相关论文: Diffusion-limited aggregation as branched growth

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…

In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volume. We obtain bounds on the speed of propagation of…

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.…

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…

We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number moments a single step of the walk has. Under various…

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…

We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…

Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…

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…

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…

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…

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…

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…

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…

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 investigate a class of aggregation-diffusion equations with strongly singular kernels and weak (fractional) dissipation in the presence of an incompressible flow. Without the flow the equations are supercritical in the sense that the…

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation…

We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment…

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…