Structural properties of hard disks in a narrow tube

Abstract

Abstract. Positional ordering of a two-dimensional fluid of hard disks is examined in such narrow tubes where only the nearest-neighbor interactions take place. Using the exact transfer-matrix method the transverse and longitudinal pressure components and the correlation function are determined numerically. Fluid-solid phase transition does not occur even in the widest tube, where the method just loses its exactness, but the appearance of the dramatic change in the equation of state and the longitudinal correlation function shows that the system undergoes a structural change from a fluid to a solid-like order. The pressure components show that the collisions are dominantly longitudinal at low densities, while they are transverse in the vicinity of close packing density. The transverse correlation function shows that the size of solid-like domains grows exponentially with increasing pressure and the correlation length diverges at close packing. It is managed to find an analytically solvable model by expanding the contact distance up to first order. The approximate model, which corresponds to the system of hard parallel rhombuses, behaves very similarly to the system of hard disks.

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

“…Equation (7) agrees with the results of Kofke and Post [30] and Varga et al [31] who considered only the case h/σ ≤ √ 3/2 in developing their transfer matrix formalism: in that special case, the step functions are all unity, because σ k,k+1 + σ k,k−1 ≥ σ k−1,k+1 ; the s i -integrations can be completed analytically, givinĝ…”

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

“…Note that the eigenfunction does not depend on the azimuthal angle (ϕ) in 3D due to symmetry reasons, i.e., ψ = ψ(y) and ψ = ψ(R) in 2D and 3D, respectively. The equation of state can be obtained from the Gibbs free energy using the following thermodynamic relation: 32 where ρ = N/L is the linear number density and L is the length of the channel. Note that the system is infinite along the horizontal axis, i.e., contrary to the MC simulation method no finite size and periodic boundary effects are present in the results.…”

Glasslike behavior of a hard-disk fluid confined to a narrow channel

“…For any finite value of this force, large fluctuations in the xcoordinates of the disks cause the time-averaged density of disks to be independent of x, so that the system is never crystalline. The static, equilibrium properties of this simple system can be determined exactly by use of the transfer matrix [6,[8][9][10][11], but the chief purpose of this paper to discuss the dynamics. The dynamical properties of our system must be determined from simulations, and to this end we have used event-driven molecular dynamics to handle the collisions of the disks with each other and with the channel walls.…”