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Related papers: Internal DLA in Higher Dimensions

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In previous works, we showed that the internal DLA cluster on \Z^d with t particles is a.s. spherical up to a maximal error of O(\log t) if d=2 and O(\sqrt{\log t}) if d > 2. This paper addresses "average error": in a certain sense, the…

Probability · Mathematics 2015-01-14 David Jerison , Lionel Levine , Scott Sheffield

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 2013-05-27 Amine Asselah , Alexandre Gaudillière

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

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…

Condensed Matter · Physics 2007-05-23 Cristopher Moore , Jonathan Machta

Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a…

Statistical Mechanics · Physics 2013-09-02 Li Deng , Yanting Wang , Zhong-Can Ou-Yang

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

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

In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…

Condensed Matter · Physics 2007-05-23 P. Ossadnik , C. -H. Lam , L. M. Sander

Diffusion limited aggregation is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the depth of the tree defined by the cluster. The existence of this…

Statistical Mechanics · Physics 2009-11-10 Dan Tillberg , Jon Machta

Diffusion Limited Aggregation (DLA) has served for forty years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references no exact result for the fractal dimension $D$ of DLA is known. In this…

Statistical Mechanics · Physics 2021-02-17 Eviatar B. Procaccia , Itamar Procaccia

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

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

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

When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial DLA is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D=1.71 arises only for very…

Statistical Mechanics · Physics 2020-04-08 Benoit B. Mandelbrot , Boaz Kol , Amnon Aharony

We consider a cluster growth model on Z^d, 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 by previous walks. It…

Probability · Mathematics 2010-05-31 Amine Asselah , Alexandre Gaudilliere

Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill…

Probability · Mathematics 2011-11-03 Hugo Duminil-Copin , Cyrille Lucas , Ariel Yadin , Amir Yehudayoff

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

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

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

A connection between fractal dimensions of "turbulent facets" and fractal dimensions in diffusion-limited aggregation (DLA) is shown. The theoretical correspondence is elucidated and an empirical support to the above claim is given.

Mathematical Physics · Physics 2020-02-07 Asher Yahalom
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