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Fine-tuning the Size and Minimizing the Noise of Solid-state Nanopores

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Published on: October 31, 2013

Corrected finite-size scaling in percolation.

Jiantong Li¹, Mikael Ostling

¹KTH Royal Institute of Technology, School of Information and Communication Technology, Electrum 229, SE-164 40 Kista, Sweden. jiantong@kth.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 11, 2012

Summary

This study introduces a new scaling theory for percolation, clarifying finite-size effects and their impact on systems like explosive percolation. The theory reveals universal scaling functions independent of boundary conditions for all systems studied.

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Area of Science:

Physics
Statistical Mechanics
Complex Systems

Background:

Percolation theory describes the formation of connected clusters in random networks.
Finite-size effects significantly influence the behavior of physical systems near critical points.
Explosive percolation exhibits a sharp, discontinuous transition, distinct from typical percolation phenomena.

Purpose of the Study:

To develop a comprehensive scaling theory for percolation phenomena.
To elucidate the fundamental nature of finite-size scaling and its effects.
To investigate the applicability of this theory to extensive systems, including explosive percolation.

Main Methods:

Development of a novel theoretical framework for percolation scaling.
Application of the theory to analyze finite-size effects in various percolation models.
Comparative analysis of scaling behaviors between normal and explosive percolation.

Main Results:

The proposed theory provides a unified understanding of finite-size scaling in percolation.
Explosive percolation follows the same scaling law as normal percolation but exhibits more pronounced finite-size effects.
Universal scaling functions were found to be independent of boundary conditions across all systems.

Conclusions:

The new scaling theory offers a robust framework for studying percolation and finite-size effects.
The findings challenge previous assumptions regarding the influence of boundary conditions on scaling functions.
This work advances the understanding of critical phenomena in complex systems.