Universal wave-number selection laws in apical growth.
Ryan Goh1, Rajendra Beekie1, Daniel Matthias2
1School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Physical Review. E
|September 15, 2016
Summary
We found boundary conditions for defect-free growth in pattern-forming systems. Universal scaling laws for wave numbers in growing domains were derived and validated through simulations.
Area of Science:
- Physics
- Applied Mathematics
Background:
- Pattern-forming dissipative systems are crucial in various scientific fields.
- Understanding defect-free growth in these systems is essential for controlling pattern formation.
Purpose of the Study:
- To identify boundary conditions enabling defect-free growth in pattern-forming dissipative systems.
- To derive universal scaling laws for wave numbers in the bulk of growing domains.
Main Methods:
- Characterization of boundary conditions for defect-free growth.
- Derivation of universal scaling laws based on strain-displacement relations for striped patterns.
- Direct numerical simulations of Swift-Hohenberg, complex Ginzburg-Landau, Cahn-Hilliard, and reaction-diffusion equations.
Main Results:
- Identified specific classes of boundary conditions that permit defect-free pattern formation and growth.
- Derived universal scaling laws for the wave number in the bulk of growing domains.
- Validated theoretical predictions against simulation results across multiple pattern-forming models.
Conclusions:
- The derived scaling laws provide a universal description of pattern selection in growing domains.
- The findings offer insights into controlling pattern formation in physical and biological systems.
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