电场控制下的回卷波和螺旋波

发布时间：2018-02-28 10:10

本文关键词： 回卷波湍流态控制螺旋波漂移极化电场交流电场　出处：《浙江大学》2017年博士论文　论文类型：学位论文

【摘要】：在远离平衡态的各种物理、化学和生物系统中,广泛地存在各种波斑图。近年来发现可激发系统中的螺旋波以及螺旋波湍流态和心动过速、心颤等心脏疾病的紧密联系更是让控制这样的波斑图的研究成为了一个热点。二维螺旋波的失稳机制有很多种,比如对行波的长波微扰引起的爱克豪斯失稳和由于多普勒效应引起的漫游失稳。三维螺旋波,又称为回卷波,是二维螺旋波在空间上第三维的拓展。将每层二维螺旋波的拓扑缺陷点连起来,就形成了三维回卷波的奇异线。任何能引起二维螺旋波失稳的机制都可以引起三维回卷波的失稳。然而,在二维螺旋波稳定、严格旋转的参数区域,三维回卷波也可能因为奇异线负张力而发展成时空湍流态。由于奇异线负张力引起的回卷波失稳已经在著名的Belousov-Zhabotinsky (简称BZ)化学反应中被观察到。在本文,我们采用加一个圆极化电场的方法来稳定在三维可激发化学介质中的由于奇异线负张力而形成的湍流态。这个稳定机制是由于外场引起了回卷波的锁相,从而使得奇异线的张力变正。锁相条件、正奇异线张力条件和相对更高频率的条件,共同促成了从湍流态到有序的转变。一个线性的基于响应函数的理论为在旋转外场的作用下奇异线张力由负到正作了解释,而且其预测与数值模拟的结果达到了非常好的吻合。因为三维可激发系统中由奇异线负张力引起的回卷波湍流态被认为与心室纤维性颤动可能有密切关系,所以研究消除湍流的方法有着重要的意义。接下来,我们研究螺旋波在不同外场下的直线漂移情况。无论是在理论、模拟,还是实验上,螺旋波的漂移在斑图动力学里都是一个重要而且基本的问题。当交流电场和极化电场的频率是螺旋波本征频率的两倍的时候,螺旋波会表现为直线漂移。然而,关于此现象的定量理论解释还是缺乏。我们用响应函数理论,提出了螺旋波在电场作用下漂移的一个定量的理论解释。该理论给出了关于螺旋波漂移速度的大小和方向的一个明确清晰的方程。无论是在强激发还是弱激发介质,数值模拟得到的结果都和理论结果有一个定量的吻合。因为交流电场和极化电场都已经在BZ化学反应中被实现,因此本论文中提到的所有现象都可能在实验中得以实现。
[Abstract]:In various physical, chemical and biological systems far from the equilibrium state, a wide variety of wave patterns have been found. In recent years, it has been found that helical waves, turbulent spiral waves and tachycardia can be excited in the system, The close connection of heart disease such as heart fibrillation makes the study of controlling such wave pattern a hot spot. There are many kinds of instability mechanisms of two-dimensional spiral wave. For example, the Eckhouse instability caused by the long-wave perturbation of traveling waves and the roaming instability caused by the Doppler effect. Three dimensional spiral waves, also known as echo waves, Is the third dimension of the two-dimensional helical wave in space. The topological defects of each layer of the two-dimensional helical wave are connected together. Any mechanism that can cause the instability of the two-dimensional spiral wave can cause the instability of the three-dimensional echo wave. However, in the parametric region where the two-dimensional spiral wave is stable and strictly rotates, Three-dimensional echo waves may also develop into spatio-temporal turbulent states due to the negative tension of singular lines. The instability of the rewind waves due to the negative tension of singular lines has been observed in the famous chemical reaction of Belousov-Zhabotinsky. We use a circular polarized electric field to stabilize the turbulent state in a three-dimensional excited chemical medium due to the negative tension of singularities. This stabilization mechanism is due to the phase-locking of the rewind waves caused by the external field. So that the tension of the singular line becomes positive, the phase-locked condition, the positive singular line tension condition, and the condition of relatively high frequency, A linear theory based on response function explains the singular line tension from negative to positive under the action of the external rotating field. The predicted results are in good agreement with the numerical results, because the rewind turbulence induced by the singular line negative tension in the three-dimensional system is considered to be closely related to the ventricular fibrillation. So it is of great significance to study the method of eliminating turbulence. Next, we study the linear drift of helical waves in different external fields, whether in theory, simulation or experiment. The drift of helical wave is an important and fundamental problem in pattern dynamics. When the frequency of alternating current field and polarization electric field is twice the intrinsic frequency of spiral wave, the helical wave will behave as linear drift. The quantitative explanation of this phenomenon is still lacking. We use the response function theory. A quantitative theoretical explanation of helical wave drift under the action of electric field is presented. The theory gives a clear and clear equation about the magnitude and direction of helical wave drift velocity, whether in strongly excited or weakly excited medium. The numerical simulation results are in good agreement with the theoretical results. Because the alternating current field and polarization electric field have been realized in BZ chemical reaction, all the phenomena mentioned in this paper may be realized in the experiment.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O415

【相似文献】