Bond percolation critical probability bounds for three Archimedean lattices

Abstract Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: .7385 < pc ((3, 12 2 ) bond) < .7449, .6430 < pc((4, 6, 12) bond) < .7376, Consequently, the bond percolation critical probability of the (3, 12 2 ) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 12 2 ) bond percolation critical probability is possibly the largest of any vertex-transitive graph with bond percolation critical probability that is strictly less than one

Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Molecular charge transport : relating orbital structures to the conductance properties

In this thesis I describe the relation between the chemical structure of small organic molecules and their conductance properties.LEI Universiteit LeidenQuantum Matter and Optic