scholarly journals NONLINEAR DYNAMICS OF ONE-DIMENSIONAL CRYSTALLINE BEAM (Ⅲ)

1990 ◽  
Vol 39 (8) ◽  
pp. 25
Author(s):  
SHAO MING-ZHU ◽  
I. HOFMANN ◽  
LUO SHI-YU
Keyword(s):  
Nonlinear Dynamics ◽  
One Dimensional

Nonlinear dynamics over rough topography: homogeneous and stratified quasi-geostrophic theory

2003 ◽  
Vol 474 ◽  
pp. 299-318 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Nonlinear Dynamics ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Small Scale ◽  
Stratified Fluids ◽  
Homogeneous Case ◽  
Bottom Boundary ◽  
One Dimensional ◽  
Averaged Equations ◽  
Large Scale Flow

The weakly nonlinear dynamics of quasi-geostrophic flows over a one-dimensional, periodic or random, small-scale topography is investigated using an asymptotic approach. Averaged (or homogenized) evolution equations which account for the flow–topography interaction are derived for both homogeneous and continuously stratified quasi-geostrophic fluids. The scaling assumptions are detailed in each case; for stratified fluids, they imply that the direct influence of the topography is confined within a thin bottom boundary layer, so that it is through a new bottom boundary condition that the topography affects the large-scale flow. For both homogeneous and stratified fluids, a single scalar function entirely encapsulates the properties of the topography that are relevant to the large-scale flow: it is the correlation function of the topographic height in the homogeneous case, and a linear transform thereof in the continuously stratified case.Some properties of the averaged equations are discussed. Explicit nonlinear solutions in the form of one-dimensional travelling waves can be found. In the homogeneous case, previously studied by Volosov, they obey a second-order differential equation; in the stratified case on which we focus they obey a nonlinear pseudodifferential equation, which reduces to the Peierls–Nabarro equation for sinusoidal topography. The known solutions to this equation provide examples of nonlinear periodic and solitary waves in continuously stratified fluid over topography.The influence of bottom topography on large-scale baroclinic instability is also examined using the averaged equations: they allow a straightforward extension of Eady's model which demonstrates the stabilizing effect of topography on baroclinic instability.

Generating Chaotic Secure Sequences with Desired Statistical Properties and High Security

1997 ◽  
Vol 07 (01) ◽  
pp. 205-213 ◽  
Author(s):  
Zhou Hong ◽  
Ling Xieting
Keyword(s):  
Nonlinear Dynamics ◽  
Distribution Function ◽  
Correlation Dimension ◽  
Linear Complexity ◽  
Statistical Properties ◽  
Linear Feedback ◽  
One Dimensional ◽  
Chaotic Sequences ◽  
Chaotic Signals ◽  
Feedback Shift Register

This work proposes a class of one-dimensional analogue chaotic signals which have perfect statistical properties. A non-invertible transformation is introduced to generate a class of binary (symbolic) chaotic sequences with desired distribution function and correlation function. These binary chaotic secure sequences are proven to have near-ideal linear complexity and infinite large discrete correlation dimension, thus they cannot be reconstructed by linear-feedback shift-register (LFSR) techniques or nonlinear dynamics (NLD) forecasting in finite order.

Nonlinear Dynamics of the Woodpecker Toy

2001 ◽  
Author(s):  
Remco I. Leine ◽  
Christoph Glocker ◽  
Dick H. van Campen
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Behaviour ◽  
One Dimensional ◽  
Nonsmooth Mechanics ◽  
Rigid Multibody

Abstract This paper studies bifurcations in systems with impact and friction, modeled with a rigid multibody approach. Knowledge from the field of Nonlinear Dynamics is therefore combined with theory from the field of Nonsmooth Mechanics. The nonlinear dynamics is studied of a commercial wooden toy. The toy shows complex dynamical behaviour but can be studied with a one-dimensional map, which allows for a thorough analysis of the bifurcations.

Nonlinear Dynamics of Exciton-Polariton Condensates in a One-Dimensional Lattice

2016 ◽  
Vol 37 (5) ◽  
pp. 511-520
Author(s):  
Martin V. Charukhchyan ◽  
Igor Yu. Chestnov ◽  
Alexander P. Alodjants ◽  
Oleg A. Egorov
Keyword(s):  
Nonlinear Dynamics ◽  
Dimensional Lattice ◽  
One Dimensional

Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling

2018 ◽  
Vol 106 ◽  
pp. 310-316
Author(s):  
Srđan Kostić ◽  
Nebojša Vasović ◽  
Kristina Todorović ◽  
Igor Franović
Keyword(s):  
Nonlinear Dynamics ◽  
Seismic Cycle ◽  
Phenomenological Modeling ◽  
One Dimensional

Numerical Simulation of Drill-String Dynamics with an Initial Curvature

2015 ◽  
Vol 799-800 ◽  
pp. 523-527 ◽  
Author(s):  
Almaz Sergaliyev ◽  
Aliya Umbetkulova
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Numerical Analysis ◽  
Variational Principle ◽  
Cross Section ◽  
Drill String ◽  
Finite Deformations ◽  
One Dimensional ◽  
Initial Curvature ◽  
Transverse Vibrations

This work is devoted to modeling of nonlinear dynamics of the rotating drill-string taking into account initial curvature and finiteness of deformations. The drill-string is compressed by variable axial force. The case of flat bending of the drill-string with an initial curvature is studied, where drill-string considered as a one-dimensional rotating rod of a symmetric cross-section. A nonlinear model is developed on the basis of the variational principle Ostrogradsky-Hamilton and the theory of finite deformations. The numerical analysis of the model is carried out. The influence of bending forms and initial curvature of the drill-string on the amplitude of transverse vibrations is established.

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