Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

Surface and Colloid Science

Numerical Initial Value Problems in Ordinary Differential Equations

New force fields for carbon dioxide and nitrogen are introduced that quantitatively reproduce the vapor–liquid equilibria (VLE) of the neat systems and their mixtures with alkanes. In addition to the usual VLE calculations for pure CO2 and N2, calculations of the binary mixtures with propane were used in the force-field development to achieve a good balance between dispersive and electrostatic (quadrupole–quadrupole) interactions. The transferability of the force fields was then assessed from calculations of the VLE for the binary mixtures with n-hexane, the binary mixture of CO2/N2, and the ternary mixture of CO2 /N2/propane. The VLE calculations were carried out using configurational-bias Monte Carlo simulations in either the grand canonical ensemble with histogram–reweighting or in the Gibbs ensemble.

Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen

For hard spheres in an external field it is shown that free energy density functionals of the type suggested by Percus [J. Chem. Phys. 75, 1316 (1981)] lead to certain approximations to the Born–Green–Yvon equation. For two functionals these approximations are worked out explicitly as well as are the expressions for the chemical potential and the direct correlation function of the homogeneous fluid. This formal relationship explains why results obtained from a Born–Green–Yvon approach and from coarse grained free energy density functionals are mostly rather similar. Moreover, a functional for the chemical potential derived by Robledo [J. Chem. Phys. 72, 1701 (1980)] from potential distribution theory is compared with the expressions from the Percus approach.

Relationship between free energy density functional, Born–Green–Yvon, and potential distribution approaches for inhomogeneous fluids

The density functional theory of Meister and Kroll for nonuniform simple fluids [Phys. Rev. A 31, 4055, (1985)] is modified in order to take into account pair correlations in the attractive energy term. The theory is applied for the calculation of density profiles of argon in the case of the free liquid surface and in the case of adsorption on ‘‘solid carbon dioxide.’’ For the gas–liquid interface the theory yields dew and bubble densities, which are in good agreement with computer simulations. For the adsorption of argon on solid CO2, the first‐order thin‐film to thick‐film transition is confirmed.

Johann Fischer

Papers

Relationship between free energy density functional, Born–Green–Yvon, and potential distribution approaches for inhomogeneous fluids

The role of attractive intermolecular forces in the density functional theory of inhomogeneous fluids

Intermolecular force parameters for unlike pairs

Liquid argon in a cylindrical carbon pore: molecular dynamics and born-green-yvon results

Construction and application of physically based equations of state: Part I. Modification of the BACK equation