Related papers: Discrete Growth Models
We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to $10^8$ particles). We observe that DLA clusters undergo strongly anisotropic…
Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…
These lecture notes on 2D growth processes are divided in two parts. The first part is a non-technical introduction to stochastic Loewner evolutions (SLEs). Their relationship with 2D critical interfaces is illustrated using numerical…
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…
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…
We present an unified approach on the behavior of two random growth models (external DLA and internal DLA) on infinite graphs, the second one being an internal counterpart of the first one. Even though the two models look pretty similar,…
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…
The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely…
Diffusion limited aggregation is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the depth of the tree defined by the cluster. The existence of this…
We present two different projects. The first one is related to the development of a semi-analytic model to follow the formation, the evolution and chemical enrichment of cluster galaxies in a hierarchical dark matter model. The second…
The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
This paper is devoted to study a model of individual clustering with two specific reproduction rates in two space dimensions. Given q > 2 and an initial condition in W 1,q (\Omega), the local existence and uniqueness of solution have been…
We develop a technique for probing harmonic measure of the diffusion limited aggregation (DLA) cluster surface with the variable size particle and generate one thousand clusters with 50 million particles using original off-lattice…
We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.
I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the…
The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…
This thesis establishes new quantitative records in several problems of incidence geometry and growth. After the necessary background in Chapters 1, 2 and 3, the following results are proven. Chapter 4 gives new results in the incidence…
Diffusion-Limited Aggregation (DLA) is a cluster-growth model that consists in a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which…
Results from a modified Diffusion Limited Aggregation (DLA) model are presented. The modifications of the classical DLA model are in the attachment to the cluster rules and in the scheme of particle generation/killing. In the classical DLA…