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Register a new userBenchmarking boron carbide equation of state using computation and experiment
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Boron carbide (B$_4$C) is of both fundamental scientific and practical interest in inertial confinement fusion (ICF) and high energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B$_4$C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Greens function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B$_4$C over a broad range of temperatures ($sim$6$times$10$^3$--5$times$10$^8$ K) and densities (0.025--50 g/cm$^{3}$). We assess that the largest discrepancies between theoretical predictions are $lesssim$5% near the compression maximum at 1--2$times10^6$ K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are $sim$18% and occur at temperatures between 6$times$10$^3$--2$times$10$^5$ K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. In addition, we have developed three new equation of state models and applied them to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.
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The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (ACTEX), and all-electron Greens function Korringa-Kohn-Rostoker (MECCA), and compute the pressure and internal energy of BN over a broad range of densities ($rho$) and temperatures ($T$). Our experiments were conducted at the Omega laser facility and measured the Hugoniot of BN to unprecedented pressures (12--30 Mbar). The EOSs computed using different methods cross validate one another, and the experimental Hugoniot are in good agreement with our theoretical predictions. We assess that the largest discrepancies between theoretical predictions are $<$4% in pressure and $<$3% in energy and occur at $10^6$ K. We find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the warm-dense regime. Moreover, SQ and FOE data have significantly smaller error bars than PIMC, and so represent significant advances for efficient computation at high $T$. We also construct tabular EOS models and clarify the ionic and electronic structure of BN over a broad $T-rho$ range and quantify their roles in the EOS. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material.
We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1$times$10$^4$-5.2$times$10$^8$ K) and densities (0.25-49 g/cm$^3$), and experimental shock Hugoniot data at unprecedented high pressures (5608$pm$118 GPa). The calculations are performed with full, first-principles methods combining path integral Monte Carlo (PIMC) at high temperatures and density functional theory molecular dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference $<$1.5 Hartree/boron in energy and $<$5% in pressure) at 5.1$times$10$^5$ K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semi-empirical EOS table (LEOS 50). We investigate the self diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high pressure and temperature conditions We study the performance sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on comparison of the first-principles calculations with LEOS 50 via 1D hydrodynamic simulations. The results are valuable for future theoretical and experimental studies and engineering design in high energy density research. (LLNL-JRNL-748227)
We report a numerical study of the equation of state of crystalline body-centered-cubic (BCC) hydrogen, tackled with a variety of complementary many-body wave function methods. These include continuum stochastic techniques of fixed-node diffusion and variational quantum Monte Carlo, and the Hilbert space stochastic method of full configuration-interaction quantum Monte Carlo. In addition, periodic coupled-cluster methods were also employed. Each of these methods is underpinned with different strengths and approximations, but their combination in order to perform reliable extrapolation to complete basis set and supercell size limits gives confidence in the final results. The methods were found to be in good agreement for equilibrium cell volumes for the system in the BCC phase, with a lattice parameter of 3.307 Bohr.
We present a suite of programs to determine the ground state of the time-independent Gross-Pitaevskii equation, used in the simulation of Bose-Einstein condensates. The calculation is based on the Optimal Damping Algorithm, ensuring a fast convergence to the true ground state. Versions are given for the one-, two-, and three-dimensional equation, using either a spectral method, well suited for harmonic trapping potentials, or a spatial grid.
Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can be reached and their functioning guaranteed. This review provides a brief overview of the known characterization methods of certification, benchmarking, and tomographic recovery of quantum states and processes, as well as their applications in quantum computing, simulation, and communication.
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