Rigorous proof of a phase transition of parallelizability in a one-dimensional structure assembly

In this paper, we prove the existence of a phase transition of parallelizability in the assembly of one-dimensional chains. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Authors: Kobayashi, Ikumi, Shin-ichi Sasa
Format: Article
Language:English
Subjects:
Assembly
Efficiency
Phase transitions
Transition points
Online Access:Get full text
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Summary:In this paper, we prove the existence of a phase transition of parallelizability in the assembly of one-dimensional chains. 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. By evaluating the parallel efficiency on each side of the transition point, we show the existence of a phase transition in this system.
ISSN:2331-8422