There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Intermolecular And Surface Forces

http://static.sif.it/SIF/resources/public/files/va2012/likos_0710.pdf

Effective interactions in soft condensed matter physics

Development of theories of inhomogeneous fluids, J.S. Rowlinson statistical mechanical sum rules, J.R. Henderson density functionals in the theory of non-uniform fluids, R. Evans integral equation theories for inhomogeneous fluids, Douglas Henderson inhomogeneous two-dimensional plasmas, B. Jancovici statistical mechanics of electrolytes at interfaces, L. Blum and Douglas Henderson wetting experiments, Carl Franck fluids between walls and in pores, Marcelo Lozada-Cassou freezing, A.D.J. Haymet nucleation, David W. Oxtoby liquid crystals, J.F. Marko nature of microemulsion, K.A. Dawson and Christopher J. Mundy kinetic theory of strongly inhomogeneous fluids, H. Ted Davis.

Fundamentals of Inhomogeneous Fluids

Vegard's law is an approximate empirical rule which holds that a linear relation exists, at constant temperature, between the crystal lattice constant of an alloy and the concentrations of the constituent elements. Applications of a density-functional theory of nonuniform fluid mixtures to the fluid-solid transition of simple binary mixtures of hard spheres demonstrates the importance of relative atomic sizes in determining lattice constants and suggests that for sufficiently small disparities in atomic size Vegard's law may also hold along the fluid-solid coexistence curve.

Vegard's law.

A new formulation of the weighted-density approximation (WDA), as currently applied in the theory of nonuniform classical liquids, is presented. This modified weighted-density approximation retains a key feature of the original approximation by including correlations, at least approximately, to all orders in the functional expansion of the excess free energy. It continues to require as input only the two-particle direct correlation function of the uniform liquid. In contrast to the original WDA, however, practical implementation of the modified WDA demands considerably less computational e6ort. When applied to the freezing of the hard-sphere liquid, the results obtained previously with the original WDA, already in good agreement with simulation, are reproduced quite accurately. It is concluded that in its new formulation the WDA is now just as simple to implement as the widely used Ramakrishnan-Yussouff' theory. But as with the original WDA the new formulation more accurately describes the freezing of hard spheres and is more soundly based in the sense of including correlations to all orders.

Modified weighted-density-functional theory of nonuniform classical liquids

A method is presented for determining the static structure factor S(Q) of a uniform bulk fluid, for all wave-vector magnitudes Q, from computer simulation data for a finite (N-particle) system. The method is based on the usual Fourier transform relation between S(Q) and the radial distribution function g(r) and on the theory of explicit finite-size effects, in particular a Taylor-series expansion, in powers of 1/N, for ${\mathit{g}}_{\mathit{N}}$(r), the N-particle counterpart of g(r). A time-dependent generalization of the method to the intermediate scattering function I(Q,t) is also presented. Implicit finite-size effects are also considered, but are found to be negligible for systems to which we have applied the method. \textcopyright{} 1996 The American Physical Society.

Finite-size effects in molecular dynamics simulations: Static structure factor and compressibility. I. Theoretical method

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modeling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.

Alan R. Denton

Papers

Vegard's law.

Modified weighted-density-functional theory of nonuniform classical liquids

Finite-size effects in molecular dynamics simulations: Static structure factor and compressibility. I. Theoretical method

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels.

Weighted-density-functional theory of nonuniform fluid mixtures: Application to freezing of binary hard-sphere mixtures.