相关论文: Diffusion-limited aggregation in channel geometry
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
Finding a suitable density function is essential for density-based clustering algorithms such as DBSCAN and DPC. A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in these…
We study a rotor-router version of the internal diffusion-limited aggregation introduced by J.Propp. The existing estimations of boundary fluctuations of the aggregation cluster show that they grow not faster than $O(\log r)$ with the…
We present results from a detailed simulation of a quasi-2D dissipative granular gas, kept in a non-condensed steady state via vertical shaking over a rough substrate. This gas shows a weak power-law decay in the tails of its Pair…
Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
We study internal diffusion-limited aggregation with random starting points on Z^d. In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
We study the structure and growth of a difusion-limited aggregate (DLA) for which the constitutive units remain mobile during the aggregation process. Contrary to DLA where far from equilibrium conditions are the prevalent factor for…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as…
We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
We study the fractal and multifractal properties (i.e. the generalized dimensions of the harmonic measure) of a 2-parameter family of growth patterns that result from a growth model that interpolates between Diffusion Limited Aggregation…