Related papers: Sublogarithmic fluctuations for internal DLA
Using stochastic conformal mappings we study the effects of anisotropic perturbations on diffusion limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant…
We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number moments a single step of the walk has. Under various…
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…
In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the…
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…
We measure the multiscaling behavior of large off-lattice diffusion limited aggregates (DLA). In contrast to previous studies we now find a continuous dependence of the multiscaling dimensions $D(x)$ on the relative distance $x=r/R_g$ to…
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 consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $\pi/4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^a$ all new…
Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in…
Let each of n particles starting at the origin in Z^2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) of n occupied sites is (with high…
We identify sources of systematic error in traditional simulations of the Witten-Sander model of diffusion-limited aggregation (DLA) on a square lattice. We present an algorithm that reduces these biases to below $10^{-12}$. We grow…
Using off-lattice noise reduction it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of…
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 Internal Diffusion Limited Aggregation has been introduced by Diaconis and Fulton in 1991. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated…
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of…
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…
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 give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process.…
We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…