Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer–Meshkov instability – CORRIGENDUM

This paper is devoted to one of the methods of symbolic computation, which based on perturbation theory and constructed in the framework of matrix formalism. This method can be used for solving optimization problems and preliminary modeling in accelerator physics. There are presented the main theoretical positions and demonstration the result of this method on example of one of classical problems.

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Nonlinear Dynamics, Symmetry and Perturbation Theory in

Encyclopedia of Complexity and Systems Science ◽

10.1007/978-3-642-27737-5_361-3 ◽

2014 ◽

pp. 1-33

Author(s):

Giuseppe Gaeta

Keyword(s):

Nonlinear Dynamics ◽

Perturbation Theory

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Multistability and Bifurcation Topology in Electrostatically Coupled Nanobeams Under Parametric Resonance

Volume 4: 22nd Design for Manufacturing and the Life Cycle Conference; 11th International Conference on Micro- and Nanosystems ◽

10.1115/detc2017-67588 ◽

2017 ◽

Author(s):

Diala Bitar ◽

Najib Kacem ◽

Noureddine Bouhaddi

Keyword(s):

Nonlinear Dynamics ◽

Perturbation Theory ◽

Numerical Simulations ◽

Numerical Method ◽

Parametric Resonance ◽

Parametric Excitation ◽

Nonlinear Differential Equations ◽

Asymptotic Numerical Method ◽

Sensing Applications ◽

Fifth Order

The collective nonlinear dynamics of electrostatically coupled nanobeams under parametric excitation is modeled and investigated, while including the main sources of nonlinearities up to the fifth order. The normalized nonlinear differential equations are solved using secular perturbation theory. Numerical simulations have been performed using the Asymptotic Numerical Method for two and three coupled nanobeams. It is shown that, the fifth order nonlinearity leads to an increase in the number of multimodal solutions and their complexity in term of bifurcation topology. This model can be exploited to design arrays of NEMS with high performances for sensing applications.

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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