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We explore the impact of volume exclusion on the local assembly of linearphysical 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 ofthese networks whose distant parts are sequentially connected by links with avery large aspect ratio. We show that the kinetics of link adhesion islogarithmic, as opposed to the algebraic growth in lower dimensions, and weattribute this qualitatively different behavior to a spontaneous delay ofdepletion forces caused by the 3D nature of the problem. Equally important, wefind that this slow kinetics is metastable, allowing us to analytically predictan algebraic growth due to the formation of local bundles. Our findings offer abenchmark to study the local assembly of physical networks, with implicationsfor non-equilibrium nest-like packings.

Logarithmic kinetics and bundling in physical networks