Bloch front

The dependence of the wave propagation direction on the coefficient /3 can be used to trap kinks and Bloch fronts. Such traps can be designed by creating spatial regions, where the coefficient j3 is locally changed to reverse the propagation velocity. The left pane in Fig. 7.3 shows an example of a kink trap in the oiie-dmiensioiial medinm at the 1 1 resonance. The value... 

B. Marts, A. Hagberg, E. Meron, and A. L. Lin. Bloch-Front turbulence in a periodically forced Belousov-Zhabotinsky reaction. Phys. Rev. Lett., 93 108305, 2004. 

Our attention is focused on the properties of periodic trains formed by kinks or traveling Bloch walls. Our analysis reveals that, depending on the parameters of the oscillatory medium and the spatial period of a train, it can undergo a reversal of its propagation direction [19]. We show how this phenomenon can be used to design traps for traveling kinks and Bloch walls. Furthermore, we find that a new kind of patterns - twisted rotated spiral waves - exist in oscillatory media under the conditions of front propagation reversal. 

The above analysis shows that front propagation reversal occurs near any n 1 resonance. For ji = I, stationary kinks (i.e., 27r-froiits) and periodic sequences of standing kinks are possible (the existence of stationary solitary kinks under global feedback conditions has previously been shown [15]). For 71 = 1, stationary tt-fronts represent standing Bloch walls or their periodic secjuences. Such standing structures are oscillation amplitude does not vanish here. 

Fig. 7,4. Trapping of kinks and Blocli fronts in the two-diniensional medium. The coefficient is set to = 5 and decreased to = 1.8 in the rectangiitar central region. The medium parainetei-s are the same as in Fig. 7.2. The system size is 1000 x 1000. Upper panek Kink trap in 1 1 resonance. The snapshots of the spatial distribution of Rctj are taken at t = 0000, t — 19000 and ( = 32000. Lower panel Bloch wave trap in 2 1 resonance. Snapshots the spatial distribution of Re>7 at t = 2000. ( = lOOOO and ( = 46800. (B = 0.061)...

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