Computational Cost Reduction and Validation of Cluster-Cluster Aggregation Model

CLUSTER ALGEBRAS AND CLUSTER CATEGORIES

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

Topological properties of diffusion limited aggregation and cluster - cluster aggregation

The detailed topological or ‘connectivity’ properties of the clusters formed in diffusion limited aggregation (DLA) and cluster-cluster aggregation (CCA) are considered for spatial dimensions d = 2,3 and 4. Specifically, for both aggregation phenomena we calculate the fractal dimension d,,, = i-’ defined by e R d m l n where e is the shortest path between two points separated by a Pythagorean d...

Persistence in cluster-cluster aggregation.

Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining int...

Simulating and Visualising Sedimentary Cluster-Cluster Aggregation

Recent simulations of diffusion limited cluster-cluster aggregation (DLCA) have shown systematic inhomogeneities in the shape and orientation of clusters formed when a sedimentary force is applied. Using custom simulation and visualisation techniques and programs we have carried out a microscopic study of these sedimentary inhomogeneities and have mapped out the model parameter space. We find v...

Aggregation Point Cluster − to − Cluster Data Path Aggregation