双层非线性耦合反应扩散系统中复杂Turing斑图

采用双层耦合的Brusselator模型, 研究了两个子系统非线性耦合时Turing 模对斑图的影响, 发现两子系统Turing 模的波数比和耦合系数的大小对斑图的形成起着重要作用. 模拟结果表明: 斑图类型随波数比值的增加, 从简单斑图发展到复杂斑图; 非线性耦合项系数在0–0.1时, 系统1中短波模在系统2失稳模的影响下不仅可形成简单六边形、四边形和条纹斑图, 两模共振耦合还可以形成蜂窝六边形、超六边形和复杂的黑眼斑图等超点阵图形, 首次在一定范围内调整控制参量观察到由简单正四边形向超六边形斑图的转化过程; 耦合系数在0.1–1时, 系统1中短波模与系统2失稳模未发生共振耦合仅观察到与系统2相同形状的简单六边形、四边形和条纹斑图. 关键词： Brusselator模型 非线性耦合 Turing模     

双层耦合Lengel-Epstein模型中的超点阵斑图

用双层耦合的Lengel-Epstein模型, 研究了两个子系统的图灵模对斑图的影响,发现其波数比在斑图的形成和选择过程中起着重要作用.当波数比为1时,双层系统未能发生耦合,只能出现条纹和六边形斑图;当波数比处于1-√17 的范围时,两子系统发生耦合,图灵模之间发生共振相互作用,得到种类丰富的超点阵斑图,包括暗点、点-棒和复杂超六边、Ⅰ-型和Ⅱ-型白眼、类蜂窝和环状超六边等斑图;当波数比大于√17 , 系统选择的斑图类型不再变化,均为环状超六边斑图.数值模拟得到的条纹、六边形、超六边点阵、Ⅱ-型白眼斑图和类蜂窝斑图均已在介质阻挡放电系统实验中观察到. 另外,还得到了超点阵斑图的波数随两个扩散系数乘积D_uD_v的变化曲线,发现其随的D_uD_v增大而减小. 关键词： 耦合系统 超点阵 波数比 数值模拟     

双层耦合非对称反应扩散系统中的振荡图灵斑图

采用线性耦合Brusselator模型和Lengyel-Epstein模型,数值研究了双层耦合非对称反应扩散系统中振荡图灵斑图的动力学,并分析了图灵模、高阶模以及霍普夫模之间的相互作用及其对振荡图灵斑图的影响.模拟结果表明,在Lengyel-Epstein模型激发的超临界图灵模k_1的激励下,Brusselator模型中处于霍普夫区域的高阶模3~(1/2)k_1被激发,这两个模式相互作用从而产生了同步振荡六边形斑图.随着控制参数b的增加,该振荡六边形斑图首先经历倍周期分岔进入双倍振荡周期,经历多倍振荡周期后,在霍普夫模式的参与下,最终进入时空混沌态.同步振荡六边形斑图形成的条件是Brusselator模型中的次临界图灵模k_2的本征值高度低于处于霍普夫区域的高阶图灵模3~(1/2)k_1的本征值高度,且两个图灵模之间不存在空间共振关系.当两个图灵模满足空间共振时,系统优先选择空间共振模式,从而产生超点阵斑图.霍普夫模和图灵模共同作用下只能产生非同步振荡图灵斑图.此外,耦合强度对振荡图灵斑图也有重要的影响.     

空间周期性驱动对双层耦合反应扩散系统中图灵斑图的影响

周期性驱动是控制斑图最有效的方式之一,因此一直是斑图动力学研究的一大热点.自然界中的斑图形成系统大多是多层耦合的非线性系统,周期性驱动对这些多层耦合系统的作用机理人们还不甚了解.本文通过耦合Brusselator (Bru)系统和Lengyel-Epstein (LE)系统,并给LE系统施加一个空间周期性驱动来研究外部驱动对多层耦合系统中图灵斑图的影响.研究发现,只要外部驱动与Bru系统的超临界图灵模(内部驱动模)两者中的一个为长波模时,就可以将LE系统中的次临界图灵模激发,3个模式共同作用从而形成具有3个空间尺度的复杂斑图.若外部驱动和内部驱动模均为短波模,则无法激发此系统的本征次临界图灵模,但满足空间共振时也可以产生超点阵斑图.若LE系统的本征模为超临界图灵模,其自发形成的六边形斑图只有在外部驱动强度较大的情况下才能够产生响应,且其空间对称性受到外部驱动波数的影响.     

氩气/空气介质阻挡放电自组织超六边形斑图实验研究

采用双水电极介质阻挡放电装置,在氩气/空气混合气体放电中,在三种边界条件下得到了一种新型的超六边形斑图.给出了超六边形斑图的傅里叶变换及其不同模强度随旋转角的变化.实验测量了超六边形斑图随空气含量和外加电压变化的相图.研究了超六边形斑图的时空动力学,发现超六边形斑图是由两套子结构嵌套而成.在四边形边界条件下,研究了放电面积的大小对斑图模式选择的影响.发现超四边形斑图的形成受边界条件影响很大,而超六边形斑图则是自组织的结果. 关键词： 介质阻挡放电 超六边形斑图 时空动力学 边界条件     

双层耦合非对称反应扩散系统中的超点阵斑图

通过线性耦合Brusselator模型和Lengyel-Epstein模型,数值研究了双层耦合非对称反应扩散系统中图灵模之间的相互作用以及斑图的形成机理.模拟结果表明,合适的波数比以及相同的对称性是两个图灵模之间达到空间共振的必要条件,而耦合强度则直接影响了图灵斑图的振幅大小.为了保证对称性相同,两个图灵模的本征值高度要位于一定的范围内.只有失稳模为长波模时,才能对另一个图灵模产生调制作用,并形成多尺度时空斑图.随着波数比的增加,短波模子系统依次经历黑眼斑图、白眼斑图以及时序振荡六边形斑图的转变.研究表明失稳图灵模与处于短波不稳定区域的高阶谐波模之间的共振是产生时序振荡六边形的主要原因.     

介质阻挡放电系统中超四边形斑图形成的实验研究

采用水电极介质阻挡放电装置,在氩气和空气的混合气体放电中,对超四边形斑图的形成进行了实验研究.发现随着外加电压的升高,斑图类型经历了四边形斑图、准超点阵斑图、超四边形斑图、条纹斑图或六边形斑图的演化顺序.对这些斑图进行了傅里叶谱分析,得到了空间模式随电压的变化关系.此外,在外加电压升高的过程中,出现了具有不同空间尺度的两种超四边形斑图,它们满足不同的驻波条件.分析了壁电荷在超四边形斑图形成中的作用.实验测量了斑图类型随气隙间距和外加电压变化的相图以及超四边形斑图随气隙间距和气隙气压变化的相图.测量了击穿电 关键词： 介质阻挡放电 斑图 壁电荷 放电参量     

不同结构六边形斑图演化过程光谱特性

采用发射光谱法,研究了水电极介质阻挡放电中具有相同对称性的3种不同结构的六边形斑图演化过程的光谱特性。实验结果表明,随着外加电压的增加,放电首先形成六边形点阵斑图,然后是空心六边形斑图,最后是蜂窝六边形斑图。利用氩原子696.5 nm(2P_2→1S_5)谱线的展宽、氩原子763.2 nm(2P_6→1S_5)与772.1 nm(2P_2→1S_3)两条谱线强度比法和氮分子第二正带系(C~3Π_u→B~3Π_g)的发射谱线,研究上述3种斑图的电子密度、电子激发温度及分子振动温度。结果发现,随着外加电压的升高,六边形点阵斑图、空心六边形斑图和蜂窝六边形斑图的电子密度逐渐减小,而电子激发温度和分子振动温度逐渐增加。等离子体状态的改变直接影响着斑图的自组织。     

大气压氩气介质阻挡放电中的四边形斑图和六边形斑图

在大气压氩气介质阻挡放电中，研究了斑图形成随放电条件的变化.观察到随电压的增加，斑图经历六边形—四边形—具有辉光背景的四边形—具有辉光背景的六边形的转变过程.其空间波长与放电丝密度也随之改变.在一定的放电条件下，斑图涌现出辉光背景，此时空间波长与放电丝密度保持不变，但放电丝每半周期放电脉冲数由一次变为两次. 关键词： 介质阻挡放电 四边形斑图 六边形斑图 空间波长     

介质阻挡放电中两种不同时空对称性的六边形发光斑图

采用水电极介质阻挡放电装置，在大气压氩气放电中，在低电压区和高电压区，观察到两种具有不同时空特性的六边形点阵发光斑图.低压区的六边形斑图空间波长及单元直径均小于高压区的六边形斑图的相应量；高压区的六边形斑图具有较亮的背景，而低压区的六边形则没有.通过对两种六边形发光斑图进行时空动力学测量，发现低压区六边形是由两套长方形子点阵嵌套而成的，且这两套子点阵的出现顺序交替变化；而高压区六边形点阵斑图的所有单元基本是同步的.最后讨论了壁电荷对斑图的时空动力学行为的影响. 关键词： 介质阻挡放电 六边形斑图 时间相关性     

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.     

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.     

Superlattice Patterns in Coupled Turing Systems

In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Three different coupling methods have been used in order to investigate the mode interaction between the two Turing modes. It is proved in the simulations that interaction between activators in the two sub-systems leads to spontaneous formation of black eye pattern and/or white eye patterns while interaction between inhibitors leads to spontaneous formation of super-hexagonal pattern. It is also demonstrated that the same symmetries of the two modes and suitable wavelength ratio of the two modes should also be satisfied to form superlattice patterns.     

六边形格子态斑图的数值模拟

采用双层耦合的Lengel-Epstein模型, 通过改变两子系统图灵模的强度比, 获得了四种的六边形格子态和多种非格子态结构. 模拟结果表明: 反应扩散系统的格子态结构由三套子结构叠加而成, 是两图灵模的波数比和强度比共同作用的结果, 两模的强度比决定了三波共振的具体模式; 另外, 系统选择格子态斑图所需的两图灵模的强度比大于非格子态斑图的强度比; 逐步增加两图灵模强度比, 出现的斑图趋于从复杂到简单变化. 深入研究发现: 不同互质数对(a, b)对应的格子态斑图的稳定性不同, 其中(3, 2)对应的格子态结构最为稳定.     

Turing patterns beyond hexagons and stripes

The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing pattern's wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.     

Superlattice Turing structures in a photosensitive reaction-diffusion system

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.