Fine-grained domain counting and percolation analysis in two-dimensional lattice systems with linked lists

We present a fine-grained approach to identify clusters and perform percolation analysis in a two-dimensional (2D) lattice system. In our approach, we develop an algorithm based on the linked-list data structure whereby the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from the Mott insulator to the superfluid phase of bosons in 2D square optical lattices. The results obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute the correlation length using definitions based on percolation theory and use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we compute the critical exponent ν which quantify the divergence of the correlation length ξ across the phase transition and the fractal dimension of the hulls of the superfluid clusters.

Parallelization of the Hoshen-Kopelman Algorithm Using a Finite State Machine

In applications such as landscape ecology, computer mod eling is used to assess habitat fragmentation and its ecological implications. Maps (two-dimensional grids) of habitat clusters or patches are analyzed to determine the number, location, and sizes of clusters. Recently, improved sequential and parallel implementations of the Hoshen- Kopelman cluster identification algorithm have been designed. These implementations use a finite state ma chine to reduce redundant integer comparisons during the cluster identification process. The sequential implementa tion for large maps performs cluster identification by par titioning the map along row boundaries and merging the results of the partitions. The parallel implementation on a 32-processor Thinking Machines CM-5 provides an effi cient mechanism for performing cluster identification in parallel. Although the sequential implementation achieved promising speed improvements ranging from 1.39 to 2.00 over an existing Hoshen-Kopelman implementation, the parallel implementation achieved a minimum speedup of 5.41 over the improved sequential implementation, exe cuted on a Sun SPARCstation 10.

Parallel Models of Animal Migration in Northern Yellowstone National Park

In landscape ecology, computer models are developed to simulate the migration of animal groups as they ex ist in nature. Typically, these models are sequential, and the animal groups move and forage in sequence. In this work, we discuss a parallel implementation of the NOYELP (NOrthern YELlowstone national Park) model on a 32-processor Thinking Machines CM-5. NOYELP is a spatially explicit, individual-based model that simulates the search, movement, and foraging activities of groups of animals across the northern por tion of Yellowstone National Park. NOYELP is primarily used to study the effects of fire-scale and pattern on the winter foraging dynamics and survival of free- ranging bison and elk groups. Separate versions of a parallel NOYELP model (referred to as PNOYELP) with different degrees of data-sharing and message-passing are used to study the effects on travel distances and semi-annual energy-gain statistics. Comparisons of these statistics with the sequential NOYELP model are made, and reasonable speed improvements (ranging from 2.8 to 6.7) for PNOYELP on the CM-5 over the sequential model on a Sun SPARCstation 10 are re ported.