Geodesic
Jamming coverage of blocks on a cubic lattice
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 82-93

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In this paper the discrete block jamming model on a cubic lattice is investigated by means of mathematical and computer simulation. A block ($k^3$-mer) with side length $k$ represents $k \times k \times k$ occupied nodes on the lattice. The start coordinates of the blocks are randomly generated uniformly distributed integers. The blocks do not overlap with each other. Periodic boundary conditions are used in the modelling. A blocks maximum packing algorithm is developed and a computer program is written to implement the mathematical model. A method for estimating of critical values by maximum lattice fill is proposed. The values of the jamming thresholds for many $k$ in the range from $2$ to $80$ were determined. Several estimates of the jamming threshold at $k\rightarrow \infty$ are obtained. The results of the paper suggest that the jamming threshold does not depend on the linear size of the lattice.
Keywords: jamming coverage, block, $k^3$-mer, cubic lattice, random sequential adsorption, percolation theory. 
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     author = {K. A. Ebert and M. M. Buzmakova and S. V. Rusakov},
     title = {Jamming coverage of blocks on a cubic lattice},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {82--93},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2024_17_4_a6/}
}
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K. A. Ebert; M. M. Buzmakova; S. V. Rusakov. Jamming coverage of blocks on a cubic lattice. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 82-93. http://geodesic.mathdoc.fr/item/VYURU_2024_17_4_a6/