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Minimization of instabilities in growing interfaces: a variational approach
Eduardo O Dias1, José A Miranda1
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
This study introduces a variational control method to minimize interfacial deformations during pattern formation in crystal growth and electric discharge. This approach offers precise control over complex spatial structures for technological applications.
Area of Science:
- Physics
- Materials Science
Background:
- Mullins-Sekerka and electric breakdown instabilities drive complex pattern formation.
- Dendritic crystals and treelike electric discharges are common outcomes.
- Controlling these patterns is crucial for technological applications.
Purpose of the Study:
- To develop a variational approach for controlling pattern formation.
- To systematically find conditions that minimize interfacial deformations.
- To enable manipulation and stabilization of complex spatial structures.
Main Methods:
- Employed a variational approach to identify optimal growth conditions.
- Utilized linear stability calculations.
- Applied 2D and 3D contour-dynamics models.
Main Results:
- Demonstrated effective minimization of interfacial deformations.
- Identified conditions for controlled pattern growth.
- Validated the method for crystal growth and electric discharge phenomena.
Conclusions:
- The variational control method offers precise manipulation of pattern formation.
- This technique stabilizes complex spatial structures.
- It has broad implications for technological applications in materials science and physics.
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