Molecular dynamics study of six-dimensional hard hypersphere crystals.

Six-dimensional hard hypersphere systems in the A, D, and E crystalline phases have been studied using event-driven molecular dynamics simulations in periodic, skew cells that reflect the underlying lattices. In all the simulations, the systems had sufficient numbers of hyperspheres to capture the first coordination shells, and the larger simulations also included the complete second coordination shell. The equations of state, for densities spanning the fluid, metastable fluid, and solid regimes, were determined.

Fluid-solid demixing in four and five dimensional asymmetric binary hard hypersphere mixtures.

Additive asymmetric binary mixtures of hard hyperspheres in four and five dimensions are investigated by Monte Carlo simulations. These investigations probe systems with diameter ratios of 0.4 and 0.

Five dimensional binary hard hypersphere mixtures: A Monte Carlo study.

Additive binary mixtures of five dimensional hyperspheres were investigated by Monte Carlo simulations. Both equal packing fraction and equal mole fraction systems with diameter ratios of 0.4 and 0.

Phase transitions in four-dimensional binary hard hypersphere mixtures.

Previous Monte Carlo investigations of binary hard hyperspheres in four-dimensional mixtures are extended to higher densities where the systems may solidify. The ratios of the diameters of the hyperspheres examined were 0.4, 0.

Monte Carlo study of four dimensional binary hard hypersphere mixtures.

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.

The fluid to solid phase transition of hard hyperspheres in four and five dimensions.

Molecular dynamics and Monte Carlo simulations are performed for four- and five-dimensional hard hyperspheres at a variety of densities, ranging from the fluid state to the solid regime of A(4), D(4), D(4)*, and D(5) lattices. The equation of state, the radial distribution functions, and the average number of hyperspheres in a coordination layer are determined. The equations of state are in excellent agreement with values obtained from both theoretical approaches and other simulations.

The equation of state of hard hyperspheres in nine dimensions for low to moderate densities.

The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or singularities on or near the negative density axis, in qualitative agreement with the recently solved Percus-Yevick equation of state in nine dimensions.

Structure factor for hard hyperspheres in higher dimensions.

The structure factor for hard hyperspheres in two to eight dimensions is computed by Fourier transforming the pair correlation function obtained by computer simulation at a variety of densities. The resulting structure factors are compared to the known Percus-Yevick equations for odd dimensions and to the model proposed by Leutheusser [J. Chem.

The equation of state of hard hyperspheres in four and five dimensions.

The equation of state of hard hyperspheres in four and five dimensions is calculated from the value of the pair correlation function at contact, as determined by Monte Carlo simulations. These results are compared to equations of state obtained by molecular dynamics and theoretical approaches. In all cases the agreement is excellent.

The structure of hyperspherical fluids in various dimensions.

The structure of hard, hyperspherical fluids in dimension one, two, three, four, and five has been examined by calculating the pair correlation function using a Monte Carlo simulation. The pair correlation functions match known results in one, two, and three dimensions. The contact value of the pair correlation functions in all the different dimensions agrees well with the theory of Song, Mason, and Stratt [J.