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Fingering in a channel and tripolar Loewner evolutions
Miguel A Durán1, Giovani L Vasconcelos
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil. mdr1@df.ufpe.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
This study explores Laplacian growth models in channels using tripolar Loewner evolutions. Researchers found that interface growth forms steadily moving fingers, with tip competition emerging in asymmetric configurations.
Area of Science:
- Physics
- Applied Mathematics
Background:
- Laplacian growth models describe phenomena like crystal growth and fluid dynamics.
- Channel geometry presents unique challenges for interface evolution studies.
Purpose of the Study:
- To investigate Laplacian growth models within channel geometries.
- To analyze fingered growth using tripolar Loewner evolutions.
- To develop and examine a generalized model for interface growth.
Main Methods:
- Utilizing the formalism of tripolar Loewner evolutions with fixed channel corners and the point at infinity.
- Revisiting fingered growth and deriving exact solutions for stationary driving functions.
- Formulating a generalized tripolar Loewner equation for interface growth.
Main Results:
- Exact solutions for stationary driving functions in fingered growth were presented.
- The growing interface was shown to evolve into a steadily moving finger.
- Tip competition was observed for nonsymmetric initial configurations with multiple tips.
Conclusions:
- Tripolar Loewner evolutions provide a robust framework for studying Laplacian growth in channels.
- The generalized model successfully captures the dynamics of steadily moving fingers and tip competition.
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