The Modeling of Ion Oscillations in Rapidly Oscillating Quadrupole Fields when Crossing the Mathieu Diagram Stability Boundaries

2021 ◽  
Author(s):  
Eugenie V. Mamontov ◽  
Roman N. Dyatlov ◽  
Alexander A. Dvagilev ◽  
Olga V. Melnik
Keyword(s):  
Stability Boundaries

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Stability boundaries of gas hydrates helped by methane—structure-H hydrates of methylcyclohexane and cis-1,2-dimethylcyclohexane

2003 ◽  
Vol 58 (2) ◽  
pp. 269-273 ◽  
Author(s):  
Toshiyuki Nakamura ◽  
Takashi Makino ◽  
Takeshi Sugahara ◽  
Kazunari Ohgaki
Keyword(s):  
Gas Hydrates ◽  
Stability Boundaries

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

On stability boundaries of conservative systems

2001 ◽  
Vol 52 (4) ◽  
pp. 669-679 ◽  
Author(s):  
P. Seyranian ◽  
A. A. Mailybaev
Keyword(s):  
Stability Boundaries ◽  
Conservative Systems

Two-stream and filamentation instabilities for a light ion beam—plasma system

1987 ◽  
Vol 37 (3) ◽  
pp. 373-382 ◽  
Author(s):  
Toshio Okada ◽  
Winfried Schmidt
Keyword(s):  
Proton Beam ◽  
Size Effects ◽  
Ion Beam ◽  
Plasma Heating ◽  
Finite Size ◽  
Stability Conditions ◽  
Plasma System ◽  
Finite Size Effects ◽  
Stability Boundaries ◽  
Gas Discharges

Electrostatic two-stream and electromagnetic filamentation instabilities for a light ion beam penetrating a plasma are investigated. The dispersion relations of these instabilities including the effect of plasma heating by the ion beam are solved analytically and numerically. Stability conditions are derived for propagation through a plasma. Attention is paid to the finite size effects of beams with small diameters of the order 0·1 cm typical for pinched gas discharges. The results are illustrated by plotting stability boundaries for a 100 keV proton beam propagating through a plasma.

Vibration Control of a Beam Embedded With an Electrorheological Fluid

1995 ◽  
Author(s):  
Tyler J. Selstad ◽  
Kambiz Farhang ◽  
David Chelidze
Keyword(s):  
Control Method ◽  
Structural Member ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Parametric Stability ◽  
Stability Boundaries ◽  
Electrical Field Strength ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Er Fluid

Abstract Electrorheological (ER) fluids are known to exhibit damping and stiffness properties which are highly dependent on the induced electrical field strength within the ER medium. Incorporation of ER fluid within a structural member then provides a means of stiffness and damping variation of the member. A structural member with embedded ER fluid is considered. Equations governing the axial and transverse motions of the member are reduced to a system of linear ordinary differential equations with time-varying coefficients. Application of the multiple time scales method results in amplitude-frequency relations. A control method is considered in which the effect of embedded ER fluid damping modulation using a simple harmonic excitation voltage on the parametric stability boundaries of the member is examined. Results indicate that the parametric stability boundaries can change effecting various modulation amplitudes and frequencies.

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