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Related Experiment Videos

Roughening and inclination of competition interfaces.

Pablo A Ferrari¹, James B Martin, Leandro P R Pimentel

¹Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970 São Paulo, Brazil. pablo@ime.usp.br

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

|April 12, 2006

Summary

This summary is machine-generated.

A phase transition in cluster growth dynamics alters interface behavior from random to deterministic. Fluctuations follow Kardar-Parisi-Zhang (KPZ) or initial condition scales, depending on the final shape.

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Area of Science:

Statistical Physics
Surface Growth Models
Phase Transitions

Background:

Understanding interface dynamics in growing systems is crucial.
Competition between growing clusters presents complex behaviors.

Purpose of the Study:

To analyze the interface competition between two growing clusters.
To investigate phase transitions and fluctuation scaling in a simplified growth model.

Main Methods:

Formal computations and analytical solutions were employed.
Analysis of interface inclination and macroscopic shape.
Characterization of fluctuation scaling.

Main Results:

A phase transition was identified for the interface's asymptotic inclination.
The transition shifts the macroscopic shape from curved (random) to noncurved (deterministic).
Fluctuation scaling depends on the final profile: Kardar-Parisi-Zhang (KPZ) for curved/flat, Gaussian for noncurved.

Conclusions:

The study reveals a critical point at stationary growth for fluctuation behavior.
Interface dynamics exhibit distinct scaling regimes based on macroscopic shape.
Analytical solutions provide insights into complex growth phenomena.