Related papers: Diffusion-limited aggregation: A relationship betw…
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…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
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…
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…
We present a Molecular Dynamics study of large Lennard-Jones clusters evolving on a crystalline surface. The static and the dynamic properties of the cluster are described. We find that large clusters can diffuse rapidly, as experimentally…
Using molecular dynamic simulations we study a waterlike model confined between two fixed hydrophobic plates. The system is tested for density, diffusion and structural anomalous behavior and compared with the bulk results. Within the range…
Aggregation of ice crystals is a key process governing precipitation. Individual ice crystals exhibit considerable diversity of shape, and a wide range of physical processes could influence their aggregation; despite this we show that a…
Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…
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…
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential equations known as aggregation-diffusion equations.…
Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths.…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
Results from a modified Diffusion Limited Aggregation (DLA) model are presented. The modifications of the classical DLA model are in the attachment to the cluster rules and in the scheme of particle generation/killing. In the classical DLA…
Experimental and modeling/simulation studies of phase equilibrium and growth morphologies of novel polymer-dispersed liquid crystal (PDLC) mixtures of PS (polystyrene) and liquid crystals that exhibit a direct isotropic/smectic-A (lamellar)…
This article concerns the correspondence between thermodynamics and the morphology of simple fluids in terms of clusters. Definitions of clusters providing a geometric interpretation of the liquid-gas phase transition are reviewed with an…
In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…
We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…
The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of…