Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength (TPCS) on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Di et al., [Phys. Rev. E 85 (2012) 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength （TPCS） on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Diet al., [Phys. Rev. E 85 （2012） 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.     

局部不均匀性对时空系统振荡频率的影响

以复金兹堡一朗道方程为模型,利用数值实验方法观察了时空系统中螺旋波斑图的演化行为,发现在局域非均匀参数条件下,系统的螺旋波可以受到该杂质区域的影响而演化成为稳定的靶波.研究表明,内传的螺旋波转换为稳定靶波的必要条件是非杂质系统和杂质系统的振荡频率相等且小于系统的固有频率,并在参数一频率空间形成一个特殊的V形区域,进一步分析表明,该V形区域具有左右对称、两侧靶波传播方向相反以及随杂质区域参数α_2的增大而向参数β_2减小方向平移等性质.     

Suppression of Spiral Waves and Spatiotemporal Chaos Under Local Self-adaptive Coupling Interactions

In this paper, a close-loop feedback control is imposed locally on the Fitzhugh-Nagumo (FHN) system to suppress the stable spirals and spatiotemporal chaos according to the principle of self-adaptive coupling interaction. The simulation results show that an expanding target wave is stimulated by the spiral waves under dynamic control period when a local area of 5×5 grids is controlled, or the spiral tip is driven to the board of the system. It is also found that the spatiotemporal chaos can be suppressed to get a stable homogeneous state within 50 time units as two local grids are controlled mutually. The mechanism of the scheme is briefly discussed.     

Dynamics of spiral waves under phase feedback control in a Belousov-Zhabotinsky reaction

Feedback control of spiral waves by the phases of the spiral tip is investigated experimentally in a light-sensitive Belousov-Zhabotinsky reaction. The phases of rotation (Psi(r)) and meandering (Psi(m)) of the spiral tip are obtained in real time during experiments. It is found that, for both meandering and rigid rotating spirals, one can manipulate the spirals to move with any arbitrary paths by the feedback signals derived from Psi(r). Synchronization between meandering and rotation dynamics can be induced when both Psi(m) and Psi(r) are used simultaneously as control signals. Experimental findings are compared well with numerical simulations of the Oregonator model.     

Multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games

We study the formation of multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games with mobile individuals. We discover a set of seed distributions of species, which is able to produce multi-armed spirals and multi-pairs antispirals with a finite number of arms and pairs based on stochastic processes. The joint spiral waves are also predicted by a theoretical model based on partial differential equations associated with specific initial conditions. The spatial entropy of patterns is introduced to differentiate the multi-armed spirals and multi-pairs antispirals. For the given mobility, the spatial entropy of multi-armed spirals is higher than that of single armed spirals. The stability of the waves is explored with respect to individual mobility. Particularly, we find that both two armed spirals and one pair antispirals transform to the single armed spirals. Furthermore, multi-armed spirals and multi-pairs antispirals are relatively stable for intermediate mobility. The joint spirals with lower numbers of arms and pairs are relatively more stable than those with higher numbers of arms and pairs. In addition, comparing to large amount of previous work, we employ the no flux boundary conditions which enables quantitative studies of pattern formation and stability in the system of stochastic interactions in the absence of excitable media.     

Geometric diagnostics of complex patterns: spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripe-like patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh-Benard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers (Pr approximately > 1). In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.     

Size transition of spiral waves using the pulse array method

The domain size of spiral waves is an important issue in studies of two-dimensional (2D) spatiotemporal patterns. In this work, we use the 2D complex Ginzburg--Landau equation (CGLE) as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.     

Transition from spirals to defect-mediated turbulence driven by a doppler instability

A transition from rotating chemical spirals to turbulence is observed in experiments on the Belousov-Zhabotinsky reaction. The transition occurs when the waves near the spiral tip spontaneously break, generating defects. Measurements reveal that this defect-mediated turbulence is caused by the Doppler effect on the traveling waves. The observations are in good accord with numerical simulations and theory.     

Emergence and transitions of dynamic patterns of thickness oscillation of the plasmodium of the true slime mold Physarum polycephalum

The emergence and transitions of various spatiotemporal patterns of thickness oscillation were studied in the freshly isolated protoplasm of the Physarum plasmodium. New patterns, such as standing waves, and chaotic and rotating spirals, developed successively before the well-documented synchronous pattern appeared. There was also a spontaneous opposite transition from synchrony to chaotic and rotating spirals. Rotating spiral waves were observed in the large migrating plasmodium, where the vein structures were being destroyed. Thus, the Physarum plasmodium exhibits versatile patterns, which are generally expected in coupled oscillator systems. This paper discusses the physiological roles of spatiotemporal patterns, comparing them with other biological systems.     

非均匀可激发介质中的稀密螺旋波

在非均匀可激发介质中,采用Barkley模型数值模拟了稀螺旋波和密螺旋波, 并对二者的动力学行为随参数的变化进行了研究. 结果发现:稀螺旋波的旋转频率随参数b的增加迅速减小,之后趋于饱和, 显示出不同于密螺旋波的行为;两种螺旋波的周期和波长随参数ε 和非均匀区域尺寸R的增加而增加,相对稀螺旋波而言,密螺旋波的性质对R的依赖更为敏感; 稀螺旋波端点的波速随R的增加而减小,与密螺旋波波速变化趋势相反. 另外,由于非均匀区域的影响,当ε 或b 超过某一临界值时,螺旋波臂上出现缺陷点.     

三层弱循环耦合可激发介质中螺旋波动力学

采用Bär模型研究了具有循环反馈耦合的三层可激发介质中的螺旋波动力学行为,数值模拟结果显示: 在耦合强度较小时, 在各子系统中可观察到螺旋波漂移或漫游; 当耦合强度稍大时, 相互作用既可以使螺旋波漫游或漂移出系统边界而使子系统回到静息态,还可以使子系统的螺旋波态转变为靶波或湍流态, 并观察到子系统的渐近态依赖初值现象; 继续增大耦合强度, 三个子系统的螺旋波可达到近似广义同步; 当耦合强度更大时, 螺旋波演化为湍流态.     

气体放电系统中多臂螺旋波的数值分析

采用Purwins的三变量模型, 在二维空间对气体放电系统中多臂螺旋波的形成和转化进行了数值研究. 通过分析方程参数对系统空间的影响, 确定了系统获得稳定螺旋波的参数空间; 得到了斑图由简单静态六边形到螺旋波的演化过程, 分析了螺旋波的形成机制和时空特性; 进一步获得六种不同臂数的多臂螺旋波斑图(例如: 双臂、三臂、四臂、五臂、六臂和七臂螺旋波). 结果表明: 螺旋波斑图出现在图灵-霍普夫(Turing-Hopf)空间, 是Turing模和Hopf模相互竞争、相互作用的结果; 不同臂数的螺旋波波头均在持续地旋转运动, 其运动速度随螺旋波臂数的增加而增大; 随着螺旋波臂数的增加, 其波头的运动形式愈加复杂; 由于受微扰及边界条件的影响, 多臂螺旋波可以向臂数少一的螺旋波发生转变, 数值模拟结果与实验结果符合较好. 关键词： 螺旋波 数值模拟 气体放电     

Tracking target and spiral waves

A new algorithm for analyzing the evolution of patterns of spiral and target waves in large aspect ratio chemical systems is introduced. The algorithm does not depend on finding the spiral tip but locates the center of the pattern by a new concept, called the spiral focus, which is defined by the evolutes of the actual spiral or target wave. With the use of Gaussian smoothing, a robust method is developed that permits the identification of targets and spirals foci independently of the wave profile. Examples of an analysis of long image sequences from experiments with the Belousov-Zhabotinsky reaction catalyzed by ruthenium-tris-bipyridyl are presented. Moving target and spiral foci are found, and the speed and direction of movement of single as well as double spiral foci are investigated. For the experiments analyzed in this paper it is found that the movement of a focus correlates with foci in the immediate neighborhood independently of how they were created. (c) 2002 American Institute of Physics.     

Dual-band asymmetric electromagnetic wave transmission for dual polarizations in chiral metamaterial structure

In this paper, we propose a chiral metamaterial structure that enables dual-band asymmetric transmission effect for different linearly polarized electromagnetic waves. The metamaterial is composed of metallic spirals with two split-ring resonators sandwiching a dielectric slab and connecting with via hole. Strong one-way transmission of two orthogonally polarized waves at different frequency bands has been confirmed through both full-wave simulation and test on fabricated prototype at the microwave band. Analysis also shows such asymmetric transmission can be attributed to the induced asymmetric current distributions in the spiral that support strong polarization conversion and cross-polarization transmission. By scaling down the metamaterial structure, the concept could also be utilized at other frequency bands, such as submillimeter or even terahertz band and find applications in designing one-way electromagnetic wave devices or polarization spectral filters.     

螺旋线型三导体脉冲形成线快波抵消方法

针对螺旋线型三导体脉冲形成线的快波振荡问题,提出一种阻抗分两段阶梯变化的螺旋线结构,分析了此类螺旋线快波反射与慢波反射相互抵消快波的条件,给出两段变阻抗螺旋线慢波系数之间的关系式以及匝数密度之比计算方法,通过仿真计算证明该方法能有效消除快波反射对螺旋线输出脉冲的影响。     

Resetting wave forms in dictyostelium territories

The mechanism by which spiral wave patterns appear in populations of Dictyostelium was probed experimentally by external chemical perturbation. Spiral waves, which often arise from the breakup of circular waves driven by pacemakers, typically entrain those pacemakers. We studied these processes by resetting the waves with a spatially uniform pulse of extrinsic cyclic AMP. A pattern of spirals reappeared if resetting was early in the signaling stage, but only targets emerged following late resetting, in a manner analogous to cardiac defibrillation. This supports recent hypotheses that wave pattern selection naturally occurs by slow temporal variation of the excitability of the cells.     

Calculation of the Lyman-α asymmetry in a dense,partially-ionized hydrogen plasma

The asymmetry of the hydrogen resonance line Lyman-α is calculated. The electron perturbers are treated by the impact approximation and the ion perturbers by the quasistatic approximation. Contributions to the quasi-static ion broadening from first- and second-order asymmetry terms are included in the calculations, i.e. contributions from the quadrupolar ion-atom interaction and the quadratic Stark effect.The asymmetry at small separations from the line centre is unaffected by the inclusion of the second-order correction and remains slightly larger than the experimentally determined asymmetry. At larger separations from the line centre, the inclusion of the second-order correction causes a decrease in asymmetry due primarily to the quadratic Stark effect. For these larger separations from the line centre, rather poor agreement is obtained between theory and the experimental results of Boldt and Cooper.