A Mathematical Theory for Random Solid Packings

Zong, Chuanming

doi:10.48550/arxiv.1410.1102

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…The set containing the placed particles is called a saturated random packing. Besides modeling absorption layers, such packings have a large variety of applications including soft matter [2,3], telecommunication [4], information theory [5] and mathematics [6].…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions in random sequential adsorption

Cieśla¹,

Ziff²

2018

J. Stat. Mech.

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The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.

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Section: Introductionmentioning

confidence: 99%

Boundary conditions in random sequential adsorption

Cieśla¹,

Ziff²

2018

J. Stat. Mech.

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“…The name of RSA is related to irreversible adsorption processes where particles are randomly placed on a surface or interface [3,4,5] -one iteration of RSA algorithm corresponds to one adsorption attempt of a single M. Smoluchowski Institute of Physics, Jagiellonian University, Lojasiewicza 11, 30-348 Cracow, Poland particle. However, RSA applications are much wider including soft matter [6], telecommunication [7], information theory [8] and mathematics [9].…”

Section: Introductionmentioning

confidence: 99%

Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing

Cieśla

2016

J Stat Phys

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The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three dimensional packings were supported by analytical calculations valid for any dimension d. It has been shown that the number of iterations needed to generate finite saturated packing is subject to Pareto distribution with exponent −1 − 1/d and the median of this distribution scales with packing size according to the power-law characterized by exponent d. Obtained results can be used in designing effective random sequential adsorption simulations.

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“…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 The RSA algorithm is based on consecutive tries to add a particle to a packing.…”

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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A Mathematical Theory for Random Solid Packings

Cited by 4 publications

References 21 publications

Boundary conditions in random sequential adsorption

Boundary conditions in random sequential adsorption

Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing

Shapes for maximal coverage for two-dimensional random sequential adsorption

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