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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…

Statistical Mechanics · Physics 2009-11-10 S. C. Ferreira

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…

Statistical Mechanics · Physics 2023-10-19 Uriel Villanueva-Alcalá , José R. Nicolás-Carlock , Denis Boyer

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…

Probability · Mathematics 2007-12-31 Lionel Levine

We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…

Combinatorics · Mathematics 2019-02-11 Kiana Mittelstaedt

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…

Probability · Mathematics 2018-04-13 Eviatar B. Procaccia , Ron Rosenthal , Yuan Zhang

Internal diffusion-limited aggregation is a growth model based on random walk in Z^d. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in Z^2 for which the limiting shape is a…

Probability · Mathematics 2010-08-17 Wouter Kager , Lionel Levine

Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d > 2. We show that A(t) is approximately spherical, up to an O(\sqrt{\log t}) error.

Probability · Mathematics 2011-02-01 David Jerison , Lionel Levine , Scott Sheffield

Diffusion limited aggregation (DLA) is a well studied phenomenon in which diffusing particles cumulatively aggregate on a starting fixed seed point, forming a pattern which is fractal in structure. Here we report an interesting DLA process…

Pattern Formation and Solitons · Physics 2025-04-21 Suvrajyoti Chatterjee , Saba Firoze , Tabish Qureshi

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…

Statistical Mechanics · Physics 2007-05-23 Benny Davidovich , Itamar Procaccia

We show that various surface parameters in two-dimensional diffusion limited aggregation (DLA) grow linearly with the number of particles. We find the ratio of the average length of the perimeter and the accessible perimeter of a DLA…

Statistical Mechanics · Physics 2010-02-19 A. A. Saberi

We study the generalized diffusion-limited aggregates (DLA), with two seeds placed at distance d lattice units and investigate the probability p(d) that the patterns generated from those seeds get connected. In this model, one can vary the…

Pattern Formation and Solitons · Physics 2007-05-23 Deepak N. Bankar , P. M. Gade , A. V. Limaye , A. G. Banpurkar

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…

Statistical Mechanics · Physics 2009-11-11 Leonard M. Sander , Ellak Somfai

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…

Soft Condensed Matter · Physics 2019-01-15 Swetlana Jungblut , Jan-Ole Joswig , Alexander Eychmüller

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…

Probability · Mathematics 2011-11-21 Amine Asselah , Alexandre Gaudilliere

Diffusion Limited Aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the…

Statistical Mechanics · Physics 2009-10-31 Benny Davidovitch , Anders Levermann , Itamar Procaccia

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…

Condensed Matter · Physics 2007-05-23 Hernan A. Makse , Shlomo Havlin , H. Eugene Stanley

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…

Statistical Mechanics · Physics 2017-11-08 Denis S. Grebenkov , Dmitry Beliaev

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

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…

Statistical Mechanics · Physics 2009-11-10 H. G. E. Hentschel , M. N. Popescu , F. Family

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…

Statistical Mechanics · Physics 2012-07-31 S. H. Ebrahimnazhad Rahbari , A. A. Saberi