Homotopic Arnold tongues deformation of the MHD α2‐dynamo
Homotopic Arnold tongues deformation of the MHD α2‐dynamo
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MHD α2âdynamo 的同位阿诺德舌头变形
DOI：
10.1002/pamm.200810719
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Kirillov O.N.
中科院分区：
文献类型：
--
作者：
Gunther U;Kirillov O.N.
我们考虑一个平均场α2 -发电机，参数α(r)=α0+γΔα(r)，参数β∈[0,1]插值在Dirichlet（理想，β=0）和Robin（物理现实，β=1）边界条件之间。结果表明，在同伦变形下，β=1处的振荡解的区域结束于β=0处的魔鬼点。当β=0时，底层的恶魔点网络实质上决定了特征值的编排，从而决定了β=1时发电机不稳定性的特征。利用微扰理论，我们导出了α0βγ‐空间中共振（Arnold’s）舌的一阶近似，其结果是由Δα(r)的傅里叶系数选择的魔鬼点附近的锥体。三维舌的空间方向由锥体顶端的恶魔交叉所涉及的模式的克莱恩特征决定。Krein空间诱导的共振区几何解释了寻找导致振荡发电机的α‐剖面的微妙之处，它明确地预测了谱异常点的位置，这是最近地磁场极性反转理论的重要组成部分。（©2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim）
We consider a mean–field α2–dynamo with helical turbulence parameter α(r)=α0+γΔα(r) and a boundary homotopy with parameter β∈[0,1] interpolating between Dirichlet (idealized, β=0) and Robin (physically realistic, β=1) boundary conditions. It is shown that the zones of oscillatory solutions at β=1 end up at the diabolical points for β=0 under the homotopic deformation. The underlying network of the diabolical points for β=0 substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for β=1. Using perturbation theory we derive the first–order approximations to the resonance (Arnold's) tongues in the α0βγ‐space, which turn out to be cones in the vicinity of the diabolical points, selected by the Fourier coefficients of Δα(r). The space orientation of the 3D tongues is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space induced geometry of the resonance zones explains the subtleties in finding α‐profiles leading to oscillatory dynamos, and it explicitly predicts the locations of the spectral exceptional points, which are important ingredients in the recent theories of polarity reversals of the geomagnetic field. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
凯尔迪什链的崩溃和连续非保守系统的稳定性
DOI：
10.1137/s0036139902414720
发表时间：
2004
期刊：
SIAM J. Appl. Math.
影响因子：
--
作者：
A. P. Seyranian;Oleg N. Kirillov
通讯作者：
Oleg N. Kirillov
摩擦声学中的亚临界颤振
DOI：
10.1098/rspa.2008.0021
发表时间：
2008
期刊：
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
影响因子：
--
作者：
Kirillov O.N.
通讯作者：
Kirillov O.N.