相关论文: Multifractal Dimensions for Branched Growth
We measure the multiscaling behavior of large off-lattice diffusion limited aggregates (DLA). In contrast to previous studies we now find a continuous dependence of the multiscaling dimensions $D(x)$ on the relative distance $x=r/R_g$ to…
We develop a technique for probing harmonic measure of the diffusion limited aggregation (DLA) cluster surface with the variable size particle and generate one thousand clusters with 50 million particles using original off-lattice…
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…
We present a novel method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and non-overlapping coverage) in order to reduce edge effects, improve…
We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible…
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…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
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…
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of…
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…
Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are…
What is the scaling limit of diffusion limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the {\em dielectric breakdown model}…
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…
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…
We extend the conformal mapping approach elaborated for the radial Diffusion Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in particular a complex function which allows to grow a cylindrical cluster using as…
We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form $D(x)\sim D_0|x|^\alpha$ in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the…
Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here, one such mixed model, the quenched trap model (QTM) on fractal lattices, is investigated. It is…
Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb-model is a simplified description of diffusion on percolation…
We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip-splitting of branches forms a fixed…
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…