منابع مشابه
Diffusion Limited Aggregation on the Boolean Lattice
In the Diffusion Limited Aggregation (DLA) process on on Z, or more generally Z, particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}, in which pa...
متن کاملDiffusion-Limited Aggregation on Curved Surfaces
We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusionlimited-aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere (K > 0) and pseudo-sphere (K < 0)...
متن کاملDiffusion Limited Aggregation on a Cylinder
We consider the DLA process on a cylinder G × 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(2−ε) |G|, the time it takes the cluster to reach the m-th layer of the cylinder is at most of order m · |G| log log|G| . In particular we get examples of infinite Cayley graphs of degree 5, ...
متن کاملSlippery diffusion-limited aggregation.
Colloidal particles that interact through strong, short-range, secondary attractions in liquids form irreversible "slippery" bonds that are not shear-rigid. Through event-driven simulations of slippery attractive spheres, we show that space-filling fractal clusters still emerge from the process of "slippery" diffusion-limited aggregation (DLA). Although slippery and classic DLA clusters have th...
متن کاملTransport-limited aggregation.
Diffusion-limited aggregation (DLA) and its variants provide the simplest models of fractal patterns, such as colloidal clusters, electrodeposits, and lightning strikes. The original model involves random walkers sticking to a growing cluster, but recently DLA (in the plane) has been reformulated in terms of stochastic conformal maps. This fruitful new perspective provides the exact Laplacian c...
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ژورنال
عنوان ژورنال: Philosophy & Public Affairs
سال: 2017
ISSN: 0048-3915
DOI: 10.1111/papa.12097