scholarly journals Numerical Simulation of the Behaviors of the Bray-Liebhafsky Oscillating Chemical Reaction by a Four-variable Model

2017 ◽  
Vol 56 (2) ◽  
Author(s):  
Jie Ren ◽  
Jinzhang Gao ◽  
Wu Yang
Keyword(s):  
Numerical Simulation ◽  
Rate Constants ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Periodic Oscillation ◽  
Variable Model ◽  
Independent Variables ◽  
Oscillating Reaction ◽  
Oscillating Chemical Reaction

Based on a ten-step chemical model involving the concentrations of I<sub>2</sub>(aq), O<sub>2</sub>(aq), and the intermediates of I<sup>-</sup> and HIO<sub>2</sub>, four independent variables and seven irreversible steps, the nonlinear behavior of Bray-Liebhafsky (BL) oscillating reaction was investigated. The results showed that with different values of initial concentrations of reactants in the process of simulation, both periodic oscillation and chaotic behavior could be observed. In addition, at the same initial concentrations and rate constants, the system becomes more and more regular after being chaos. That is to say, the translation from chaos to periodic oscillation at the same initial conditions appeared in the BL system. The nonlinear behavior of system was also investigated briefly

A GALLERY OF CHUA ATTRACTORS: PART I

2007 ◽  
Vol 17 (01) ◽  
pp. 1-60 ◽  
Author(s):  
ELEONORA BILOTTA ◽  
PIETRO PANTANO ◽  
FAUSTO STRANGES
Keyword(s):  
Parameter Space ◽  
Chaotic Systems ◽  
Recent Literature ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Experimental Investigations ◽  
Contemporary Science ◽  
Complex Picture ◽  
Chua Oscillator

Chua Oscillator exhibits a wide variety of nonlinear behavior and has become a paradigm for theoretical and experimental investigations of chaotic systems. An initial exploration of the parameter space for the circuit shows that the system and its generalizations generates a broad range of very different strange attractors. In the work described in this paper, we constructed "a gallery" of these attractors, including patterns that have never previously been observed. We identified the regions of parameter space occupied by each attractor and the initial conditions leading to production of the attractor. System behavior was characterized using time series, FFT graphs and in some cases Lyapunov exponents. In this way we created a complex picture of chaos, which we divided into six parts. The first, we publish here. The rest of our work will be published in subsequent issues of this journal. In this first paper, we describe how to build Chua Oscillator and some of its generalizations, as proposed in the recent literature. We introduce the main features that characterize the chaotic behavior of each of these systems. Finally, we offer hints on the mechanisms underlying synchronization between pairs of coupled Chua Oscillators. The investigation of chaos allows for the emergence of a complex picture, which could improve our knowledge of these challenging phenomena in contemporary science.

Numerical Simulation on Temperature Field in Multi-Layers Inside-Beam Powder Feeding when Laser Cladding

2012 ◽  
Vol 499 ◽  
pp. 114-119 ◽  
Author(s):  
Ming Di Wang ◽  
Shi Hong Shi ◽  
X.B. Liu ◽  
Cheng Fa Song ◽  
Li Ning Sun
Keyword(s):  
Numerical Simulation ◽  
Heat Source ◽  
Laser Beam ◽  
Cooling Rate ◽  
Light Source ◽  
Laser Cladding ◽  
Laser Scanning ◽  
Initial Conditions ◽  
Cladding Layer ◽  
Powder Feeding

Numerical simulation of laser cladding is the main research topics for many universities and academes, but all researchers used the Gaussian laser light source. Due to using inside-beam powder feeding for laser cladding, the laser is dispersed by the cone-shaped mirror, and then be focused by the annular mirror, the laser can be assumed as the light source of uniform intensity.In this paper,the temperature of powder during landing selected as the initial conditions, and adopting the life-and-death unit method, the moving point heat source and the uniform heat source are realized. In the thickness direction, using the small melt layer stacking method, a finite element model has been established, and layer unit is acted layer by layer, then a virtual reality laser cladding manu-facturing process is simulated. Calculated results show that the surface temperature of the cladding layer depends on the laser scanning speed, powder feed rate, defocus distance. As cladding layers increases, due to the heat conduction into the base too late, bath temperature will gradually increase. The highest temperature is not at the laser beam, but at the later point of the laser beam. In the clad-ding process, the temperature cooling rate of the cladding layer in high temperature section is great, and in the low-temperature, cooling rate is relatively small. These conclusions are also similar with the normal laser cladding. Finally, some experiments validate the simulation results. The trends of simulating temperature are fit to the actual temperature, and the temperature gradient can also ex-plain the actual shape of cross-section.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

scholarly journals A computational framework for finding parameter sets associated with chaotic dynamics

2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Computational Framework ◽  
Independent Variables ◽  
Systems Model ◽  
Small Support

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

Research on a complete model of cosmological evolution a classical scalar field with a Higgs potential. II. Numerical simulation

2021 ◽  
pp. 147-151
Author(s):  
Yu.G. Ignat’ev ◽  
◽  
A.R. Samigullina ◽  
Keyword(s):  
Numerical Simulation ◽  
Computer Simulation ◽  
Scalar Field ◽  
Initial Conditions ◽  
Higgs Field ◽  
Hubble Constant ◽  
Cosmological Evolution ◽  
Higgs Potential ◽  
Complete Model ◽  
Expansion Stage

A study and computer simulation of a complete model of the cosmological evolution of a classical scalar field with a Higgs potential is carried out without the assumption that the Hubble constant is nonnegative. It is shown that in most cases of initial conditions the cosmological model passes from the expansion stage to the compression stage. Thus, cosmological models based on the classical Higgs field are unstable with respect to finite perturbations.

scholarly journals Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation.

2006 ◽  
Vol 53 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Ramón Varón ◽  
Matilde E Fuentes ◽  
Manuela García-Moreno ◽  
Francisco Garcìa-Sevilla ◽  
Enrique Arias ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Time Course ◽  
Initial Conditions ◽  
Reaction Scheme ◽  
Complete Analysis ◽  
Zymogen Activation ◽  
Relative Contribution ◽  
Starting Point ◽  
Definition Of

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

scholarly journals Determine of the wave equation in the task of electrical oscillations

2018 ◽  
Vol 184 ◽  
pp. 01023
Author(s):  
Gordana V. Jelić ◽  
Vladica Stanojević ◽  
Dragana Radosavljević
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Mathematical Physics ◽  
Equation Of Motion ◽  
Independent Variables ◽  
Equations Of Mathematical Physics ◽  
Basic Equations ◽  
Derivatives Of ◽  
Two Independent Variables ◽  
Transverse Oscillations

One of the basic equations of mathematical physics (for instance function of two independent variables) is the differential equation with partial derivatives of the second order (3). This equation is called the wave equation, and is provided when considering the process of transverse oscillations of wire, longitudinal oscillations of rod, electrical oscillations in a conductor, torsional vibration at waves, etc… The paper shows how to form the equation (3) which is the equation of motion of each point of wire with abscissa x in time t during its oscillation. It is also shown how to determine the equation (3) in the task of electrical oscillations in a conductor. Then equation (3) is determined, and this solution satisfies the boundary and initial conditions.

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