Chirality effect on the global structure of spiral-domain patterns in the two-dimensional complex Ginzburg-Landau equation.
It is well known that in the single-spiral-stable parameter regimes of the two-dimensional complex Ginzburg-Landau equation, spiral-domain patterns spontaneously appear. These patterns are disordered cells of frozen spiral waves well separated by thin walls (shocks), and to a good approximation, the walls are segments of hyperbolas. In this paper, we take a closer look at the global structure of spiral-domain patterns by using rigorous mathematical analysis and considering the unusual effect of the chirality (handedness) of spiral wave. An equation that determines the slope of the shock line is derived. We generalize this analytical method to study the interaction of a pair of spirals with different rotation frequencies, and obtain the geometrical structures of the shock line and the wave front of the invasion wave in transient processing.
Zhan
Meng
M
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China. zhanmeng@wipm.ac.cn
Luo
Jinming
J
Gao
Jihua
J