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Related papers: Fluctuating diffusion-limited aggregates

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The two-dimensional comb lattice $C_2$ is a natural spanning tree of the Euclidean lattice $\mathbb{Z}^2$. We study three related cluster growth models on $C_2$: internal diffusion limited aggregation (IDLA), in which random walkers move on…

Probability · Mathematics 2012-04-13 Wilfried Huss , Ecaterina Sava

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the…

Chemical Physics · Physics 2018-08-03 Zhijie Xu , Paul Meakin

We study one-dimensional multi-particle Diffusion Limited Aggregation (MDLA) at its critical density $\lambda=1$. Previous works have verified that the size of the aggregate $X_t$ at time $t$ is $t^{1/2}$ in the subcritical regime and…

Probability · Mathematics 2020-09-11 Dor Elboim , Danny Nam , Allan Sly

Actin growth is a fundamental biophysical process and it is, at the same time, a prototypical example of diffusion-mediated surface growth. We formulate a coupled chemo-mechanical, one-dimensional growth model encompassing both material…

Soft Condensed Matter · Physics 2020-01-03 Rohan Abeyaratne , Eric Puntel , Giuseppe Tomassetti

Recently, the diffusion-limited cluster aggregation (DLCA) model was restudied as a real-world example of showing discontinuous percolation transitions (PTs). Because a larger cluster is less mobile in Brownian motion, it comes into contact…

Statistical Mechanics · Physics 2012-10-08 Y. S. Cho , Y. W. Kim , B. Kahng

A concentration difference of particles across a membrane perforated by pores will induce a diffusive flux. If the diffusing objects are of the same length scale as the the pores, diffusion may not be simple, objects can move into the pore…

Soft Condensed Matter · Physics 2015-05-18 Robert S. Shaw , Norman H. Packard

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum…

Mesoscale and Nanoscale Physics · Physics 2017-09-13 F. Evers , P. Schmitteckert

A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge…

Statistical Mechanics · Physics 2010-03-09 David A. Head , Hajime Tanaka

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 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

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

Machine Learning · Computer Science 2022-09-01 Xingchao Liu , Lemeng Wu , Mao Ye , Qiang Liu

We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with boundary $\Gamma$, where the behavior at the boundary is sticky. The construction covers…

Probability · Mathematics 2015-01-14 Martin Grothaus , Robert Voßhall

Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…

Statistical Mechanics · Physics 2007-05-23 Robin C. Ball , Neill E. Bowler , Leonard M. Sander , Ellak Somfai

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

We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…

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

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of…

Probability · Mathematics 2010-12-24 Lionel Levine , Yuval Peres

Flow-induced aggregation of colloidal particles leads to aggregates with fairly high fractal dimension () which are directly responsible for the observed rheological properties of sheared dispersions. We address the problem of the decrease…

Soft Condensed Matter · Physics 2009-06-05 A. Zaccone , M. Soos , M. Lattuada , M. U. Baebler , M. Morbidelli

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…

Statistical Mechanics · Physics 2016-10-05 A. G. Cherstvy , R. Metzler

We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process.…

Probability · Mathematics 2012-03-30 Tobias Friedrich , Lionel Levine

We study active run-and-tumble particles with an additional two-state internal variable characterizing their motile or non-motile state. Motile particles change irreversibly into non-motile ones upon collision with a non-motile particle.…

Soft Condensed Matter · Physics 2018-11-27 Matteo Paoluzzi , Marco Leoni , M Cristina Marchetti