Unpinning the spiral waves by using parameter waves

The spiral waves anchored to heterogeneous areas are more difficult to control and eliminate than freely rotating ones in homogenous mediums. To eliminate pinned spiral waves, the resistant force should be provided to resist the pinning force. Other than advection field, we introduce parametric wave to play the role of providing resistant force. It is found that the parametric wave with large enough amplitude and proper frequency can unpin and eliminate the spiral wave successfully. The capability of parametric wave in providing resistant force is dependent on its amplitude and frequency sensitively. On the basis of parametric wave, the dependence of pinning force on the size and level of heterogeneity is further confirmed.     

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.     

Kinematics of rigidly rotating spiral waves

Spiral waves rigidly rotating in excitable media are studied by use of a free-boundary approach. This study reveals the selection principle which determines the shape and the rotation frequency of spiral waves in an unbounded medium with a given excitability. It is shown that a rigidly rotating spiral in a medium with a strongly reduced refractoriness is supported within a range of the medium excitability restricted by two universal limits. At the low excitability limit the spiral core radius diverges, while at the high excitability limit it vanishes. The simulations performed for the medium excitability higher than the high excitability limit reveal nonstationary rotating waves, which considerably differ from well-studied meandering spiral waves. It is shown how the proposed free-boundary approach can be extended to the case of an arbitrary refractoriness. The predictions of the free-boundary approach are in good agreement with the results from numerical simulations of the underlying reaction-diffusion model and with asymptotics derived earlier for highly and weakly excitable media.     

Nonlinear fast growth of water waves under wind forcing

In the wind-driven wave regime, the Miles mechanism gives an estimate of the growth rate of the waves under the effect of wind. We consider the case where this growth rate, normalised with respect to the frequency of the carrier wave, is of the order of the wave steepness. Using the method of multiple scales, we calculate the terms which appear in the nonlinear Schrödinger (NLS) equation in this regime of fast-growing waves. We define a coordinate transformation which maps the forced NLS equation into the standard NLS with constant coefficients, that has a number of known analytical soliton solutions. Among these solutions, the Peregrine and the Akhmediev solitons show an enhancement of both their lifetime and maximum amplitude which is in qualitative agreement with the results of tank experiments and numerical simulations of dispersive focusing under the action of wind.     

Partial waves in coupled spiral lines

The slow-wave system consists of two parallel spirals of rectangular cross section wound on insulating rods; the mode of winding and excitation conditicns may vary. The field expressions and dispersion equations are derived for four possible cases. The results can be used to choose a slow-wave system with given dispersion features.     

FitzHugh-Nagumo系统中螺旋波的控制

采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进 关键词： 螺旋波 相空间压缩 FitzHugh-Nagumo方程     

Motion of spiral tip driven by local forcing in excitable media

We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.     

The mixed PDE for amplifying spiral waves

A special class of solutions of the wave equations is determined by a mixed-type PDE. Two kinds of well-posed boundary-value problems are solved. The equation has the following interesting property: it is a mixed equation of the first class and behaves as a mixed equation of the second class in large regions.Dedicated to Professor L. K. Hua.     

Nonlinear spiral waves in a galactic disk

An analytical solution of the nonlinear dynamic equations for a galactic disk is found. This solution describes the spiral design of spiral galaxies. The logarithmic profile of the spiral design and relatively larger density fluctuations as compared to velocity-field fluctuations are explained. Breaking of the obtained solution takes place for a certain critical amplitude. This can be a mechanism for the formation of galactic shocks and narrow star formation regions.     

Surface spiral waves in a filamentary vortex

Second-order [ O(k(2)), k = omega/c] nondipole effects in soft-x-ray photoemission are demonstrated via an experimental and a theoretical study of angular distributions of neon valence photoelectrons in the 100-1200 eV photon-energy range. A newly derived theoretical expression for nondipolar angular distributions characterizes the second-order effects using four new parameters with primary contributions from pure-quadrupole and octupole-dipole interference terms. Independent-particle calculations of these parameters account for a significant portion of the existing discrepancy between experiment and theory for Ne 2p first-order nondipole parameters.     

Motion of spiral waves induced by local pacing

The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.      

Nonstationary rotation of spiral waves: Three-dimensional effect

Nonstationary rotation of spiral waves was studied in experiments with the chemical active medium (the Belousov-Zhabotinsky reaction). It was shown that nonstationarity in some cases is a result of nonuniformity of the reaction throughout the solution depth due to nonuniform saturation with oxygen from the surface to bottom of the solution. Numerical experiments confirm the experimental data. It was shown numerically that this type of nonuniformity can lead to nonstationary rotation of spiral waves.     

Superspiral structures of meandering and drifting spiral waves

The spatiotemporal superstructure of meandering and drifting spiral waves is explained analytically. It is also demonstrated that the Hopf eigenmode that causes the transition to meandering waves is weakly exponentially localized at onset but grows exponentially slightly before onset.     

Projective synchronization of two coupled excitable spiral waves

Interaction of two identical excitable spiral waves in a bilayer system is studied. We find that the two spiral waves can be completely synchronized if the coupling strength is sufficiently large. Prior to the complete synchronization, we find a new type of weak synchronization between the two coupled systems, i.e., the spiral wave of the driven system has the same geometric shape as the spiral wave of the driving system but with a much lower amplitude. This general behavior, called projective synchronization of two spiral waves, is similar to projective synchronization of two coupled nonlinear oscillators, which has been extensively studied before. The underlying mechanism is uncovered by the study of pulse collision in one-dimensional systems.     

Light induced annihilation and shift of spiral waves

The light-induced collapse of a pair of spiral waves was studied in a chemically active medium based on the photosensitive Ru(bpy)(3)-catalyzed Belousov-Zhabotinsky reaction. Spiral waves annihilate only if the light intensity is increased in proper phase relative to the spiral waves' rotation. Otherwise, the distance between spiral wave cores increases and the pair survives. Computer simulations reveal the mechanism which forces the spiral waves to collide and annihilate. It is based on the shift of a single spiral wave upon an instantaneous decrease of excitability of the medium. (c) 1996 American Institute of Physics.     

Rotating spiral waves in a modified Fitz-Hugh-Nagumo model

A modified Fitz-Hugh-Nagumo model (a two-variable reaction-diffusion system with an excitable kinetics and a diffusing fast variable) was used to study numerically the rotating waves in a circular domain and in a two-dimensional ring. Large deviations from a Wiener type of behaviour of rotating spiral waves were revealed. We have shown that there are conditions under which: (i) vortices can appear in a medium with a hole but do not exist in a disk; (ii) two kinds of vortices with considerably differing periods can occur in the same ring; (iii) there is a non-monotonic dependence of vortex period on the hole size. These phenomena are believed to take place in myocardial tissue and in chemical active media. The conditions under which they could be observed experimentally are discussed.     

Synchronizing spiral waves in a coupled Rossler system

The synchronisation of spiral patterns in a drive-response R6ssler system is studied. The existence of three types of synchronisation is revealed by inspecting the coupling parameter space. Two transient stages of phase synchronisation and partial synchronisation are observed in a comparatively weak feedback coupling parameter regime, whilst complete synchronisation of spirals is found with strong negative couplings. Detailed observations of the synchronous process, such as oscillatory frequencies, parameters mismatches and amplitude variations, etc, are investigated via numerical simulations.