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Register a new userEfficient Implementations of Molecular Dynamics Simulations for Lennard-Jones Systems
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Efficient implementations of the classical molecular dynamics (MD) method for Lennard-Jones particle systems are considered. Not only general algorithms but also techniques that are efficient for some specific CPU architectures are also explained. A simple spatial-decomposition-based strategy is adopted for parallelization. By utilizing the developed code, benchmark simulations are performed on a HITACHI SR16000/J2 system consisting of IBM POWER6 processors which are 4.7 GHz at the National Institute for Fusion Science (NIFS) and an SGI Altix ICE 8400EX system consisting of Intel Xeon processors which are 2.93 GHz at the Institute for Solid State Physics (ISSP), the University of Tokyo. The parallelization efficiency of the largest run, consisting of 4.1 billion particles with 8192 MPI processes, is about 73% relative to that of the smallest run with 128 MPI processes at NIFS, and it is about 66% relative to that of the smallest run with 4 MPI processes at ISSP. The factors causing the parallel overhead are investigated. It is found that fluctuations of the execution time of each process degrade the parallel efficiency. These fluctuations may be due to the interference of the operating system, which is known as OS Jitter.
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We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width $D$. The pore walls are assumed to be flat and structureless, and attract one component of the mixture (A) with the same strength. The pair-wise interactions between the particles is modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S.~K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E {bf 72}, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly 2-$d$ geometry is also discussed.
The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets is found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well defined core or surface. The environment of the nucleating droplets form randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. We also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the efficiency of particle swaps into equilibrium molecular dynamics (MD) simulations. We first develop a hybrid MD/MC scheme combining molecular dynamics with the original swap Monte Carlo. We implement this hybrid method in LAMMPS, a software package employed by a large community of users. Secondly, we define a continuous time version of the swap algorithm where both the positions and diameters of the particles evolve via Hamiltons equations of motion. For both algorithms, we discuss in detail various technical issues as well as the optimisation of simulation parameters. We compare the numerical efficiency of all available swap algorithms and discuss their relative merits.
The phase diagram of the prototypical two-dimensional Lennard-Jones system, while extensively investigated, is still debated. In particular, there are controversial results in the literature as concern the existence of the hexatic phase and the melting scenario. Here, we study the phase behaviour of 2D LJ particles via large-scale numerical simulations. We demonstrate that at high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. As the temperature decreases, the density range where the hexatic phase occurs shrinks so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.
The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, $langle K rangle$, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that $langle K rangle$ increases exponentially with $beta = 1/k_BT$ and with pressure, $P$ in agreement with previous results in the literature. A method is illustrated for using $langle K rangle (beta, P)$ to generate a phase diagram for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
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