Phase transition of parallelizability in assembly systems

TL;DR

This paper investigates a phase transition in the feasibility of efficient parallel assembly, defining a measure called parallel efficiency and demonstrating a transition point where assembly shifts from feasible to infeasible.

Contribution

It introduces a novel phase transition framework for parallel assembly systems and models this transition analytically in large systems.

Findings

Identification of a non-analytic change in parallel efficiency

Demonstration of phase transition in two analyzable models

Characterization of the transition point in assembly feasibility

Abstract

We propose a phase transition on the feasibility of efficient parallel assembly. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. We present two analyzable models to demonstrate this phase transition in the limit of infinite system size.