Evolution Of Spatiotemporal Correlation Of Patterns In A Liquid Crystal Layer Under AC Electrical Driving

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.