English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Recent studies have established a connection between the macroscopicmechanical response of polymeric materials and the statistics of the shortestpath (SP) length between distant nodes in the polymer network. Since thesestatistics can be costly to compute and difficult to study theoretically, weintroduce a branching random walk (BRW) model to describe the SP statisticsfrom the coarse-grained molecular dynamics (CGMD) simulations of polymernetworks. We postulate that the first passage time (FPT) of the BRW to a giventermination site can be used to approximate the statistics of the SP betweendistant nodes in the polymer network. We develop a theoretical framework forstudying the FPT of spatial branching processes and obtain an analyticalexpression for estimating the FPT distribution as a function of the cross-linkdensity. We demonstrate by extensive numerical calculations that thedistribution of the FPT of the BRW model agrees well with the SP distributionfrom the CGMD simulations. The theoretical estimate and the correspondingnumerical implementations of BRW provide an efficient way of approximating theSP distribution in a polymer network. Our results have the physical meaningthat by accounting for the realistic topology of polymer networks, extensivebond-breaking is expected to occur at a much smaller stretch than that expectedfrom idealized models assuming periodic network structures. Our work presentsthe first analysis of polymer networks as a BRW and sets the framework fordeveloping a generalizable spatial branching model for studying the macroscopicevolution of polymeric systems.

Modeling Shortest Paths in Polymeric Networks using Spatial Branching Processes