We report on the completion of the first version of a new-generation simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains state-of-the-art modules for the equations of state and thermonuclear reaction networks. The FLASH code was developed to study the problems of nuclear flashes on the surfaces of neutron stars and white dwarfs, as well as in the interior of white dwarfs. We expect, however, that the FLASH code will be useful for solving a wide variety of other problems. This first version of the code has been subjected to a large variety of test cases and is currently being used for production simulations of X-ray bursts, Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and thermonuclear flame fronts. The FLASH code is portable and already runs on a wide variety of massively parallel machines, including some of the largest machines now extant.

https://iopscience.iop.org/article/10.1086/317361/pdf

Flash: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes

FLASH: Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes

The processes that lead to charging of dust grains in a plasma are briefly reviewed. Whereas for single grains the results have been long known, the reduction of the average charge on a grain by 'Debye screening' has only recently been discovered. This reduction can be important in the Jovian ring and in the rings of Uranus. The emerging field of gravitoelectrodynamics which deals with the motion of charged grains in a planetary magnetosphere is then reviewed. Important mechanisms for distributing grains in radial distance are due to stochastic fluctuations of the grain charge and a systematic variation due to motion through plasma gradients. The electrostatic levitation model for the formation of spokes is discussed, and it is shown that the radial transport of dust contained in the spokes may be responsible for the rich radial structure in Saturn's rings. Finally, collective effects in dusty plasmas are discussed which affect various waves, such as density waves in planetary rings and low-frequency plasma waves. The possibility of charged grains forming a Coulomb lattice is briefly described.

Dusty plasmas in the solar system

Neutron Stars 1: Equation of State and Structure

Complex (dusty) plasmas: current status, open issues, perspectives

Exact results for the Madelung constants and first order anharmonic energies are given for the inverse power potentials with the Coulomb potential as the softest example. Similar exact results are obtained using the analysis of Rosenfeld on the {Gamma} {yields} {infinity} limit for the OCP internal energy, direct correlation function, screening function, and bridge functions. Knowing these exact limits for the fluid phase of the OCP allows one to determine the nature of the thermal corrections to the strongly coupled results. Solutions of the HNC equation modified with the hard sphere bridge function give an example.

Analytic Properties of The OCP Ionic Mixtures in the Strongly Coupled Fluid State

Within the random-phase approximation (RPA) or ring sum, the ground-state correlation energy for a uniform gas of charged particles with density parameter {ital r}{sub {ital s}} tends as {ital r}{sub {ital s}}{r arrow}{infinity} to ({minus}0.803 Ry) {ital r}{sub {ital s}}{sup {minus}3/4}. This limit holds for fermions, as for bosons and distinguishable particles. For electrons, the next term in the low-density expansion (of order {ital r}{sub {ital s}}{sup {minus}1}) cancels the exchange energy. Corrections to RPA must cancel the {ital r}{sub {ital s}}{sup {minus}3/4} term, and can modify the {ital r}{sub {ital s}}{sup {minus}1} term.

Low-density limit of the correlation energy in the random-phase approximation for charged particles of arbitrary statistics.

We describe a mixed expansion method that combines the best features of the virial and activity expansions The mixed expansion has the important feature that it can be applied to mixtures of plasma and neutrals that involve both attractive and repulsive interactions

Combined activity-virial expansions

The fluid to crystalline solid first order phase transition of the classical one component plasma (OCP) has been studied by Monte Carlo simulation in three dimensions for temperatures below the thermodynamic freezing temperature (Γ = Z2e2/akT = 180, a = Wigner-Zeitz radius). With N = 686 we found freezing from a metastable supercooled fluid into microcrystals for values of Γ ranging from 250 to 700. In one case, Γ = 500, the system froze into a perfect bcc lattice from a random start. With more particles the system froze into two or more crystals one bcc and one fcc and smaller examples of hcp. The lattice planes were examined and various kinds of crystal defects could be observed. We developed a program for determining the local environment of each particle as bcc, fcc, hcp, or fluid in order to identify microcrystals in the system at any stage of the freezing process. Generally freezing proceeds rapidly when any single miciutrystal attains a sufficient size or roughly 60 to 70 particles. The observations of freezing seem to agree with classical nucleation theory. No separate glass phase (non-crystalline) was seen.

H. E. DeWitt

Papers

Analytic Properties of The OCP Ionic Mixtures in the Strongly Coupled Fluid State

Low-density limit of the correlation energy in the random-phase approximation for charged particles of arbitrary statistics.

Combined activity-virial expansions

Numerical Simulation of Coulombic Freezing

Critical indices for the charged Bose gas