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Multiparticle diffusion-limited aggregation with strip geometry

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  • Meakin, Paul

Abstract

Two finite density versions of the multiparticle DLA model have been investigated on strips of width L lattice units with periodic boundary conditions. In model I single particles are added to the deposit at the position in which they first attempt to step onto the deposit and in model II particles directly and indirectly connected to the deposit (via nearest neighbor occupancy) are added when they first contact the growing deposit. For model I the growth of the deposit mass crosses over from t12 dependence in the low density/short time limit to M ∼ t in the high density/long time limit. For model II a similar crossover is found but as the density approaches the percolation threshold the deposit mass is found to grow according to M ∼ tδ with δ having a value of about 4/3. These results help to resolve some apparent discrepancies between the results of earlier work on closely related models by Voss and by Meakin and Deutch.

Suggested Citation

  • Meakin, Paul, 1988. "Multiparticle diffusion-limited aggregation with strip geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 1-19.
    • Handle: RePEc:eee:phsmap:v:153:y:1988:i:1:p:1-19
    DOI: 10.1016/0378-4371(88)90098-2
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    Cited by:

    1. Zhang, Ligen & Yang, Z.R., 1997. "A solvable aggregation-annihilation chain model with n species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 441-448.
    2. Sang Bub Lee, & Amar, J.G. & Family, F., 1997. "Thin film growth of incompatible materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 337-354.
    3. Bershadskii, A., 1997. "Critical multifractality near monofractal states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 238(1), pages 1-8.
    4. Mašić, Nikola & Djordjević, Zorica V., 1990. "Multifractal nature of the first passage time for biased diffusion on percolation clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(2), pages 560-564.
    5. Bershadskii, A., 1997. "Branched critical multifractality and morphological phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 79-90.
    6. Meakin, Paul, 1989. "Reaction and adsorption on multifractal substrates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(1), pages 21-36.
    7. Meakin, Paul & Jøssang, Torstein & Feder, Jens, 1993. "A two dimensional reaction-limited selective dissolution model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 196(4), pages 481-504.

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