外界场作用下的波前曲率关系和波形变化

基金项目: 国家自然科学基金资助项目(19902005)

Curvature Relation of Wave Front and Wave Changing in External Field

1.
Department of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China;

摘要: 研究外界场作用下，激发介质的波前曲率关系和波形变化．理论分析波前曲率关系，得到外界场作用下，波前的法向速度与波前平均曲率、平面波速和外界场之间的线性关系．数值分析外界场作用下，激发介质的Bar-Eiswirth模型，得到外界场作用下激发介质的波形图案．这里的理论分析、数值结果与BZ反应的实验结果完全一致，从而解释了外界场作用下的BZ现象，且由数值结果可知激发介质包含丰富的波形图案．
- 激波介质 /
- 螺旋波 /
- 图案 /
- 外界场
Abstract: The changing of wave structure in excitable media in external field is studied and the curvature relation of wave front is analyzed. Under external stimulus the normal velocity of wave front has linear relation with mean curvature of wave front, plane velocity and external field. The simulation methods have been used to analyze Bar-Eiswirth model with external field and obtain the wave pattern of excitable media contained external stimulus. These theoretical analysis and simulation results are identical with experiments of BZ reaction. So the results here theoretically explain the BZ phenomenon under external field and the simulation results here have rich wave patterns.
- excitable medium /
- spiral wave /
- pattern /
- external field

[1]	欧阳颀.反应扩散系统中的斑图动力学[M].非线性科学丛书.上海：上海科技教育出版社，2000.
[2]	Winfree A T.The Geometry of Biological Time,Second Edition.[M].New York:Springer, 2000.
[3]	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.
[4]	Tyson J,Keener J P.The dynamics of scroll waves in excitable media[J].SIAM, Rev,1992,34(1):1—39. doi: 10.1137/1034001
[5]	Krinsky V, Hamm E,Voignier V.Dense and sparse vortices in excitable media drift in opposite directions in electric field[J].Phys Rev,1996,76(20):3854—3857.
[6]	Pertrov V,Ouyang qi,Swinney H L.Resonant pattern formation in a chemical system[J].Nature,1997,388(6643):655—657. doi: 10.1038/41732
[7]	Steinbock O,Zykov V,Muller S.Control of spiral-wave dynamics in active media by periodic modulation of excitability[J].Nature,1993,366(6453):322—324. doi: 10.1038/366322a0
[8]	Vinson M,Mironov S,Pertsov A.Control of spiral orientation and lifetime of scroll rings in excitable media[J].Nature,1997,386(6624):477—480. doi: 10.1038/386477a0
[9]	Barkley D.Euclidean symmetry and the dynamics of rotating spiral waves[J].Phys Rev Lett,1994,72(1):164—167. doi: 10.1103/PhysRevLett.72.164
[10]	Dowle M,Mantel R M,Barkley D.Fast simulations of waves in three-dimensional excitable media[J].Int J Bif Chaos,1997,7(11):2529—2546. doi: 10.1142/S0218127497001692