Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers

Abstract

In this paper, we study the trapping problem in two representative polymer networks, Cayley trees and Vicsek fractals, which separately model dendrimers and regular hyperbranched polymers. Our goal is to explore the impact of trap location on the efficiency of trapping in these two important polymer systems, with the efficiency being measured by the average trapping time (ATT) that is the average of source-to-trap mean first-passage time over every staring point in the whole networks. For Cayley trees, we derive an exact analytic formula for the ATT to an arbitrary trap node, based on which we further obtain the explicit expression of ATT for the case that the trap is uniformly distributed. For Vicsek fractals, we provide the closed-form solution for ATT to a peripheral node farthest from the central node, as well as the numerical solutions for the case when the trap is placed on other nodes. Moreover, we derive the exact formula for the ATT corresponding to the trapping problem when the trap has an uniform distribution over all nodes. Our results show that the influence of trap location on the trapping efficiency is completely different for the two polymer networks. In Cayley trees, the leading scaling of ATT increases with the shortest distance between the trap and the central node, implying that trap's position has an essential impact on the trapping efficiency; while in Vicsek fractals, the effect of location of the trap is negligible, since the dominant behavior of ATT is identical, respective of the location where the trap is placed. We also present that for all cases of trapping problems being studied, the trapping process is more efficient in Cayley trees than in Vicsek fractals. We demonstrate that all differences related to trapping in the two polymer systems are rooted in their underlying topological structures.

Definitive version accepted for publication in The Journal of Chemical Physics

References in corpus (16)

• First-passage times in complex scale-invariant media
• Exact mean first-passage time on the T-graph
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Determining mean first-passage time on a class of treelike regular fractals
• Exact solution of mean geodesic distance for Vicsek fractals
• Trapping in complex networks
• Trapping in dendrimers and regular hyperbranched polymers
• Mean first-passage time for random walks on the T-graph
• Trapping time statistics and efficiency of transport of optical excitations in dendrimers
• Mean first-passage time for random walks in general graphs with a deep trap
• Anomalous behavior of trapping on a fractal scale-free network
• Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs
• Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap

Cited by in corpus (5)

• Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications
• Exact results for the first-passage properties in a class of fractal networks
• First encounters on Bethe Lattices and Cayley Trees
• Maximal entropy random walk improves efficiency of trapping in dendrimers
• Mean trapping time for an arbitrary node on regular hyperbranched polymers