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In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at equilibrium, comparing novel methodologies of event-chain Monte Carlo variants, specifically the Newtonian event-chain and straight event-chain algorithms. We systematically analyze both event-based and CPU time-based efficiency in liquid and solid phases, aiming to elucidate the microscopic mechanisms underlying structural relaxation. Our results demonstrate how chain length or duration, system size, and phase state influence the efficiency of diffusion dynamics, including hopping motion. This work provides insights into optimizing simulation techniques for highly packed systems and has the potential to improve our understanding of diffusion dynamics even in complex many-body systems., Comment: 11 pages, 6 figures, to appear in J. Chem. Phys

In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular jamming transitions and various aspects of the behavior of active matter. However, conventional techniques (based on a fixed-distance cutoff or the Voronoi construction) have mainly been applied to equilibrated, homogeneous, and monodisperse particle systems. In this paper, we implement simple and efficient methods for local structure analysis in nonequilibrium, inhomogeneous, and polydisperse hard disk systems. We show how these novel methods can overcome the difficulties encountered by conventional techniques, as well as demonstrating some applications., Comment: 16 pages, 15 figures

Particle dynamics in supercooled liquids are often dominated by string-like motions in which lines of particles perform activated hops cooperatively. The structural features triggering these motions, crucial in understanding glassy dynamics, remain highly controversial. We experimentally study microscopic particle dynamics in colloidal glass formers at high packing fractions. With a small polydispersity leading to glass-crystal coexistence, a void in the form of a vacancy in the crystal can diffuse reversibly into the glass and further induces string-like motions. In the glass, a void takes the form of a quasi-void consisting of a few neighboring free volumes and is transported by the string-like motions it induces. In fully glassy systems with a large polydispersity, similar quasi-void actions are observed. The mobile particles cluster into string-like or compact geometries, but the compact ones can further be broken down into connected sequences of strings, establishing their general importance., Comment: main text 5 pages 4 figures + supplymentary material 24 pages 23 figures (Ancillary files), 2020 Nov accepted by Physical Review Letter

We investigate numerically the applicability of dynamic facilitation (DF) theory for glass-forming binary hard disk systems where supercompression is controlled by pressure. By using novel efficient algorithms for hard disks, we are able to generate equilibrium supercompressed states in an additive non-equimolar binary mixture, where micro-crystallization and size segregation do not emerge at high average packing fractions. Above an onset pressure where collective heterogeneous relaxation sets in, we find that relaxation times are well described by a "parabolic law" with pressure. We identify excitations, or soft-spots, that give rise to structural relaxation, and find that they are spatially localized, their average concentration decays exponentially with pressure, and their associated energy scale is logarithmic in the excitation size. These observations are consistent with the predictions of DF generalized to systems controlled by pressure rather than temperature., Comment: 6 pages, 3 figures, to appear in Phys. Rev. Lett

We simulate crystallization and melting with local Monte Carlo (LMC), event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD) in systems with up to one million three-dimensional hard spheres. We illustrate that our implementations of the three algorithms rigorously coincide in their equilibrium properties. We then study nucleation in the NVE ensemble from the fcc crystal into the homogeneous liquid phase and from the liquid into the homogeneous crystal. ECMC and EDMD both approach equilibrium orders of magnitude faster than LMC. ECMC is also notably faster than EDMD, especially for the equilibration into a crystal from a disordered initial condition at high density. ECMC can be trivially implemented for hard-sphere and for soft-sphere potentials, and we suggest possible applications of this algorithm for studying jamming and the physics of glasses, as well as disordered systems., Comment: 7 pages, 7 figures

We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase., Comment: 9 pages, 8 figures, 2 tables

Higher order parameters in the hard disk fluid are computed to investigate the number, the life time and size of transient crystal nuclei in the pre-freezing phase. The methodology introduces further neighbor shells bond orientational order parameters and coarse-grains the correlation functions needed for the evaluation of the stress autocorrelation function for the viscosity. We successfully reproduce results by the previous collision method for the pair orientational correlation function, but some two orders of magnitude faster. This speed-up allows calculating the time dependent four body orientational correlation between two different pairs of particles as a function of their separation, needed to characterize the size of the transient crystals. The result is that the slow decay of the stress autocorrelation function near freezing is due to a large number of rather small crystal nuclei lasting long enough to lead to the molasses tail., Comment: 10 pages, 11 figures, to appear in J. Chem. Phys

We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological Langevin-type theory describing the fluctuation of center of mass height, which was originally constructed for a one-dimensional granular gas on a vibrating bottom plate, was generalized to any dimensionality, even for the case in which the vibrating bottom plate is replaced by a thermal wall. The theory predicts a fluctuation-dissipation relation known to be satisfied at equilibrium, with a modification that replaces the equilibrium temperature by an effective temperature defined by the center of mass kinetic energy. To test the validity of the fluctuation-dissipation relation, we performed extensive and accurate event-driven molecular dynamics simulations for the model system with a thermal wall at the bottom. The power spectrum and response function of the center of mass height were measured and closely compared with theoretical predictions. It is shown that the fluctuation-dissipation relation for the granular system is satisfied, especially in the high-frequency (short time) region, for a wide range of system parameters. Finally, we describe the relationship between systematic deviations in the low-frequency (long time) region and the time scales of the driven granular system., Comment: 13 pages, LaTeX, 12 figures. Version 2: changes in the text

The molasses tail in dense hard core fluids is investigated by extensive event-driven molecular dynamics simulation through the orientational autocorrelation functions. Near the fluid-solid phase transition, there exist three regimes in the relaxation of the pair orientational autocorrelation function, namely the kinetic, molasses (stretched exponential), and diffusional power decay. The density dependence of both the molasses and diffusional power regimes are evaluated and the latter compares with theoretical predictions in three dimensions. The largest cluster at the freezing density of only a few sphere diameter in size persist for only about 30 picoseconds (~ 2.8 x 10^{-11}[s]). The most striking observation through the bond orientatinal order parameter is the dramatic increase of the cluster size as the freezing density is approached., Comment: 12 pages, 8 figures, 3 tables, To appear in the Proceedings of YKIS2009 Frontiers in Nonequilibrium Physics, Progress of Theoretical Physics Supplement (2010).

We propose a novel approach based on a Langevin equation for fluctuating motion of the center of mass of granular media fluidized by energy injection from a bottom plate. In this framework, the analytical solution of the Langevin equation is used to derive analytic expressions for several macroscopic quantities and the power spectrum for the center of mass. In order to test our theory, we performed event-driven molecular dynamics simulations for one- and two-dimensional systems. Energy is injected from a vibrating bottom plate in the one-dimensional case and from a thermal wall at the bottom in the two-dimensional case. We found that the theoretical predictions are in good agreement with the results of those simulations under the assumption that the fluctuation-dissipation relation holds in the case of nearly elastic collisions between particles. However, as the inelasticity of the interparticle collisions increases, the power spectrum for the center of mass obtained by the simulations gradually deviates from the prediction of theoretical curve. Connection between this deviation and violation of the fluctuation-dissipation relation is discussed., Comment: 13 pages, 11 figures; corrected typos, to be published in the AIP Conference Proceedings of the IUTAM-ISIMM Symposium "Mathematical and Physical Instances of Granular Flows" held in Reggio Calabria, September 14-18, 2009

We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this framework, we derive analytical expressions for several macroscopic quantities. We also predict the power spectrum for the height of the center of mass. We find good agreement between our theoretical predictions and extensive event-driven molecular dynamics simulations., Comment: 11 pages, 3 figures, to be published in J. Phys. Soc. Jpn

Alder and Wainwright discovered the slow power decay $\sim t^{-d/2}$ ($d$:dimension) of the velocity autocorrelation function in moderately dense hard sphere fluids using the event-driven molecular dynamics simulations. In the two-dimensional case, the diffusion coefficient derived using the time correlation expression in linear response theory shows logarithmic divergence, which is called the ``2D long-time-tail problem''. We revisited this problem to perform a large-scale, long-time simulation with one million hard disks using a modern efficient algorithm and found that the decay of the long tail in moderately dense fluids is slightly faster than the power decay ($\sim 1/t$). We also compared our numerical data with the prediction of the self-consistent mode-coupling theory in the long time limit ($\sim 1/(t\sqrt{\ln{t}})$)., Comment: 5 pages, 5 figures, to appear in Phys. Rev. E

We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbulence. There are four typical stages in the freely evolving inelastic hard disk system, which are homogeneous, shearing (vortex), clustering and final state. In the shearing stage, the self-organized macroscopic coherent vortices become dominant. In the clustering stage, the energy spectra are close to the expectation of Kraichnan-Batchelor theory and the squared two-particle separation strictly obeys Richardson law., Comment: 4 pages, 4 figures, to be published in PRE

Molecular dynamics study on the granular bifurcation in a simple model is presented. The model consists of hard disks, which undergo inelastic collisions; the system is under the uniform external gravity and is driven by the heat bath. The competition between the two effects, namely, the gravitational force and the heat bath, is carefully studied. We found that the system shows three phases, namely, the condensed phase, locally fluidized phase, and granular turbulent phase, upon increasing the external control parameter. We conclude that the transition from the condensed phase to the locally fluidized phase is distinguished by the existence of fluidized holes, and the transition from the locally fluidized phase to the granular turbulent phase is understood by the destabilization transition of the fluidized holes due to mutual interference., Comment: 35 pages, 17 figures, to be published in PRE

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker., Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.5

A simple and efficient algorithm of the molecular-dynamics simulation of the hard disk system based on the Event-Driven method is developed. From the analysis of algorithm, the complexity is O(log N) per 1 event, and the constant coefficient of the complexity is smaller than conventional efficient algorithm based on the concept of Cell-Crossing Event. The maximum performance more than 460 millions of collisions per CPU-hour on the Alpha600 compatible in 2500 particle system is achieved. An extension to the infinite-space system based on this algorithm is also proposed., Comment: 13 pages, including 2 figures

We performed numerical simulations on a two-dimensional inelastic hard disk system under gravity with a heat bath to study the dynamics of granular fluidization. Upon increasing the temperature of the heat bath, we found that three phases, namely, the condensed phase, locally fluidized phase, and granular turbulent phase, can be distinguished using the maximum packing fraction and the excitation ratio, or the ratio of the kinetic energy to the potential energy.It is shown that the system behavior in each phase is very different from that of an ordinary vibrating bed., Comment: 4 pages, including 5 figures