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We had established inner and outer fluctuation for the internal DLA cluster when all walks are launched from the origin. In obtaining the outer fluctuation, we had used a deep lemma of Jerison, Levine and Sheffield, which estimate roughly…
Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…
We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible…
Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed…
We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
For a class of aggregation models on the integer lattice $\mathbb{Z}^d$, $d\geq 2$, in which clusters are formed by particles arriving one after the other and sticking irreversibly where they first hit the cluster, including the classical…
We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of…
Irreversible diffusion limited cluster aggregation (DLCA) of hard spheres was simulated using Brownian cluster dynamics. Bound spheres were allowed to move freely within a specified range, but no bond breaking was allowed. The structure and…
In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…
Diffusion-limited cluster aggregation (DLCA) is a well established model for the formation of highly porous low-density non-equilibrium structures. One of the main conclusions of the previous studies considering this model is that the…
Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and…
Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill…
Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a…
We study the scaling limits of three different aggregation models on the integer lattice Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform…
Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good…