Spatiotemporal synchronization

In the other type of self-organization (dynamic self-organization), spontaneous ordering of the systems occurs under thermodynamically non-equilibrium conditions, in which various ordered structures with wavelengths tens to hundreds of thousands times larger than the size of the system components are formed by spatiotemporal synchronization of various factors [10-12]. The spatiotemporal order... 

Oscillations connected with adsorbate-induced surface restructuring were studied also in [29]. The model used was aimed at mimicking oscillations in NO reduction by H2 on a mesoscopic Pt particle containing two catalytically active (100) areas connected by an inactive (111) area that only adsorbed NO reversibly. NO diffusion on and between facets was much faster than other steps. The results obtained show that the coupling of the catalytically active sublattices may synchronize nearly harmonic oscillations observed on these sublattices and also may result in the appearance of aperiodic partially synchronized oscillations. The spatiotemporal patterns corresponding to these regimes are nontrivial. In particular, the model predicts that, due to phase separation, the reaction may be accompanied by the formation of narrow NO-covered zones on the (100) sublattices near the (lOO)-(lll) boundaries. These zones partly prevent NO supply from the (111) sublattice to the (100) sublattices. 

All the complex behavior described so far in this Chapter arises from the diffusive coupling of the local dynamics which in the homogeneous case have simple fixed points as asymptotic states. If the local dynamics becomes more complex, the range of possible dynamic behavior in the presence of diffusion becomes practically unlimited. It is clear that coupling chaotic subsystems could produce an extremely rich dynamics. But even the case of periodic local dynamics does so. Diffusively coupled chemical or biological oscillators may become synchronized (Pikovsky et ah, 2003), or rather additional instabilities may arise from the spatial coupling. This may produce target waves, spiral patterns, front instabilities and several different types of spatiotemporal chaos or phase turbulence (Kuramoto, 1984). 

H. G. Winful and L. Rahman. Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers. Phys. Rev. Lett, 65 1575, 1990. 

Rate oscillations, spatiotemporal patterns and chaos, e.g. dissipative structures were also observed in heterogeneous catalytic reactions. If compared with pattern formation in homogeneous systems, the surface studies introduced new aspects, like anisotropic diffusion, and the possibility of global synchronization via the gas phase. Application of field electron and field ion microscopy to the study of oscillatory surface reactions provided the capability of obtaining images with near-atomic resolution. The most extensively studied reaction is CO oxidation, which is catalyzed by group VIII noble metals. 

Spontaneous Symmetry-Breaking. The amoeba s circular deformation (i.e., synchronous expanding movements of all branches) would be inevitable if realizable spatiotemporal patterns were limited to circularly symmetric ones. However, we observed that the amoeba produces various symmetry-broken patterns, and the pattern varies nonperiodically in a complex manner. As shown in Fig. 3A, the symmetry was spontaneously broken as a defective site was created in the periphery. The defective site was exclusively expanded at a velocity relatively larger than that of the rest, and developed into a distinct branch having enough occupying area inside the neuron 8 to evoke the illumination. 

Pfurtscheller, G., B. Graimann, J.E. Huggins, S.P. Ixvine, and L.A. Schuh. 2003. Spatiotemporal patterns of beta desynchronization and gamma synchronization in corticographic data during self-paced movement. Clinical Neurophysiology 114(7) 1226-1236. 

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