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1.
Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system
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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. 相似文献
2.
采用双层线性耦合Lengyel-Epstein模型,在二维空间对简单正四边和超点阵四边形进行了数值分析.结果表明:当两子系统波数比N1时,随耦合强度的增大,基模的波矢空间共振形式发生改变,系统由简单六边形自发演化为结构复杂的新型斑图,除已报道的超六边形外,还获得了简单正四边和多种超点阵四边形,包括大小点、点线、白眼和环状超四边等斑图.当耦合系数α和β在一定范围内同步增大时,两子系统形成相同波长的Ⅰ型简单正四边;当α和β不同步增大时,由于两图灵模在短波子系统形成共振,系统斑图经相变发生Ⅰ型正四边→Ⅱ型正四边→超点阵四边形的转变;当系统失去耦合作用时,短波子系统波长为λ的Ⅰ型正四边斑图迅速失稳并形成波长为λ/N的Ⅰ型正四边,随模拟时间的延长,两子系统中不同波长的正四边均会经相变发生Ⅰ型正四边→Ⅱ型正四边→六边形的转变. 相似文献
3.
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. 相似文献
4.
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 相似文献
5.
Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes 总被引:1,自引:0,他引:1
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. 相似文献
6.
Turing patterns beyond hexagons and stripes 总被引:1,自引:0,他引:1
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. 相似文献
7.
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 相似文献
8.
W.L. Bloss 《Solid State Communications》1983,48(10):927-931
The collective plasmon excitations of a superlattice are investigated in both the classical and quantum limits. Using a model that is applicable to superlattices whose constituent layers are either semiconductor- semiconductor, semiconductor-metal, or metal-metal, we show that the surface plasmon interface modes of each layer (slab) couple via the long range Coulomb interaction into two bands of plasmons with dispersion along the superlattice axis. Results for plasmon dispersion are presented for the classical limit (de Broglie wavelength less than the layer width) where the response is treated via a solution of Maxwell's equations using the bulk 3-D dielectric constant to describe each intervening layer. These results are compared to the plasmon dispersion in the quantum regime where the wave-vector frequency dependent dielectric constant of the superlattice is calculated taking into account quantization effects (subband structure). The relationship between the modes in both limits is derived. 相似文献
9.
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 相似文献
10.
11.
12.
The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states.
When the system is driven by two commensurate frequencies, a variety of interesting superlattice type states are generated
via a number of different 3-wave resonant interactions. These states occur either as symmetry-breaking bifurcations of hexagonal
patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated
by the two forcing frequencies. Near the system’s bicritical point, a well-defined region of phase space exists in which a
highly disordered state, both in space and time, is observed. We first show that this state results from the competition between
two distinct nonlinear super-lattice states, each with different characteristic temporal and spatial symmetries. After characterizing
the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled.
Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a
third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency
used. This technique can also excite rapid switching between different nonlinear states. 相似文献
13.
用等效介质理论计算了半无限侧向铁磁/铁磁超晶格的推迟模式.且以Co/Ni体系超晶格为例具体计算了该超晶格的表面模式和体模式,展示出一些与磁性/非磁性超晶格不同的有趣性质.侧向磁性/磁性超晶格具有较复杂的推迟模式,这是一种具有高度一般性的体系,在改变构成超晶格的两种铁磁层的厚度的比值、外场时,可以调节两支表面模式的频率以及体模式的频带,这种调节作用是与两种铁磁层的饱和磁化值有关的.当饱和磁化值相差较大时,调制效果是很明显的.当第二种铁磁介质饱和磁化值趋于零时,该体系演变成熟知的磁性/非磁性超晶格.当取麦克斯
关键词:
铁磁/铁磁超晶格
推迟模式
等效介质理论
自旋波谱 相似文献
14.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed. 相似文献
15.
Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the nonmonotonic dispersion relation of a ferrofluid. 相似文献
16.
17.
Baumberger F Hengsberger M Muntwiler M Shi M Krempasky J Patthey L Osterwalder J Greber T 《Physical review letters》2004,92(1):016803
The interaction of the Shockley surface state with the step lattice of vicinal Cu(111) leads to the formation of an electronic superlattice state. On Cu(443), where the average terrace length forms a "shape resonance" with the Fermi wavelength, we find a step-lattice-induced band-gap opening at the Fermi level. A gap magnitude >200 meV is inferred from high resolution photoemission experiments and line shape analysis. The corresponding energy gain with respect to a gapless case is approximately 11 meV/unit cell, and is a substantial contribution to the stabilization of the step lattice. 相似文献
18.
The Bloch spinors, energy spectrum, and spin density in energy bands are studied for a two-dimensional electron gas (2DEG)
with Rashba spin-orbit (SO) interaction subject to the one-dimensional (1D) periodic electrostatic potential of a lateral
superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed
quasi-momentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections
in these states have components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion
curves due to the interplay between the SO and periodic terms is observed, thus, leading to the spin flip. The relation between
the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice
in the presence of an external electric field is predicted.
The text was submitted by the authors in English. 相似文献
19.
G.Gonzalez de la Cruz A. Tselis J.J. Quinn 《Journal of Physics and Chemistry of Solids》1983,44(8):807-812
Electronic collective modes in a semiconductor superlattice structure are studied within the self-consistent field approach. Plasmon and magneto-plasmon dispersion relations are obtained for the cases of strong and weak coupling between layers. The interaction of these collective modes with optical phonons is also investigated. 相似文献
20.
We study spontaneous pattern formation in a glass-forming nematic liquid crystal during the magnetically induced dynamic Fréedericksz
transition. Pattern growth rates and wavelengths as functions of the magnetic field are extracted from optical transmission
textures of thin planar cells. The characteristics of the observed stripe pattern can be related to viscoelastic parameters
of the nematic by means of a linear stability analysis of director fluctuation modes. The viscous properties of the material
allow to vary the time scales of the experiment with temperature by orders of magnitude, leaving the spatial structure of
the pattern essentially unchanged. We find that the ratios of shear and rotational viscosity coefficients relevant for the
pattern wavelength selection remain constant in the temperature range investigated, whereas their absolute values change by
almost two orders.
Received 23 November 2001 and Received in final form 19 April 2002 相似文献