Particle Swap Research Articles

Irreversible MonteCarlo Algorithms for Hard Disk Glasses: From Event-Chain to Collective Swaps.

Equilibrium sampling of the configuration space in disordered systems requires algorithms that bypass the glassy slowing down of the physical dynamics. Irreversible MonteCarlo algorithms breaking detailed balance successfully accelerate sampling in some systems. We first implement an irreversible event-chain MonteCarlo algorithm in a model of continuously polydisperse hard disks. The effect of collective translational moves marginally affects the dynamics and results in a modest speedup that decreases with density. We then propose an irreversible algorithm performing collective particle swaps which outperforms all known MonteCarlo algorithms. We show that these collective swaps can also be used to prepare very dense jammed packings of disks.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Exceptionally dense and resilient critically jammed polydisperse disk packings.

Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are protocol dependent. Here, we demonstrate that this variability can be systematically traced to structural measures of packing, as well as to energy measures inside the jammed regime. A novel generalized simultaneous particle swap algorithm constructs overjammed states of desired energy, which upon decompression lead to predictable critical packing fractions. Thus, for a given set of particle sizes, states with extraordinarily high critical packing fractions can be found efficiently, which sustain substantial shear strain and preserve their special structure over the entire jammed domain. The close relation revealed here between the energy landscape of overjammed soft-particle packings and the behavior near the jamming transition points towards new ways of understanding and constructing disordered materials with exceptional properties.

Continuous fractional component Gibbs ensemble Monte Carlo

A continuous fractional component (CFC) approach increases the probability of particle swaps in the context of vapor-liquid equilibrium simulations using the Gibbs ensemble Monte Carlo algorithm. Two variants of the CFC approach are compared for simulations of pure Lennard-Jones (LJ) fluids and binary LJ mixtures as examples. The details of an exemplary CFC implementation are presented. Recommendations are provided to reduce the effort required for the suggested problems.

Diffusion-Coefficient Power Laws and Defect-Driven Glassy Dynamics in Swap Acceleration.

Particle swaps can drastically accelerate dynamics in glass. The mechanism is expected to be vital for a fundamental understanding of glassy dynamics. To extract defining features, we propose a partial swap model with a fraction ϕ_{s} of swap-initiating particles, which can only swap locally with each other or with regular particles. We focus on the swap-dominating regime. At all temperatures studied, particle diffusion coefficients scale with ϕ_{s} in unexpected power laws with temperature-dependent exponents, consistent with the kinetic picture of glassy dynamics. At small ϕ_{s}, swap initiators, becoming defect particles, induce remarkably typical glassy dynamics of regular particles. This supports defect models of glass.

Physical swap dynamics, shortcuts to relaxation, and entropy production in dissipative Rydberg gases.

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids

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 Hamilton’s 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.

Complex Crystals from Size-Disperse Spheres.

Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long history of research, the conditions under which nonuniform particles crystallize and which crystal forms is still not well understood. Here, we demonstrate that hard spheres with Gaussian radius distribution and dispersity up to 19% always crystallize if compressed slowly enough, and they do so in surprisingly complex ways. This result is obtained by accelerating event-driven simulations with particle swap moves for static dispersity and particle resize moves for dynamic dispersity. Above 6% dispersity, AB_{2} Laves, AB_{13}, and a region of Frank-Kasper phases are found. The Frank-Kasper region includes a quasicrystal approximant with Pearson symbol oS276. Our findings are relevant for ordering phenomena in soft matter and alloys.

Assessment and Optimization of Configurational-Bias Monte Carlo Particle Swap Strategies for Simulations of Water in the Gibbs Ensemble.

Particle swap moves between phases are usually the rate-limiting step for Gibbs ensemble Monte Carlo (GEMC) simulations of fluid phase equilibria at low reduced temperatures because the acceptance probabilities for these moves can become very low for molecules with articulated architecture and/or highly directional interactions. The configurational-bias Monte Carlo (CBMC) technique can greatly increase the acceptance probabilities, but the efficiency of the CBMC algorithm is influenced by multiple parameters. In this work we assess the performance of different CBMC strategies for GEMC simulations using the SPC/E and TIP4P water models at 283, 343, and 473 K, demonstrate that much higher acceptance probabilities can be achieved than previously reported in the literature, and make recommendations for CBMC strategies leading to optimal efficiency.

Improved Monte Carlo Scheme for Efficient Particle Transfer in Heterogeneous Systems in the Grand Canonical Ensemble: Application to Vapor-Liquid Nucleation.

Reformulation of existing Monte Carlo algorithms used in the study of grand canonical systems has yielded massive improvements in efficiency. Here we present an energy biasing scheme designed to address targeting issues encountered in particle swap moves using sophisticated algorithms such as the Aggregation-Volume-Bias and Unbonding-Bonding methods. Specifically, this energy biasing scheme allows a particle to be inserted to (or removed from) a region that is more acceptable. As a result, this new method showed a several-fold increase in insertion/removal efficiency in addition to an accelerated rate of convergence for the thermodynamic properties of the system.

Hybrid Monte Carlo simulation of a glass-forming binary mixture

We propose a different, hybrid Monte Carlo algorithm that combines configurational bias particle swaps with parallel tempering. We use this algorithm to simulate a standard model of a glass-forming binary mixture above and below the so-called mode-coupling temperature T(MCT). We find that an ansatz that was used previously to extrapolate thermodynamic quantities to temperatures below T(MCT) breaks down in the vicinity of the mode-coupling temperature. We also find that the Adam-Gibbs relations D(alpha)exp(-a/TS(c)) and tau(alpha)exp(b/TS(c)), which connect the diffusion coefficient D and the relaxation time tau with the configurational entropy S(c), are valid for all temperatures for which the configurational and vibrational contributions to the free energy decouple.

Direct Gibbs Ensemble Monte Carlo Simulations for Solid−Vapor Phase Equilibria: Applications to Lennard−Jonesium and Carbon Dioxide

The Gibbs ensemble Monte Carlo method of Panagiotopoulos is extended to calculations of solid−vapor coexistence curves. As in the original Gibbs ensemble method, the new technique makes use of two simulation boxes that are in thermodynamic contact. However, the box that contains the solid phase is elongated along one axis and contains only a slab of solid material surrounded on both sides by vapor. Aggregation-volume-bias Monte Carlo moves are used to sample transfers from the solid to the vapor and vice versa in this box, whereas the usual particle swap moves are applied to transfers between the solid−vapor box and the other box that contains a bulk vapor phase. Volume moves for the solid−vapor box use separate displacements of individual cell lengths or of individual H-matrix elements. As one approaches the triple-point temperature from below, increased disorder at the solid−vapor interface is observed, and once the triple-point temperature is exceeded, the entire solid slab converts to a liquid. The us...

Fast Monte Carlo algorithm for supercooled soft spheres.

We present a nonlocal Monte Carlo algorithm with particle swaps that greatly accelerates thermalization of soft sphere binary mixtures in the glassy region. Our first results show that thermalization of systems of hundreds of particles is achievable, and find behavior compatible with a thermodynamic glass transition.

Adiabatic Nuclear and Electronic Sampling Monte Carlo Simulations in the Gibbs Ensemble: Application to Polarizable Force Fields for Water

The adiabatic nuclear and electronic sampling Monte Carlo algorithm (ANES-MC) is extended to simulations in the Gibbs ensemble. Whereas the maximum displacements used for translational, rotational, and volume trial moves can be adjusted to foster efficient sampling in the adiabatic limit, the transfer (swap) of particles always causes a major disturbance of the electronic structures of the two phases (supplying and receiving the particle). To reequilibrate the electronic structures requires additional sampling of the electronic degrees of freedom. A simple, distance-dependent criterion for the preferential selection of the electronic degrees of freedom, for which a move is to be attempted, is shown to improve the efficiency of the particle swap move. The ANES-MC algorithm is applied to the polarizable simple point charge-fluctuating charge (SPC−FQ) and transferable intermolecular potential 4 point-fluctuating charge (TIP4P−FQ) models proposed by Rick et al. (J. Chem. Phys. 1994, 101, 6141). For both models simulations were performed using the standard constraint on the neutrality of individual molecules. In addition, for the SPC−FQ model the use of a constraint on the neutrality of an entire phase was investigated, which allows for intermolecular charge transfer. Simulations in the Gibbs ensemble were performed to calculate the vapor−liquid coexistence curves from 323 to 523 K, whereas simulations in the grand canonical ensemble were performed for the near-critical region. Dielectric constants at different state points were calculated from canonical ensemble simulations. Neither the SPC−FQ nor the TIP4P−FQ force fields give a satisfactory description of the vapor−liquid equilibria. In particular, the critical temperature is greatly underestimated by both models. Although intermolecular charge transfer has only a very small influence on the internal energy and the radial distribution functions at ambient conditions and along the coexistence curve, it increases the dielectric constant by approximately 30%.

Vapour liquid equilibria of Lennard-Jones model mixtures from the NpT plus test particle method

The NpT+test particle method for the calculation of vapour liquid phase equilibria (VLE) is applied to ten binary Lennard-Jones mixtures which were studied previously with the Gibbs ensemble (Harismiadis et al., 1991). The present method uses one simulation for the description of the liquid. For the vapour two simulations are required at higher densities, whilst at lower vapour densities the Haar-Shenker-Kohler (HSK) equation of state is used. The chemical potentials from simulation are calculated by Widom's test particle insertion method (Widom, 1963) and adjusted with the results from the particle swap method, which yields the differences of the chemical potentials. Additionally, VLE results are obtained by using the Fischer-Lago-Bohn perturbation theory for the liquid and the HSK equation for the vapour. A comparison of the new simulation results with those of the Gibbs ensemble shows qualitative agreement but in most cases smaller error bars and considerably less scatter of the present data. Moreover, the simulations confirm the good to excellent performance of the perturbation theory.

Chemical potential, partial enthalpy and partial volume of mixtures by NPT molecular dynamics

Equilibrium NPT molecular dynamics computer simulations have been used to determine the chemical potential, partial enthalpy and partial volume of model Ar/Kr-like mixtures using the non-intrusive particle insertion and particle swap techniques devised by P. Sindzingre et al. [Chem. Phys. 129 (1989) 213]. Both species are represented by single-site Lennard-Jones (LJ) pair potentials with Lorentz-Berthelot rules for the cross-species interactions. In this report we use these techniques to examine further (a) the relative convergence statistics of the particle swap and particle insertion methods for these properties for model argon-krypton mixtures, and (b) to investigate the effect of changing the relative values of the LJ well-depth, ϵ, and core-diameter, σ, for the two species. If the two species in the binary mixture are labelled A and B, we show that species A → B virtual particle swaps and B → A swaps lead to statistically identical values for the difference in the chemical potentials, partial enthalpies and partial volumes between the two species. This confirms that no bias is introduced in the sampling of phase space by this method. Over the whole phase diagram and especially in the vicinity of the fluid-solid coexistence line, the particle swap method converges significantly more rapidly than the particle insertion method for the difference in chemical potential of the two species, partial enthalpy and partial volume of each species. Also, we find that, using the particle swap method, the difference in the chemical potential converges more rapidly than the differences in the partial enthalpy and volume. We use the swap technique to investigate the effects of changing the molecular potential parameters on the partial properties. We consider artificial binary mixtures con- structed from various choices of the σ Ar, σ Kr, ϵ Ar and ϵ Kr given to the two species. We discover that the effects of the argon and krypton LJ parameters largely cancel for the mixture thermodynamic properties. Arbitrary combinations of these parameters can give rise to more extreme composition dependence for the average and partial properties. The partitioned and partial enthalpies provide a useful probe of the local structural changes accompanying probe particle insertion.

Chemical Potential, Partial Enthalpy and Partial Volume of Mixtures byNPTMolecular Dynamics

Abstract Equilibrium NPT molecular dynamics computer simulations have been used to determine the chemical potential, partial enthalpy and partial volume of model Ar-Kr mixtures using newly devised non-intrusive particle insertion and particle swap techniques [P. Sindzingre et al. Chemical Physics, 129 (1989) 213]. In this report we examine, for the first time, in some detail the relative convergence statistics of the particle swap and particle insertion methods for these properties for binary Lennard-Jones (LJ) mixtures. Both species are represented by single-site Lennard-Jones pair potentials with Lorentz-Berthelot rules for the cross-species interactions. We show that, over the whole phase diagram and especially in the vicinity of the fluid-solid coexistence line, the particle swap method gives significantly better statistics than the particle insertion method for the difference in chemical potential of the two species, partial enthalpy and partial volume of each species. Also, we find that, using the p...