Off-lattice Eden-C cluster growth model

Abstract

A non-trivial cluster growth model, equivalent to the lattice-free Eden-C model, is proposed. The model is constructed by randomly adding contiguous circles without overlapping. Large-scale computer simulations show the interior density is constant at 0.650, while the boundary is fractal, with a thickness proportional to the 0.396 power of the mean radius.

Packing Fraction of a Two-dimensional Eden Model with Random-Sized Particles

“…These asymptotic values φ R are considerably smaller than On the other hand, the unfilled circles represent the particles generated between N T = 2500 and 3000. Note that the circles exist in the bulk of the cluster, whereas the active particles exist on only the cluster boundary found by Wang et al 14) φ = 0.78, which was conjectured for the two-dimensional random loose-packed limit. 21) On the other hand, the value of φ R 's are larger than φ = 0.547 for our model evaluated in the random sequential adsorption (RSA) configuration, which is generated by sequentially placing disks of equal size randomly into a region without overlapping.…”

“…However, hitherto there has been no theoretical study focusing on the situation where the particle size is random, although bulk properties of this model have been investigated quantitatively from the viewpoint of pattern formation such as the compact structure 13) and the packing fraction. 14) Wang et al 14) discussed the packing fraction of the Eden model with uniformsized particles.…”

A dynamical model for fractal and compact growth in supercooled systems

“…(2) For cases of isotropic growth, any growth process simulated on a square lattice must bear the unrealistic effect of lattice-imposed anisotropy [54,55]. Potential solutions to this problem include the development of an off-lattice [57] or anisotropycorrected [58] version of the model. (3) For cases of shallow temperature quench, the growth dynamics is typically limited by the diffusion of latent heat [ 25,[59][60][61][65][66][67][68][69][70].…”

“…To understand how a particular growth pattern is formed, computer growth models are often employed to simulate the underlying growth process. Well-known examples include the models of diffusion-limited aggregation (DLA) [35][36][37][38][39] (and relevant diffusion-based models [40,41]), cluster-cluster aggregation (CCA) [42] and percolation [43][44][45][46][47][48][49][50][51][52] for the growth of fractal-like clusters, as well as Eden's model [53,54], including its noise-reduced [55,56], off-lattice [57] and anisotropy-corrected [58] variants, for the growth of compact-like structures. Such growth models, which do not involve any detailed molecular mechanism, provides a unified description of growth processes across different experimental systems.…”

Strategies for optimize off-lattice aggregate simulations

“…In this model, new particles are sequentially added to the empty neighborhood of the cluster without overlap with previously aggregated particles [16,17]. Although the Eden model is unrealistic from the biological point of view, it produces com-pact aggregates with a nontrivial interface scaling usually analyzed through the interface width w [18].…”