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Percolation and jamming properties in particle shape-controlled seeded growth model

  • Regular Article – Statistical and Nonlinear Physics
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Abstract

We consider the percolation model with nucleation and simultaneous growth of multiple finite clusters, taking the initial seed concentration \(\rho \) as a tunable parameter. Growing objects expand with constant speed, filling the nodes of the triangular lattice according to rules that control their shape. As growing objects of predefined shape, we consider needle-like objects and “wrapping” objects whose size is gradually increased by wrapping the walks in several different ways, making triangles, rhombuses, and hexagons. Growing random walk chains are also analyzed as an example of objects whose shape is formed randomly during the growth. We compare the percolation properties and jamming densities of the systems of various growing shapes for a wide range of initial seed densities \(\rho < 0.5\). To gain a basic insight into the structure of the jammed states, we consider the size distribution of deposited growing objects. The presence of the most numerous and the largest growing objects is recorded for the system in the jamming state. Our results suggest that at sufficiently low seed densities \(\rho \), the way of the object growth has a substantial influence on the percolation threshold. This influence weakens with increasing \(\rho \) and ceases near the value of the site percolation threshold for monomers on the triangular lattice, \(\rho _\text {p}^* = 0.5\).

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and there are no experimental data.]

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Acknowledgements

This work was supported by the Ministry of Education, Science, and Technological Development of the Republic of Serbia. Numerical simulations were run on the PARADOX supercomputing facility at the Scientific Computing Laboratory of the Institute of Physics Belgrade.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, 71000, Bosnia and Herzegovina

    D. Dujak

  2. Polytechnic Faculty, University of Zenica, Zenica, Bosnia and Herzegovina

    A. Karač

  3. Faculty of Engineering, Trg D. Obradovića 6, Novi Sad, 21000, Serbia

    Lj. Budinski-Petković

  4. Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, Zemun, 11080, Belgrade, Serbia

    Z. M. Jakšić & S. B. Vrhovac

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Contributions

Study conception and design: S. B. Vrhovac and Lj. Budinski-Petković; Analysis and interpretation of numerical data: D. Dujak, A. Karač and Z. M. Jakšić; Development of the numerical simulations: D. Dujak and A. Karač; Drafting of manuscript: S. B. Vrhovac and Lj. Budinski-Petković; Critical revision: S. B. Vrhovac, Lj. Budinski-Petković and Z. M. Jakšić

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Correspondence to S. B. Vrhovac.

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Dujak, D., Karač, A., Budinski-Petković, L. et al. Percolation and jamming properties in particle shape-controlled seeded growth model. Eur. Phys. J. B 95, 143 (2022). https://doi.org/10.1140/epjb/s10051-022-00401-1

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