Destabilization of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">m</mml:mi><mml:mspace /><mml:mo>=</mml:mo><mml:mspace /><mml:mn>1</mml:mn><mml:mn /></mml:math>Diocotron Mode in Non-neutral Plasmas

Finn, John M.; del‐Castillo‐Negrete, Diego; Barnes, D. C.

doi:10.1103/physrevlett.84.2401

Cited by 14 publications

(10 citation statements)

References 18 publications

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“…2,3 For example, the knowledge of several largest Lyapunov exponents can be used for chaos control through "unstable periodic orbit stabilization" 3,4,62,63 or for characterization of different types of chaos synchronization [64][65][66] in plasma or electronic devices.…”

Section: Discussionmentioning

confidence: 99%

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Lyapunov stability of charge transport in miniband semiconductor superlattices

et al. 2013

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Section: Discussionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] Such systems can demonstrate a variety of dynamical behavior, including deterministic chaos. 5,[8][9][10] However, stability analysis (even numerical) of the systems away from the equilibrium still remains a nontrivial problem.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov stability of charge transport in miniband semiconductor superlattices

et al. 2013

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“…As a mathematical model of TED we consider the self-consistent system of the one-dimensional current continuity and the Poisson equation, which are used widely to describe charge transport processes in solid state and plasma physics, including Pierce beam-plasma system [33], non-neutral plasma [34], simple plasma diodes [35,36], semiconductors [37,38], organic field-effect transistors [39], etc. Such model was shown to demonstrate a variety of nonlinear phenomena including developing instabilities of electron transport in Pierce diode [40] and semiconductor structures [37], developing of turbulence [41] and bifurcations in plasma drift waves [42,43].…”

Section: Modelmentioning

confidence: 99%

Lyapunov analysis of the spatially discrete-continuous system dynamics

Maksimenko

Hramov

Короновский

et al. 2017

Chaos, Solitons & Fractals

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Citation: MAXIMENKO, V.A. ... et al, 2017. Lyapunov analysis of the spatially discrete-continuous system dynamics. Chaos, Solitons and Fractals, 104, Additional Information:• This paper was accepted for publication in the journal Chaos, Soli- AbstractThe spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable andPreprint submitted to Elsevier August 31, 2017inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

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“…Of course, as with conventional fluid experiments there are aspects of the electron vortex system which fall outside of the 2D fluid analogy. In electron vortex experiments the confinement geometry and the electron parameters are adjusted to eliminate or minimize these non-2D effects, which can include frequency shifts [23], mode instabilities [31,11] and temperature-dependent transport [30].…”

Section: Comparisonsmentioning

confidence: 99%

Using Global Interpolation to Evaluate the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements

Platte¹,

Rossi²,

Mitchell³

2009

SIAM J. Sci. Comput.

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Abstract. This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios. When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptical fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement between the three approaches.

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Destabilization of them=1Diocotron Mode in Non-neutral Plasmas

Cited by 14 publications

References 18 publications

Lyapunov stability of charge transport in miniband semiconductor superlattices

Lyapunov stability of charge transport in miniband semiconductor superlattices

Lyapunov analysis of the spatially discrete-continuous system dynamics

Using Global Interpolation to Evaluate the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements

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