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We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the emph{on}-collision statistical properties. We analyze the distribution functions of velocity, free flight time and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single particle dynamical properties behave analogously in collisional and continuous time representations, exhibiting apparent crossovers between the fluid and the solid phase. We find that, both in collisional and continuous time representation, the mean square displacement, velocity autocorrelation functions, intermediate scattering functions and self part of the van Hove function (propagator), closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids and supercooled liquids close to the glass or jamming transition.
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.
We consider a modification of the well studied Hamiltonian Mean-Field model by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate numerically its dynamics. Our results show that the outcom
We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to $exp{({const} beta)}$ in the Ising, $sqrt{beta}$ in the classi
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 f
A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low density phase is liqui