Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions

For inhomogeneous systems with interfaces, the inclusion of long-range dispersion interactions is necessary to achieve consistency between molecular simulation calculations and experimental results. For accurate and efficient incorporation of these contributions, we have implemented a particle-particle particle-mesh (PPPM) Ewald solver for dispersion ($r^{-6}$) interactions into the LAMMPS molecular dynamics package. We demonstrate that the solver's $\mathcal{O}(N\log N)$ scaling behavior allows its application to large-scale simulations. We carefully determine a set of parameters for the solver that provides accurate results and efficient computation. We perform a series of simulations with Lennard-Jones particles, SPC/E water, and hexane to show that with our choice of parameters the dependence of physical results on the chosen cutoff radius is removed. Physical results and computation time of these simulations are compared to results obtained using either a plain cutoff or a traditional Ewald sum for dispersion.Comment: 31 pages, 9 figure

Accelerating scientific codes by performance and accuracy modeling

Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used suboptimally. In a typical scenario, accuracy requirements are imposed, and attained through suboptimal performance. In this paper, we present a methodology for the automatic selection of parameters for simulation codes, and a corresponding prototype tool. To be amenable to our methodology, the target code must expose the parameters affecting accuracy and performance, and there must be formulas available for error bounds and computational complexity of the underlying methods. As a case study, we consider the particle-particle particle-mesh method (PPPM) from the LAMMPS suite for molecular dynamics, and use our tool to identify configurations of the input parameters that achieve a given accuracy in the shortest execution time. When compared with the configurations suggested by expert users, the parameters selected by our tool yield reductions in the time-to-solution ranging between 10% and 60%. In other words, for the typical scenario where a fixed number of core-hours are granted and simulations of a fixed number of timesteps are to be run, usage of our tool may allow up to twice as many simulations. While we develop our ideas using LAMMPS as computational framework and use the PPPM method for dispersion as case study, the methodology is general and valid for a range of software tools and methods

Capillary waves at the liquid-vapor interface and the surface tension of water models

Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.Comment: 11 pages, 8 figures, 7 tables. Accepted for publication in J. Chem. Phys. [v2: Added references, corrected minor errors

Coating thickness and coverage effects on the forces between silica nanoparticles in water

The structure and interactions of coated silica nanoparticles have been studied in water using molecular dynamics simulations. For 5 nm diameter amorphous silica nanoparticles we studied the effects of varying the chain length and grafting density of polyethylene oxide (PEO) on the nanoparticle coating's shape and on nanoparticle-nanoparticle effective forces. For short ligands of length $n=6$ and $n=20$ repeat units, the coatings are radially symmetric while for longer chains ($n=100$) the coatings are highly anisotropic. This anisotropy appears to be governed primarily by chain length, with coverage playing a secondary role. For the largest chain lengths considered, the strongly anisotropic shape makes fitting to a simple radial force model impossible. For shorter ligands, where the coatings are isotropic, we found that the force between pairs of nanoparticles is purely repulsive and can be fit to the form $(R/2r_\text{core}-1)^{-b}$ where $R$ is the separation between the center of the nanoparticles, $r_\text{core}$ is the radius of the silica core, and $b$ is measured to be between 2.3 and 4.1.Comment: 20 pages, 6 figure

Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices

In this paper, we extend our analysis of lattice systems using the wavelet transform to systems for which exact enumeration is impractical. For such systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm, which hierarchically coarse-grains a lattice model by computing the probability distribution for successively larger block spins. We demonstrate that although the method perturbs the system by changing its Hamiltonian and by allowing block spins to take on values not permitted for individual spins, the results obtained agree with the analytical results in the preceding paper, and ``converge'' to exact results obtained in the absence of coarse-graining. Additionally, we show that the decorrelation time for the WAMC is no worse than that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed from data performed in several short simulations to estimate the results that would be obtained from the original simulation. Although the algorithm is not asymptotically faster than traditional MMC, because of its hierarchical design, the new algorithm executes several orders of magnitude faster than a full simulation of the original problem. Consequently, the new method allows for rapid analysis of a phase diagram, allowing computational time to be focused on regions near phase transitions.Comment: 11 pages plus 7 figures in PNG format (downloadable separately

pMSSM Benchmark Models for Snowmass 2013

We present several benchmark points in the phenomenological Minimal Supersymmetric Standard Model (pMSSM). We select these models as experimentally well-motivated examples of the MSSM which predict the observed Higgs mass and dark matter relic density while evading the current LHC searches. We also use benchmarks to generate spokes in parameter space by scaling the mass parameters in a manner which keeps the Higgs mass and relic density approximately constant.Comment: 10 pages, 6 figure

Coarse-Graining Using Wavelet-Accelerated Monte Carlo

We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations. Previously, it was applied to simulations examining the structure of individual polymer chains in solution using up to four levels of coarse- graining (Ismail et al., J. Chem. Phys., 2005, 122, 234901 and Ismail et al., J. Chem. Phys., 2005, 122, 234902), recovering the correct scaling behavior in the coarse-grained representation. In the present work, we extend this method to the study of polymer solutions, deriving the bonded and non-bonded potentials between coarse-grained superatoms from the single chain statistics. A universal scaling function is obtained, which does not require recalculation of the potentials as the scale of the system is changed. To model semi-dilute polymer solutions, we assume the intermolecular potential between the coarse- grained beads to be equal to the non-bonded potential, which is a reasonable approximation in the case of semidilute systems. Thus, a minimal input of microscopic data is required for simulating the systems at the mesoscopic scale. We show that coarse-grained polymer solutions can reproduce results obtained from the more detailed atomistic system without a significant loss of accuracy