交变电场驱动下混沌液晶斑图的时空相关性演化
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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。
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.
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。
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.
引文
[1]Thomas H. Maugh II. Edward N. Lorenz, Scientist Developed Influential Chaos theory[J]]. Deathwatch.17, May.2008
[2]E. Lorenz. Deterministic Nonperiodic Flow[J]. Journal of the Atmospheric Sciences,20:130, Mar.1963
[3]徐泽西.“蝴蝶效应”和“混沌理论”[J].百科知识,6：19,2009
[4]J. Thompson, H. Stewart, R. Ghaffari, et al. Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists[M]. Great Britain:Jhon Wiley & Sons Ltd.,1988
[5]刘秉政、彭建华.非线性动力学[M].北京：高等教育出版社,2005
[6]吴积亲.混沌理论与创新探讨[J].绥化学院学报,2,27：1,2007
[7]杨君慧.混沌理论与蝴蝶效应视角下的全球金融危机[J].浙江金融,2,2009
[8]张彩霞.基于混沌理论的控制系统及应用[J].自动化仪器仪表,6,2007
[9]费燕.混沌理论及其在工程中的应用[J].中国高新技术企业,6,2009
[10]吴祥兴.混沌学导论[M].上海：上海科技文献出版社,1996
[11]杨维明.时空混沌和耦合映像格子[M].上海：上海科技文献出版社,1994
[12]陈宇环、易称福.时空混沌理论及其在保密通信中的应用[J].信息技术与信息化,2：20,2008
[13]J. Kosterlitz and D. Thouless. Ordering, Metastability and Phase Transitions in Two-demesional Systems. J. Phys. C:Solid State Phys.,6:1181,1973
[14]E. Bodenschatz, W. Zimmerman and L. Kramer. On Electrically Driven Pattern-forming Instabilities in Planar Nematics. J. Phys. France 49,11:1875-1899,1988
[15]R. Anugraha, K. Tamura and Y. Hidaka, et la. Order-Disorder Phase Transition in a Chaotic System. Phys.Rev.Lett.100:164503, Apr.2008
[16]K. Tamura, R. Anugraha and R. Matsuo, et la. Control Parameter Dependence of Spatial Domain Structures in Soft-Mode Turbulence. Phys. Soc. Jpn.75,6:063801, Jun.2006
[17]M. Tribelsky and K. Tsuboi. New Scenario for Transition to Turbulence? Phys. Rev. Lett.76, 10:1631, Mar.1996
[18]彼得·J·柯林斯.液晶——自然界中的奇妙物象[M].阮丽真.上海：上海科技教育出版社,2007.7
[19]郭琦、陈莜、吴一军等.液晶的性质及应用[EB／OL].http://www.chem.pku.edu.cn/bianj/paper/05/10.pdf,2009.12
[20]陈珺.液晶技术及应用[J].卫生职业教育,26：15,2008
[21]小林俊介.液晶显示技术的进展历程[J].现代显示,12：6,1997
[22]陈庆新.液晶显示技术的发展与展望[J].电声技术,9：16,1995
[23]于天池、高伟光、邹滨雁.液晶电光效应的应用研究[J].大连交通大学学报,28：1,2007.3
[24]郭琦、龙云、于聪等.液晶的性质及其在生物方面的应用[EB／OL].http://www.chem.pku.edu.cn/bianj/paper/05/12.pdf,2009.12
[25]李兰英、武长城、姚康德.生物液晶[J].化学通报,10：745,2005
[26]欧阳钟灿、刘寄星.从肥皂泡到液晶生物膜[M].科学家谈物理(第二辑)湖南：湖南教育出版社,1994.8
[27]王瑾菲、蒲永平、杨公安等.高分子液晶材料的应用及发展趋势[J].陶瓷,3：16,2009
[28]张江涛、何军、尹少辉.液晶分子模拟理论及其应用[J].科研报告,36：20,2008
[29]杨傅子.近期液晶研究中的几个新方向——液晶非显示应用基础研究的进展[J].物理学进展,28:2,2008.6
[30]Y. Hidaka, J. Huh and K. Hayashi, et la. Soft-mode Turbulence in Electrohydrodynamic Convection of a Homeotropically Aligned Nematic Layer. American Physical Society,56,6: R6259, Dec.1997
[31]M. Cross, D. Meiron and Y. Tu. Chaotic Domain:A Numerical Investigation[J]. Chaos,4:4, 1994
[32]Nathan Becker and Guenter Ahlers. Local wave director analysis of domain chaos in Rayleigh-B'enard convection[J]. Journal of Statistical Mechanics, P12002, Dec.,2006
[33]杨胡江、肖井华、蒋达娅.液晶物性实验介绍[J].大学物理,24:3,2005
[34]高鸿锦、董友梅.液晶与平板显示技术[M].北京：北京邮电大学出版社,2007
[35]李丽、王振领.Matlab工程计算及应用[M].北京：人民邮电出版社,2001
[36]赵国瑞、汪大民菊、陆明.计算机软件技术基础[M].天津：天津大学出版社,2004
[37]S. Lippman、J. Lajoie、B. Moo. C++ Primer中文版[M].李师贤译.北京：：人民邮电出版社,2009
[38]叶卫平、方安平、于本方.Origin 7.0科技绘图及数据分析[M].北京：机械工业出版社,2004
[39]郁道银、谈衡英.工程光学[M].北京：机械工业出版社,2003
[2]E. Lorenz. Deterministic Nonperiodic Flow[J]. Journal of the Atmospheric Sciences,20:130, Mar.1963
[3]徐泽西.“蝴蝶效应”和“混沌理论”[J].百科知识,6：19,2009
[4]J. Thompson, H. Stewart, R. Ghaffari, et al. Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists[M]. Great Britain:Jhon Wiley & Sons Ltd.,1988
[5]刘秉政、彭建华.非线性动力学[M].北京：高等教育出版社,2005
[6]吴积亲.混沌理论与创新探讨[J].绥化学院学报,2,27：1,2007
[7]杨君慧.混沌理论与蝴蝶效应视角下的全球金融危机[J].浙江金融,2,2009
[8]张彩霞.基于混沌理论的控制系统及应用[J].自动化仪器仪表,6,2007
[9]费燕.混沌理论及其在工程中的应用[J].中国高新技术企业,6,2009
[10]吴祥兴.混沌学导论[M].上海：上海科技文献出版社,1996
[11]杨维明.时空混沌和耦合映像格子[M].上海：上海科技文献出版社,1994
[12]陈宇环、易称福.时空混沌理论及其在保密通信中的应用[J].信息技术与信息化,2：20,2008
[13]J. Kosterlitz and D. Thouless. Ordering, Metastability and Phase Transitions in Two-demesional Systems. J. Phys. C:Solid State Phys.,6:1181,1973
[14]E. Bodenschatz, W. Zimmerman and L. Kramer. On Electrically Driven Pattern-forming Instabilities in Planar Nematics. J. Phys. France 49,11:1875-1899,1988
[15]R. Anugraha, K. Tamura and Y. Hidaka, et la. Order-Disorder Phase Transition in a Chaotic System. Phys.Rev.Lett.100:164503, Apr.2008
[16]K. Tamura, R. Anugraha and R. Matsuo, et la. Control Parameter Dependence of Spatial Domain Structures in Soft-Mode Turbulence. Phys. Soc. Jpn.75,6:063801, Jun.2006
[17]M. Tribelsky and K. Tsuboi. New Scenario for Transition to Turbulence? Phys. Rev. Lett.76, 10:1631, Mar.1996
[18]彼得·J·柯林斯.液晶——自然界中的奇妙物象[M].阮丽真.上海：上海科技教育出版社,2007.7
[19]郭琦、陈莜、吴一军等.液晶的性质及应用[EB／OL].http://www.chem.pku.edu.cn/bianj/paper/05/10.pdf,2009.12
[20]陈珺.液晶技术及应用[J].卫生职业教育,26：15,2008
[21]小林俊介.液晶显示技术的进展历程[J].现代显示,12：6,1997
[22]陈庆新.液晶显示技术的发展与展望[J].电声技术,9：16,1995
[23]于天池、高伟光、邹滨雁.液晶电光效应的应用研究[J].大连交通大学学报,28：1,2007.3
[24]郭琦、龙云、于聪等.液晶的性质及其在生物方面的应用[EB／OL].http://www.chem.pku.edu.cn/bianj/paper/05/12.pdf,2009.12
[25]李兰英、武长城、姚康德.生物液晶[J].化学通报,10：745,2005
[26]欧阳钟灿、刘寄星.从肥皂泡到液晶生物膜[M].科学家谈物理(第二辑)湖南：湖南教育出版社,1994.8
[27]王瑾菲、蒲永平、杨公安等.高分子液晶材料的应用及发展趋势[J].陶瓷,3：16,2009
[28]张江涛、何军、尹少辉.液晶分子模拟理论及其应用[J].科研报告,36：20,2008
[29]杨傅子.近期液晶研究中的几个新方向——液晶非显示应用基础研究的进展[J].物理学进展,28:2,2008.6
[30]Y. Hidaka, J. Huh and K. Hayashi, et la. Soft-mode Turbulence in Electrohydrodynamic Convection of a Homeotropically Aligned Nematic Layer. American Physical Society,56,6: R6259, Dec.1997
[31]M. Cross, D. Meiron and Y. Tu. Chaotic Domain:A Numerical Investigation[J]. Chaos,4:4, 1994
[32]Nathan Becker and Guenter Ahlers. Local wave director analysis of domain chaos in Rayleigh-B'enard convection[J]. Journal of Statistical Mechanics, P12002, Dec.,2006
[33]杨胡江、肖井华、蒋达娅.液晶物性实验介绍[J].大学物理,24:3,2005
[34]高鸿锦、董友梅.液晶与平板显示技术[M].北京：北京邮电大学出版社,2007
[35]李丽、王振领.Matlab工程计算及应用[M].北京：人民邮电出版社,2001
[36]赵国瑞、汪大民菊、陆明.计算机软件技术基础[M].天津：天津大学出版社,2004
[37]S. Lippman、J. Lajoie、B. Moo. C++ Primer中文版[M].李师贤译.北京：：人民邮电出版社,2009
[38]叶卫平、方安平、于本方.Origin 7.0科技绘图及数据分析[M].北京：机械工业出版社,2004
[39]郁道银、谈衡英.工程光学[M].北京：机械工业出版社,2003