Random sequential adsorption

Feder, Jens

doi:10.1016/0022-5193(80)90358-6

Cited by 636 publications

(550 citation statements)

References 26 publications

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“…Included in the table is the stopping density φ stop , relative system volume L d /v 1 (1/2) for the largest system, where v 1 (1/2) is the volume of a hypersphere, and the total number of configurations n conf . The results for d = 1, 2 and 3 agree well with known results for these dimensions [17,18,20,21,22]. We see that the stopping density φ stop is very nearly equal to the saturation density φ s for all dimensions, except for d = 1 where these two quantities are identical.…”

Section: A Saturation Densitysupporting

confidence: 88%

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Random sequential addition of hard spheres in high Euclidean dimensions

2006

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Sphere packings in high dimensions have been the subject of recent theoretical interest. Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in d-dimensional Euclidean space R d in the infinitetime or saturation limit for the first six space dimensions (1 ≤ d ≤ 6). Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each of these dimensions. We find that for 2 ≤ d ≤ 6, the saturation density φ s scales with dimension as φ s = c 1 /2 d + c 2 d/2 d , where c 1 = 0.202048 and c 2 = 0.973872. We also show analytically that the same density scaling persists in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by φ s ≥ (d + 2)(1 − S 0 )/2 d+1 , where S 0 ∈ [0, 1] is the structure factor at k = 0 (i.e., infinite-wavelength number variance) in the high-dimensional limit.We prove rigorously that a Palàsti-like conjecture (the saturation density in R d is equal to that of the one-dimensional problem raised to the dth power) cannot be true for RSA hyperspheres.We demonstrate that the structure factor S(k) must be analytic at k = 0 and that RSA packings for 1 ≤ d ≤ 6 are nearly "hyperuniform." Consistent with the recent "decorrelation principle," we find that pair correlations markedly diminish as the space dimension increases up to six. We also obtain kissing (contact) number statistics for saturated RSA configurations on the surface of a ddimensional sphere for dimensions 2 ≤ d ≤ 5 and compare to the maximal kissing numbers in these dimensions. We determine the structure factor exactly for the related "ghost" RSA packing in R d and show that its distance from "hyperuniformity" increases as the space dimension increases, approaching a constant asymptotic value of 1/2. Our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions.

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Section: A Saturation Densitysupporting

confidence: 88%

“…[17]. For 2 ≤ d < ∞, an exact determination of φ(∞) is not possible, but estimates for it have been obtained via computer experiments in two dimensions (circular disks) [18,20] and three dimensions (spheres) [21,22]. However, estimates of the saturation density φ(∞) in higher dimensions have heretofore not been obtained.…”

Section: Introductionmentioning

confidence: 99%

Random sequential addition of hard spheres in high Euclidean dimensions

2006

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“…Thus, a particle arriving at the surface is accepted if it does not overlap with a previously adsorbed one; otherwise it is rejected. Specific quantities, such as the maximum coverage of the surface, or jamming limit, are in accordance with some experimental results [3] [4] [5], so it was concluded that RSA was a good model when particles diffuse to the surface. However, further numerical studies which took into account the diffusion showed discrepancies in the pair distribution function [6].…”

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Influence of hydrodynamic interactions on the adsorption process of large particles

Pagonabarraga

Rubı́

1994

Phys. Rev. Lett.

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“…Rényi 2 introduced another famous one-dimensional RSA problem-the parking of cars along an unmarked curb. Feder 3 helped to make RSA a very popular tool for modeling monolayers obtained as a result of irreversible adsorption [4][5][6] . More recently, random packings generated by RSA have been of interest in a number of scientific fields, e.g., soft matter [7][8][9] , surface science 10 , mathematics 11 , telecommunication 12 and information theory 13 .…”

Section: Introductionmentioning

confidence: 99%

Shapes for maximal coverage for two-dimensional random sequential adsorption

Cieśla

Pajk

Ziff

2015

Phys. Chem. Chem. Phys.

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The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to the maximum packing fraction of ellipsoids and spherocylinders and higher than other studied shapes. Discussion why this shape is beneficial for random sequential adsorption is given.

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Random sequential adsorption

Cited by 636 publications

References 26 publications

Random sequential addition of hard spheres in high Euclidean dimensions

Random sequential addition of hard spheres in high Euclidean dimensions

Influence of hydrodynamic interactions on the adsorption process of large particles

Shapes for maximal coverage for two-dimensional random sequential adsorption

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