Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma

Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of $9.83 \times 10^{-4}\rm \leq \rho \leq 0.153 \rm gcm^{-3}$ and $5000 \leq T \leq 250 000 \rm K$. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.Comment: 12 pages, 21 figures, submitted for Phys. Rev.

All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

We develop an all-electron path integral Monte Carlo (PIMC) method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements with core electrons. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at temperatures of (2.5-7.5)$\times10^5$ K and both methods together form a coherent equation of state (EOS) over a density-temperature range of 3--12 g/cm$^3$ and 10$^4$--10$^9$ K

Numerical Investigation of the Influence of Span-wise Force Variation in Circular Cylinders Undergoing Vortex Induced Vibrations at High Reynolds Number

The focus of this research is on the development of a new approach for simulating vortex induced vibrations on marine risers at high Reynolds numbers. This method considers the span-wise variation of the lift and drag forces, and determines the moment acting on the cylinder. The predicted motion then consists of a rotational component to accompany the traditional cross-stream and stream-wise translations normally associated with vortex induced vibrations. This was accomplished by describing the motion of the cylinder using a set of springs and dampers. A moment acting on the cylinder causes the springs on one end to compress, and stretch on the other, thus rotating the cylinder. A Large Eddy Simulation (LES) computational fluid dynamics code running on 16 3Ghz processors was used to calculate the unsteady flow and at each time step the hydrodynamic forces acting on the cylinder were calculated in a separate routine based on the pressure distribution around the cylinder. This information was then used to solve two second-order ordinary differential equations, which gave the velocity and displacement of the cylinder in cross-flow and rotational planes. This information was transferred back to the code where the cylinder was displaced and another cycle of calculations was started. The simulated results showed that the correlation length was higher for a cylinder subject to pure translation compared to a cylinder free to translate and rotate in the cross-stream direction. This has implications for current numerical and experimental techniques since it has been traditionally assumed that the flow around a circular cylinder becomes two-dimensional during vortex induced vibrations. Consequently, empirical,numerical and experimental models have generally only considered cross stream and/or stream-wise translation. The extent to which the experimental apparatus or harmonic model may have influenced the behavior of the riser by eliminating span-wise amplitude variation is important information that should be considered for future riser designs

Equations of state and stability of MgSiO3_3 perovskite and post-perovskite phases from quantum Monte Carlo simulations

We have performed quantum Monte Carlo (QMC) simulations and density functional theory (DFT) calculations to study the equations of state of MgSiO$_3$ perovskite (Pv) and post-perovskite (PPv), up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground state energies were derived using QMC and the temperature dependent Helmholtz free energies were calculated within the quasi-harmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO$_3$ agree well with experiments, and better than those from generalized gradient approximation (GGA) calculations. The Pv-PPv phase boundary calculated from our QMC equations of states is also consistent with experiments, and better than previous LDA calculations. We discuss the implications for double crossing of the Pv-PPv boundary in the Earth

Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen

A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by Gaussians with the mean, width and amplitude as variational parameters. The method is illustrated for the particle in an external field problem, the hydrogen molecule and dense hydrogen where the molecular, the dissociated and the plasma regime are described. Structural and thermodynamic properties (energy, equation of state and shock Hugoniot) are presented.Comment: 26 pages, 13 figures. submitted to Phys. Rev. E, October 199

Rocky core solubility in Jupiter and giant exoplanets

Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10000 K, implying significant redistribution of rocky core material in Jupiter and larger exoplanets

Austenite to ferrite transformation kinetics during continuous cooling

The austenite decomposition has been investigated in a hypo-eutectoid plain carbon steel under continuous cooling conditions using a dilatometer and a Gleeble 1500 thermomechanical simulator. The experimental results were used to verify model calculations based on a fundamental approach for the dilute ternary systems Fe-C-Mn. The austenite to ferrite transformation start temperature can be predicted from a nucleation model for slow cooling rates. The formation of ferrite nuclei takes place with equilibrium composition on austenite grain boundaries. The nuclei are assumed to have a pill box shape in accordance with minimal interfacial energy. For higher cooling rates, early growth has to be taken into account to describe the transformation start. In contrast to nucleation, growth of the ferrite is characterized by paraequilibrium; i.e. only carbon can redistribute, whereas the diffusion of Mn is too slow to allow full equilibrium in the ternary system. However, Mn segregation to the moving ferrite-austenite interface has to be considered. The latter, in turn, exerts a solute drag effect on the boundary movement. Thus, growth kinetics is controlled by carbon diffusion in austenite modified by interfacial segregation of Mn. Employing a phenomenological segregation model, good agreement has been achieved with the measurements

The effect of differential rotation on Jupiter's low-degree even gravity moments

The close-by orbits of the ongoing Juno mission allow measuring with unprecedented accuracy Jupiter's low-degree even gravity moments J(2), J(4), J(6), and J(8). These can be used to better determine Jupiter's internal density profile and constrain its core mass. Yet the largest unknown on these gravity moments comes from the effect of differential rotation, which gives a degree of freedom unaccounted for by internal structure models. Here considering a wide range of possible internal flow structures and dynamical considerations, we provide upper bounds to the effect of dynamics (differential rotation) on the low-degree gravity moments. In light of the recent Juno gravity measurements and their small uncertainties, this allows differentiating between the various models suggested for Jupiter's internal structure.Israeli Ministry of Science; Minerva foundation; Federal German Ministry of Education and Research; Helen Kimmel Center for Planetary Science at the Weizmann Institute of Science; CNES; BSF; NSF; Juno project6 month embargo; Published Online: 19 June 2017This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Path integral Monte Carlo simulation of charged particles in traps

This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as a small perturbation. For weakly coupled systems many efficient theoretical and computational techniques do exist. However, for strongly interacting systems such as nonideal gases or plasmas, strongly correlated electrons and so on, perturbation methods fail and alternative approaches are needed. Among them, an extremely successful one is the Monte Carlo (MC) method which we are going to consider in this chapter.Comment: 18 pages, based on talks on Hareaus school on computational methods, Greifswald, September 200