Logarithmic kinetics and bundling in physical networks

TL;DR

This paper investigates how volume exclusion influences the assembly kinetics of 3D physical networks, revealing logarithmic growth in link formation and the emergence of metastable bundles, which differ from lower-dimensional behaviors.

Contribution

The study introduces a minimal 3D model to analyze network assembly, highlighting the logarithmic kinetics and metastability due to bundle formation, advancing understanding of physical network growth.

Findings

Link adhesion kinetics are logarithmic in 3D networks.

Metastable slow kinetics allow algebraic bundle growth.

Provides a benchmark for studying non-equilibrium packings.

Abstract

We explore the impact of volume exclusion on the local assembly of linear physical networks, where nodes and links are hard-core rigid objects. To do so, we introduce a minimal 3D model that helps us zoom into confined regions of these networks whose distant parts are sequentially connected by links with a very large aspect ratio. We show that the kinetics of link adhesion is logarithmic, as opposed to the algebraic growth in lower dimensions, and we attribute this qualitatively different behavior to a spontaneous delay of depletion forces caused by the 3D nature of the problem. Equally important, we find that this slow kinetics is metastable, allowing us to analytically predict an algebraic growth due to the formation of local bundles. Our findings offer a benchmark to study the local assembly of physical networks, with implications for non-equilibrium nest-like packings.