A Solver for Complex-Valued Parametric Linear Systems

This work reports on a new software for solving linear systems involving affine-linear dependencies between complex-valued interval parameters. We discuss the implementation of a parametric residual iteration for linear interval systems by advanced communication between the system Mathematica and the library C-XSC supporting rigorous complex interval arithmetic. An example of AC electrical circuit illustrates the use of the presented software.

An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

We develop a simplified implementation of the Hoshen-Kopelman cluster counting algorithm adapted for honeycomb networks. In our implementation of the algorithm we assume that all nodes in the network are occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determines which nodes belong to each cluster. The network information is stored into two sets of data. The first one is related to the connectivity of the nodes and the second one to the state of links. The algorithm finds all clusters in only one scan across the network and thereafter cluster relabeling operates on a vector whose size is much smaller than the size of the network. Counting the number of clusters of each size, the algorithm determines the cluster size probability distribution from which the mean cluster size parameter can be estimated. Although our implementation of the Hoshen-Kopelman algorithm works only for networks with a honeycomb (hexagonal) structure, it can be easily changed to be applied for networks with arbitrary connectivity between the nodes (triangular, square, etc.). The proposed adaptation of the Hoshen-Kopelman cluster counting algorithm is applied to studying the thermal degradation of a graphene-like honeycomb membrane by means of Molecular Dynamics simulation with a Langevin thermostat. ACM Computing Classification System (1998): F.2.2, I.5.3.