Molecular dynamics simulation should be combined with modern supercomputer technologies to obtain meaningful results in reasonable time. Widely used simulation software in MD is LAMMPS. It produces a dump with computational results of simulation, and such a large amount of data should be post-processed. However, LAMMPS does not provide ready-to-use utilities that would do it. In this paper we present the developed algorithm for LAMMPS output data processing for nucleation process. The analysis of implementation performance shows that it is shading that takes most of the time, hence, it should provide the greatest room for future optimization.
One of the problems to be solved with the use of modern supercomputer
technologies is the molecular dynamics (MD) simulation of metastable phase states
and phase transitions. The rst stage of a new thermodynamic phase formation is
nucleation. Nucleation is widespread in both nature and technological processes
during which the phase transitions occur [
A popular method of nucleation study is molecular dynamics (MD)
simulations [
Using the coordinates and velocities of the particles at a speci c point of time,
one can compute [
The most widely used MD simulation software is the LAMMPS system [
Several computational experiments for studying the nucleation properties were conducted at the Institute of Thermophysics. For modeling homogeneous nucleation, the Lennard-Jones (LJ) liquid gas mixture of methane and nitrogen is considered. The system under study contains N = 32000 LJ particles. The particles are placed in a cubic box with periodic boundary conditions (PBC) as presented in Fig. 1. Isothermal entry into metastable states of mixture is implemented by lowering the density through stretching the whole cell and then scaling the particles' coordinates accordingly.
For study of heterogeneous nucleation, the system of LJ particles (model liquids consisting of monocenter molecules) placed between two at crystalline walls is used, as shown in Fig. 2. The appearance of the vapor phase on the walls simulates the heterogeneous nucleation (Fig. 3).
An important property of nucleation is the rate of nucleation, which equals
the average number of nuclei of a new phase formed per unit volume per unit
time [
As a result of numerical experiments in simulation of molecular dynamics, the LAMMPS system produces a text le with the coordinates of the particles. It is required to post-process these results to calculate the various characteristics of the models. For the homogeneous nucleation experiment with the gas mixture in cells with the periodic boundaries, we need to nd an empty cluster with the maximum radius and then evaluate the parameters of the cluster such as volume, center of mass coordinates, and particles' density distribution.
We developed a four-step (Fig. 5) algorithm for detecting empty spaces: 1. Discretization of space. The model space is partitioned into equal cells, which are cubes with sides parallel to the model sides. The number of cubes is pre-selected so that each single particle of the model \gets" nclast partition cubes. 2. Shading non-empty cubes. The cubes the centers of which are less than the distance Rnearest away from some particle are shaded. 3. Clustering empty cubes. Unmarked cubes are clustered using the breadth- rst search (BFS) algorithm. We assume that the two cubes belong to the same cluster if they share at least one edge. 4. Finding the cluster center. We determine the cells with the most distance from each other for the clusters in all three dimensions and calculate the center of the cluster.
The algorithm was implemented using C++ with Intel Compiler. The current implementation is capable of processing existing LAMMPS output les with particle coordinates. The advantage of such an approach is the ability to process the data from previously conducted experiments.
To analyze the performance of the implementation, the numerical experiments on specially prepared test data were carried out. The Intel Xeon X5675 processor was used during the experiments. Our implementation processed one frame with 1000000 particles and 300 partition cubes per particle (nclast) in 440 seconds (including input/output time). The achieved performance is practical for frame numbers between 100 and 200.
The performance of the implementation was studied with the help of the Intel VTune Ampli er pro ler software. Shading takes 94% of the time on test data, 2% are occupied by BFS, and 1% by other tasks (discretization of the space, nding the cluster center, data input/output, etc.). Hence, shading o ers the greatest room for optimization. We presented an algorithm for post-processing the MD simulation results: nding the biggest empty cluster and evaluating its parameters|the radius, the volume, the center of coordinates, and the particles' density distribution. Directions of future work include improving the performance of the algorithm implementation using parallel computing in order to process frames with millions of particles. In addition, we plan to develop and implement algorithms for post-processing of heterogeneous nucleation simulation results (contact angle, tensor of pressure, etc.). The post-processing programs will be implemented as plugins for LAMMPS.
Acknowledgements The work was supported by the Research Program of Ural Branch of RAS, project no. 15-7-12-8 and the Russian Foundation for Basic Research, project no. 15-08-03399. Our study was performed using the Uran supercomputer of the Krasovskii Institute of Mathematics and Mechanics.