Zhang, Z., Mohanty, S., Blanchet, J., & Cai, W. (2024). Modeling shortest paths in polymeric networks using spatial branching processes. Journal of the Mechanics and Physics of Solids, 187, 105636. https://doi.org/10.1016/j.jmps.2024.105636
Abstract
Recent studies have established a connection between the macroscopic mechanical response of polymeric materials and the statistics of the shortest path (SP) length between distant nodes in the polymer network. Since these statistics can be costly to compute and difficult to study theoretically, we introduce a branching random walk (BRW) model to describe the SP statistics from the coarse-grained molecular dynamics (CGMD) simulations of polymer networks. We postulate that the first passage time (FPT) of the BRW to a given termination site can be used to approximate the statistics of the SP between distant nodes in the polymer network. We develop a theoretical framework for studying the FPT of spatial branching processes and obtain an analytical expression for estimating the FPT distribution as a function of the cross-link density. We demonstrate by extensive numerical calculations that the distribution of the …
Authors
Zhenyuan Zhang, Shaswat Mohanty, Jose Blanchet, Wei Cai
Publication date
2024/6/1
Journal
Journal of the Mechanics and Physics of Solids
Volume
187
Pages
105636
Publisher
Pergamon
