Related papers: Diffusion-limited aggregation as branched growth
We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes…
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state…
The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…
Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a…
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 study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient $(D)$ of a Brownian particle on the distribution width $(\varepsilon)$ of…
We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…
The prediction of diffusion in solids is necessary to understand the microstructure evolution in materials out of equilibrium. Although one can reasonably predict diffusive transport coefficients using atomistic methods, these approaches…
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $\pi/4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^a$ all new…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…
We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation, in radial symmetry, in an elastic field of a screw dislocation subject to the flux conservation…