Structure of Wave Front and Organization Center in Excitable Media
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摘要: 通过建立波前曲面上的移动坐标系和边界层内的摄动分析，研究激发介质的波前曲面和组织中心的结构，得到波前曲面所满足的特征方程，组织中心所满足的一般方程．这些特征方程表明激发介质的波前曲面具有扭曲型回卷波、Mbius带型结构等变化；组织中心的轨迹具有打结、连结型的环型结构．得到的理论结果不仅解释了BZ化学反应产生的波形图案，而且给出一般激发介质波前曲面和组织中心可能出现的变化．Abstract: With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer, the structures of wave front and organization center in excitable media were studied. The eikonal equation of wave front surface and general equation of organization center were obtained. These eikonal equations reveal the wave front surfaces have structures of twisted scroll wave and M bius band, the organization centers have structures of knotted and linked ring. These theoretical results not only explain the wave patterns of BZ chemical reaction but also give several possibility structures of wave front surface and organization center in general excitable media.
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Key words:
- excitable media /
- wave front /
- organization center
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[1] Winfree A T.The Geometry of Biological Time[M].Second Edition.NY:Springer-Verlag,2000. [2] Perez-Munuzuri V, Aliev R，Vasiev B，et al.Super-spiral structure in an excitable medium[J].Nature,1991,353(24):740—742. doi: 10.1038/353740a0 [3] Pertsov A,Aliev R，Krinsky V. Three-dimensional twisted vortices in an excitable chemical medium[J].Nature,1991,354(31):419—421. doi: 10.1038/354419a0 [4] Jahnke W, Skaggs W，Winfree A T.Chemical vortex dynamics in the BZ reaction and in the 2-variable Oregonator model[J].J Chem Phys,1989,93(1):740—749. doi: 10.1021/j100339a047 [5] Winfree A T. Stable particle-like solutions to the nonlinear wave equations of three-dimensional excitable media[J].SIAM Rev,1990,32(1): 1—53. doi: 10.1137/1032001 [6] Hofer T,Sherraff J，Maini P. Cellular pattern formation during dictyostelium aggregation[J].Phys D,1995,85(3):425—444. doi: 10.1016/0167-2789(95)00075-F [7] Fagen X,Zhilin Q，Garfinkel A. Dynamics of reentry around an obstacle in cardiac tissue[J].Phys Rev E,1998,58(5):6355—6358. doi: 10.1103/PhysRevE.58.6355 [8] Keener J. The dynamics of three-dimensional scroll waves in excitable media [J].Phys D,1988,31(2):269—276. doi: 10.1016/0167-2789(88)90080-2 [9] Winfree A T. Persistent tangled vortex rings in generic excitable media[J].Phys D,1995,84(1):126—136. doi: 10.1016/0167-2789(95)00025-Y [10] DING Da-fu,FENG Zu-kang.Nonlinear wave dynamics in excitable media[J].Progress in Physics,1991,11(2):214—244. [11] Grindrod P.Patterns and Waves[M].Oxford Applied Mathematics and Computer Science Series.Oxford: Clarendon Press,1991. [12] 刘深泉.激发介质中螺旋波的波尖运动[J].物理学报,1998,47(7): 1057—1063. [13] 刘深泉，陆启韶，黄克累.单扩散回卷波组织中心的运动[J].应用数学和力学, 1999,20(4):398—404. -
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