Shyi-Long Lee

Multifractal analysis of diffusion-limited reactions over surfaces of diffusion-limited aggregates

Abstract Simulations of diffusion-limited reactions over surfaces of Witten—Sander diffusion-limited aggregates (DLA) were performed using a Monte Carlo random walk algorithm. Multifractal analyses were then carried out on the reaction probability distribution to investigate the effect of fractal environment of DLA surfaces on model chemical reactions. Multifractality of the reaction probability distribution in DLA was revealed from analysis of size effects. Comparisons were made to diffusion-limited reactions over Cantor set and devils staircase reported by Avnir et al.

Topological analysis of the eigenvectors of the adjacency matrices in graph theory: Degenerate case

Abstract Vertex- and edge-signed graphs were used to represent the eigenvectors and their internal connectivities of the adjacency matrix of a chemical graph. Simple net sign analysis of the edge-signed graphs was found to yield the correct energy ordering of the eigenvectors in most chemical graphs. For degenerate cases a more complicated net sign analysis is proposed to overcome the ambiguity originating from the different choices of the set of eigenvectors.

Simulation of diffusion-limited aggregation: effects of launching boundary shape and non-fixed centre

Abstract Simulations of the Witten—Sander model of diffusion-limited aggregation (DLA) were performed using modified versions in which a square launching boundary and a non-fixed centre were adopted. Square launching boundary leads to an isotropic fractal instead of the diamond-shape cluster found in the conventional simulation using circular releasing boundary. The nonfixed centre model displays a similar feature as that found in Levy-flight-trajectory simulations which bridge two limiting aggregation models, i.e. the Eden model and the Witten—Sander model.

Topological analysis of some special of graphs. Hypercubes

Abstract A general strategy was proposed for generating the eigenvectors and the eigenvalues of some special classes of graphs from the well-known chemical graphs such as the complete graph of order 2, K 2 , which is isomorphic to the hydrogen-suppressed ethene. Hypercubes were used as examples to illustrate the elegance of this method. Net sign analysis were also performed for hypercubes. The parallel relationships between the ordering of net signs and the ordering of eigenvalues of hypercubes were found to be strictly valid.

Net signs and eigenvalues of molecular graphs: some analogies

Abstract A number of analogies which exist between the net signs and the eigenvalues of molecular graphs are pointed out. In particular, a pairing-theorem-type regularity holds for the net signs of bipartite graphs (i.e. molecular graphs of alternant hydrocarbons).

Effect of lateral interactions beyond nearest-neighbors on size and shape of non-equilibrium island on surfaces

Abstract Monte Carlo simulations were performed to investigate the island formation of adsorbates on surfaces. The surface is modeled by a N × N square lattice. The adsorbates are initially random distributed over the lattice. The movement of each adsorbate is then monitored by a random walk algorithm. Lateral interactions containing contributions from up to the fourth coordination shell are considered. Inclusion of interactions among diagonal neighbors is found to play a key role for the formation of non-equilibrium island. The effect of the interactions contributed from the third and fourth coordination shell on the island shape is discussed.

Effect of structural modifications on electron delocalization of mixed-valence biferrocenium systems

Abstract Deviations of the cyclopentadienyl ring from the parallel positions were found to correlate quite well with the critical temperatures of delocalization—localization transition for mixed-valence bifferocenium cation salts on Mossbauer time scale. The observations can be rationalized by examining the variations of HOMOLUMO gap of the CpFeCp monomer unit as the angle of ∠ CpFeCp changes induced via ligand substitutions on the terminal Cp rings.

Two-dimensional topologies and clustering on zeolite surfaces. A Monte Carlo study

Abstract Monte Carlo simulations were carried out to investigate the clustering of adatoms on zeolite surfaces. The zeolite surface is built up by repeated template which models the smallest building unit. The movement of each adatom is then monitored by a random walk algorithm. Lateral interactions beyond nearest-neighbor interactions are considered. Eight types of zeolite surfaces were used to demonstrate the influence of pore size and topology on the clustering rate. Zeolite with larger pore size is found to have a lower clustering rate. Higher symmetry of zeolite surface topology instead leads to a higher clustering rate.