【作者】 张鸣；

【导师】 肖井华；

【作者基本信息】 北京邮电大学 ， 物理电子学， 2010， 硕士

【摘要】 混沌理论自20世纪60年代建立以来,就一直吸引着众多领域的科学家,其中较为复杂的时空混沌动力学更是近来研究的热点。液晶材料现已被广泛应用到生产、生活的各个领域,而交变电场驱动下的液晶层就是一个典型的时空混沌系统。在外加电场的作用下,液晶分子将改变其自身的排列形式,从而产生特定的斑图。研究交变电场驱动下时空混沌的液晶斑图的演化规律,可以丰富时空混沌的理论研究。同时,系统地整理液晶的相变规律,还可以为今后同类型、甚至其他液晶材料的广泛应用、以及大规模生产提供定量的参考依据,甚至更为挖掘液晶材料的创新应用提供一些启发。液晶斑图的形成与驱动电压的幅值和频率有着非常密切的关系。本文通过学习混沌的基本理论和总结液晶研究的当前发展状况,提出了一套适用于液晶相变研究的基本方法。文中构建了定量描述相变规律的时空相关函数,以及通过区域频谱分析法获得纹理角度特征的图像信息处理算法。设计并完成了“观测交变电场驱动下时空混沌液晶斑图演变”的实验。根据实验观测所得的大量数据,定性总结了液晶斑图所具有的多种相态,以及它们在不同电压幅值和频率下相互演化的基本趋势。同时,分别计算了暂态斑图和稳态斑图的频谱、纹理角度分布特征、时空相关性等参数,从而定量地描述了液晶斑图在具有确定电压和频率的交变信号驱动下演化的过程。此外,还总结了在不同驱动频率、不同驱动电压、不同的驱动信号加载方式、以及不同类型的周期驱动信号下斑图形成的规律。更多还原

【Abstract】 Since 1960s, chaos theory has attracted a large number of scientists in variety of fields. Recently, the complex spatiotemporal chaotic dynamics, an important branch of chaos theory, have become a research hot spot. Liquid crystal(LC), which has been widely applied to modern industrial production, is a typical spatiotemporal chaotic system under alternating current(AC) driving. Under the influence of the electric field, the LC molecules will change their original arrangement, resulting in certain patterns. Study on the evolution of spatiotemporal chaotic patterns of LC will enrich and advance the theoretical study of spatiotemporal chaos. In the meantime, systematically concluded rules of phase transition in LC, will provide quantitative reference data for the future widespread application as well as large-scale production of the similar type of LC materials. It may also inspire new ideas for innovative applications of LC.The formation of liquid crystal pattern relates to the driving voltage amplitude and frequency. In this paper, we introduced the basic theory of chaos, summarized the current development of LC research and proposed a solution about how to study the phase transition in LC. First, we found a spatiotemporal correlation function and the image processing algorithms using local spectrum method. Then we designed and performed the experiment of "Spatiotemporal chaotic pattern evolution and phase transition liquid crystal under AC driving". According to the data obtained from our observation, we summarized the evolution tendency of LD patterns in different phases under different amplitude and frequency of electric field qualitatively. Then we calculated the spectrums of the LD pattern, the distribution of the azimuthal angle of the patterns, spatiotemporal correlation and some other relative parameters to quantitatively describe the rules of pattern evolution under electric driving with certain amplitudes and frequencies. In addition, we also summarized the formation of LC patterns in different driving conditions, such as different amplitude，different frequency, changing driving signal as well as different kinds of periodic driving.更多还原