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

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

A potential model intended to be a general purpose model for the condensed phases of water is presented. TIP4P/2005 is a rigid four site model which consists of three fixed point charges and one Lennard-Jones center. The parametrization has been based on a fit of the temperature of maximum density (indirectly estimated from the melting point of hexagonal ice), the stability of several ice polymorphs and other commonly used target quantities. The calculated properties include a variety of thermodynamic properties of the liquid and solid phases, the phase diagram involving condensed phases, properties at melting and vaporization, dielectric constant, pair distribution function, and self-diffusion coefficient. These properties cover a temperature range from 123to573K and pressures up to 40000bar. The model gives an impressive performance for this variety of properties and thermodynamic conditions. For example, it gives excellent predictions for the densities at 1bar with a maximum density at 278K and an aver...

http://cacharro.quim.ucm.es/publicaciones/JCP_123_234505_2005.pdf

A general purpose model for the condensed phases of water: TIP4P/2005

Thermodynamic integration along a path that coincides with the saturation line is proposed as an efficient means for evaluation of phase equilibria by molecular simulation. The technique allows coexistence to be determined by just one simulation, without ever attempting or performing particle insertions. Prior knowledge of one coexistence point is required to start the procedure. Integration then advances from this state according to the Clapeyron formula—a first‐order ordinary differential equation that prescribes how the pressure must change with temperature to maintain coexistence. The method is unusual in the context of thermodynamic integration in that the path is not known at the outset of the process; results from each simulation determine the course that the integration subsequently takes. Predictor–corrector methods among standard numerical techniques are shown to be particularly well suited for this type of integration. A typical integration step along the saturation line proceeds as follows: An increment in the temperature is chosen, and the saturation pressure at the new temperature is ‘‘predicted’’ from previous data (the initial coexistence datum and/or previous simulations). Simultaneous but independent NPT simulations of the coexisting phases are initiated at the said conditions. Averages taken throughout the simulations are repeatedly used to ‘‘correct’’ the estimate of the pressure to convergence. Thus strictly the pressure is not fixed during the simulation. Vapor–liquid coexistence of the van der Waals model is first used to study the numerical integration method without the complications of molecular simulation. In a second application the phase envelope of the Lennard‐Jones model fluid is computed, and many variations of the technique are examined. Overall, the results are remarkably consistent and in agreement with previous simulation studies. Difficulty is encountered upon approach of the critical point, but, by artificially coupling the simulation volumes, the method remains effective in this regime so long as a suitably small integration step is employed. Many extensions and improvements of the technique are discussed.

/pdf/direct-evaluation-of-phase-coexistence-by-molecular-2ejawao1pf.pdf

Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line

A method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation. Given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line. In each simulation, the pressure is adjusted to satisfy chemical potential equality according to the Gibbs-Duhem equation. Each coexistence point is determined by just one simulation, and particle insertions are never performed or attempted. Vapourliquid coexistence for the Lennard-Jones model is evaluated, and extensions are discussed.

Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation

Properties of coexisting fluid and solid phases of the Lennard-Jones model potential are reported. The melting line, representing equilibrium between the solid and liquid phases, is computed by performing a thermodynamic integration along a path that follows the coexistence line itself, according to the Gibbs-Duhem integration method recently introduced by us. Monte Carlo simulations are conducted to compute the quantities needed by the method; two system sizes, with particles numbering approximately 100 and 500, respectively, are examined. The starting point for the integration is the soft sphere system obtained in the limit of high temperature. The procedure terminates at the solid-liquid-vapour triple point, and thus the entire melting line is determined. Our results for the melting pressure are about 10% higher than those reported previously in the literature, while the triple point temperature we compute is in accord with the established value. An analysis of the approach to the high-temperature limi...

Thermodynamic and structural properties of model systems at solid-fluid coexistence. ii: melting and sublimation of the lennard-jones system

An analysis is presented of the average probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move acceptance probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the acceptance probability.

On the acceptance probability of replica-exchange Monte Carlo trials

A general formalism and methodology are presented for the Monte Carlo simulation of equilibria in multicomponent systems, and are applied to the study of phase equilibrium in a model binary mixture, and to phase and chemical equilibrium in the ternary mixture Br2−Cl2−BrCl. Very good agreement with available experimental data is obtained. The formalism is based upon an ensemble in which the ratios of all fugacities to a reference fugacity are imposed. Simulations of mixtures performed in this ensemble fluctuate in composition while keeping constant the total number of particles. The reference fugacity is computed by integration of simulation averages of the composition for varying values of the fugacity ratios. Several features of the approach are: (1) it can be readily applied to mixtures of any number of components, even to polydisperse systems, with little additional computational effort; (2) the chemical potential of only one species at one state need be evaluated by conventional techniques, regardless...

David A. Kofke

Papers

Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line

Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation

Thermodynamic and structural properties of model systems at solid-fluid coexistence. ii: melting and sublimation of the lennard-jones system

On the acceptance probability of replica-exchange Monte Carlo trials

Monte Carlo simulation of multicomponent equilibria in a semigrand canonical ensemble