The site and bond explosive percolation models are carefully defined and studied on a square latt... more The site and bond explosive percolation models are carefully defined and studied on a square lattice. From the cluster distribution function and the behavior of the second largest cluster, it is shown that the duality in which the transition is discontinuous exists for the pairs of the site model and the corresponding bond model which relatively enhances the intra-bond occupation. In contrast the intra-bond-suppressed models which have no corresponding site models undergo the continuous transition and satisfy the normal scaling ansatz as ordinary percolation.
We investigate the kinetics of bimolecular chemical reactions A+A→0 and A+B→0 on weighted scale-f... more We investigate the kinetics of bimolecular chemical reactions A+A→0 and A+B→0 on weighted scale-free networks (WSFNs) with degree distribution P(k)∼k^{-γ} . On WSFNs, a weight w{ij} is assigned to the link between node i and j . We consider the symmetric weight given as w{ij}=(k{i}k{j})^{μ} , where k{i} and k{j} are the degree of node i and j . The hopping probability T{ij} of a particle from node i to j is then given as T{ij}∝(k{i}k{j})^{μ} . From a mean-field analysis, we analytically show in the thermodynamic limit that the kinetics of A+A→0 and A+B→0 are identical and there exist two crossover μ values, μ{1c}=γ-2 and μ{2c}=(γ-3)/2 . The density of particles ρ(t) algebraically decays in time t as t^{-α} with α=1 for μ<μ{2c} and α=(μ+1)/(γ-μ-2) for μ{2c}≤μ<μ{1c} . For μ≥μ{1c} , ρ decays exponentially. With the mean-field rate equation for ρ(t) , we also analytically show that the kinetics on the WSFNs is mapped onto that on unweighted SFNs with P(k)∼k^{-γ^{'}} with γ^{'}=(μ+γ)/(μ+1) .
The site and bond explosive percolation models are carefully defined and studied on a square latt... more The site and bond explosive percolation models are carefully defined and studied on a square lattice. From the cluster distribution function and the behavior of the second largest cluster, it is shown that the duality in which the transition is discontinuous exists for the pairs of the site model and the corresponding bond model which relatively enhances the intra-bond occupation. In contrast the intra-bond-suppressed models which have no corresponding site models undergo the continuous transition and satisfy the normal scaling ansatz as ordinary percolation.
We investigate the kinetics of bimolecular chemical reactions A+A→0 and A+B→0 on weighted scale-f... more We investigate the kinetics of bimolecular chemical reactions A+A→0 and A+B→0 on weighted scale-free networks (WSFNs) with degree distribution P(k)∼k^{-γ} . On WSFNs, a weight w{ij} is assigned to the link between node i and j . We consider the symmetric weight given as w{ij}=(k{i}k{j})^{μ} , where k{i} and k{j} are the degree of node i and j . The hopping probability T{ij} of a particle from node i to j is then given as T{ij}∝(k{i}k{j})^{μ} . From a mean-field analysis, we analytically show in the thermodynamic limit that the kinetics of A+A→0 and A+B→0 are identical and there exist two crossover μ values, μ{1c}=γ-2 and μ{2c}=(γ-3)/2 . The density of particles ρ(t) algebraically decays in time t as t^{-α} with α=1 for μ<μ{2c} and α=(μ+1)/(γ-μ-2) for μ{2c}≤μ<μ{1c} . For μ≥μ{1c} , ρ decays exponentially. With the mean-field rate equation for ρ(t) , we also analytically show that the kinetics on the WSFNs is mapped onto that on unweighted SFNs with P(k)∼k^{-γ^{'}} with γ^{'}=(μ+γ)/(μ+1) .
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