A. Toth et al., SIGNAL TRANSMISSION IN CHEMICAL-SYSTEMS - PROPAGATION OF CHEMICAL WAVES THROUGH CAPILLARY TUBES, Journal of physical chemistry, 98(2), 1994, pp. 522-531
The propagation of chemical waves through narrow channels has been inv
estigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are
connected by precision-bore capillary tubes of different internal diam
eters. A wave initiated on one side of an otherwise impenetrable barri
er enters and travels through the capillary tube, forming a hemisphere
of excited solution at the exit. When the tube diameter is greater th
an a critical value, the excitation serves to initiate a circular wave
in the second compartment; otherwise, the hemisphere collapses and no
wave is initiated. Electrochemically generated periodic wave trains g
ive rise to resonance patterns characterized by firing numbers 1/n, wh
ere n = 1, 2, etc. is the number of waves entering the tube for every
wave exiting. These firing numbers correspond to one branch of a Farey
tree; higher periodic resonances in modeling calculations indicate th
at more fully developed Farey sequences may also occur. A one-dimensio
nal mapping procedure is proposed to describe the appearance and order
ing of the resonance patterns.