Liquid-hexatic transition for soft disks.

We study the liquid-hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse mth power of the separation, the liquid-hexatic phase transition is continuous for m=12 and m=8, while it is of first order for m=24. The critical power m for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for m=12 implies that the two-dimensional Lennard-Jones model has a continuous liquid-hexatic transition at high temperatures. We also study the Weeks-Chandler-Andersen model and find a continuous transition at high temperatures that is consistent with the soft-disk case for m=12. Pressure data as well as our implementation are available from an open-source repository.

Hard-disk pressure computations-a historic perspective.

We discuss pressure computations for the hard-disk model performed since 1953 and compare them to the results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental efforts to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository.

Hard-disk dipoles and non-reversible Markov chains.

We benchmark event-chain Monte Carlo (ECMC) algorithms for tethered hard-disk dipoles in two dimensions in view of application of ECMC to water models in molecular simulation. We characterize the rotation dynamics of dipoles through the integrated autocorrelation times of the polarization. The non-reversible straight, reflective, forward, and Newtonian ECMC algorithms are all event-driven and only move a single hard disk at any time. They differ only in their update rules at event times. We show that they realize considerable speedups with respect to the local reversible Metropolis algorithm with single-disk moves. We also find significant speed differences among the ECMC variants. Newtonian ECMC appears particularly well-suited for overcoming the dynamical arrest that has plagued straight ECMC for three-dimensional dipolar models with Coulomb interactions.

Large-scale dynamics of event-chain Monte Carlo.

Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulations. Rather than imposing detailed balance on the transition probabilities, the method enforces a weaker global-balance condition in order to guarantee convergence to equilibrium. In this paper, we generalize the factor-field variant of ECMC to higher space dimensions. In the two-dimensional fluid phase, factor-field ECMC saturates the lower bound z=0 for the dynamical scaling exponent for local dynamics, whereas molecular dynamics is characterized by z=1 and local Metropolis Monte Carlo by z=2. In the presence of hexatic order, factor fields are not found to speed up the convergence. We note that generalizations of factor fields could couple to orientational order.

Phase Separation by Entanglement of Active Polymerlike Worms.

We investigate the aggregation and phase separation of thin, living T. tubifex worms that behave as active polymers. Randomly dispersed active worms spontaneously aggregate to form compact, highly entangled blobs, a process similar to polymer phase separation, and for which we observe power-law growth kinetics. We find that the phase separation of active polymerlike worms does not occur through Ostwald ripening, but through active motion and coalescence of the phase domains. Interestingly, the growth mechanism differs from conventional growth by droplet coalescence: the diffusion constant characterizing the random motion of a worm blob is independent of its size, a phenomenon that can be explained from the fact that the active random motion arises from the worms at the surface of the blob. This leads to a fundamentally different phase-separation mechanism that may be unique to active polymers.

Event-chain Monte Carlo with factor fields.

We study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular dynamics. We show, using simulations, that the autocorrelation time grows only with the square root of the system size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.

All-atom computations with irreversible Markov chains.

We apply the irreversible event-chain Monte Carlo (ECMC) algorithm to the simulation of dense all-atom systems with long-range Coulomb interactions. ECMC is event-driven and exactly samples the Boltzmann distribution. It neither uses time-step approximations nor spatial cutoffs on the range of the interaction potentials. Most importantly, it need not evaluate the total Coulomb potential and thus circumvents the major computational bottleneck of traditional approaches. It only requires the derivatives of the two-particle Coulomb potential, for which we discuss mutually consistent choices. ECMC breaks up the total interaction potential into factors. For particle systems made up of neutral dipolar molecules, we demonstrate the superior performance of dipole-dipole factors that do not decompose the Coulomb potential beyond the two-molecule level. We demonstrate that these long-range factors can nevertheless lead to local lifting schemes, where subsequently moved particles are mostly close to each other. For the simple point-charge water model with flexible molecules (SPC/Fw), which combines the long-ranged intermolecular Coulomb potential with hydrogen-oxygen bond-length vibrations, a flexible hydrogen-oxygen-hydrogen bond angle, and Lennard-Jones oxygen-oxygen potentials, we break up the potential into factors containing between two and six particles. For this all-atom liquid-water model, we demonstrate that the computational complexity of ECMC scales very well with the system size. This is achieved in a pure particle-particle framework, without the interpolating mesh required for the efficient implementation of other modern Coulomb algorithms. Finally, we discuss prospects and challenges for ECMC and outline several future applications.

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations.

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)]PRLTAO0031-900710.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films.

Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model. Height profiles are monitored as a function of time after heating the system above its glass-transition temperature and their time dependence is fitted to the theory of capillary leveling. Results show that the viscosity is not constant, but time dependent. In addition to providing a complementary insight about the local inner mechanisms, our simulations of the capillary-leveling process therefore probe the viscoelasticity of the polymer and not only its viscosity, in contrast to most experimental approaches.

Nonequilibrium Tuning of the Thermal Casimir Effect.

In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Casimir forces between two plates containing Brownian charges can be modulated by decorrelating the system through the application of an electric field, which generates a nonequilibrium steady state with a constant current in one or both plates, reducing the ensuing fluctuation-generated normal force while at the same time generating a lateral drag force. This hypothesis is confirmed by detailed numerical simulations as well as an analytical approach based on stochastic density functional theory.

The range and nature of effective interactions in hard-sphere solids.

Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals.

General theory of asymmetric steric interactions in electrostatic double layers.

We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important. We generalise lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other existing lattice gas approximations, not based on the Flory-Huggins Ansatz. Within the methodology presented we also invoke more realistic equations of state, such as the Carnahan-Starling approximation, that are not based on the lattice gas approximation and lead to thermodynamic functions and properties that differ strongly from the lattice gas case. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation.

Convexity and Stiffness in Energy Functions for Electrostatic Simulations.

We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true fluctuations of electrolytes and thus the one-loop correction to mean field theory-including the Debye-Hückel correction to the free energy of ionic solutions. We also compare the functionals for use in numerical optimization of a mean field model of a charged polymer and show that different functionals have very different stiffnesses leading to substantial differences in accuracy and speed.

Cavity averages for hard spheres in the presence of polydispersity and incomplete data.

We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are available-volume and free-volume methods. We add a third one, which we call available volume after take-out, and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics: In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalists for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful.

Fluctuation-induced forces governed by the dielectric properties of water-A contribution to the hydrophobic interaction.

The hydrophobic interaction between objects immersed in water is typically attractive and adds to the well-known van der Waals interaction. The former supposedly dominates the latter on nanometric distances and could be of major importance in the assembly of biologic objects. Here, we show that the fluctuation-induced attraction between two objects immersed in a correlated dielectric medium which models water is the sum of a van der Waals term and a short-range contribution that can be identified as part of the hydrophobic interaction. In this framework, we calculate analytically the fluid correlation function and the fluctuation-induced interaction between small and extended inclusions embedded in water and we characterize the hydrophobic terms.

Phonons in two-dimensional soft colloidal crystals.

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.

Anisotropic elasticity in confocal studies of colloidal crystals.

We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods based on the fast Fourier transform. In certain situations of high symmetry we find exact analytic results for the projected fluctuations.

Simple glass models and their quantum annealing.

We study first-order quantum phase transitions in mean-field spin glasses. We solve the quantum random energy model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all "random first-order" models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.

Fluctuation-induced interactions between dielectrics in general geometries.

We study thermal Casimir and quantum nonretarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant, which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product of determinants. We compare the approximations of pairwise additivity and proximity force with our numerical methods. We propose a "factorization approximation" that gives rather good numerical results in the geometries that we study.

Boundary conditions in local electrostatics algorithms.

We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We first show how to implement constant-potential, Dirichlet boundary conditions by introducing extra Monte Carlo moves to the algorithm. Second, we show the interest of the algorithm for studying systems which require anisotropic electrostatic boundary conditions for simulating planar geometries such as membranes.