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Related papers: Anisotropic Diffusion Limited Aggregation

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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

Using event-driven kinetic Monte-Carlo simulations we investigate the early stage of non-equilibrium surface growth in a generic model with anisotropic interactions among the adsorbed particles. Specifically, we consider a two-dimensional…

Soft Condensed Matter · Physics 2018-10-24 Thomas Martynec , Sabine H. L. Klapp

We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the…

Statistical Mechanics · Physics 2007-05-23 Ellak Somfai , Robin C. Ball , Jason P. DeVita , Leonard M. Sander

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…

Statistical Mechanics · Physics 2007-05-23 Martin Z. Bazant , Jaehyuk Choi , Benny Davidovitch

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

Mesoscale and Nanoscale Physics · Physics 2025-04-02 Nilotpal Chakraborty , Markus Heyl , Roderich Moessner

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low…

Statistical Mechanics · Physics 2007-05-23 Mogens H. Jensen , Anders Levermann , Joachim Mathiesen , Benny Davidovitch , Itamar Procaccia

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

In the Diffusion Limited Aggregation (DLA) process on on $\mathbb{Z}^2$, or more generally $\mathbb{Z}^d$, particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a…

Probability · Mathematics 2017-12-25 Alan Frieze , Wesley Pegden

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 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

We study internal diffusion limited aggregation (DLA) on the two dimensional comb lattice. The comb lattice is a spanning tree of the euclidean lattice, and internal DLA is a random growth model, where simple random walks, starting one at a…

Probability · Mathematics 2014-01-28 Amine Asselah , Houda Rahmani

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

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

In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution with mean $\mu$, independently of all other…

Mathematical Physics · Physics 2020-09-15 Vladas Sidoravicius , Balazs Rath

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

Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and…

Pattern Formation and Solitons · Physics 2020-01-27 J. R. Nicolás-Carlock , J. M. Solano-Altamirano , J. L. Carrillo-Estrada

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

We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if…

Probability · Mathematics 2015-11-24 A. Asselah , E. Cirillo , E. Scoppola , B. Scoppola

We study the horizontal expansion of vertically confined ultra-cold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is…

I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the…

patt-sol · Physics 2009-10-30 Thomas C. Halsey