Abstract
We study a heretofore ignored class of spiral patterns in oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of r, thereby turning off the instability at large r. They are uniquely determined by matching to this outer condition, lifting a degeneracy in the set of steady-state solutions of the original equations. Unlike the well-studied spiral which acts as a wave source, has a simple core structure and is insensitive to the details of the boundary on which no-flux conditions are imposed, these new spirals are wave sinks, have non-monotonic wavefront curvature near the core, and can be patterned by the form of the spatial boundary. We predict that these anomalous spirals could be produced in nonlinear optics experiments via spatially modulating the gain of the medium.
Original language | English |
---|---|
Article number | 063026 |
Journal | New Journal of Physics |
Volume | 19 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2017 |
Bibliographical note
Publisher Copyright:© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Funding
The research ofDAKis supported by the US-Israel Binational Science Foundation under grant 2015619. The research of HL is supported by the National Science Foundation Center for Theoretical Biological Physics (Grant NSF PHY-1427654).We also gratefully acknowledge the hospitality of the Aspen Center for Physics, where this work was started.
Funders | Funder number |
---|---|
US-Israel Binational Science Foundation | 2015619 |
Directorate for Mathematical and Physical Sciences | 1427654 |
Center for Theoretical Biological Physics | NSF PHY-1427654 |
Keywords
- complex Ginzburg-Landau equation
- frequency selection
- oscillatory media
- spiral waves