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Related Experiment Video

Updated: Jun 22, 2026

Precise, High-throughput Analysis of Bacterial Growth

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Parameter-free scaling relation for nonequilibrium growth processes.

Yen-Liang Chou¹, Michel Pleimling

¹Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA.

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

|June 13, 2009

Summary

A new parameter-free scaling relation provides a complete data collapse for nonequilibrium growth processes. This method surpasses the limitations of the Family-Vicsek relation in analyzing various growth models.

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Area of Science:

Physics
Materials Science
Statistical Mechanics

Background:

Nonequilibrium growth processes are fundamental in various scientific fields.
Existing scaling relations, like the Family-Vicsek relation, have limitations in describing complex growth dynamics.

Purpose of the Study:

To introduce and validate a novel parameter-free scaling relation for nonequilibrium growth.
To demonstrate the universality and effectiveness of this new relation across diverse growth models.

Main Methods:

Application of a parameter-free scaling relation to analyze nonequilibrium growth phenomena.
Testing the relation against established models: competitive growth, random deposition with diffusion, and restricted solid-on-solid models.
Comparative analysis with the Family-Vicsek relation.

Main Results:

Achieved a complete data collapse for large classes of nonequilibrium growth processes using the parameter-free relation.
Demonstrated superior performance compared to the Family-Vicsek relation, highlighting its limitations.
Validated the relation across models with varying complexities, including temperature-dependent diffusion.

Conclusions:

The proposed parameter-free scaling relation offers a robust and universal tool for studying nonequilibrium growth.
This new relation overcomes key limitations of previous methods, enabling more accurate data analysis.
It provides a powerful framework for understanding surface growth dynamics in diverse physical systems.