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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…

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…

Statistical Mechanics · Physics 2009-08-21 F. Mohammadi , A. A. Saberi , S. Rouhani

We revisit Kesten's argument for the upper bound on the growth rate of DLA. We are able to make the argument robust enough so that it applies to many graphs, where only control of the heat kernel is required. We apply this to many examples…

Probability · Mathematics 2017-05-18 Itai Benjamini , Ariel Yadin

We discuss the scaling of characteristic lengths in diffusion limited aggregation (DLA) clusters in light of recent developments using conformal maps. We are led to the conjecture that the apparently anomalous scaling of lengths is due to…

Statistical Mechanics · Physics 2009-10-31 E. Somfai , L. M. Sander , R. C. Ball

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…

Other Condensed Matter · Physics 2015-05-20 E. B. Postnikov , A. B. Ryabov , A. Loskutov

We explore the macroscopic consequences of lattice anisotropy for Diffusion Limited Aggregation (DLA) in three dimensions. Simple cubic and BCC lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the…

Statistical Mechanics · Physics 2007-05-23 Nicholas R. Goold , Ellak Somfai , Robin C. Ball

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation…

Statistical Mechanics · Physics 2007-05-23 S. G. Alves , S. C. Ferreira

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…

Statistical Mechanics · Physics 2009-10-31 Boaz Kol , Amnon Aharony

The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA…

Statistical Mechanics · Physics 2009-11-07 Felipe Barra , Benny Davidovitch , Itamar Procaccia

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…

Condensed Matter · Physics 2009-10-22 P. L. Krapivsky

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…

Soft Condensed Matter · Physics 2009-03-25 Sujin Babu , Jean-Christophe Gimel , Taco Nicolai

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\tau$ as $\tau^{-\alpha}$. Depending on the exponent $\alpha$, the scaling of tree depth with tree size $n$ displays a…

Populations and Evolution · Quantitative Biology 2015-02-04 Stephanie Keller-Schmidt , Murat Tugrul , Victor M. Eguiluz , Emilio Hernandez-Garcia , Konstantin Klemm

We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is…

Statistical Mechanics · Physics 2007-05-23 R. C. Ball , E. Somfai

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from…

Probability · Mathematics 2008-07-04 Bo Chen , Daniel Ford , Matthias Winkel

Consider a family of random ordered graph trees $(T_n)_{n\geq 1}$, where $T_n$ has $n$ vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled…

Probability · Mathematics 2012-10-24 David A. Croydon

For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established…

Computational Physics · Physics 2007-05-23 Jie Ren , Wen-Xu Wang , Gang Yan , Bing-Hong Wang

We prove that the one dimensional Multi-Particle Diffusion Limited Aggregation model has linear growth whenever the particle density exceeds 1 answering a question of Kesten and Sidoravicius. As a corollary we prove linear growth in all…

Probability · Mathematics 2016-09-27 Allan Sly

In this paper we study the structure of the limit aggregate $A_\infty = \bigcup_{n\geq 0} A_n$ of the one-dimensional long range diffusion limited aggregation process defined in [AABK09]. We show (under some regularity conditions) that for…

Probability · Mathematics 2015-04-07 Gideon Amir

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…

Statistical Mechanics · Physics 2007-05-23 Alessandro Taloni , Emanuele Caglioti , Vittorio Loreto , Luciano Pietronero

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…

Discrete Mathematics · Computer Science 2021-12-20 Nicolas Bitar , Eric Goles , Pedro Montealegre