%0 Book Section %1 statphys23_0366 %A Proykova, A.I. %A Karadjov, B. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K fractal growth non-equilibrium percolation statphys23 topic-9 %T Conditional Deposition of Particles on a Surface – a Fractal versus Non-fractal Dimension of the Percolating Clusters %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=366 %X The formation of a real surface is influenced by a large number of factors and it is almost impossible to distinguish all of them. The hope is, however, that there is a small number of basic 'laws' determining the morphology and the dynamics of the growth. The action of these basic laws can be described in microscopic detail through discrete growth models that mimic essential physics bypassing some of the less important details. We propose a parametric model for studying the non-equilibrium interfaces: particles, deposited on a surface, stick conditionally with a probability $ømega(łambda)$, where $łambda$ is a controlling parameter; $= 0$ corresponds to a 2D percolation on a square lattice 1. We start with an empty surface, chose a site $i$ at random, and release a particle. The particle is seeded in $i$ with a probability $ømega(łambda)$ which is: (a) $= 1$, if either all neighbors are empty, or only one site is occupied; (b) $= 1/łambda$ if two opposite neighbors are occupied; (c) $ømega=1/łambda^2$ if three neighbors are occupied. The parameter $łambda$ could take any positive real value. Here we present results for $=2, 2, 3, 4$. Unlike the known Alexandrowitz's algorithm where the sites visited previously are marked and excluded from the further trials, our model counts all the empty sites in every trial. The deposition of particles continues until a concentration $c $ 0,1 is reached. The concentration is defined as the ratio of N (number of particles) and LxL (number of cells). The time for deposition of N particles is scaled by the number of trial steps, e.g. it depends on $ømega(łambda)$ and increases with the concentration. This is a simulation of a hampered aggregation of non-diffusive particles. For some critical particle concentrations $p_c(łambda)$, the connecting clusters are fractals. A technique, which is a modification of the box-counting method (Parrinello), has been worked out for determining the fractal dimension. An object-oriented code (C++) has been developed for the Monte Carlo part of the calculations. This style of coding allows an abstract definition of the ‘nearest neighbors’ and by changing the number of neighbors one can solve 2D, 3D or higher-dimensional problems implementing the same code. Other applications can be simulated with our model: a transition from an insulating surface to a metallic one, if the particles are metal atoms or a change of the social communications influenced by mass media 2.\ References: 1 Stauffer D and Aharony A 1991 Introduction to Percolation Theory 2nd edn. (London: Taylor and Francis). 2 Proykova A and Stauffer D, Physica A, vol 312/1-2 pp 300-304, (2002).

@incollection{statphys23_0366, abstract = {The formation of a real surface is influenced by a large number of factors and it is almost impossible to distinguish all of them. The hope is, however, that there is a small number of basic 'laws' determining the morphology and the dynamics of the growth. The action of these basic laws can be described in microscopic detail through discrete growth models that mimic essential physics bypassing some of the less important details. We propose a parametric model for studying the non-equilibrium interfaces: particles, deposited on a surface, stick conditionally with a probability $\omega(\lambda)$, where $\lambda$ is a controlling parameter; $\lambda = 0$ corresponds to a 2D percolation on a square lattice [1]. We start with an empty surface, chose a site $\it i$ at random, and release a particle. The particle is seeded in $\it i$ with a probability $\omega(\lambda)$ which is: (a) $\omega = 1$, if either all neighbors are empty, or only one site is occupied; (b) $\omega = 1/\lambda$ if two opposite neighbors are occupied; (c) $\omega=1/{\lambda}^2$ if three neighbors are occupied. The parameter $\lambda$ could take any positive real value. Here we present results for $\lambda =\sqrt 2, 2, 3, 4$. Unlike the known Alexandrowitz's algorithm where the sites visited previously are marked and excluded from the further trials, our model counts all the empty sites in every trial. The deposition of particles continues until a concentration $c \in $ [0,1] is reached. The concentration is defined as the ratio of N (number of particles) and LxL (number of cells). The time for deposition of N particles is scaled by the number of trial steps, e.g. it depends on $\omega(\lambda)$ and increases with the concentration. This is a simulation of a hampered aggregation of non-diffusive particles. For some critical particle concentrations $p_c(\lambda)$, the connecting clusters are fractals. A technique, which is a modification of the box-counting method (Parrinello), has been worked out for determining the fractal dimension. An object-oriented code (C++) has been developed for the Monte Carlo part of the calculations. This style of coding allows an abstract definition of the ‘nearest neighbors’ and by changing the number of neighbors one can solve 2D, 3D or higher-dimensional problems implementing the same code. Other applications can be simulated with our model: a transition from an insulating surface to a metallic one, if the particles are metal atoms or a change of the social communications influenced by mass media [2].\ References: [1] Stauffer D and Aharony A 1991 Introduction to Percolation Theory 2nd edn. (London: Taylor and Francis). [2] Proykova A and Stauffer D, Physica A, vol 312/1-2 pp 300-304, (2002).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Proykova, A.I. and Karadjov, B.}, biburl = {https://www.bibsonomy.org/bibtex/272ec8e458f9b7a3315a343004990add0/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {46cf9c79411050fcc6ac4ef442ad0b3f}, intrahash = {72ec8e458f9b7a3315a343004990add0}, keywords = {fractal growth non-equilibrium percolation statphys23 topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Conditional Deposition of Particles on a Surface – a Fractal versus Non-fractal Dimension of the Percolating Clusters}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=366}, year = 2007 }