Paris car parking problem for partially oriented discorectangles on a line

Connectedness percolation in the random sequential adsorption packings of elongated particles

“…For 2D systems with h > 1, a wide variety of monotonic and non-monotonicφ(ε) dependencies have been observed. Particularly, for the system with PBCs (systems with size 32ε×32ε were used to imitate an infinitely large system) the maximum in theφ(ε) dependence can be explained a a result the competition between the particles' orientational degrees of freedom and the excluded area effects [14,15,21]. Monotonicφ(ε) dependencies have only been observed in strongly confined systems with h < 3.…”

“…For larger distances (h ≥ 10) between the walls, there were powerlike dependencies δ ∝ ε α with exponent 0.25 < α < 1. Finally, for the imitated infinite systems (systems with PBCs applied in both the horizontal (x) and the vertical (y) directions and of the system size 32ε × 32ε [21]) the value α ≈ 0.25 was estimated. Obtained data evidenced that the confinement between walls resulted in a weakening of connectivity along the vertical axis y( ) and an enhancement of it across the horizontal axis x(↔).…”

“…The width of the slit was varied within h ∈ [1; 80] and periodic boundary conditions (PBCs) were used in the vertical (y) direction. The comparative data to mimic infinite systems were obtained using PBCs applied in both the horizontal (x) and the vertical (y) directions using a system size of 32ε × 32ε (more detailed information can be found elsewhere [21]).…”

“…For elongated particles, RSA is a challenging problem that has been the ongoing focus of many researchers. The RSA packings of ellipses [10,11], rectangles [12,13], discorectangles [14,15], and other elongated objects [6,[16][17][18][19][20][21] with different aspect ratios (length-to-width ratios ε = l/d), have been analyzed. In many cases, intriguing non-monotonic ϕ(ε) dependencies have been observed.…”

Relaxation of saturated random sequential adsorption packings of discorectangles aligned on a line

“…The different 1D-RSA problems for particles with arbitrary shapes, e.g., segments (sticks), disks, ellipses, rectangles, discorectangles, etc., have been analyzed [7][8][9]. For elongated particles, this problem is commonly referred to as the "Paris car parking problem" [10]. For the parking of 1D segments of identical length, the kinetics of the RSA have been described analytically [1,2].…”