Nonlinear dynamics and two-dimensional solitons for spin-1 ferromagnets with biquadratic exchange

In this paper, the two-dimensional nonlinear dynamics are investigated for the nonplanar nonlinear vibrations of an axially accelerating moving viscoelastic beam with in-plane and out-of-plane vibrations by the harmonic differential quadrature method (HDQM). The coupled nonlinear partial differential equations for the two-dimensional nonplanar nonlinear vibrations are discretized in space and time domains using HDQM and Runge-Kutta-Fehlberg methods respectively. Based on the numerical solutions, the nonlinear dynamical behaviors such as bifurcations and chaotic motions of the nonlinear system are investigated by using of the phase portrait and the bifurcation diagrams. The bifurcation diagrams for the in-plane and out-of-plane displacements via the mean axial velocity and the amplitude of velocity fluctuation are respectively presented while other parameters are fixed.

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Nonlinear dynamics and chaos

10.1093/oso/9780198708636.003.0013 ◽

2018 ◽

Author(s):

Joseph F. Boudreau ◽

Eric S. Swanson

Keyword(s):

Nonlinear Dynamics ◽

Lyapunov Exponent ◽

Chaotic Behavior ◽

Phase Portraits ◽

Nonlinear Ordinary Differential Equations ◽

Two Dimensional ◽

Kam Theorem ◽

Physical Systems ◽

Nonlinear Dynamics And Chaos ◽

Iterative Maps

Simple maps and dynamical systems are used to explore chaos in nature. The discussion starts with a review of the properties of nonlinear ordinary differential equations, including the useful concepts of phase portraits, fixed points, and limit cycles. These notions are developed further in an examination of iterative maps that reveal chaotic behavior. Next, the damped driven oscillator is used to illustrate the Lyapunov exponent that can be used to quantify chaos. The famous KAM theorem on the conditions under which chaotic behavior occurs in physical systems is also presented. The principle is illustrated with the Hénon-Heiles model of a star in a galactic environment and billiard models that describe the motion of balls in closed two-dimensional regions.

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Two-dimensional nonlinear dynamics of four driven vortices

Physical Review E ◽

10.1103/physreve.49.2062 ◽

1994 ◽

Vol 49 (3) ◽

pp. 2062-2069 ◽

Cited By ~ 8

Author(s):

P. N. Guzdar ◽

J. M. Finn ◽

A. V. Rogalsky ◽

J. F. Drake

Keyword(s):

Nonlinear Dynamics ◽

Two Dimensional

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Advances in two-dimensional gel matching technology

Biochemical Society Transactions ◽

10.1042/bst0320511 ◽

2004 ◽

Vol 32 (3) ◽

pp. 511-516 ◽

Cited By ~ 7

Author(s):

S. Church

Keyword(s):

Nonlinear Dynamics ◽

Image Analysis ◽

Gel Electrophoresis ◽

Two Dimensional ◽

Analysis Software ◽

Two Dimensional Gel Electrophoresis ◽

Software Products ◽

Large Numbers ◽

Noise Contamination ◽

The Impact

For many years, two-dimensional gel electrophoresis has been the method of choice for the investigation of complex mixtures of proteins. Although there are a number of emerging technologies that can be applied to proteomics, none can yet yield routinely the breadth of information available from two-dimensional gels. To be able to obtain instant information regarding molecular mass and pI, as well as to highlight quickly the expression changes or unique proteins across a gel series requires sophisticated and powerful image analysis software. The range of software products offered by Nonlinear Dynamics covers all levels of user application and throughput, from the user-guided Phoretix two-dimensional approach, when working with a small number of gels, to the automatic processing of large numbers of gels with minimal user intervention with Progenesis. Integration of the analysis software with powerful database components allows advanced gel comparisons and data mining to be performed with statistical verification of the results. Spot pick lists can be quickly created and automatically linked to a number of commercially available spot picking robots further increasing the support for proteomics research. The importance of image analysis for accurate, reliable and meaningful results will be discussed. Recent advances in development, with particular attention placed on the impact of noise contamination within gels, are illustrated and how the Progenesis product from Nonlinear Dynamics can be utilized to get the most from two-dimensional gel electrophoresis is shown.

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