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Entropy, Volume 22, Issue 2 (February 2020) – 131 articles

Cover Story (view full-size image): In recent years, analysis of the organization and performance of football teams has undergone a methodological revolution, thanks to emergent technologies recording player activity during a match. Nowadays, it is possible to measure all events occurring on the pitch (passes, interceptions, shots, goals, fouls, etc.) with precise temporal and spatial coordinates. In this paper, we investigated the spatial and temporal entropies of football teams, focusing on the locations of all passes made during a match and the evolution of the organization of the corresponding passing networks. The analysis of football teams as time-evolving networks reveals interesting insights about what network parameters behave more/less randomly and, therefore, could be used as indicators for the prediction of future events. View this paper.
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23 pages, 3145 KiB  
Article
A Novel Multi-Criteria Decision-Making Model for Building Material Supplier Selection Based on Entropy-AHP Weighted TOPSIS
by Chun-Ho Chen
Entropy 2020, 22(2), 259; https://doi.org/10.3390/e22020259 - 24 Feb 2020
Cited by 154 | Viewed by 9767
Abstract
The type of criterion weight can be distinguished according to different decision methods. Subjective weights are given by decision makers based on their knowledge, experience, expertise, and other factors. Objective weights are obtained through multi-step calculations of the evaluation matrix constructed from the [...] Read more.
The type of criterion weight can be distinguished according to different decision methods. Subjective weights are given by decision makers based on their knowledge, experience, expertise, and other factors. Objective weights are obtained through multi-step calculations of the evaluation matrix constructed from the actual information about the evaluation criteria of the alternatives. A single consideration of these two types of weights often results in biased results. In addition, in order to build an effective supply chain source, buyers must find suitable quality products and/or service providers in the process of supplier selection. Based on the above reasons, it is difficult to accurately select the appropriate alternative. The main contribution of this paper is to combine entropy weight, analytic hierarchy process (AHP) weight, and the technique for order preference by similarity to an ideal solution (TOPSIS) method into a suitable multi-criteria decision making (MCDM) solution. The TOPSIS method is extended with entropy-AHP weights, and entropy-AHP weights are used instead of subjective weights. A novel decision-making model of TOPSIS integrated entropy-AHP weights is proposed to select the appropriate supplier. Finally, we take the selection of building material suppliers as an example and use sensitivity analysis to show that the combination of the TOPSIS method based on entropy-AHP weights can effectively select the appropriate supplier. Full article
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24 pages, 2462 KiB  
Article
Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design
by Zhihang Xu and Qifeng Liao
Entropy 2020, 22(2), 258; https://doi.org/10.3390/e22020258 - 24 Feb 2020
Cited by 6 | Viewed by 4195
Abstract
Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a [...] Read more.
Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments. Full article
(This article belongs to the Section Multidisciplinary Applications)
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11 pages, 3606 KiB  
Article
Characteristics of Nonthermal Dupree Diffusion on Space-Charge Wave in a Kappa Distribution Plasma Column with Turbulent Diffusion
by Myoung-Jae Lee and Young-Dae Jung
Entropy 2020, 22(2), 257; https://doi.org/10.3390/e22020257 - 24 Feb 2020
Cited by 2 | Viewed by 2061
Abstract
The nonthermal diffusion effects on the dispersion equations of ion-acoustic space-charge wave (SCW) in a nonthermal plasma column composed of nonthermal turbulent electrons and cold ions are investigated based on the analysis of normal modes and the separation of variables. It is found [...] Read more.
The nonthermal diffusion effects on the dispersion equations of ion-acoustic space-charge wave (SCW) in a nonthermal plasma column composed of nonthermal turbulent electrons and cold ions are investigated based on the analysis of normal modes and the separation of variables. It is found that the real portion of the wave frequency of the SCW in a Maxwellian plasma is greater than that in a nonthermal plasma. It is also found that the magnitude of the damping rate of the SCW decreases with an increase of the spectral index of the nonthermal plasma. It is also shown that the magnitude of the scaled damping rate increases with an increase of the Dupree diffusion coefficient. Moreover, the influence of the nonthermal character of the nonthermal plasma on the damping rate is found to be more significant in turbulent plasmas with higher diffusion coefficient. The variations of the wave frequency and the growth rate due to the characteristics of nonthermal diffusion are also discussed. Full article
(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)
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14 pages, 496 KiB  
Article
Phylogenetic Analysis of HIV-1 Genomes Based on the Position-Weighted K-mers Method
by Yuanlin Ma, Zuguo Yu, Runbin Tang, Xianhua Xie, Guosheng Han and Vo V. Anh
Entropy 2020, 22(2), 255; https://doi.org/10.3390/e22020255 - 23 Feb 2020
Cited by 11 | Viewed by 3100
Abstract
HIV-1 viruses, which are predominant in the family of HIV viruses, have strong pathogenicity and infectivity. They can evolve into many different variants in a very short time. In this study, we propose a new and effective alignment-free method for the phylogenetic analysis [...] Read more.
HIV-1 viruses, which are predominant in the family of HIV viruses, have strong pathogenicity and infectivity. They can evolve into many different variants in a very short time. In this study, we propose a new and effective alignment-free method for the phylogenetic analysis of HIV-1 viruses using complete genome sequences. Our method combines the position distribution information and the counts of the k-mers together. We also propose a metric to determine the optimal k value. We name our method the Position-Weighted k-mers (PWkmer) method. Validation and comparison with the Robinson–Foulds distance method and the modified bootstrap method on a benchmark dataset show that our method is reliable for the phylogenetic analysis of HIV-1 viruses. PWkmer can resolve within-group variations for different known subtypes of Group M of HIV-1 viruses. This method is simple and computationally fast for whole genome phylogenetic analysis. Full article
(This article belongs to the Special Issue Statistical Inference from High Dimensional Data)
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19 pages, 1671 KiB  
Review
Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review
by Miao Cai, Peng Cui, Yikang Qin, Daoshuang Geng, Qiqin Wei, Xiyou Wang, Daoguo Yang and Guoqi Zhang
Entropy 2020, 22(2), 254; https://doi.org/10.3390/e22020254 - 23 Feb 2020
Cited by 12 | Viewed by 5535
Abstract
Understanding the defect characterization of electronic and mechanical components is a crucial step in diagnosing component lifetime. Technologies for determining reliability, such as thermal modeling, cohesion modeling, statistical distribution, and entropy generation analysis, have been developed widely. Defect analysis based on the irreversibility [...] Read more.
Understanding the defect characterization of electronic and mechanical components is a crucial step in diagnosing component lifetime. Technologies for determining reliability, such as thermal modeling, cohesion modeling, statistical distribution, and entropy generation analysis, have been developed widely. Defect analysis based on the irreversibility entropy generation methodology is favorable for electronic and mechanical components because the second law of thermodynamics plays a unique role in the analysis of various damage assessment problems encountered in the engineering field. In recent years, numerical and theoretical studies involving entropy generation methodologies have been carried out to predict and diagnose the lifetime of electronic and mechanical components. This work aimed to review previous defect analysis studies that used entropy generation methodologies for electronic and mechanical components. The methodologies are classified into two categories, namely, damage analysis for electronic devices and defect diagnosis for mechanical components. Entropy generation formulations are also divided into two detailed derivations and are summarized and discussed by combining their applications. This work is expected to clarify the relationship among entropy generation methodologies, and benefit the research and development of reliable engineering components. Full article
(This article belongs to the Section Entropy Reviews)
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10 pages, 757 KiB  
Article
(1,0)-Super Solutions of (k,s)-CNF Formula
by Zufeng Fu, Daoyun Xu and Yongping Wang
Entropy 2020, 22(2), 253; https://doi.org/10.3390/e22020253 - 23 Feb 2020
Cited by 3 | Viewed by 2511
Abstract
A (1,0)-super solution is a satisfying assignment such that if the value of any one variable is flipped to the opposite value, the new assignment is still a satisfying assignment. Namely, every clause must contain at least two satisfied literals. Because of its [...] Read more.
A (1,0)-super solution is a satisfying assignment such that if the value of any one variable is flipped to the opposite value, the new assignment is still a satisfying assignment. Namely, every clause must contain at least two satisfied literals. Because of its robustness, super solutions are concerned in combinatorial optimization problems and decision problems. In this paper, we investigate the existence conditions of the (1,0)-super solution of ( k , s ) -CNF formula, and give a reduction method that transform from k-SAT to (1,0)- ( k + 1 , s ) -SAT if there is a ( k + 1 , s )-CNF formula without a (1,0)-super solution. Here, ( k , s ) -CNF is a subclass of CNF in which each clause has exactly k distinct literals, and each variable occurs at most s times. (1,0)- ( k , s ) -SAT is a problem to decide whether a ( k , s ) -CNF formula has a (1,0)-super solution. We prove that for k > 3 , if there exists a ( k , s ) -CNF formula without a (1,0)-super solution, (1,0)- ( k , s ) -SAT is NP-complete. We show that for k > 3 , there is a critical function φ ( k ) such that every ( k , s ) -CNF formula has a (1,0)-super solution for s φ ( k ) and (1,0)- ( k , s ) -SAT is NP-complete for s > φ ( k ) . We further show some properties of the critical function φ ( k ) . Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
19 pages, 2411 KiB  
Article
Semi-Supervised Bidirectional Long Short-Term Memory and Conditional Random Fields Model for Named-Entity Recognition Using Embeddings from Language Models Representations
by Min Zhang, Guohua Geng and Jing Chen
Entropy 2020, 22(2), 252; https://doi.org/10.3390/e22020252 - 22 Feb 2020
Cited by 20 | Viewed by 4582
Abstract
Increasingly, popular online museums have significantly changed the way people acquire cultural knowledge. These online museums have been generating abundant amounts of cultural relics data. In recent years, researchers have used deep learning models that can automatically extract complex features and have rich [...] Read more.
Increasingly, popular online museums have significantly changed the way people acquire cultural knowledge. These online museums have been generating abundant amounts of cultural relics data. In recent years, researchers have used deep learning models that can automatically extract complex features and have rich representation capabilities to implement named-entity recognition (NER). However, the lack of labeled data in the field of cultural relics makes it difficult for deep learning models that rely on labeled data to achieve excellent performance. To address this problem, this paper proposes a semi-supervised deep learning model named SCRNER (Semi-supervised model for Cultural Relics’ Named Entity Recognition) that utilizes the bidirectional long short-term memory (BiLSTM) and conditional random fields (CRF) model trained by seldom labeled data and abundant unlabeled data to attain an effective performance. To satisfy the semi-supervised sample selection, we propose a repeat-labeled (relabeled) strategy to select samples of high confidence to enlarge the training set iteratively. In addition, we use embeddings from language model (ELMo) representations to dynamically acquire word representations as the input of the model to solve the problem of the blurred boundaries of cultural objects and Chinese characteristics of texts in the field of cultural relics. Experimental results demonstrate that our proposed model, trained on limited labeled data, achieves an effective performance in the task of named entity recognition of cultural relics. Full article
(This article belongs to the Special Issue Information Theory and Graph Signal Processing)
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14 pages, 5353 KiB  
Article
Self-Propulsion Enhances Polymerization
by Maximino Aldana, Miguel Fuentes-Cabrera and Martín Zumaya
Entropy 2020, 22(2), 251; https://doi.org/10.3390/e22020251 - 22 Feb 2020
Cited by 3 | Viewed by 3180
Abstract
Self-assembly is a spontaneous process through which macroscopic structures are formed from basic microscopic constituents (e.g., molecules or colloids). By contrast, the formation of large biological molecules inside the cell (such as proteins or nucleic acids) is a process more akin to self-organization [...] Read more.
Self-assembly is a spontaneous process through which macroscopic structures are formed from basic microscopic constituents (e.g., molecules or colloids). By contrast, the formation of large biological molecules inside the cell (such as proteins or nucleic acids) is a process more akin to self-organization than to self-assembly, as it requires a constant supply of external energy. Recent studies have tried to merge self-assembly with self-organization by analyzing the assembly of self-propelled (or active) colloid-like particles whose motion is driven by a permanent source of energy. Here we present evidence that points to the fact that self-propulsion considerably enhances the assembly of polymers: self-propelled molecules are found to assemble faster into polymer-like structures than non self-propelled ones. The average polymer length increases towards a maximum as the self-propulsion force increases. Beyond this maximum, the average polymer length decreases due to the competition between bonding energy and disruptive forces that result from collisions. The assembly of active molecules might have promoted the formation of large pre-biotic polymers that could be the precursors of the informational polymers we observe nowadays. Full article
(This article belongs to the Special Issue Thermodynamics and Entropy for Self-Assembly and Self-Organization)
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16 pages, 1670 KiB  
Article
Spin Glasses in a Field Show a Phase Transition Varying the Distance among Real Replicas (And How to Exploit It to Find the Critical Line in a Field)
by Maddalena Dilucca, Luca Leuzzi, Giorgio Parisi, Federico Ricci-Tersenghi and Juan J. Ruiz-Lorenzo
Entropy 2020, 22(2), 250; https://doi.org/10.3390/e22020250 - 22 Feb 2020
Cited by 3 | Viewed by 4413
Abstract
We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than [...] Read more.
We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h > 0 and T c ( h ) < T < T c ( h = 0 ) , of the d = 1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field. Full article
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17 pages, 4256 KiB  
Article
A Novel Counterfeit Feature Extraction Technique for Exposing Face-Swap Images Based on Deep Learning and Error Level Analysis
by Weiguo Zhang, Chenggang Zhao and Yuxing Li
Entropy 2020, 22(2), 249; https://doi.org/10.3390/e22020249 - 21 Feb 2020
Cited by 31 | Viewed by 5518
Abstract
The quality and efficiency of generating face-swap images have been markedly strengthened by deep learning. For instance, the face-swap manipulations by DeepFake are so real that it is tricky to distinguish authenticity through automatic or manual detection. To augment the efficiency of distinguishing [...] Read more.
The quality and efficiency of generating face-swap images have been markedly strengthened by deep learning. For instance, the face-swap manipulations by DeepFake are so real that it is tricky to distinguish authenticity through automatic or manual detection. To augment the efficiency of distinguishing face-swap images generated by DeepFake from real facial ones, a novel counterfeit feature extraction technique was developed based on deep learning and error level analysis (ELA). It is related to entropy and information theory such as cross-entropy loss function in the final softmax layer. The DeepFake algorithm is only able to generate limited resolutions. Therefore, this algorithm results in two different image compression ratios between the fake face area as the foreground and the original area as the background, which would leave distinctive counterfeit traces. Through the ELA method, we can detect whether there are different image compression ratios. Convolution neural network (CNN), one of the representative technologies of deep learning, can extract the counterfeit feature and detect whether images are fake. Experiments show that the training efficiency of the CNN model can be significantly improved by the ELA method. In addition, the proposed technique can accurately extract the counterfeit feature, and therefore achieves outperformance in simplicity and efficiency compared with direct detection methods. Specifically, without loss of accuracy, the amount of computation can be significantly reduced (where the required floating-point computing power is reduced by more than 90%). Full article
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18 pages, 1585 KiB  
Article
Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells
by Benjamin Maldon, Ngamta Thamwattana and Maureen Edwards
Entropy 2020, 22(2), 248; https://doi.org/10.3390/e22020248 - 21 Feb 2020
Cited by 8 | Viewed by 3173
Abstract
Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion [...] Read more.
Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells. Under linear diffusion and recombination, this paper provides analytical solutions to the diffusion equation. Further, Lie symmetry analysis is adopted in order to explore analytical solutions to physically relevant special cases of the nonlinear diffusion equations. While analytical solutions may not be possible, we provide numerical solutions, which are in good agreement with the results given in the literature. Full article
(This article belongs to the Special Issue Applications of Nonlinear Diffusion Equations)
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26 pages, 427 KiB  
Article
The Self-Simulation Hypothesis Interpretation of Quantum Mechanics
by Klee Irwin, Marcelo Amaral and David Chester
Entropy 2020, 22(2), 247; https://doi.org/10.3390/e22020247 - 21 Feb 2020
Cited by 11 | Viewed by 92812
Abstract
We modify the simulation hypothesis to a self-simulation hypothesis, where the physical universe, as a strange loop, is a mental self-simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle [...] Read more.
We modify the simulation hypothesis to a self-simulation hypothesis, where the physical universe, as a strange loop, is a mental self-simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle of efficient language axiom. This leads to ontological interpretations about quantum mechanics. We also discuss some implications of the self-simulation hypothesis such as an informational arrow of time. Full article
(This article belongs to the Special Issue Quantum Spacetime and Entanglement Entropy)
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29 pages, 1577 KiB  
Article
Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources
by Burhan Gulbahar
Entropy 2020, 22(2), 246; https://doi.org/10.3390/e22020246 - 21 Feb 2020
Cited by 2 | Viewed by 3312
Abstract
Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource [...] Read more.
Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures. Full article
(This article belongs to the Special Issue Quantum Entanglement)
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20 pages, 3228 KiB  
Article
Input Pattern Classification Based on the Markov Property of the IMBT with Related Equations and Contingency Tables
by István Finta, Sándor Szénási and Lóránt Farkas
Entropy 2020, 22(2), 245; https://doi.org/10.3390/e22020245 - 21 Feb 2020
Viewed by 2325
Abstract
In this contribution, we provide a detailed analysis of the search operation for the Interval Merging Binary Tree (IMBT), an efficient data structure proposed earlier to handle typical anomalies in the transmission of data packets. A framework is provided to decide under which [...] Read more.
In this contribution, we provide a detailed analysis of the search operation for the Interval Merging Binary Tree (IMBT), an efficient data structure proposed earlier to handle typical anomalies in the transmission of data packets. A framework is provided to decide under which conditions IMBT outperforms other data structures typically used in the field, as a function of the statistical characteristics of the commonly occurring anomalies in the arrival of data packets. We use in the modeling Bernstein theorem, Markov property, Fibonacci sequences, bipartite multi-graphs, and contingency tables. Full article
(This article belongs to the Section Complexity)
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8 pages, 1136 KiB  
Article
Entropy of Conduction Electrons from Transport Experiments
by Nicolás Pérez, Constantin Wolf, Alexander Kunzmann, Jens Freudenberger, Maria Krautz, Bruno Weise, Kornelius Nielsch and Gabi Schierning
Entropy 2020, 22(2), 244; https://doi.org/10.3390/e22020244 - 21 Feb 2020
Cited by 5 | Viewed by 3821
Abstract
The entropy of conduction electrons was evaluated utilizing the thermodynamic definition of the Seebeck coefficient as a tool. This analysis was applied to two different kinds of scientific questions that can—if at all—be only partially addressed by other methods. These are the field-dependence [...] Read more.
The entropy of conduction electrons was evaluated utilizing the thermodynamic definition of the Seebeck coefficient as a tool. This analysis was applied to two different kinds of scientific questions that can—if at all—be only partially addressed by other methods. These are the field-dependence of meta-magnetic phase transitions and the electronic structure in strongly disordered materials, such as alloys. We showed that the electronic entropy change in meta-magnetic transitions is not constant with the applied magnetic field, as is usually assumed. Furthermore, we traced the evolution of the electronic entropy with respect to the chemical composition of an alloy series. Insights about the strength and kind of interactions appearing in the exemplary materials can be identified in the experiments. Full article
(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)
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27 pages, 12869 KiB  
Article
A Novel Five-Dimensional Three-Leaf Chaotic Attractor and Its Application in Image Encryption
by Tao Wang, Liwen Song, Minghui Wang, Shiqiang Chen and Zhiben Zhuang
Entropy 2020, 22(2), 243; https://doi.org/10.3390/e22020243 - 21 Feb 2020
Cited by 4 | Viewed by 2678
Abstract
This paper presents a novel five-dimensional three-leaf chaotic attractor and its application in image encryption. First, a new five-dimensional three-leaf chaotic system is proposed. Some basic dynamics of the chaotic system were analyzed theoretically and numerically, such as the equilibrium point, dissipative, bifurcation [...] Read more.
This paper presents a novel five-dimensional three-leaf chaotic attractor and its application in image encryption. First, a new five-dimensional three-leaf chaotic system is proposed. Some basic dynamics of the chaotic system were analyzed theoretically and numerically, such as the equilibrium point, dissipative, bifurcation diagram, plane phase diagram, and three-dimensional phase diagram. Simultaneously, an analog circuit was designed to implement the chaotic attractor. The circuit simulation experiment results were consistent with the numerical simulation experiment results. Second, a convolution kernel was used to process the five chaotic sequences, respectively, and the plaintext image matrix was divided according to the row and column proportions. Lastly, each of the divided plaintext images was scrambled with five chaotic sequences that were convolved to obtain the final encrypted image. The theoretical analysis and simulation results demonstrated that the key space of the algorithm was larger than 10150 that had strong key sensitivity. It effectively resisted the attacks of statistical analysis and gray value analysis, and had a good encryption effect on the encryption of digital images. Full article
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19 pages, 1596 KiB  
Article
Influential Nodes Identification in Complex Networks via Information Entropy
by Chungu Guo, Liangwei Yang, Xiao Chen, Duanbing Chen, Hui Gao and Jing Ma
Entropy 2020, 22(2), 242; https://doi.org/10.3390/e22020242 - 21 Feb 2020
Cited by 82 | Viewed by 6487
Abstract
Identifying a set of influential nodes is an important topic in complex networks which plays a crucial role in many applications, such as market advertising, rumor controlling, and predicting valuable scientific publications. In regard to this, researchers have developed algorithms from simple degree [...] Read more.
Identifying a set of influential nodes is an important topic in complex networks which plays a crucial role in many applications, such as market advertising, rumor controlling, and predicting valuable scientific publications. In regard to this, researchers have developed algorithms from simple degree methods to all kinds of sophisticated approaches. However, a more robust and practical algorithm is required for the task. In this paper, we propose the EnRenew algorithm aimed to identify a set of influential nodes via information entropy. Firstly, the information entropy of each node is calculated as initial spreading ability. Then, select the node with the largest information entropy and renovate its l-length reachable nodes’ spreading ability by an attenuation factor, repeat this process until specific number of influential nodes are selected. Compared with the best state-of-the-art benchmark methods, the performance of proposed algorithm improved by 21.1%, 7.0%, 30.0%, 5.0%, 2.5%, and 9.0% in final affected scale on CEnew, Email, Hamster, Router, Condmat, and Amazon network, respectively, under the Susceptible-Infected-Recovered (SIR) simulation model. The proposed algorithm measures the importance of nodes based on information entropy and selects a group of important nodes through dynamic update strategy. The impressive results on the SIR simulation model shed light on new method of node mining in complex networks for information spreading and epidemic prevention. Full article
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15 pages, 1167 KiB  
Article
Entropy-Based Measures of Hypnopompic Heart Rate Variability Contribute to the Automatic Prediction of Cardiovascular Events
by Xueya Yan, Lulu Zhang, Jinlian Li, Ding Du and Fengzhen Hou
Entropy 2020, 22(2), 241; https://doi.org/10.3390/e22020241 - 20 Feb 2020
Cited by 14 | Viewed by 2620
Abstract
Surges in sympathetic activity should be a major contributor to the frequent occurrence of cardiovascular events towards the end of nocturnal sleep. We aimed to investigate whether the analysis of hypnopompic heart rate variability (HRV) could assist in the prediction of cardiovascular disease [...] Read more.
Surges in sympathetic activity should be a major contributor to the frequent occurrence of cardiovascular events towards the end of nocturnal sleep. We aimed to investigate whether the analysis of hypnopompic heart rate variability (HRV) could assist in the prediction of cardiovascular disease (CVD). 2217 baseline CVD-free subjects were identified and divided into CVD group and non-CVD group, according to the presence of CVD during a follow-up visit. HRV measures derived from time domain analysis, frequency domain analysis and nonlinear analysis were employed to characterize cardiac functioning. Machine learning models for both long-term and short-term CVD prediction were then constructed, based on hypnopompic HRV metrics and other typical CVD risk factors. CVD was associated with significant alterations in hypnopompic HRV. An accuracy of 81.4% was achieved in short-term prediction of CVD, demonstrating a 10.7% increase compared with long-term prediction. There was a decline of more than 6% in the predictive performance of short-term CVD outcomes without HRV metrics. The complexity of hypnopompic HRV, measured by entropy-based indices, contributed considerably to the prediction and achieved greater importance in the proposed models than conventional HRV measures. Our findings suggest that Hypnopompic HRV assists the prediction of CVD outcomes, especially the occurrence of CVD event within two years. Full article
(This article belongs to the Special Issue Application of Information Theory and Entropy in Cardiology)
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12 pages, 290 KiB  
Article
Global Geometry of Bayesian Statistics
by Atsuhide Mori
Entropy 2020, 22(2), 240; https://doi.org/10.3390/e22020240 - 20 Feb 2020
Cited by 1 | Viewed by 2859
Abstract
In the previous work of the author, a non-trivial symmetry of the relative entropy in the information geometry of normal distributions was discovered. The same symmetry also appears in the symplectic/contact geometry of Hilbert modular cusps. Further, it was observed that a contact [...] Read more.
In the previous work of the author, a non-trivial symmetry of the relative entropy in the information geometry of normal distributions was discovered. The same symmetry also appears in the symplectic/contact geometry of Hilbert modular cusps. Further, it was observed that a contact Hamiltonian flow presents a certain Bayesian inference on normal distributions. In this paper, we describe Bayesian statistics and the information geometry in the language of current geometry in order to spread our interest in statistics through general geometers and topologists. Then, we foliate the space of multivariate normal distributions by symplectic leaves to generalize the above result of the author. This foliation arises from the Cholesky decomposition of the covariance matrices. Full article
(This article belongs to the Special Issue Information Geometry III)
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22 pages, 2665 KiB  
Review
Complexity Analysis of EEG, MEG, and fMRI in Mild Cognitive Impairment and Alzheimer’s Disease: A Review
by Jie Sun, Bin Wang, Yan Niu, Yuan Tan, Chanjuan Fan, Nan Zhang, Jiayue Xue, Jing Wei and Jie Xiang
Entropy 2020, 22(2), 239; https://doi.org/10.3390/e22020239 - 20 Feb 2020
Cited by 64 | Viewed by 9329
Abstract
Alzheimer’s disease (AD) is a degenerative brain disease with a high and irreversible incidence. In recent years, because brain signals have complex nonlinear dynamics, there has been growing interest in studying complex changes in the time series of brain signals in patients with [...] Read more.
Alzheimer’s disease (AD) is a degenerative brain disease with a high and irreversible incidence. In recent years, because brain signals have complex nonlinear dynamics, there has been growing interest in studying complex changes in the time series of brain signals in patients with AD. We reviewed studies of complexity analyses of single-channel time series from electroencephalogram (EEG), magnetoencephalogram (MEG), and functional magnetic resonance imaging (fMRI) in AD and determined future research directions. A systematic literature search for 2000–2019 was performed in the Web of Science and PubMed databases, resulting in 126 identified studies. Compared to healthy individuals, the signals from AD patients have less complexity and more predictable oscillations, which are found mainly in the left parietal, occipital, right frontal, and temporal regions. This complexity is considered a potential biomarker for accurately responding to the functional lesion in AD. The current review helps to reveal the patterns of dysfunction in the brains of patients with AD and to investigate whether signal complexity can be used as a biomarker to accurately respond to the functional lesion in AD. We proposed further studies in the signal complexities of AD patients, including investigating the reliability of complexity algorithms and the spatial patterns of signal complexity. In conclusion, the current review helps to better understand the complexity of abnormalities in the AD brain and provide useful information for AD diagnosis. Full article
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21 pages, 2725 KiB  
Article
Biometric Identification Method for Heart Sound Based on Multimodal Multiscale Dispersion Entropy
by Xiefeng Cheng, Pengfei Wang and Chenjun She
Entropy 2020, 22(2), 238; https://doi.org/10.3390/e22020238 - 20 Feb 2020
Cited by 25 | Viewed by 3215
Abstract
In this paper, a new method of biometric characterization of heart sounds based on multimodal multiscale dispersion entropy is proposed. Firstly, the heart sound is periodically segmented, and then each single-cycle heart sound is decomposed into a group of intrinsic mode functions (IMFs) [...] Read more.
In this paper, a new method of biometric characterization of heart sounds based on multimodal multiscale dispersion entropy is proposed. Firstly, the heart sound is periodically segmented, and then each single-cycle heart sound is decomposed into a group of intrinsic mode functions (IMFs) by improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN). These IMFs are then segmented to a series of frames, which is used to calculate the refine composite multiscale dispersion entropy (RCMDE) as the characteristic representation of heart sound. In the simulation experiments I, carried out on the open heart sounds database Michigan, Washington and Littman, the feature representation method was combined with the heart sound segmentation method based on logistic regression (LR) and hidden semi-Markov models (HSMM), and feature selection was performed through the Fisher ratio (FR). Finally, the Euclidean distance (ED) and the close principle are used for matching and identification, and the recognition accuracy rate was 96.08%. To improve the practical application value of this method, the proposed method was applied to 80 heart sounds database constructed by 40 volunteer heart sounds to discuss the effect of single-cycle heart sounds with different starting positions on performance in experiment II. The experimental results show that the single-cycle heart sound with the starting position of the start of the first heart sound (S1) has the highest recognition rate of 97.5%. In summary, the proposed method is effective for heart sound biometric recognition. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications)
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10 pages, 658 KiB  
Article
Thermodynamic and Transport Properties of Equilibrium Debye Plasmas
by Gianpiero Colonna and Annarita Laricchiuta
Entropy 2020, 22(2), 237; https://doi.org/10.3390/e22020237 - 20 Feb 2020
Cited by 4 | Viewed by 3046
Abstract
The thermodynamic and transport properties of weakly non-ideal, high-density partially ionized hydrogen plasma are investigated, accounting for quantum effects due to the change in the energy spectrum of atomic hydrogen when the electron–proton interaction is considered embedded in the surrounding particles. The complexity [...] Read more.
The thermodynamic and transport properties of weakly non-ideal, high-density partially ionized hydrogen plasma are investigated, accounting for quantum effects due to the change in the energy spectrum of atomic hydrogen when the electron–proton interaction is considered embedded in the surrounding particles. The complexity of the rigorous approach led to the development of simplified models, able to include the neighbor-effects on the isolated system while remaining consistent with the traditional thermodynamic approach. High-density conditions have been simulated assuming particle interactions described by a screened Coulomb potential. Full article
(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)
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17 pages, 730 KiB  
Article
Estimating Differential Entropy using Recursive Copula Splitting
by Gil Ariel and Yoram Louzoun
Entropy 2020, 22(2), 236; https://doi.org/10.3390/e22020236 - 19 Feb 2020
Cited by 14 | Viewed by 4211
Abstract
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals [...] Read more.
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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6 pages, 733 KiB  
Article
Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field
by Edward Bormashenko
Entropy 2020, 22(2), 235; https://doi.org/10.3390/e22020235 - 19 Feb 2020
Cited by 10 | Viewed by 3081
Abstract
The second part of this paper develops an approach suggested in Entropy 2020, 22(1), 11; which relates ordering in physical systems to symmetrizing. Entropy is frequently interpreted as a quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and [...] Read more.
The second part of this paper develops an approach suggested in Entropy 2020, 22(1), 11; which relates ordering in physical systems to symmetrizing. Entropy is frequently interpreted as a quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are vague and subjective, to a great extent. This leads to numerous misinterpretations of entropy. We propose that the disorder is viewed as an absence of symmetry and identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We explore the initially disordered system of elementary magnets exerted to the external magnetic field H . Imposing symmetry restrictions diminishes the entropy of the system and decreases its temperature. The general case of the system of elementary magnets demonstrating j-fold symmetry is studied. The T j = T j interrelation takes place, where T and T j are the temperatures of non-symmetrized and j-fold-symmetrized systems of the magnets, correspondingly. Full article
(This article belongs to the Section Statistical Physics)
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13 pages, 9366 KiB  
Article
Diffusion Barrier Performance of AlCrTaTiZr/AlCrTaTiZr-N High-Entropy Alloy Films for Cu/Si Connect System
by Chunxia Jiang, Rongbin Li, Xin Wang, Hailong Shang, Yong Zhang and Peter K. Liaw
Entropy 2020, 22(2), 234; https://doi.org/10.3390/e22020234 - 19 Feb 2020
Cited by 28 | Viewed by 3811
Abstract
In this study, high-entropy alloy films, namely, AlCrTaTiZr/AlCrTaTiZr-N, were deposited on the n-type (100) silicon substrate. Then, a copper film was deposited on the high-entropy alloy films. The diffusion barrier performance of AlCrTaTiZr/AlCrTaTiZr-N for Cu/Si connect system was investigated after thermal annealing for [...] Read more.
In this study, high-entropy alloy films, namely, AlCrTaTiZr/AlCrTaTiZr-N, were deposited on the n-type (100) silicon substrate. Then, a copper film was deposited on the high-entropy alloy films. The diffusion barrier performance of AlCrTaTiZr/AlCrTaTiZr-N for Cu/Si connect system was investigated after thermal annealing for an hour at 600 °C, 700 °C, 800 °C, and 900 °C. There were no Cu-Si intermetallic compounds generated in the Cu/AlCrTaTiZr/AlCrTaTiZr-N/Si film stacks after annealing even at 900 °C through transmission electron microscopy (TEM) and atomic probe tomography (APT) analysis. The results indicated that AlCrTaTiZr/AlCrTaTiZr-N alloy films can prevent copper diffusion at 900 °C. The reason was investigated in this work. The amorphous structure of the AlCrTaTiZr layer has lower driving force to form intermetallic compounds; the lattice mismatch between the AlCrTaTiZr and AlCrTaTiZ-rN layers increased the diffusion distance of the Cu atoms and the difficulty of the Cu atom diffusion to the Si substrate. Full article
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18 pages, 5195 KiB  
Article
Musical Collaboration in Rhythmic Improvisation
by Shinnosuke Nakayama, Vrishin R. Soman and Maurizio Porfiri
Entropy 2020, 22(2), 233; https://doi.org/10.3390/e22020233 - 19 Feb 2020
Cited by 4 | Viewed by 3818
Abstract
Despite our intimate relationship with music in every-day life, we know little about how people create music. A particularly elusive area of study entails the spontaneous collaborative musical creation in the absence of rehearsals or scripts. Toward this aim, we designed an experiment [...] Read more.
Despite our intimate relationship with music in every-day life, we know little about how people create music. A particularly elusive area of study entails the spontaneous collaborative musical creation in the absence of rehearsals or scripts. Toward this aim, we designed an experiment in which pairs of players collaboratively created music in rhythmic improvisation. Rhythmic patterns and collaborative processes were investigated through symbolic-recurrence quantification and information theory, applied to the time series of the sound created by the players. Working with real data on collaborative rhythmic improvisation, we identified features of improvised music and elucidated underlying processes of collaboration. Players preferred certain patterns over others, and their musical experience drove musical collaboration when rhythmic improvisation started. These results unfold prevailing rhythmic features in collaborative music creation while informing the complex dynamics of the underlying processes. Full article
(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)
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20 pages, 3012 KiB  
Article
Short-Time Estimation of Fractionation in Atrial Fibrillation with Coarse-Grained Correlation Dimension for Mapping the Atrial Substrate
by Aikaterini Vraka, Fernando Hornero, Vicente Bertomeu-González, Joaquín Osca, Raúl Alcaraz and José J. Rieta
Entropy 2020, 22(2), 232; https://doi.org/10.3390/e22020232 - 19 Feb 2020
Cited by 5 | Viewed by 2719
Abstract
Atrial fibrillation (AF) is currently the most common cardiac arrhythmia, with catheter ablation (CA) of the pulmonary veins (PV) being its first line therapy. Ablation of complex fractionated atrial electrograms (CFAEs) outside the PVs has demonstrated improved long-term results, but their identification requires [...] Read more.
Atrial fibrillation (AF) is currently the most common cardiac arrhythmia, with catheter ablation (CA) of the pulmonary veins (PV) being its first line therapy. Ablation of complex fractionated atrial electrograms (CFAEs) outside the PVs has demonstrated improved long-term results, but their identification requires a reliable electrogram (EGM) fractionation estimator. This study proposes a technique aimed to assist CA procedures under real-time settings. The method has been tested on three groups of recordings: Group 1 consisted of 24 highly representative EGMs, eight of each belonging to a different AF Type. Group 2 contained the entire dataset of 119 EGMs, whereas Group 3 contained 20 pseudo-real EGMs of the special Type IV AF. Coarse-grained correlation dimension (CGCD) was computed at epochs of 1 s duration, obtaining a classification accuracy of 100% in Group 1 and 84.0–85.7% in Group 2, using 10-fold cross-validation. The receiver operating characteristics (ROC) analysis for highly fractionated EGMs, showed 100% specificity and sensitivity in Group 1 and 87.5% specificity and 93.6% sensitivity in Group 2. In addition, 100% of the pseudo-real EGMs were correctly identified as Type IV AF. This method can consistently express the fractionation level of AF EGMs and provides better performance than previous works. Its ability to compute fractionation in short-time can agilely detect sudden changes of AF Types and could be used for mapping the atrial substrate, thus assisting CA procedures under real-time settings for atrial substrate modification. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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12 pages, 3853 KiB  
Article
A Multiple-Input Multiple-Output Reservoir Computing System Subject to Optoelectronic Feedbacks and Mutual Coupling
by Xiurong Bao, Qingchun Zhao and Hongxi Yin
Entropy 2020, 22(2), 231; https://doi.org/10.3390/e22020231 - 18 Feb 2020
Cited by 8 | Viewed by 3018
Abstract
In this paper, a multiple-input multiple-output reservoir computing (RC) system is proposed, which is composed of multiple nonlinear nodes (Mach–Zehnder modulators) and multiple mutual-coupling loops of optoelectronic delay lines. Each input signal is added into every mutual-coupling loop to implement the simultaneous recognition [...] Read more.
In this paper, a multiple-input multiple-output reservoir computing (RC) system is proposed, which is composed of multiple nonlinear nodes (Mach–Zehnder modulators) and multiple mutual-coupling loops of optoelectronic delay lines. Each input signal is added into every mutual-coupling loop to implement the simultaneous recognition of multiple route signals, which results in the signal processing speed improving and the number of routes increasing. As an example, the four-route input and four-route output RC is simultaneously realized by numerical simulations. The results show that this type of RC system can successfully recognize the four-route optical packet headers with 3-bit, 8-bit, 16-bit, and 32-bit, and four-route independent digital speeches. When the white noise is added to the signals such that the signal-to-noise ratio (SNR) of the optical packet headers and the digital speeches are 35 dB and 20 dB respectively, the normalized root mean square errors (NRMSEs) of the signal recognition are all close to 0.1. The word error rates (WERs) of the optical packet header recognition are 0%. The WER of the digital speech recognition is 1.6%. The eight-route input and eight-route output RC is also numerically simulated. The recognition of the eight-route 3-bit optical packet headers is implemented. The parallel processing of multiple-route signals and the high recognition accuracy are implemented by this proposed system. Full article
(This article belongs to the Special Issue Entropy-Based Algorithms for Signal Processing)
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12 pages, 3259 KiB  
Article
High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette
by Maryam Sadeghilaridjani, Saideep Muskeri, Mayur Pole and Sundeep Mukherjee
Entropy 2020, 22(2), 230; https://doi.org/10.3390/e22020230 - 18 Feb 2020
Cited by 22 | Viewed by 3712
Abstract
There is a strong demand for materials with inherently high creep resistance in the harsh environment of next-generation nuclear reactors. High entropy alloys have drawn intense attention in this regard due to their excellent elevated temperature properties and irradiation resistance. Here, the time-dependent [...] Read more.
There is a strong demand for materials with inherently high creep resistance in the harsh environment of next-generation nuclear reactors. High entropy alloys have drawn intense attention in this regard due to their excellent elevated temperature properties and irradiation resistance. Here, the time-dependent plastic deformation behavior of two refractory high entropy alloys was investigated, namely HfTaTiVZr and TaTiVWZr. These alloys are based on reduced activity metals from the 4-5-6 elemental palette that would allow easy post-service recycling after use in nuclear reactors. The creep behavior was investigated using nano-indentation over the temperature range of 298 K to 573 K under static and dynamic loads up to 5 N. Creep stress exponent for HfTaTiVZr and TaTiVWZr was found to be in the range of 20–140 and the activation volume was ~16–20b3, indicating dislocation dominated mechanism. The stress exponent increased with increasing indentation depth due to a higher density of dislocations and their entanglement at larger depth and the exponent decreased with increasing temperature due to thermally activated dislocations. Smaller creep displacement and higher activation energy for the two high entropy alloys indicate superior creep resistance compared to refractory pure metals like tungsten. Full article
(This article belongs to the Special Issue Future Directions of High Entropy Alloys)
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17 pages, 4275 KiB  
Article
Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation
by A. K. Alzahrani, S. Sivasankaran and M. Bhuvaneswari
Entropy 2020, 22(2), 229; https://doi.org/10.3390/e22020229 - 18 Feb 2020
Cited by 21 | Viewed by 2604
Abstract
The goal of the current numerical simulation is to explore the impact of aspect ratio, thermal radiation, and entropy generation on buoyant induced convection in a rectangular box filled with Casson fluid. The vertical boundaries of the box are maintained with different constant [...] Read more.
The goal of the current numerical simulation is to explore the impact of aspect ratio, thermal radiation, and entropy generation on buoyant induced convection in a rectangular box filled with Casson fluid. The vertical boundaries of the box are maintained with different constant thermal distribution. Thermal insulation is executed on horizontal boundaries. The solution is obtained by a finite volume-based iterative method. The results are explored over a range of radiation parameter, Casson fluid parameter, aspect ratio, and Grashof number. The impact of entropy generation is also examined in detail. Thermal stratification occurs for greater values of Casson liquid parameters in the presence of radiation. The kinetic energy grows on rising the values of Casson liquid and radiation parameters. The thermal energy transport declines on growing the values of radiation parameter and it enhances on rising the Casson fluid parameter. Full article
(This article belongs to the Special Issue Thermal Radiation and Entropy Analysis)
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