Bijective mapping between the eigenvalue spectrum of a Karle–Hauptman matrix and its phases

2008 ◽  
Vol 64 (6) ◽  
pp. 698-700 ◽  
Author(s):  
A. C. Ralph
Keyword(s):  
Eigenvalue Spectrum ◽  
Bijective Mapping

scholarly journals Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Hwancheol Jeong ◽  
Chulwoo Jung ◽  
Seungyeob Jwa ◽  
Jangho Kim ◽  
Jeehun Kim ◽  
...  
Keyword(s):  
Chiral Symmetry ◽  
Dirac Operators ◽  
Eigenvalue Spectrum

The eigenvalue spectrum of domain decomposed preconditioners

1991 ◽  
Vol 8 (4-5) ◽  
pp. 389-410 ◽  
Author(s):  
D. Goovaerts ◽  
T.F. Chan ◽  
Robert Piessens
Keyword(s):  
Eigenvalue Spectrum

scholarly journals The non-modal onset of the tearing instability

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
D. MacTaggart
Keyword(s):  
Initial Conditions ◽  
Linear Equations ◽  
Initial Perturbation ◽  
Transient Growth ◽  
Tearing Mode ◽  
Eigenvalue Spectrum ◽  
Tearing Instability ◽  
Set Up ◽  
Solution Behaviour ◽  
Physical Quantities

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number$S$increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the$L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as$O(S^{1/4})$on time scales of$O(S^{1/4})$for$S\gg 1$. This behaviour is much faster than the time scale$O(S^{1/2})$when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

Eigenvalue spectrum and synchronizability of multiplex chain networks

2020 ◽  
Vol 537 ◽  
pp. 122631 ◽  
Author(s):  
Yang Deng ◽  
Zhen Jia ◽  
Guangming Deng ◽  
Qiongfen Zhang
Keyword(s):  
Eigenvalue Spectrum
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