Oil–water two-phase flow pattern analysis with ERT based measurement and multivariate maximum Lyapunov exponent

Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.

Analysis of Electrogastrograms of Elderly Gastrectomized Subjects by Using Maximum Lyapunov Exponent

Not much data are available regarding the electrical activity in the stomachs and intestines of elderly gastrectomized patients The purpose of this study was to determine the feasibility of using a complex dynamic method to analyze the electrogastrograms （EGGs） of healthy young, healthy elderly, and gastrectomized elderly male individuals. The authors analyzed the EGGs by using the maximum Lyapunov exponent （MLE）, which is one of the indices of the chaotic characteristics of time series. Significant differences were observed between the MLEs estimated from the, EGGs of the young and elderly individuals for most of the temporal intervals. The authors＇ data indicate that the EGGs of elderly gastrectomized subjects might be distinguished from the EGGs of healthy elderly individuals on the basis of the MLE distribution.

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.

The Nonlinear Bifurcation and Chaos of Coupled Heave and Pitch Motions of a Truss Spar Platform

This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincare maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave fre- quency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional temately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Nonlinear characteristics of induced spontaneous combustion process of sulfide ores

To investigate the relationship between nonlinear parameters and spontaneous combustion tendency of sulfide ores, nine different sulfide ore samples were taken from a pyrite mine in China, and induced spontaneous combustion experiment was carried out in the laboratory. Different stages of the induced spontaneous combustion process were studied by integrating wavelet technology and nonlinear dynamics theory. The results show that ignition points of all the ore samples are above 330 ℃, indicating that sulfide ores of the pyrite mine are difficult to combust spontaneously under normal mining conditions. Spontaneous combustion process includes three stages： incubation stage, development stage and approaching stage. The average temperature rising rate of the three stages are 1.0 ~C/min, 2.0 ~C/min and 4.2 ~C/min, respectively. During the spontaneous combustion process, mean values of approximate entropy and correlation dimension increase at first, and then decrease in the following stage. The mean value of the maximum Lyapunov exponent increases with the passage of reaction time. In a whole, correlation among the three nonlinear parameters firstly weakens, then enhances, and the best correlation period is at approaching stage. As ignition point increases, the maximum Lyapunov exponent of approaching stage decreases. Therefore, combustible tendency of sulfide ores could be qualitatively evaluated based on the maximum Lyapunov exponent of this stage.

Partition airflow varying features of chaos-theory-based coalmine ventilation system and related safety forecasting and forewarning system

To realize real-time monitoring and short-term forecasting and forewarning of coalmine ventilation systems(CVS), in this paper, we first established a joint surface and underground CVS safety management system consisting of main ventilation fan, safety-partition linked passageways, and air-required locations. We then applied chaos theory to identify the air quantity and gas concentration of underground partition boundaries, and adopted a fixed data quantity, multi-step progressive, weighted first-order local-domain method to setup a chaos prediction model and a CVS safety forecasting and forewarning system formed by the normal change level, orange forewarning level, and red alarm level. We next conduct the on-field application of the system in a coalmine in Jining, Shandong, China. The results showed that (1) in the statistical scale of 5 min, the changes in both air quantity and gas concentration along CVS partition airflow boundaries were characteristic of chaos and could be used for short-term chaos prediction, and the latter was more chaotic than the former;(2) the setup chaos prediction model had a higher prediction precision and the established safety prediction system could not only predict the variation in CVS stability but also reflect the rationality of underground mining intensity. Thus, this CVS safety forecasting and forewarning system is of better application value.

Stochastic Resonance as a Mathematical Model of an Electrogastrogram

An electrogastrogram （EGG） is a recording of the electrical activity in the stomach, as measured on the abdominal surface. In this study, the goal is to obtain a mathematical model of an EGG; to achieve this, the EGG of 14 subjects （seven males and seven females） will be obtained. Initially, the Wayland algorithm to the EGG to measure the degree of determinism is applied. However, it could not be determined whether the EGG could be generated by a chaotic process. In addition, the waveform of the electric potential in the interstitial cells of Cajal is similar to the graphs of the numerical solutions to the Van der Pol equation. Therefore, the Van der Pol equation to a periodic function was added, and random white noise was used to represent the intestinal motility and other biosignals. The EGG and numerical solutions were compared and evaluated on the basis of the translation error （Etrans） in the Wayland algorithm and the maximum Lyapunov exponent （2） in Rosenstein＇s algorithm. By projecting the data from an obtained stationary EGG from the subjects, along with the numerical solutions, onto the Etrans-λ plane, the affinity between them was qualitatively evaluated. The EGG was well described by stochastic resonance from the stochastic differential equations.

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.