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Related Experiment Video

Updated: May 7, 2026

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Isotropic model for cluster growth on a regular lattice.

Christian A Yates¹, Ruth E Baker

¹Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom.

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

|September 17, 2013

Summary

This study explores a novel cluster growth model, revealing circular clusters without anisotropy. A new nonmonotonic surface scaling relationship was discovered, challenging traditional universality class classifications in cluster aggregation.

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Last Updated: May 7, 2026

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production

Published on: March 27, 2017

Area of Science:

Statistical Mechanics
Computational Physics
Materials Science

Background:

Traditional cluster growth models on lattices exhibit anisotropy.
Existing models often struggle with inherent lattice-induced directional bias.
Ferreira Jr. and Alves introduced a model producing isotropic, circular clusters.

Purpose of the Study:

Analyze the Ferreira Jr. and Alves stochastic cluster growth model.
Investigate cluster anisotropy and surface scaling properties.
Adapt the model using a mitosis-like growth mechanism.

Main Methods:

Analysis of a stochastic cluster growth model.
Introduction of a rearrangement algorithm simulating cell splitting.
Examination of surface scaling in "1+1" dimensions.
Comparison with traditional cluster growth models and Family-Vicsek scaling.

Main Results:

The model consistently produces circular clusters, even with reduced noise.
A novel, nonmonotonic surface thickness scaling relationship was identified in "1+1" dimensions.
This scaling behavior deviates significantly from the established Family-Vicsek scaling.

Conclusions:

The adapted cluster growth model exhibits unique scaling properties.
The findings challenge the universal applicability of traditional universality class classifications for certain growth models.
Models not solely dependent on surface considerations may require new classification frameworks.