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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

In the classical model of Diffusion Limited Aggregation (DLA), introduced by Witten and Sander, the process begins with a single particle cluster placed at the origin of a space, and then, one at a time, particles make a random walk from…

Probability · Mathematics 2026-04-29 Colin Cooper , Alan Frieze

Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph $G$, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the…

Probability · Mathematics 2022-02-04 Nico Heizmann

We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear…

Statistical Mechanics · Physics 2009-11-11 Benny Davidovitch , Jaehyuk Choi , Martin Z. Bazant

Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The…

Computational Engineering, Finance, and Science · Computer Science 2016-11-17 Tuomo Sipola , Fengyu Cong , Tapani Ristaniemi , Vinoo Alluri , Petri Toiviainen , Elvira Brattico , Asoke K. Nandi

Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…

Statistical Mechanics · Physics 2007-05-23 Benny Davidovich , M. J. Feigenbaum , H. G. E. Hentschel , Itamar Procaccia

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…

Condensed Matter · Physics 2009-10-28 Thomas C. Halsey , Katsuya Honda , Bertrand Duplantier

Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by…

Probability · Mathematics 2025-10-16 Amine Asselah , Vittoria Silvestri , Lorenzo Taggi

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…

Statistical Mechanics · Physics 2009-11-11 M. Tasinkevych , J. M. Tavares , F. de los Santos

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

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 extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of dynamical scale invariance in the coarsening of two-dimensional DLAs (diffusion-limited aggregates) as described by the Cahn-Hilliard equation. Existence of a second…

Disordered Systems and Neural Networks · Physics 2007-05-23 Massimo Conti , Baruch Meerson , Pavel V. Sasorov

A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…

Chaotic Dynamics · Physics 2007-05-23 A. Loskutov , D. Andrievsky , V. Ivanov , K. Vasiliev , A. Ryabov

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the…

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

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal…

Statistical Mechanics · Physics 2008-10-02 Anton Yu. Menshutin , Lev N. Shchur , Valery M. Vinokour

Internal DLA is a discrete random growth model describing growing clusters of particles. Its limiting shape and fluctuations are well understood when the underlying graph is the $d$-dimensional lattice or the cylinder $\mathbb{Z}_N \times…

Probability · Mathematics 2026-04-24 Ahmed Bou-Rabee , Vittoria Silvestri , Ariel Yadin

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 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…

Statistical Mechanics · Physics 2009-11-07 H. George E. Hentschel , Anders Levermann , Itamar Procaccia

We consider a cluster growth model on the d-dimensional lattice, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied…

Probability · Mathematics 2013-06-03 Amine Asselah , Alexandre Gaudilliere

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,…

Probability · Mathematics 2019-07-04 Ecaterina Sava-Huss