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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.

Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding of the subject., Comment: 8 pages, 5 figures, 1 table We have performed numerical calculation through MATLAB and added the numerical results to this new version in order to have better comparison the classical results with that of quantum. In this manuscript, we added one co-author (M.E. Samei) for his contribution on numerical calculation

We propose two different derivations of Pythagoras Theorem and apply the same to study discrete and continuum states., Comment: Earlier model has been generalized