Related papers: Attracted Diffusion-Limited Aggregation
The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact…
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…
A generalized form of the Hastings and Levitov (HL) algorithm for simulation of diffusion-limited aggregation (DLA) restricted in a sector geometry is studied. It is found that this generalization with uniform measure produces "wedge-like"…
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…
We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput…
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…
The growth of a diffusion limited aggregation (DLA) cluster with mass $M$ and radius of gyration $R$ is described by a set of growth probabilities $\{ p_i\}$, where $p_i$ is the probability that the perimeter site $i$ will be the next to…
We extend the conformal mapping approach elaborated for the radial Diffusion Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in particular a complex function which allows to grow a cylindrical cluster using as…
We study the fractal and multifractal properties (i.e. the generalized dimensions of the harmonic measure) of a 2-parameter family of growth patterns that result from a growth model that interpolates between Diffusion Limited Aggregation…
A connection between fractal dimensions of "turbulent facets" and fractal dimensions in diffusion-limited aggregation (DLA) is shown. The theoretical correspondence is elucidated and an empirical support to the above claim is given.
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…
A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define…
Aggregation phenomena are ubiquitous in nature, encompassing out-of-equilibrium processes of fractal pattern formation, important in many areas of science and technology. Despite their simplicity, foundational models such as…
Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are…
We have combined the original diffusion-limited aggregation model introduced by Witten and Sander with the surface thermodynamics of the growing solid aggregate. The theory is based on the consideration of the surface chemical potential as…
Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the…
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…
We study the structure and growth of a difusion-limited aggregate (DLA) for which the constitutive units remain mobile during the aggregation process. Contrary to DLA where far from equilibrium conditions are the prevalent factor for…
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…
Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…