The Study of Percolation with the Presence of Extended Impurities
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Date
2017-09-18
Journal Title
Journal ISSN
Volume Title
Journal Title
Journal of Statistical Mechanics: Theory and Experiment
Volume Title
2017
Article Title
093202
Publisher
Institute of Physics Publishing
Abstract
In the preceding paper, Budinski-Petković et al (2016 J. Stat. Mech. 053101) studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths ℓ. For a wide range of impurity concentrations p, percolation threshold θp∗ is determined for k-mers, angled objects and triangles of two different sizes. For sufficiently large impurities, percolation threshold θp∗ of all examined objects increases with concentration p, and this increase is more prominent for impurities of a larger length ℓ. We determine the critical concentrations of pc∗ defects above which it is not possible to achieve percolation for a given object, for impurities of various lengths ℓ. It is found that the critical concentration pc∗ of finite-size impurities decreases with the length ℓ of impurities. In the case of deposition of larger objects an exception occurs for point-like impurities when critical concentration pc∗ of monomers is lower than pc∗ for the dimer impurities. At relatively low concentrations p, the presence of small impurities (but not point-like) stimulates the percolation for larger depositing objects.