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In the experiment, bubbles were generated from the brass nozzle with the inner diameter of 1.1 mm submerged in the glass tank (400 × 400 × 700 mm) filled with distillated water. Pressure fluctuations and signal from the laser-ph...
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In the experiment, bubbles were generated from the brass nozzle with the inner diameter of 1.1 mm submerged in the glass tank (400 × 400 × 700 mm) filled with distillated water. Pressure fluctuations and signal from the laser-phototransistor sensor were recorded simultaneously. The movement of bubble wall was measured using a high speed camera and image processing technique. Results of analysis of images have been correlated with pressure and laser-phototransistor signals. In the analysis the Fourier spectrum, wavelet spectrum and non-linear methods (mutual information, attractor reconstruction, largest Lyapunov exponent and correlation dimension) have been used.The three applied in the paper techniques of measurement of dynamical properties of bubbling allow us to discuss in detail the mechanisms of different chaotic behaviors of bubbling. Two ranges of the air volume flow rate with different kinds of bubble chaotic behaviors have been identified. For the air volume flow rate less than 0.2 1/min the air pressure chaotic fluctuations do not cause the significant chaotic changes of bubble departure frequencies. When the air volume flow rate increases above the 0.21/min, the interaction between departing bubbles causes nonperiodic bubble wall movement, and then the appearance of chaotic changes of bubble departure frequency.
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The dynamics of bubble departures (at a frequency of ?=3 Hz) from a glass nozzle submerged in a tank filled with distilled water has been experimentally and theoretically studied. The volume of the system that supplies air to the ...
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The dynamics of bubble departures (at a frequency of ?=3 Hz) from a glass nozzle submerged in a tank filled with distilled water has been experimentally and theoretically studied. The volume of the system that supplies air to the nozzle (plenum chamber volume) and the air volume flow rate were changed in the experiment. The air pressure, bubble paths and liquid flow inside the nozzle were simultaneously recorded using a data acquisition system and a high-speed camera. It was shown that an increase in the plenum chamber volume leads to an increase in the intensity of the occurrences of chaotic changes in the subsequent waiting times. The analysis of the mechanism of the stability loss of the periodic bubble departures was based on changes in the time of the air pressure, the depth of the liquid penetration into the nozzle, the time of the bubble growth, the waiting time, and the bubble paths and their sizes, which is presented in this paper. The results of the analysis are compared with simulations that are based on the models of bubble growth and liquid flow inside the nozzle during the waiting time. It was shown that the air pressure rise, Δ_(Pl) during the waiting time is a non-linear function of the gas pressure after the bubble departure and the liquid velocity around the nozzle outlet. The nonlinearity of Δ_(Pl) increases when the plenum chamber volume increases, and it decreases when the air volume flow rate increases.
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A new approach is proposed for evaluating the quality of fluorescent particle image velocimetry (F-PIV) measurements for different superficial gas velocities (U-G) in a bubble column (1.0 m longx0.145 m i.d.) using chaos analysis....
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A new approach is proposed for evaluating the quality of fluorescent particle image velocimetry (F-PIV) measurements for different superficial gas velocities (U-G) in a bubble column (1.0 m longx0.145 m i.d.) using chaos analysis. The 2D velocity fields of a F-PIV system were obtained in a 0.145x0.10 m area located 0.552 m above the gas distributor. Four thousand pairs of images were obtained at a frequency of 4.2 Hz at nine radial positions for superficial gas velocities (UG) of 0.158, 0.528, 2.106 and 4.212x10(-2) m/s. Using the standard cross-correlation (SCC) approach, PIV quality was analyzed for the velocity module and its components by investigating the cross-correlation coefficient (CCC), the signal-to-noise ratio (SNR) and the uncertainty (CS method) estimated by correlation statistics. Moreover, it was possible to extract the velocity fluctuation series for chaos analysis (correlation dimension, D-ML, and standard deviation of the correlation integral, DevML). The effect of the quality of F-PIV measurements evaluated by chaos analysis is based on the noise limitation in amplitude and normalization of the integral correlation distances. The results presented similarities in the behavior of the PIV uncertainty and chaotic parameters along the radius for all UG investigated. For this reason, chaos analysis can be used in other PIV processing settings where quality indicators, such as uncertainty, SNR and CCC, do not exist. Thus, it was possible to use this analysis to gain a better understanding of the nonlinear interactions in a bubble column as well as the performance of a PIV post-processing filter in order to reduce the effect of noise.
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The paper investigates the dynamics of bubble departures from a glass nozzle submerged in a tank filled with distilled water. Air pressure and liquid flow inside the nozzle are simultaneously recorded using a data acquisition syst...
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The paper investigates the dynamics of bubble departures from a glass nozzle submerged in a tank filled with distilled water. Air pressure and liquid flow inside the nozzle are simultaneously recorded using a data acquisition system and a high speed camera. The recurrence plot and cross recurrence plot methods are used to identify the loss of synchronization between air pressure fluctuations and the depth of liquid flow inside the nozzle during chaotic bubble departures. We claim that the synchronization between pressure fluctuations and the depth of liquid penetration inside the nozzle is suppressed during chaotic bubble departures. The experimental results show agreement with the numerical findings. The results demonstrate that the non-linearities of processes occurring during liquid penetration inside the nozzle have a significant impact on the synchronization between the time histories of pressure and the corresponding depths of liquid penetration inside the nozzle.
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Experiments carried out to study the liquid displacements in bubble columns via the computer automated radioactive particle tracking technique are analyzed by means of Labrangian and qualitative dynamics tools. The Lagrangian appr...
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Experiments carried out to study the liquid displacements in bubble columns via the computer automated radioactive particle tracking technique are analyzed by means of Labrangian and qualitative dynamics tools. The Lagrangian approach yields the detalied motion sequences of the trancer as entrained by the fast ascending bubbles or by the liquid flow alongside the column walls. The qualitative dynamics tools, on the other hand, provide prima facie corroburation ofchaos in liquid motion based on an analysis of the volume-averaged Kol,mogorov entropy and the mutual informations function. Other features of the liquid hydrodynamics due to changes in column diameter and operating pressure are inspected. By increasing pressure the attractor's correlation dimension and the information loss rate decrease, whereas the liquid flow path is dramatically affected
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We introduce Max Weber's spirit of capitalism hypothesis into a benchmark Lucas' tree asset pricing model by assuming that economic agents derive direct utility from wealth. We prove the existence of perfect foresight equilibria w...
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We introduce Max Weber's spirit of capitalism hypothesis into a benchmark Lucas' tree asset pricing model by assuming that economic agents derive direct utility from wealth. We prove the existence of perfect foresight equilibria where the price-dividend ratio displays explosive rational bubble solutions, endogenous periodic cycles and chaotic dynamics.
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Based on the signals from oil-water two-phase flow experiment, we construct and analyze recurrence networks to characterize the dynamic behavior of different flow patterns. We first take a chaotic time series as an example to demo...
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Based on the signals from oil-water two-phase flow experiment, we construct and analyze recurrence networks to characterize the dynamic behavior of different flow patterns. We first take a chaotic time series as an example to demonstrate that the local property of recurrence network allows characterizing chaotic dynamics. Then we construct recurrence networks for different oil-in-water flow patterns and investigate the local property of each constructed network, respectively. The results indicate that the local topological statistic of recurrence network is very sensitive to the transitions of flow patterns and allows uncovering the dynamic flow behavior associated with chaotic unstable periodic orbits.
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We have studied the complex dynamics of Chua's canonical circuit, a third-order nonlinear autonomous electric circuit, with a nonlinear resistor. When the v-i characteristic of the nonlinear resistor of the circuit is a smooth cub...
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We have studied the complex dynamics of Chua's canonical circuit, a third-order nonlinear autonomous electric circuit, with a nonlinear resistor. When the v-i characteristic of the nonlinear resistor of the circuit is a smooth cubic function, dynamics of the systems becomes more complex, than the case, when the v-i characteristic of the nonlinear resistor of the circuit is a piecewise linear function. Unlike the monotone bifurcation behavior of the members of Chua's circuit family with a piecewise linear resistor, forward and reverse period doublings cascades, as a parameter of the circuit is varied in a monotone way, have been observed in the circuit we have studied. Dynamics of the circuit is very sensitive to initial conditions, as forward and reverse period doubling sequences coexist with period-1 limit cycles.
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A first-order correction of the exponential divergence of trajectories in state space of a chaotic time series with noise was proposed. We demonstrated the performance for various examples using data from the Henon map, Ikeda map ...
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A first-order correction of the exponential divergence of trajectories in state space of a chaotic time series with noise was proposed. We demonstrated the performance for various examples using data from the Henon map, Ikeda map and logistic map, which were contaminated with noise. It was found that the proposed method provided a reasonable estimate of the largest Lyapunov exponent even when the noise level was as high as 30% of the signal content. The new method was not sensitive to the distribution of the noise. Furthermore, the comparison with Wolf et al. algorithm showed that our method is much better when dealing with the time series contaminated with noise. Our algorithm was also valid for more complicated chaotic dynamical systems, such as Lorenz attractor and R6ssler-hyperchaos attractor. (c) 2005 Elsevier B.V All rights reserved.
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This work aims at studying the non-linear dynamics and the flow regime transitions in bubble column reactors. For this purpose, various signal processing techniques e.g. frequency analysis, fractal analysis and deterministic chaos...
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This work aims at studying the non-linear dynamics and the flow regime transitions in bubble column reactors. For this purpose, various signal processing techniques e.g. frequency analysis, fractal analysis and deterministic chaos analysis have been applied to laser Doppler velocimetry signals. The system considered is a two-dimensional reactor allowing LDV measurements at higher void fractions than in three-dimensional systems. Each signal processing technique presents a specific capacity to describe a regime transition or a feature of the flow structure. Use of these various techniques have highlighted the occurrence of two states in the transition regime and yielded detailed information on the physical mechanisms responsible for these transitions. (C) 2003 Elsevier Science Ltd. All rights reserved. [References: 20]
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