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Scroll waves in Excitable media and the Motion of organization Center
Published in H-H Dai, P L Sachdev, Recent Advances in Differential Equations, 2020
For the wave front of a spatial scroll wave, we usually have NQ = c + DkQ, where No denotes the normal velocity of the wave front, c the plane velocity of the wave front surface and kQ the mean curvature of the wave front. Equation (3.2) shows that the organization center also has a similar relation. The only difference between them is that No, k0 degenerate into the normal velocity �and curvature k of the organization center, respectively. From the spiral wave theory we know that when the wave front satisfies the curvature relation it has the shape of a spiral wave. So we get the global structure of a scroll wave: the organization center is a vortex ring, and the intersection on the cross-section perpendicular to the axis is a spiral wave.
Deep spatio-temporal sparse decomposition for trend prediction and anomaly detection in cardiac electrical conduction
Published in IISE Transactions on Healthcare Systems Engineering, 2022
Xinyu Zhao, Hao Yan, Zhiyong Hu, Dongping Du
In the first category, most of the works have been focused on using a model-based control method to control the anomaly (Dubljevic et al., 2008). For example, Garzon et al. (Garzón et al., 2014) proposed a model-based continuous-time feedback control methodology to suppress the anomaly. Marcotte and Grigoriev (Marcotte & Grigoriev, 2016) proposed an adjoint eigenfunction method to provide localization for the dynamics and control of the unstable spiral wave. Some efforts to reduce the computational complexity, including Galerkin projection (Garzón et al., 2014) and numerical approximation (Kaboudian et al., 2019) have been proposed. However, the major limitations of the model-based methodology are that these models require all the complex dynamic models and parameters to be known, which may not be feasible in practice.
Viscoelastic Taylor–Couette instability in the Keplerian regime
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
Y. Bai, T. Vieu, O. Crumeyrolle, I. Mutabazi
The resulting pattern is formed of wavepacket with different irregular size and slow modulation in time. The axial wavelength of the spiral wave is about 1.40 in agreement with the results from linear stability analysis. The disordered nature of time-dependent patterns is the consequence of the existence of many modes near the threshold. Indeed, the linear stability has shown that in the considered interval of , there are three modes whose marginal stability curves have close minima (m = 1, m = 0 and ). We have performed a complex demodulation of the disordered patterns (Bot and Mutabazi 2000) and separated left and right travelling waves (figure 8). The two waves have different amplitudes and phases, this is the reason why their superposition does not form standing waves.
Symmetric Airy vortex and symmetric Airy vector beams
Published in Liquid Crystals, 2021
Wenxing Fu, Yaqin Zhou, Yide Yuan, Tiegang Lin, Yingjie Zhou, Tibing Zeng, Huihui Huang, Fan Fan, Shuangchun Wen
For a left circularly polarised (LCP) incident beam, the output beam is a superposition of two parts: the residual LCP component, and the transformed right circularly polarised (RCP) component with a spiral phase factor and a symmetric spatially cubic phase factor . On the contrary, for the RCP incident beam, the output beam contains the residual RCP component, and the transformed LCP component with a spiral phase factorand a symmetric spatially cubic phase factor . The residual component can be totally eliminated when the QSAP satisfies the half wave condition (Γ = π, 3π, 5π…). The different signs of the spiral and symmetric spatially cubic phase factors indicated the twist direction of the spiral wave fronts of the vortex beam and the ability to focus first and then diffuse the whole SABs, respectively. Therefore, the symmetric Airy vortex beam will be formed for the circular polarisation incident beams.