北京大学 政学者论文集（2001） 我与君政.docx

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1、CIUN.PIIYS.LETT.Vol. 18,5 6(2001) 834A Non-invasive Method of Tracing Spiral Tips ”WANG Kai(王凯)，MAO XiaoMing(毛晓明)，OU-YANG Qi(欧阳顽)Depart inent uf Physic，uid Mesoscopic Physics Laboratory Peking University, Beijing 100871(Rxxcived 27 October 2000)A new method is developed to trace the tip of spiral wa

2、ves in an excitable medium. The in/orniation of a spiraltip movement is obtained from only six probes. This method can trace the tip of a simple rotating spiral as weJJas a complex spiral tip movement. More importuitly it can be used to distinguish between a spirport unity to solve the problem. Rece

3、ntly, Hall andGlass2 proposed a method to distinguish a targetfrom a spiral. Their basic strategy is to generate an-other target wave iii the heart witli stimuli, and mea-sure the phase shift of local cardiac signals caused bythe interaction of the stimulated wave and the originalwaves, wliich gives

4、 the information of the wave type.Their method is workable in theory, but may intro-duce dangers with a large stimulation to the alreadyabnormal heart.Here, we present a non-invasive method to distin-guish between target aiid spiral using only nine localprobes. Moreover, our method can locate spiral

5、 sourceusing only six local probes in a heart in real time,wliich is a necessary step towards controlling spiralwaves in hearts. We test our method with numericalsimulations and experiments. Iii the experiment, wcuse the Belousov-Zhabotiiisky (BZ) reaction3 山 areaction-diffusion system as a model, w

6、hich can qual-itatively reflect wave behaviour in hearts.Spiral waves are the travelling waves moving out-w /2d must be met.Fig. 1. Schematic representation of the arrangement ofone group of probes. The location of the probe is respec-tively at 1, 2, and 3.The information required for tliis method i

7、s thephase difference (3$ pj) among different probes inthe same group. In order to reduce the error bar, anSupported partly by the National Natural Science Foundation of China under Grant No. 19725519 and Jun-Zheng Foundationin Peking University.2001 Chinese Physical Society and IOP Publishing Ltd83

8、6WANG Kai el al.Vol. 18average value of 5 (pj over several periods is takenas the measurement. FYom Fig. 1, it is obvious that if人d is satisfied, we liavc:27r ,. d .八% - 82 = dcosO - sin。,Arwhere (r, 0) is the polar coordinates of probe at (翁 y),by taking the spiral tip as the apex. From the cquartions we obtain:(31 丹)sin。一(夕1 一 夕3)r cos。= d,(4)27r(31 -夕2) cos 0 +(81 93)sin 0 = d.(5)AThe above equations have two solutions of A, a positiveone and a negative one. Since A must be positive,