Kolmogorov Entropy Values Research Articles

Chaotic index analysis of ethanol-based graphene nanofluid pulsating heat pipe

Pulsating heat pipes utilizing ethanol-based graphene nanofluids hold significant promise for cooling large electronic devices. However, traditional methods fall short in fully characterizing their properties due to internal phase transitions, latent heat, multiphase flow, and multi-field coupling. To address this, nonlinear chaotic analysis methods are introduced. This study constructs a vertical closed-loop pulsating heat pipe platform and applies Takens embedding theorem, phase space reconstruction theory, mutual information recursive selection method, and associative dimensionality algorithm to analyze ethanol-based graphene nanofluids with various concentrations. The investigation focuses on correlation dimensions and Kolmogorov entropy to provide numerical feedback on nanofluid concentration. Notably, ethanol-based graphene nanofluids concentrations between 0.04 wt% and 0.07 wt% exhibit an average heat transfer thermal resistance of approximately 0.74 K/W, corresponding to correlation dimension and Kolmogorov entropy values of 1.36 and 0.035, respectively. Additionally, reconstructed three-dimensional Singular Attractor phase diagrams offer morphological feedback on the pulsating heat pipe's working conditions. As the ethanol-based graphene nanofluids concentration reaches 0.35 wt%, an increase in the number of free vector points within the three-dimensional coordinate Attractor indicates localized unstable conditions in the heat pipe. Employing a wavelet noise reduction method with a soft threshold of 80 preserves the macroscopic vector flow pattern while eliminating irrelevant local information. Overall, this paper introduces novel approaches for analyzing heat transfer characteristics of graphene nanofluids in pulsating heat pipes.

A Parameter-Selection-Based Chaotic System

Control parameters play a key role in a chaotic system, where they directly determine its chaotic performance. In this brief, we propose a novel parameter-selection-based chaotic system (PSCS), where a new sequence of control parameters is generated using Kolmogorov entropy (KE). KE measures the chaotic behaviors of a chaotic system, and the positive values indicate that the system exhibits chaotic characteristics. Hence, the new sequence is formed by the parameters that yield positive KE values, which always maintain the chaotic behaviors in each iteration. Coupling the obtained sequence into a basic chaotic map, PSCS achieves a simple structure and lower computation cost. Experiments on the time complexity, NIST SP800-22 test suit, and information entropy demonstrate the good performance of the proposed PSCS.

Nonlinear time‐series analysis of optical signals to identify multiphase flow behavior in microchannels

This study provides an insight into the instability and irregularity of multiphase flows in microchannels. Using a homemade optical measuring system, time series related to two‐phase flow dynamics under different operating conditions, fluids, and channel lengths were collected and analyzed via a nonlinear characteristic parameter, Kolmogorov entropy (KE). Our results reveal that higher KE corresponds to unstable flow behavior, while lower KE refers to steady flow behavior; higher KE values appear at comparatively low or high gas flow rates, and most Taylor flow regime appeared at proper operating conditions with small KE. An equation derived based on the definition of KE is proposed to better understand KE characteristics, which include bubble break‐up impact and gas/liquid flow rate ratio. Predictions from the proposed analytical equation agree with experimental results, suggesting that the equation effectively identifies unstable flows and can be used to ensure stable and predictable multiphase flows in microchannels. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2378–2385, 2017

A New Method for Flow Regime Identification in a Fluidized Bed Based on Gamma-Ray Densitometry and Information Entropy

The accurate identification of the boundaries of the main flow regimes in fluidized beds is very important since the degrees of mixing and mass and heat transfer depend on the prevailing flow regime. Both the minimum fluidization velocity Umf (0.103 m·s−1) and the transition velocity Utrans (0.12 m·s−1) to bubbling fluidization regime have been successfully identified based on a newly developed maximum information entropy (IEmax) algorithm applied to gamma photon time series. The latter are recorded by means of gamma-ray densitometry scans performed in an air–polyethylene fluidized bed (0.438 m in ID) operated at ambient conditions. A comparison with the Kolmogorov entropy (KE) algorithm has found that the new approach yielded more accurate transition velocities. The value of Umf is also validated by means of the profiles of both bed pressure drop and bed height, respectively. It has been found, however, that these parameters are not capable of identifying the second transition velocity Utrans. It is demonstrated that the Umf value identified on the basis of IEmax is theoretically predictable. In the bubbling fluidization regime, a simple correlation between both the KE and IEmax values is developed.

Application of Chaos Analysis for the Investigation of Turbulence in Heterogeneous Bubble Columns

AbstractThe Kolmogorov entropy (KE) algorithm was applied to local gas holdup fluctuations for estimating the degree of turbulence (chaos) in a large‐scale bubble column (0.289 m ID and clear liquid height: 1.31 m). The latter was operated with nitrogen and polyalphaolefin liquid (PSS8) in the churn‐turbulent regime (0.117 ≤ Ug ≤ 0.257 m/s) at both high temperature (T = 441–468 K) and pressure (P = 1.8–2.5 MPa). Measurements in four different zones (z = 0.35, 0.67, 1.1 and 1.52 m) were performed. When the bubble coalescence is weak (local gas holdups < transitional gas holdup), the KE exhibits an initial peak (enhanced turbulence) in the first zone, then a sudden drop in the second zone and finally it increases smoothly in the upper zones. In the case of strong bubble coalescence, the KE exhibits alternating maxima and minima, i.e., instable flow patterns. It was found that at z = 1.52 m, the KE values increase with P. At higher values of T, the KE values are lower in all zones.

Kolmogorov entropy changes and cortical lateralization during complex problem solving task measured with EEG

The objective is to study changes in EEG time-domain Kolmogorov entropy and cortical lateralization of brain function areas during complex problem solving mental task in healthy human subjects. EEG data for healthy subjects are acquired during complex problem solving mental task using a net of 6 electrodes. The subject was given a nontrivial multiplication problem to solve and the signals were recorded for 10s during the task. Kolmogorov entropy values during the task were calculated. It was found that Kolmogorov entropy values were obviously greater in P4 channel (right) than ones in P3 channel (left) during complex problem solving task. It indicated that all subjects presented significant left parietal lateralization for the total frequency spectrum. These results suggest that it may be possible to noninvasively lateralize, and even eventually localize, cerebral regions essential for particular mental tasks from scalp EEG data.

Prediction of The Kolmogorov Entropy Derived from CT Data in a Bubble Column Operated under The Transition Regime and Ambient Pressure

AbstractThe Kolmogorov entropy (KE) algorithm was successfully applied to single source γ‐ray Computed Tomography (CT) data measured by three scintillation detectors in a 0.162 m‐ID bubble column equipped with a perforated plate distributor (163 holes × ∅︁ 1.32 · 10–3 m). The aerated liquid height was set at 1.8 m. Dried air was used as a gas phase, while Therminol LT (ρL = 886 kg m–3, μL = 0.88 · 10–3 Pa s, σ = 17 · 10–3 N m–1) was used as a liquid phase. At ambient pressure, the superficial gas velocity, uG, was increased stepwise with an increment of 0.01 m s–1 up to 0.2 m s–1. Based on the sudden changes in the KE values, the boundaries of the following five regimes were successfully identified: dispersed bubble regime (uG < 0.02 m s–1), first transition regime (0.02 ≤ uG < 0.08 m s–1), second transition regime (0.08 ≤ uG < 0.1 m s–1), coalesced bubble regime consisting of four regions (called 4‐region flow; 0.1 ≤ uG < 0.12 m s–1), and coalesced bubble regime consisting of three regions (called 3‐region flow; uG > 0.12 m s–1). The KE values derived from three scintillation detectors in the first transition regime were successfully correlated to both bubble frequency and bubble impact. The latter was found to be inversely proportional to the bubble Froude number. The KE model implies that the bubble size in this particular flow regime is a weak function of the orifice Reynolds number (db = 7.1 · 10–3Re0–0.05).

Dynamic cerebral autoregulation assessment using chaotic analysis in diabetic autonomic neuropathy

Cerebral autoregulation (CA) was assessed by chaotic analysis based on mean arterial blood pressure (MABP) and mean cerebral blood flow velocity (MCBFV) in 19 diabetics with autonomic neuropathy (AN) and 11 age-matched normal subjects. MABP in diabetics dropped significantly in response to tilting (91.6 +/- 14.9 vs. 74.1 +/- 13.4 mmHg, P < 0.05). Valsalva ratio of heart rate was reduced in diabetics compared to normal (1.1 +/- 0.1 vs. 1.5 +/- 0.2, P < 0.05). It indicated AN affects the vasomotor tone of peripheral vessels and baroreflex. Nonlinear results showed higher correlation dimension values of MABP and MCBFV in diabetics compared to normal, especially MABP (3.7 +/- 2.3 vs. 2.0 +/- 0.8, P < 0.05). It indicated CA is more complicated in diabetics. The lower Lyapunov exponent and the higher Kolmogorov entropy values in diabetics indicated less predictable behavior and higher chaotic degree. This study suggests impaired autoregulation would be more chaotic and less predictable.

Identification of Various Transition Velocities in a Bubble Column Based on Kolmogorov Entropy

AbstractThe Kolmogorov entropy (KE) algorithm was applied successfully to gas holdup fluctuations measured in a 0.102 m I.D. stainless steel bubble column equipped with a perforated plate distributor (19 holes ∅︁ 1 mm). Nitrogen was used as the gas, while both 1‐butanol and gasoline were used as liquids. 1‐Butanol was aerated at pressures, P = 0.1 and 0.5 MPa, whereas gasoline was aerated at P = 0.1 and 0.2 MPa. Based on the peaks in the KE values under the pressures examined in both liquids, the boundaries of the following five regimes were identified: bubbly flow, first transition, second transition, coalesced bubble (4‐region flow) and coalesced bubble (3‐region flow). As the pressure increases to P = 0.5 MPa in 1‐butanol, all four transition velocities shift to higher superficial gas velocity, uG. In addition, in gasoline at P = 0.2 MPa and uG ≤ 0.017 m s–1, the existence of a chain bubbling regime was detected, whereas in 1‐butanol at P = 0.5 MPa and uG ≤ 0.02 m s–1, both laminar and turbulent chain bubbling subregimes were identified. It was found that in 1‐butanol under ambient pressure, the second and fourth transition velocities occur earlier than in gasoline.

Flow Regime Identification in a Bubble Column Based on Both Statistical and Chaotic Parameters Applied to Computed Tomography Data

AbstractThe Kolmogorov entropy (KE) algorithm was applied successfully to single source γ‐ray Computed Tomography (CT) data measured in a 0.162 m ID bubble column equipped with a perforated plate distributor (163 holes · ∅︁ 1.32 mm). Dried air was used as the gas phase and Therminol LT (ρL = 886 kg m–3, μL = 0.88 · 10–3 Pa s, σ = 17 · 10–3 N m–1) was used as a liquid phase. Three different pressures, P, of 0.1, 0.4, and 1.0 MPa were examined. At each pressure the superficial gas velocity, uG, was increased stepwise by steps of 0.01 m s–1 up to 0.2 m s–1. The average absolute deviation (AAD) was also used as a robust statistical criterion for regime transition. At all three pressures, based on the sudden changes in both the AAD and KE values, the boundaries of the following five regimes were identified: dispersed bubble regime, first and second transition regimes, coalesced bubble regime consisting of four regions (called 4‐region flow), and coalesced bubble regime consisting of three regions (called 3‐region flow). The existence of these regimes has already been documented. As the pressure increases, the transition velocity between the dispersed bubble and first transition regimes and the transition velocity between coalesced bubble (4‐region flow) and coalesced bubble (3‐region flow) regimes shift to higher uG values. On the other hand, at P = 0.4 MPa the second transition regime starts earlier. In addition, at P = 1 MPa the transition to coalesced bubble (4‐region flow) is delayed.

Chaotic analysis for blast furnace ironmaking process

Based on the algorithm of Kolmogorov entropy presented by Grassberger and Procac cia, as the time series data of silicon content in molten iron of No.1 BF at Laiwu and No.6 BF at Linfen Iron and Steel Group Cos. to be as samples, their Kolmo gorov entropy are computed to be (01453±00151)nats·h-1-1 an d (01553±00140)nats·h-1-1, and the time scales of forecasti ng in both BFs are estimated to be about 688 and 644h respectively. Since the value of Kolmogorov entropy is finite and positive, there is chaos in both b last furnace ironmaking processes, and the idea that Kolmogorov entropy may be u sed to judge the condition of BF is presented.

Modified chaotic adding weight one_rank local_region forecasting for silicon content in molten iron of blast furnace

Based on the usual chaotic-weighting first-rank local-region forecas ting model, a modification is made for the predictor in matrix and vector simulation instead of single variant. Then the modified forec asting model is applied to pr edict silicon content in molten iron of the medium-sized blast furnace in China, and good results are obtained. Finally, we find that the value of Kolmogo rov entropy has a great effect on the hitting accuracy of the prediction .