Soliton dan DNA

Mapping Intimacies ◽

10.31219/osf.io/6bnmt ◽

2020 ◽

Author(s):

Miftachul Hadi

Keyword(s):

Nonlinear Dynamics ◽

Equation Of Motion ◽

Internal Motion ◽

Hamiltonian Model

Di artikel ini kami membahas secara ringkas DNA dan strukturnya, model DNA, DNA sebagai sistem dinamika non-linier, gerak internal DNA, juga model Hamilton untuk DNA dan persamaan geraknya. In this article we describe DNA and its structure, DNA model, DNA as nonlinear dynamics system, internal motion in DNA. Also, Hamiltonian model for DNA and its equation of motion.

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THE INTERNAL MOTION OF SUPERPARTICLE AND THE EQUATION OF MOTION OF SUPERSYMMETRIC PARTNERS

Modern Physics Letters A ◽

10.1142/s0217732395001897 ◽

1995 ◽

Vol 10 (24) ◽

pp. 1769-1776

Author(s):

OSAMU HARA

Keyword(s):

Conservation Laws ◽

Quantum Number ◽

Lorentz Invariance ◽

Equation Of Motion ◽

Internal Motion ◽

The Other

The internal motion of the superparticle and the equation of motion of its supersymmetric partners are discussed based on the conservation laws resulting from the invariances possessed by the Lagrangian of the superparticle, one of which is the Lorentz invariance and the other is to be discussed here. It is shown that this leads to the existence of a new quantum number which is related to the spin but gives information independent of it.

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Nonlinear Dynamics of a Translational FGM Plate with Strong Mode Interaction

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500311 ◽

2018 ◽

Vol 18 (03) ◽

pp. 1850031 ◽

Cited By ~ 34

Author(s):

Yan Qing Wang ◽

Jean W. Zu

Keyword(s):

Nonlinear Dynamics ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Power Law ◽

Equation Of Motion ◽

Functionally Graded ◽

Mode Interaction ◽

Dynamical Response ◽

Nonlinear Frequency ◽

Power Law Distribution

This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Kármán nonlinear geometrical relations, the equation of motion is derived from the D’Alembert’s principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge–Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted.

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Nonlinear Dynamics of Supported Cylinder Subjected to Axial Flow

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.243-249.4712 ◽

2011 ◽

Vol 243-249 ◽

pp. 4712-4717

Author(s):

Ji Duo Jin ◽

Zhao Hong Qin

Keyword(s):

Nonlinear Dynamics ◽

Flow Velocity ◽

Nonlinear Model ◽

Dynamical Behavior ◽

Axial Flow ◽

Equation Of Motion ◽

Flexible Cylinder ◽

Chaotic Motions ◽

Flutter Instability ◽

The Stability

In this paper, the stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are only the additional axial force induced by the lateral motions of the cylinder. Using six-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the quasiperiodic motion around the buckled position occurs, and this evolves into chaotic motions at higher flow.

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Perturbation analysis of the effective equation for two coupled periodically driven oscillators

Differential Equations and Nonlinear Mechanics ◽

10.1155/denm/2006/56146 ◽

2006 ◽

Vol 2006 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Andrzej Okniński ◽

Jan Kyzioł

Keyword(s):

Dynamical System ◽

Perturbation Analysis ◽

Approximate Equation ◽

Equation Of Motion ◽

Internal Motion ◽

Effective Equation ◽

Periodically Driven

Dynamics of two coupled periodically driven oscillators is analyzed via approximate effective equation of motion. The internal motion is separated off exactly and then approximate equation of motion is derived. Perturbation analysis of the effective equation is used to study the dynamics of the initial dynamical system.

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APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM II: ANALYZING CHAOTIC MOTION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127494000563 ◽

1994 ◽

Vol 04 (04) ◽

pp. 761-771 ◽

Cited By ~ 11

Author(s):

R. DOERNER ◽

B. HÜBINGER ◽

H. HENG ◽

W. MARTIENSSEN

Keyword(s):

Nonlinear Dynamics ◽

Lyapunov Exponents ◽

Time Scale ◽

Chaotic Motion ◽

Deterministic Chaos ◽

Fractal Dimensions ◽

Equation Of Motion ◽

Unstable Periodic Orbits ◽

Initial State ◽

Sensitive Dependence

Using a driven damped pendulum as a demonstration model we illustrate some fundamental concepts of nonlinear dynamics. We find deterministic chaos in the motion of the pendulum by observing its sensitive dependence on the initial state. We calculate the corresponding Lyapunov exponents from the equation of motion. The largest exponent gives the average predictability time scale. We estimate fractal dimensions of the attractor by determining the Kaplan Yorke dimension. Further we investigate the organization of unstable periodic orbits embedded in the attractor of the pendulum.

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