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Complex eigenvalues and the inverse spectral problem for transmission eigenvalues
Inverse Problems, 2013We continue our investigation of complex eigenvalues of the interior transmission problem for spherically stratified media (Leung and Colton 2012 Inverse Problems 28 075005). In this paper we show that if complex transmission values exist for a spherically stratified medium with (normalized) support in {x: |x| ⩽ 1} then they must lie in a strip ...
David Colton, Yuk-J Leung
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Controlling chaos to solutions with complex eigenvalues
Physical Review E, 2003We derive formulas for parameter and variable perturbations to control chaos using linearized dynamics. They are available irrespective of the dimension of the system, the number of perturbed parameters or variables, and the kinds of eigenvalues of the linearized dynamics. We illustrate this using the two coupled Duffing oscillators and the two coupled
Oh-Jong, Kwon, Hoyun, Lee
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First-order perturbation solution to the complex eigenvalues
Applied Mathematics and Mechanics, 1987The matrix perturbation method is extended to discrete linear nonconservative system with unsymmetric matrices. By introducing the concept of the adjoint complex eigenvector and by making use of the orthogonality relationship in the complex mode theory, the first-order perturbation solution to the complex eigenvalues is derived.
Li, Jiming, Wang, Wei
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Complex eigenvalues in scattering theory
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1959The non-relativistic problem of scattering of a particle by a target possessing discrete excited states can be expressed in terms of ‘physical’ resonance states, i.e. solutions of the wave equation for complex energy in which in the asymptotic form of the wave function in each channel one of the two possible exponential terms (which for real energy ...
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Complex Eigenvalue Analysis of Plasmonic Waveguides
Integrated Photonics Research, Silicon and Nanophotonics and Photonics in Switching, 2010Complex eigenvalue problems of plasmonic waveguide nanostructures are solved using FEM and MMP solvers. For improving MMP performance, new eigenvalue search functions are studied. Several plasmonic structures are analyzed and the field solvers are compared.
Jasmin Smajic, Christian Hafner
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Lee model with complex energy eigenvalues
Il Nuovo Cimento, 1959The Lee model with fixed point particles is investigated when complex energy eigenvalues appear in the subspace (V, N+θ). It is proved that in general such a model has no physical interpretation, at least in the usual framework. Indeed a problem in the subspace (2V+θ, V+N+2θ, 2N+3θ) is considered, and it is shown that expressions which are usually ...
Ascoli, R., Minardi, E.
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Coupled channel calculations with complex eigenvalues
Nuclear Physics A, 1970Abstract The Kapur-Peierls dispersion theory is applied to the calculation of the S -matrix for a system of coupled square wells. The energy dependence of the complex eigenvalue is investigated. The validity of a single-level approximation to the S -matrix in the framework of Kapur-Peierls theory is studied.
A. Lejeune, M.A. Nagarajan
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Complex eigenvalues in scattering theory
1997The non-relativistic problem of scattering of a particle by a target possessing discrete excited states can be expressed in terms of ‘physical’ resonance states, i.e. solutions of the wave equation for complex energy in which in the asymptotic form of the wave function in each channel one of the two possible exponential terms (which for real energy ...
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On complex eigenvalues of compartmental models
Mathematical Biosciences, 1985Abstract Conditions under which the eigenvalues of the matrix of a compartmental model have a nonzero imaginary part are studied. Inequalities for the total imaginary part are obtained. The effect of excretions and combinations of cycles on this imaginary part are studied.
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