M. López de Haro, A. Santos, S. B. Yuste
A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.
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We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.
Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behaviour of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [Commun. Phys. 2, 70 (2019)], we find that the phase behaviour of polydisperse hard-disk systems with lognormal and triangle distributions are significantly different. In polydisperse hard-disk systems of lognormal distributions, although the phase diagram appears similar to that of Gaussian-like polydisperse hard disks, the re-entrant melting of hexatic or solid phase can n…
We examine the question of the criteria of the relaxation to the equilibrium in the hard disk dynamics. In the Event-Chain Monte Carlo, we check the displacement distributions which follows to the exponential law.
Starting from the ordered state, we investigate the short-time behaviour of the hard-disk model. For the positional order, we determine the critical exponents eta and z from the dynamic relaxation of the order parameter and the cumulant with molecular dynamics simulations. The results are compared with previous Monte Carlo (MC) simulations. The bond orientational order is studied with MC dynamics.
The melting of a polydisperse hard disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation unbinding mechanism, as an extension of the 2D hard disk melting problem. We find that while there is pronounced fractionation in polydispersity, the apparent density-polydispersity gap does not increase in width, contrary to 3D polydisperse hard spheres. The point where the Young's modulus is low enough for the dislocation unbinding to occur moves with the apparent melting point, but stays wit…
A two-dimensional system of 10000 hard disks with square periodic boundary conditions, at a density in the middle of the 2-phase region predicted from equation-of-state data, when subjected to a weak external uniform force, is seen to phase separate. Thermodynamic profiles of the inhomogeneous two-phase system agree with the local density approximation (LDA) of density functional theory. There is no indication of any mesophase.
A system of smooth "frozen" Janus-type disks is studied. Such disks cannot rotate and are divided by their diameter into two sides of different inelasticities. Taking as a reference a system of colored elastic disks, we find differences in the behavior of the collisions once the anisotropy is included. A homogeneous state, akin to the homogeneous cooling state of granular gases, is seen to arise and the singular behavior of both the collisions and the precollisional correlations are highlighted.
The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound influence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were first discussed for this model. Here we reformulate hard-disk Monte Carlo algorithms in terms of another classic problem, namely the sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in 1953, appears as a sequence of random walks in high-dimensional polytopes, while the moves of the more powerful event-chain algorithm corres…
Bimodality of local structural ordering in extremely confined hard disks
结合模拟与元胞模型，发现极受限准1D硬壁通道内2D硬盘左右最近邻间距呈现仅由熵键驱动的双峰性，揭示了从类气态到类液态的交叉转变。
Molecular dynamics computer simulations of collective excitations in a system of hard disks confined to a narrow channel of the specific width, that resembles 2D triangular lattice at disk close packing, are performed. We found that transverse excitations, which for hard-disk system are absent in the limit of 1D and are of acoustic nature in the limit of 2D, in the case of q1D hard-disk system emerge in the form of transverse optical excitations and could be considered as a tool to detect the structural transition to a zigzag ordering. By analyzing density evolution of longitudinal static stru…
In this work, the effects of excluded volume are studied in the "one to five hard disks in a box" system. For one and two disks in different types of cages, the attractive and repulsive forces are calculated analytically. Attractive forces are due to excluded volume overlap, and thus allows to understand that in hard-core systems, second neighbors have an effective interaction, a fact that is usually neglected when considering only collisions with first-neighbors. The same effects are observed for numerical computations with five-disks in a box, as the distributions of distances between disks …
Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system
该理论统一了硬磁盘系统熵的广延性与强度性贡献，通过两至五个同心圆的相交公式直接计算自由体积，便于数值模拟，并可推广至硬球系统。
The freezing mechanism, recently suggested for a monodisperse hard-disk fluid [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is extended here to an equimolar binary hard-disk mixtures. We are showing that for diameter ratios, smaller than 1.15 the global orientational order parameter of the binary mixture behaves like in the case of a monodisperse fluid. Namely, by increasing the disk number density there is a tendency to form a crystalline-like phase. However, for diameter ratios larger than 1.15 the binary mixtures behave like a disordered fluid. We use some of the structural and thermodyna…
The freezing mechanism suggested for a fluid composed of hard disks [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is used here to probe the fluid-to-solid transition in a hard-dumbbell fluid composed of overlapping hard disks with a variable length between disk centers. Analyzing the trends in the shape of second maximum of the radial distribution function of the planar hard-dumbbell fluid it has been found that the type of transition could be sensitive to the length of hard-dumbbell molecules. From the ${NpT}$ Monte Carlo simulations data we show that if a hard-dumbbell length does not exce…
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