 014103) and MgO (Soubiran and Militzer 2020 Phys. Rev. Lett. 125 175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon–Glazel fit T m(P) = T 0(1 + P/a)1/c , where T 0 = 1564 K, a = 15.8037 GPa and c = 2.4154 for Be, while T 0 = 3010 K, a = 10.5797 GPa and c = 2.8683 for the MgO in the B1. For the B2 phase, we use the values a = 26.1163 GPa and c = 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid–solid–liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.

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Hwang, Yao-Hsin, Ho-Shuenn Huang, Nien-Mien Chung, and Pai-Yi Wang. "Particle method of characteristics (PMOC) for unsteady pipe flow." Journal of Hydroinformatics 15, no. 3 (December 18, 2012): 780–97. http://dx.doi.org/10.2166/hydro.2012.116.

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A novel particle method of characteristics (PMOC) to simulate unsteady pipe flows is introduced and validated in the present study. Contrary to the conventional method of characteristics (MOC), the present formulation is built by reallocating the computational nodes along the characteristic lines. Both the right- and left-running characteristics are accurately traced and imitated with their associated computational particles. The annoying numerical inconveniences in the fixed-grid arrangement due to incompatible Courant–Friedrichs–Lewy (CFL) condition by repeating solution interpolations is effectively eliminated. Special particles with dual states satisfying the Rankine–Hugoniot relations are deliberately imposed to emulate the shock structure. Efficacy of this formulation is verified by solving some benchmark problems with significant transient effects in pipe flows. Computational results of piezometric head and flow velocity are meticulously compared with available analytical solutions. It is concluded that the proposed PMOC will be a useful tool to replicate transient phenomena in pipe flows.

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ASAKURA, FUMIOKI, and MITSURU YAMAZAKI. "VISCOUS SHOCK PROFILES FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH AN UMBILIC POINT." Journal of Hyperbolic Differential Equations 06, no. 03 (September 2009): 483–524. http://dx.doi.org/10.1142/s0219891609001903.

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This article analyzes the existence of viscous shock profiles joining two states satisfying the Rankine–Hugoniot condition that comes from hyperbolic 2 × 2 systems of conservation laws having quadratic flux functions with an isolated umbilic point: the point where the characteristic speeds coincide and the Jacobian matrix of the flux functions is diagonalizable. The systems studied in this note are particularly in Schaeffer and Shearer's cases I and II which are relevant to the three-phase Buckley–Leverett model for oil reservoir flow. It is shown that any compressive and overcompressive shocks have a viscous shock profile provided that there are no undercompressive shock with viscous profile having the same propagation speed. The idea of the proof is a generalization of the first theorem of Morse to noncompact level sets. It is also shown that there exists a shock satisfying the Liu–Oleĭnik condition but having no viscous shock profile. In this case, there is an undercompressive shock with viscous shock profile.

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Batani, Dimitri, Stefano Paleari, Tommaso Vinci, Roberto Benocci, Keisuke Shigemori, Yoichiro Hironaka, Toshihiko Kadono, and Akiyuki Shiroshita. "Advances in the investigation of shock-induced reflectivity of porous carbon." Laser and Particle Beams 31, no. 3 (July 2, 2013): 457–64. http://dx.doi.org/10.1017/s026303461300030x.

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AbstractWe studied the behavior of porous carbon compressed by laser-generated shock waves. In particular, we developed a new design for targets, optimized for the investigation of carbon reflectivity at hundred-GPa pressures and eV/k temperatures. Specially designed “two-layer-two materials” targets, comprising porous carbon on transparent substrates, allowed the probing of carbon reflectivity and a quite accurate determination of the position in the P, T plane. This was achieved by the simultaneous measurement of shock breakout times, sample temperature (by optical pyrometry) and uid velocity. The experiments proved the new scheme is reliable and appropriate for reflectivity measurements of thermodynamical states lying out of the standard graphite or diamond hugoniot. An increase of reflectivity in carbon has been observed at 260 GPa and 14,000 K while no increase in reflectivity is found at 200 GPa and 20,000 K. We also discuss the role of numerical simulations in the optimization of target parameters and in clarifying shock dynamics.

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Navas-Montilla, A., P. Solán-Fustero, J. Murillo, and P. García-Navarro. "Discontinuous Galerkin well-balanced schemes using augmented Riemann solvers with application to the shallow water equations." Journal of Hydroinformatics 22, no. 5 (April 17, 2020): 1038–58. http://dx.doi.org/10.2166/hydro.2020.206.

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Abstract High order methods are becoming increasingly popular in shallow water flow modeling motivated by their high computational efficiency (i.e. the ratio between accuracy and computational cost). In particular, Discontinuous Galerkin (DG) schemes are very well suited for the resolution of the shallow water equations (SWE) and related models, being a competitive alternative to the traditional finite volume schemes. In this work, a novel framework for the construction of DG schemes using augmented Riemann solvers is proposed. Such solvers incorporate the source term at cell interfaces in the definition of the Riemann problem, allowing definition of two different inner states in the so-called star region. The benefits of this family of solvers lie in the exact preservation of the Rankine–Hugoniot condition at cell interfaces at the discrete level, ensuring the preservation of equilibrium solutions (i.e. the well-balanced property) without requiring extra corrections of the numerical fluxes. The semi-discrete DG operator becomes nil automatically under equilibrium conditions, provided the use of suitable quadrature rules. The proposed scheme is applied to the Burgers' equation with geometric source term and to the SWE. The numerical results evidence that the proposed scheme achieves the prescribed convergence rates and preserves the equilibrium states of relevance with machine precision.

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Rastogi, Vinay, Raymond F. Smith, Damian C. Swift, Richard Briggs, Martin G. Gorman, Connor Krill, Amy L. Coleman, et al. "Femtosecond diffraction studies of the sodium chloride phase diagram under laser shock compression." Journal of Applied Physics 132, no. 8 (August 28, 2022): 085901. http://dx.doi.org/10.1063/5.0094894.

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The phase diagram of sodium chloride (NaCl) under laser shock compression has been studied at Linac Coherent Light Source (LCLS) at the x-ray free-electron laser facility. Both solid–solid (B1 → B2) and solid–liquid (B2 → liquid) transitions have been observed along the Hugoniot over nanosecond time scales. By combining structural measurements through in situ x-ray diffraction, pressure determination through velocimetry, and a thermal equation-of-state, the shock-compressed data are used to constrain the phase diagram of NaCl. Transformation into the B2 phase is found to occur at 28(2) GPa, and B2–liquid coexistence is observed between 54(4) and 66(6) GPa, with near full melt at 66(6) GPa. Late-time pressure release from an initial shocked B2-state results in a B2 → B1 back transformation. Our results show agreement with previous static compression data, suggesting that the time scale for melting is very rapid and that equilibrium states in NaCl are being accessed over nanosecond time scales. A multiphase equation-of-state description of NaCl incorporated into a one-dimensional hydrocode is used to interpret pressure and temperature evolution over these rapid time scales.

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Christenson, Joel G., Laurence E. Fried, Sorin Bastea, Michael H. Nielsen, Trevor M. Willey, and Michael Bagge-Hansen. "The role of detonation condensates on the performance of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) detonation." Journal of Applied Physics 132, no. 9 (September 7, 2022): 095901. http://dx.doi.org/10.1063/5.0091799.

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Thermochemical models of detonation are widely used to estimate energy delivery, but they are based on the assumption that the carbon-rich condensates (soot) formed during detonation are very similar to bulk carbon. We present an analytic equation of state (EOS) based on experimental detonation data for soot formed during the detonation of triaminotrinitrobenzene (TATB)-based high explosives. X-ray photoelectron spectra of several detonation soots are used to determine the elemental nitrogen abundance, with surprisingly high values for TATB. The proposed TATB soot EOS is highly compressible at low pressures and shares some features of glassy carbon, exhibiting graphite- and diamond-like behavior as a function of pressure. We demonstrate the influence of formed soot on detonation performance, including a lowering of the detonation velocity at typical charge densities, and a more compressive product Hugoniot at overdriven conditions. The soot model improves the accuracy of thermochemical calculations for TATB-based explosives across a wide range of states. Detonation velocity predictions for HMX (cyclotetramethylene-tetranitramine)-TATB blends with 80% or more TATB content, as well predictions for 1,3-diamino-2,4,6-trinitrobenzene (DATB) and 3-nitro-1,2,4-triazol-5-one (NTO), which share some features with TATB, are also improved.

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MYONG, R. S., and P. L. ROE. "Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system." Journal of Plasma Physics 58, no. 3 (October 1997): 485–519. http://dx.doi.org/10.1017/s002237789700593x.

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The present study consists of two parts. Here in Part 1, a model set of conservation laws exactly preserving the MHD hyperbolic singularities is investigated to develop the general theory of the nonlinear evolution of MHD shock waves. Great emphasis is placed on shock admissibility conditions. By developing the viscosity admissibility condition, it is shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. In contrast, it turns out that the evolutionary condition is inappropriate for determining physically relevant MHD shocks. In the general non-planar case, by studying canonical cases, we show that the solution of the Riemann problem is not necessarily unique – in particular, that it depends not only on reference states but also on the associated internal structure. Finally, the stability of intermediate shocks is discussed, and a theory of their nonlinear evolution is proposed. In Part 2, the theory of nonlinear waves developed for the model is applied to the MHD problem. It is shown that the topology of the MHD Hugoniot and wave curves is identical to that of the model problem.

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Poliukhin, A. S., S. A. Dyachkov, A. A. Malyugin, and P. R. Levashov. "A wide-range semiclassical self-consistent average atom model." Physics of Plasmas 30, no. 1 (January 2023): 012711. http://dx.doi.org/10.1063/5.0130872.

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The discovery of material properties at extremes, which are essential for high energy density physics development, requires the most advanced experimental facilities, theories, and computations. Nowadays, it is possible to model properties of matter in such conditions using the state-of-the-art density functional theory (DFT) or path-integral Monte Carlo approaches with remarkable precision. However, fundamental and computational limitations of these methods impede their practical usage, while wide-range thermodynamic and transport models of plasma are required. As a consequence, an average atom (AA) framework is still relevant today and has been attracting more and more attention lately. The self-consistent field and electron density in an atomic cell is usually obtained using the Thomas–Fermi (TF), Hartree–Fock, Kohn–Sham approaches, or their extensions. In this study, we present the AA model, where semiclassical wave functions are used for bound states, while free electrons are approximated by the TF model with a thermodynamically consistent energy boundary. The model is compared in various regions of temperatures and pressures with the reference data: the Saha model for rarefied plasma, DFT for warm dense matter, and experimental shock Hugoniot data. It is demonstrated that a single AA model may provide a reasonable agreement with the established techniques at low computational cost and with stable convergence of the self-consistent field.

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Winey, J. M., Y. Toyoda, and Y. M. Gupta. "Shock-induced chemical decomposition and overdriven detonation in hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) single crystals." Journal of Applied Physics 132, no. 9 (September 7, 2022): 095905. http://dx.doi.org/10.1063/5.0108463.

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Understanding the differences in the shock compression and detonation response of insensitive high explosives (IHEs) and conventional HEs (CHEs) is a long-standing need in HE science and technology. Having previously examined 1,1-diamino-2,2-dinitroethene (FOX-7) IHE single crystals [Winey et al., J. Appl. Phys. 130, 015902 (2021)], the shock and detonation response of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX)—a widely used CHE—was determined using wave profile measurements in ∼250 μm thick single crystals shock compressed to 63 GPa. In marked contrast to FOX-7, RDX single crystals shocked along the [100] and [111] orientations showed wave profile features consistent with chemical decomposition onset at 15 GPa. These features were more pronounced for [100] RDX, suggesting a higher decomposition rate compared to [111] RDX. At 51 GPa and above, flat-topped single waves were observed for both orientations, showing the classic Chapman–Jouget (C–J) detonation response in which the decomposition is completed within the detonation front. The Hugoniot states and sound speeds determined for the detonation products were similar for both [100] and [111] orientations, showing that the overdriven detonation response for RDX does not depend on crystal orientation. The C–J pressure for RDX single crystals (35 GPa)—determined experimentally—is comparable to that of FOX-7. However, compared to FOX-7, chemical decomposition onset for RDX occurs at much lower pressures and the overdriven C–J detonation response occurs at higher pressures. The present findings constitute the first experimental comparison of the shock and detonation response of conventional and insensitive HE single crystals over a broad pressure range below and above the C–J pressure.

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SINGH, CHANDRA B., and SANDIP K. CHAKRABARTI. "MODEL DEPENDENCE OF OUTFLOW RATES FROM AN ACCRETION DISK IN PRESENCE OF A DISSIPATIVE STANDING SHOCK." International Journal of Modern Physics D 20, no. 13 (December 23, 2011): 2507–23. http://dx.doi.org/10.1142/s0218271811020482.

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Solutions of black hole accretion flows with axisymmetric shocks are obtained self-consistently when the dissipation at the post-shock flow is taken into account. The Rankine–Hugoniot relationships had to be modified suitably to incorporate the energy loss as well as possible matter loss due to outflows in the post-shock region. The outflow rate from the post-shock region is also computed self-consistently. This was done by considering the quantities in the subsonic post-shock flow as the initial condition for the conical outflow. We have several major results: we find the analytical expression of the ratio of the outflow rate and the inflow rate Rṁ. We find that Rṁ strongly depends on the model assumptions which govern the flow geometry. It appears that, (a) the outflow rate is at most a few percent of the inflow rate, (b) the outflow is absent when the shock is relatively weak, (c) the outflow rate decreases with the increase in the energy loss at the post-shock region. These conclusions are very important as they have direct bearings on the observational effects. Since spectrally soft states are generally believed to be caused by the dominance of the soft photons and almost total loss of thermal energy of the Compton cloud by inverse Comptonization, a spectrally softer state should have less outflows. The opposite is generally true: A spectrally harder state will have a stronger outflow, but the result depends on the compression ratio and the adopted model. The other major result is that the model independence of the transonic properties of the flow does not hold in presence of the loss of the energy (radiation) and mass (outflow).

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Solo, K. M., S. B. Collins, L. G. Schneider, M. R. Hajimorad, F. A. Hale, J. B. Wilkerson, A. S. Windham, D. H. Byrne, and M. T. Windham. "Evaluation of Rosa Species Accessions for Resistance to Eriophyid Mites1." Journal of Environmental Horticulture 37, no. 4 (December 1, 2019): 108–12. http://dx.doi.org/10.24266/0738-2898-37.4.108.

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Abstract Rose rosette disease, caused by rose rosette virus (RRV), is an epidemic affecting nearly every rose cultivar in the United States. The only hosts for Phyllocoptes fructiphilus, the eriophyid mite that vectors RRV, are Rosa species. Eighteen Rosa species were evaluated for mite resistance by collecting foliage samples from July to November in 2016 and 2017, from which mites were extracted. Mites were isolated through a series of sieves and counted using a stereomicroscope. The response variable was expressed as the number of mites per gram of optimal rose tissue. Mite data were evaluated to determine the peak week for mite populations for each year. The mite populations varied by rose species (α = 0.05) in 2016 but not 2017. Due to high variability in mite counts, the species were not as clearly distinguishable as expected. This high variability is likely due to factors such as differential growth rates of the roses, weather, presence of RRV in the rose, and the quality of the tissue collected throughout the season. Experimental design revisions are proposed for future studies looking at Rosa species resistance to eriophyid mite populations. Index words: rose rosette virus, rose rosette disease, Phyllocoptes fructiphilus Keifer, virus, vector. Species used in this study: Phyllocoptes fructiphilus (Keifer), Prairie Rose [Rosa arkansana (Porter), Forest Farm]; Carolina Rose [Rosa carolina (L.), Forest Farm]; Rosa clinophylla (Thory), Rogue Valley Rose; White Prairie Rose [Rosa foliolosa (Nutt.), Rogue Valley Rose]; White Prairie Rose [Rosa foliolosa (Nutt.) Antique Rose Emporium]; Father Hugo Rose [Rosa hugonis, Rogue Valley Rose]; Musk Rose [Rosa moschata (J. Herrm.), Antique Rose Emporium]; Multiflora Rose [Rosa multiflora (Thunb.)]; Shining Rose [Rosa nitida (Willd.), Rogue Valley Rose]; Shining Rose [Rosa nitida (Willd.), Antique Rose Emporium]; Nootka Rose [Rosa nutkana (C. Presl.), Rogue Valley Rose]; Tea Rose [Rosa odorata (Andrews), Foundation Plant Services, Davis, CA]; Swamp Rose [Rosa palustris (Marshall), Antique Rose Emporium]; Swamp Rose [Rosa palustris (Marshall), Ever Blooming Antique Rose Emporium]; Chestnut Rose [Rosa roxburghii (Tratt.), Antique Rose Emporium]; ‘Plena' Chestnut Rose [Rosa roxburghii (Tratt.), Rogue Valley Rose]; Rugosa Rose [Rosa rugosa (Thunb.), Bailey's Nursery]; ‘Alba' Rugosa Rose [Rosa rugosa (Thunb.), Bailey's Nursery]; Climbing Prairie Rose [Rosa setigera (Michx.), Antique Rose Emporium]; Rosa soulieana (Crép.), Ralph Moore; Virginia Rose [Rosa virginiana (Mill.), Forest Farm]; Porterfolia Memorial Rose [Rosa wichuraiana (Crép.), Antique Rose Emporium]; Mountain Woods' Rose [Rosa woodsii (Lindl.), Rogue Valley Rose].

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Aliverdiev, Abutrab A., Dimitri Batani, Luca Antonelli, Katarzyna Jakubowska, Riccardo Dezulian, Anise A. Amirova, Gaji M. Gajiev, Manoranjan Khan, and Hem C. Pant. "Use of multilayer targets for achieving off-Hugoniot states." Physical Review E 89, no. 5 (May 12, 2014). http://dx.doi.org/10.1103/physreve.89.053101.

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Shu, Hua, Jiangtao Li, Yucheng Tu, Junjian Ye, Junyue Wang, Qili Zhang, Huiru Tian, et al. "Measurement of the sound velocity of shock compressed water." Scientific Reports 11, no. 1 (March 17, 2021). http://dx.doi.org/10.1038/s41598-021-84978-0.

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AbstractThe sound velocities of water in the Hugoniot states are investigated by laser shock compression of precompressed water in a diamond anvil cell. The obtained sound velocities in the off-Hugoniot region of liquid water at precompressed conditions are used to test the predictions of quantum molecular dynamics (QMD) simulations and the SESAME equation-of-state (EOS) library. It is found that the prediction of QMD simulations agrees with the experimental data while the prediction of SESAME EOS library underestimates the sound velocities probably due to its improper accounting for the ionization processes.

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McGonegle, D., P. G. Heighway, M. Sliwa, C. A. Bolme, A. J. Comley, L. E. Dresselhaus-Marais, A. Higginbotham, et al. "Investigating off-Hugoniot states using multi-layer ring-up targets." Scientific Reports 10, no. 1 (August 6, 2020). http://dx.doi.org/10.1038/s41598-020-68544-8.

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41

Aliverdiev, Abutrab A., Dimitri Batani, Luca Antonelli, Katarzyna Jakubowska, Riccardo Dezulian, Anise A. Amirova, Gaji M. Gajiev, Manoranjan Khan, and Hem C. Pant. "Publisher's Note: Use of multilayer targets for achieving off-Hugoniot states [Phys. Rev. E89, 053101 (2014)]." Physical Review E 89, no. 5 (May 16, 2014). http://dx.doi.org/10.1103/physreve.89.059902.

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Bret, Antoine, and Ramesh Narayan. "Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas." Journal of Plasma Physics 84, no. 6 (November 15, 2018). http://dx.doi.org/10.1017/s0022377818001125.

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Collisionless shocks follow the Rankine–Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent particle-in-cell simulations reveal a significant departure from magnetohydrodynamics behaviour for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we present a non-relativistic model of the plasma evolution through the shock front, allowing for a derivation of the downstream anisotropy in terms of the field strength. Our scenario assumes double adiabatic evolution of a pair plasma through the shock front. As a result, the perpendicular temperature is conserved. If the resulting downstream is firehose stable, then the plasma remains in this state. If unstable, it migrates towards the firehose stability threshold. In both cases, the conservation equations, together with the relevant hypothesis made on the temperature, allows a full determination of the downstream anisotropy in terms of the field strength.

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Trotta, D., L. Vuorinen, H. Hietala, T. Horbury, N. Dresing, J. Gieseler, A. Kouloumvakos, et al. "Single-spacecraft techniques for shock parameters estimation: A systematic approach." Frontiers in Astronomy and Space Sciences 9 (October 19, 2022). http://dx.doi.org/10.3389/fspas.2022.1005672.

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Spacecraft missions provide the unique opportunity to study the properties of collisionless shocks utilising in situ measurements. In the past years, several diagnostics have been developed to address key shock parameters using time series of magnetic field (and plasma) data collected by a single spacecraft crossing a shock front. A critical aspect of such diagnostics is the averaging process involved in the evaluation of upstream/downstream quantities. In this work, we discuss several of these techniques, with a particular focus on the shock obliquity (defined as the angle between the upstream magnetic field and the shock normal vector) estimation. We introduce a systematic variation of the upstream/downstream averaging windows, yielding to an ensemble of shock parameters, which is a useful tool to address the robustness of their estimation. This approach is first tested with a synthetic shock dataset compliant with the Rankine-Hugoniot jump conditions for a shock, including the presence of noise and disturbances. We then employ self-consistent, hybrid kinetic shock simulations to apply the diagnostics to virtual spacecraft crossing the shock front at various stages of its evolution, highlighting the role of shock-induced fluctuations in the parameters’ estimation. This approach has the strong advantage of retaining some important properties of collisionless shock (such as, for example, the shock front microstructure) while being able to set a known, nominal set of shock parameters. Finally, two recent observations of interplanetary shocks from the Solar Orbiter spacecraft are presented, to demonstrate the use of this systematic approach to real events of shock crossings. The approach is also tested on an interplanetary shock measured by the four spacecraft of the Magnetospheric Multiscale (MMS) mission. All the Python software developed and used for the diagnostics (SerPyShock) is made available for the public, including an example of parameter estimation for a shock wave recently observed in-situ by the Solar Orbiter spacecraft.

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Journal articles on the topic 'Hugoniot states'

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