Author

Abstract

The Random Deposition model is the simplest model for surface growth, where there is no correlation between the neighbor sites of the lattice. In the Ballistic deposition model, the particles stick to the first neighbor particle; thus it is used to describe the deposition of the sticky particles. However, in many true-life phenomena involving surface growth, there is no adhesion. Instead, the friction between the particles leads to interlocking particles and the formation of porosity inside the growing bulk. Presenting a discrete 1+1 dimensional model, we study this case. In this model, if a particle is trapped between two other particles from right and left, it will stay in that position, as an equivalent for friction. The growth and roughness exponents are calculated, close to the Ballistic model, although there is no lateral growth.

Keywords

1. A L Barabási and H E Stanley, “Fractal Concepts in Surface Growth”, Cambridge University Press (1995). 2. E Ben-Jacob, O Shochet, A Tenenbaum, I Cohen, A Czirok, and T Vicsek, Fractals 2, 01 (1994) 15. 3. M Matsushita and H Fujikawa, Physica A: Statistical Mechanics and its Applications 168, 1 (1990) 498. 4. D A Weitz, M Y Lin, and C J Sandroff, Surface Science 158, 1-3 (1985) 147. 5. P Meakin, Advances in Colloid and Interface Science 28 (1987) 249. 6. H Brune, C Romainczyk, H Röder, and K Kern, Nature 369 (6480) (1994) 469. 7. A L Barabási, S V Buldyrev, S Havlin, G Huber, H E Stanley, and T Vicsek, “Surface Disordering: Growth, Roughening and Phase Transitions”, Nova Science, New York (1992). 8. J Zhang, Y C Zhang, P Alstrøm, and M T Levinsen, Physica A: Statistical Mechanics and its Applications, 189, 3-4 (1992) 383. 9. H Löwe, L Egli, S Bartlett, M Guala, and C Manes, Geophysical Research Letters 34 (2007) L21507. 10. S F Edwards,and D R Wilkinson, “The Surface Statistics of a Granular Aggregate”, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 381, 1780 (1982) 17. 11. K Kardar, G Parisi, and Y Z Zhang, Phys. Rev. Lett. 56 (1986) 889. 12. F Family and T Vicsek, Journal of Physics A: Mathematical and General 18, 2 (1985) L75. 13. M J Vold, Journal of Colloid Science 18, 7 (1963) 684. 14. P Meakin, P Ramanlal, L M Sander, and R C Ball, Physical Review A 34, 6 (1986) 5091. 15. F Family, Journal of Physics A: Mathematical and General 19, 8 (1986) L441. 16. P Meakin and R Jullien, Journal de Physique 48, 10 (1987) 1651.

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