Effective dynamics of twisted and curved scroll waves using virtual filaments.
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.
Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281 S9 WE05, 9000 Ghent, Belgium.
Hans
H
Dierckx
Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281 S9 WE05, 9000 Ghent, Belgium.
Henri
H
Verschelde