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Entropy, Volume 16, Issue 10 (October 2014) – 20 articles , Pages 5159-5600

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Article
Partial Encryption of Entropy-Coded Video Compression Using Coupled Chaotic Maps
Entropy 2014, 16(10), 5575-5600; https://doi.org/10.3390/e16105575 - 23 Oct 2014
Cited by 5 | Viewed by 2476
Abstract
Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a [...] Read more.
Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a novel scheme to efficiently secure variable length coded (VLC) multimedia bit streams, such as H.264. It is based on code word error diffusion and variable size segment shuffling. The codeword diffusion and the shuffling mechanisms are based on random operations from a secure and computationally efficient chaos-based pseudo-random number generator. The proposed scheme is ubiquitous to the end users and can be deployed at any node in the network. It provides different levels of security, with encrypted data volume fluctuating between 5.5–17%. It works on the compressed bit stream without requiring any decoding. It provides excellent encryption speeds on different platforms, including mobile devices. It is 200% faster and 150% more power efficient when compared with AES software-based full encryption schemes. Regarding security, the scheme is robust to well-known attacks in the literature, such as brute force and known/chosen plain text attacks. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Article
Contributions to the Transformation Entropy Change and Influencing Factors in Metamagnetic Ni-Co-Mn-Ga Shape Memory Alloys
Entropy 2014, 16(10), 5560-5574; https://doi.org/10.3390/e16105560 - 22 Oct 2014
Cited by 11 | Viewed by 2512
Abstract
Ni-Co-Mn-Ga ferromagnetic shape memory alloys show metamagnetic transition from ferromagnetic austenite to paramagnetic (or weak-magnetic) martensite for a limited range of Co contents. The temperatures of the structural and magnetic transitions depend strongly on composition and atomic order degree, in such a way [...] Read more.
Ni-Co-Mn-Ga ferromagnetic shape memory alloys show metamagnetic transition from ferromagnetic austenite to paramagnetic (or weak-magnetic) martensite for a limited range of Co contents. The temperatures of the structural and magnetic transitions depend strongly on composition and atomic order degree, in such a way that combined composition and thermal treatment allows obtaining martensitic transformation (MT) between any magnetic state of austenite and martensite. The entropy change ΔS measured in the magnetostructural transition comprises a magnetic contribution which depends on the type and degree of magnetic order of the related phases. Consequently, both the magnetization jump across the MT (ΔM) and ΔS are composition and atomic order dependent. Both ΔS and ΔM determine the effect of applied magnetic fields on the MT, hence knowledge and understanding of their behavior can help to approach the best conditions for magnetic field induced MT and related effects. In previous papers, we have reported findings regarding the behavior of the transformation entropy in relation to composition and atomic order in Ni50xCoxMn25+yGa25y (x = 3–8, y = 5–7) alloys. In the present paper we will review our recent results, summarizing the key findings and drawing general conclusions regarding the magnetic contribution to ΔS and the effect of different factors on the magnetic and structural properties of these metamagnetic alloys. Full article
(This article belongs to the Special Issue Entropy in Shape Memory Alloys)
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Article
Conventional Point-Velocity Records and Surface Velocity Observations for Estimating High Flow Discharge
Entropy 2014, 16(10), 5546-5559; https://doi.org/10.3390/e16105546 - 21 Oct 2014
Cited by 5 | Viewed by 2469
Abstract
Flow velocity measurements using point-velocity meters are normally obtained by sampling one, two or three velocity points per vertical profile. During high floods their use is inhibited due to the difficulty of sampling in lower portions of the flow area. Nevertheless, the application [...] Read more.
Flow velocity measurements using point-velocity meters are normally obtained by sampling one, two or three velocity points per vertical profile. During high floods their use is inhibited due to the difficulty of sampling in lower portions of the flow area. Nevertheless, the application of standard methods allows estimation of a parameter, α, which depends on the energy slope and the Manning roughness coefficient. During high floods, monitoring of velocity can be accomplished by sampling the maximum velocity, umax, only, which can be used to estimate the mean flow velocity, um, by applying the linear entropy relationship depending on the parameter, M, estimated on the basis of historical observed pairs (um, umax). In this context, this work attempts to analyze if a correlation between α and M holds, so that the monitoring for high flows can be addressed by exploiting information from standard methods. A methodology is proposed to estimate M from α, by coupling the “historical” information derived by standard methods, and “new” information from the measurement of umax surmised at later times. Results from four gauged river sites of different hydraulic and geometric characteristics have shown the robust estimation of M based on α. Full article
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Article
The Q-Exponential Decay of Subjective Probability for Future Reward: A Psychophysical Time Approach
Entropy 2014, 16(10), 5537-5545; https://doi.org/10.3390/e16105537 - 21 Oct 2014
Cited by 7 | Viewed by 2925
Abstract
This study experimentally examined why subjective probability for delayed reward decays non-exponentially (“hyperbolically”, i.e., q ˂ 1 in the q-exponential discount function) in humans. Our results indicate that nonlinear psychophysical time causes hyperbolic time-decay of subjective probability for delayed reward. Implications for [...] Read more.
This study experimentally examined why subjective probability for delayed reward decays non-exponentially (“hyperbolically”, i.e., q ˂ 1 in the q-exponential discount function) in humans. Our results indicate that nonlinear psychophysical time causes hyperbolic time-decay of subjective probability for delayed reward. Implications for econophysics and neuroeconomics are discussed. Full article
(This article belongs to the Special Issue Advances in Applied Thermodynamics)
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Article
Extreme Value Laws for Superstatistics
Entropy 2014, 16(10), 5523-5536; https://doi.org/10.3390/e16105523 - 20 Oct 2014
Cited by 5 | Viewed by 2470
Abstract
We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three [...] Read more.
We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ2-superstatistics, inverse χ2 -superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that χ2-superstatistics generally leads an extreme value statistics described by a Fréchet distribution, whereas inverse χ2 -superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution. Full article
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
Article
Directionality Theory and the Entropic Principle of Natural Selection
Entropy 2014, 16(10), 5428-5522; https://doi.org/10.3390/e16105428 - 20 Oct 2014
Cited by 11 | Viewed by 3822
Abstract
Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated [...] Read more.
Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated with population stability, and describes the number of accessible pathways of energy flow between the individuals in the population. Directionality theory is a mathematical model of the evolutionary process based on the concept evolutionary entropy as the measure of fitness. The theory predicts that the changes which occur as a population evolves from one non-equilibrium steady state to another are described by the following directionality principle–fundamental theorem of evolution: (a) an increase in evolutionary entropy when resource composition is diverse, and resource abundance constant; (b) a decrease in evolutionary entropy when resource composition is singular, and resource abundance variable. Evolutionary entropy characterizes the dynamics of energy flow between the individual elements in various classes of biological networks: (a) where the units are individuals parameterized by age, and their age-specific fecundity and mortality; where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. % This article reviews the analytical basis of the evolutionary entropic principle, and describes applications of directionality theory to the study of evolutionary dynamics in two biological systems; (i) social networks–the evolution of cooperation; (ii) metabolic networks–the evolution of body size. Statistical thermodynamics is a mathematical model of macroscopic behavior in inanimate matter based on entropy, a statistical measure which describes the number of ways the molecules that compose the a material aggregate can be arranged to attain the same total energy. This theory predicts an increase in thermodynamic entropy as the system evolves towards its equilibrium state. We will delineate the relation between directionality theory and statistical thermodynamics, and review the claim that the entropic principle for thermodynamic systems is the limit, as the resource production rate tends to zero, and population size tends to infinity, of the entropic principle for evolutionary systems. Full article
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Article
A Note on Distance-based Graph Entropies
Entropy 2014, 16(10), 5416-5427; https://doi.org/10.3390/e16105416 - 20 Oct 2014
Cited by 57 | Viewed by 3178
Abstract
A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties [...] Read more.
A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance \(k\) to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity. Full article
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
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Article
Performance Degradation Assessment of Rolling Element Bearings Based on an Index Combining SVD and Information Exergy
Entropy 2014, 16(10), 5400-5415; https://doi.org/10.3390/e16105400 - 16 Oct 2014
Cited by 8 | Viewed by 3329
Abstract
Performance degradation assessment of rolling element bearings is vital for the reliable and cost-efficient operation and maintenance of rotating machines, especially for the implementation of condition-based maintenance (CBM). For robust degradation assessment of rolling element bearings, uncertainties such as those induced from usage [...] Read more.
Performance degradation assessment of rolling element bearings is vital for the reliable and cost-efficient operation and maintenance of rotating machines, especially for the implementation of condition-based maintenance (CBM). For robust degradation assessment of rolling element bearings, uncertainties such as those induced from usage variations or sensor errors must be taken into account. This paper presents an information exergy index for bearing performance degradation assessment that combines singular value decomposition (SVD) and the information exergy method. Information exergy integrates condition monitoring information of multiple instants and multiple sensors, and thus performance degradation assessment uncertainties are reduced and robust degradation assessment results can be obtained using the proposed index. The effectiveness and robustness of the proposed information exergy index are validated through experimental case studies. Full article
(This article belongs to the Special Issue Exergy: Analysis and Applications)
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Article
On Some Properties of Tsallis Hypoentropies and Hypodivergences
Entropy 2014, 16(10), 5377-5399; https://doi.org/10.3390/e16105377 - 15 Oct 2014
Cited by 8 | Viewed by 2794
Abstract
Both the Kullback–Leibler and the Tsallis divergence have a strong limitation: if the value zero appears in probability distributions (p1, ··· , pn) and (q1, ··· , qn), it must appear in the [...] Read more.
Both the Kullback–Leibler and the Tsallis divergence have a strong limitation: if the value zero appears in probability distributions (p1, ··· , pn) and (q1, ··· , qn), it must appear in the same positions for the sake of significance. In order to avoid that limitation in the framework of Shannon statistics, Ferreri introduced in 1980 hypoentropy: “such conditions rarely occur in practice”. The aim of the present paper is to extend Ferreri’s hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties, like nonnegativity, monotonicity, the chain rule and subadditivity, are established. Full article
(This article belongs to the Section Statistical Physics)
Article
Research and Development of a Chaotic Signal Synchronization Error Dynamics-Based Ball Bearing Fault Diagnostor
Entropy 2014, 16(10), 5358-5376; https://doi.org/10.3390/e16105358 - 15 Oct 2014
Cited by 16 | Viewed by 2828
Abstract
This paper describes the fault diagnosis in the operation of industrial ball bearings. In order to cluster the very small differential signals of the four classic fault types of the ball bearing system, the chaos synchronization (CS) concept is used in this study [...] Read more.
This paper describes the fault diagnosis in the operation of industrial ball bearings. In order to cluster the very small differential signals of the four classic fault types of the ball bearing system, the chaos synchronization (CS) concept is used in this study as the chaos system is very sensitive to a system’s variation such as initial conditions or system parameters. In this study, the Chen-Lee chaotic system was used to load the normal and fault signals of the bearings into the chaos synchronization error dynamics system. The fractal theory was applied to determine the fractal dimension and lacunarity from the CS error dynamics. Extenics theory was then applied to distinguish the state of the bearing faults. This study also compared the proposed method with discrete Fourier transform and wavelet packet analysis. According to the results, it is shown that the proposed chaos synchronization method combined with extenics theory can separate the characteristics (fractal dimension vs. lacunarity) completely. Therefore, it has a better fault diagnosis rate than the two traditional signal processing methods, i.e., Fourier transform and wavelet packet analysis combined with extenics theory. Full article
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
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Article
Redundancy of Exchangeable Estimators
Entropy 2014, 16(10), 5339-5357; https://doi.org/10.3390/e16105339 - 13 Oct 2014
Viewed by 2766
Abstract
Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression [...] Read more.
Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson–Dirichlet priors (or “Chinese restaurant processes”) and the Pitman–Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Review
Quantum Computation-Based Image Representation, Processing Operations and Their Applications
Entropy 2014, 16(10), 5290-5338; https://doi.org/10.3390/e16105290 - 10 Oct 2014
Cited by 36 | Viewed by 3656
Abstract
A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and [...] Read more.
A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers. Full article
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Article
Cross-Scale Interactions and Information Transfer
Entropy 2014, 16(10), 5263-5289; https://doi.org/10.3390/e16105263 - 10 Oct 2014
Cited by 21 | Viewed by 3939
Abstract
An information-theoretic approach for detecting interactions and informationtransfer between two systems is extended to interactions between dynamical phenomenaevolving on different time scales of a complex, multiscale process. The approach isdemonstrated in the detection of an information transfer from larger to smaller time scales [...] Read more.
An information-theoretic approach for detecting interactions and informationtransfer between two systems is extended to interactions between dynamical phenomenaevolving on different time scales of a complex, multiscale process. The approach isdemonstrated in the detection of an information transfer from larger to smaller time scales ina model multifractal process and applied in a study of cross-scale interactions in atmosphericdynamics. Applying a form of the conditional mutual information and a statistical test basedon the Fourier transform and multifractal surrogate data to about a century long recordsof daily mean surface air temperature from various European locations, an informationtransfer from larger to smaller time scales has been observed as the influence of the phaseof slow oscillatory phenomena with the periods around 6–11 years on the amplitudes of thevariability characterized by the smaller temporal scales from a few months to 4–5 years.These directed cross-scale interactions have a non-negligible effect on interannual airtemperature variability in a large area of Europe. Full article
(This article belongs to the Special Issue Information in Dynamical Systems and Complex Systems)
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Article
How to Mine Information from Each Instance to Extract an Abbreviated and Credible Logical Rule
Entropy 2014, 16(10), 5242-5262; https://doi.org/10.3390/e16105242 - 09 Oct 2014
Viewed by 2646
Abstract
Decision trees are particularly promising in symbolic representation and reasoning due to their comprehensible nature, which resembles the hierarchical process of human decision making. However, their drawbacks, caused by the single-tree structure,cannot be ignored. A rigid decision path may cause the majority class [...] Read more.
Decision trees are particularly promising in symbolic representation and reasoning due to their comprehensible nature, which resembles the hierarchical process of human decision making. However, their drawbacks, caused by the single-tree structure,cannot be ignored. A rigid decision path may cause the majority class to overwhelm otherclass when dealing with imbalanced data sets, and pruning removes not only superfluousnodes, but also subtrees. The proposed learning algorithm, flexible hybrid decision forest(FHDF), mines information implicated in each instance to form logical rules on the basis of a chain rule of local mutual information, then forms different decision tree structures and decision forests later. The most credible decision path from the decision forest can be selected to make a prediction. Furthermore, functional dependencies (FDs), which are extracted from the whole data set based on association rule analysis, perform embedded attribute selection to remove nodes rather than subtrees, thus helping to achieve different levels of knowledge representation and improve model comprehension in the framework of semi-supervised learning. Naive Bayes replaces the leaf nodes at the bottom of the tree hierarchy, where the conditional independence assumption may hold. This technique reduces the potential for overfitting and overtraining and improves the prediction quality and generalization. Experimental results on UCI data sets demonstrate the efficacy of the proposed approach. Full article
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Editorial
Entropy Methods in Guided Self-Organisation
Entropy 2014, 16(10), 5232-5241; https://doi.org/10.3390/e16105232 - 09 Oct 2014
Cited by 10 | Viewed by 5818
Abstract
Self-organisation occurs in natural phenomena when a spontaneous increase in order is produced by the interactions of elements of a complex system. Thermodynamically, this increase must be offset by production of entropy which, broadly speaking, can be understood as a decrease in order. [...] Read more.
Self-organisation occurs in natural phenomena when a spontaneous increase in order is produced by the interactions of elements of a complex system. Thermodynamically, this increase must be offset by production of entropy which, broadly speaking, can be understood as a decrease in order. Ideally, self-organisation can be used to guide the system towards a desired regime or state, while "exporting" the entropy to the system's exterior. Thus, Guided Self-Organisation (GSO) attempts to harness the order-inducing potential of self-organisation for specific purposes. Not surprisingly, general methods developed to study entropy can also be applied to guided self-organisation. This special issue covers abroad diversity of GSO approaches which can be classified in three categories: information theory, intelligent agents, and collective behavior. The proposals make another step towards a unifying theory of GSO which promises to impact numerous research fields. Full article
(This article belongs to the Special Issue Entropy Methods in Guided Self-Organization)
Article
Elimination of a Second-Law-Attack, and All Cable-Resistance-Based Attacks, in the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System
Entropy 2014, 16(10), 5223-5231; https://doi.org/10.3390/e16105223 - 07 Oct 2014
Cited by 20 | Viewed by 3241
Abstract
We introduce the so far most efficient attack against the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack utilizes the lack of exact thermal equilibrium in practical applications and is based on cable resistance losses and the fact that the Second Law of [...] Read more.
We introduce the so far most efficient attack against the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack utilizes the lack of exact thermal equilibrium in practical applications and is based on cable resistance losses and the fact that the Second Law of Thermodynamics cannot provide full security when such losses are present. The new attack does not challenge the unconditional security of the KLJN scheme, but it puts more stringent demands on the security/privacy enhancing protocol than for any earlier attack. In this paper we present a simple defense protocol to fully eliminate this new attack by increasing the noise-temperature at the side of the smaller resistance value over the noise-temperature at the side with the greater resistance. It is shown that this simple protocol totally removes Eve’s information not only for the new attack but also for the old Bergou-Scheuer-Yariv attack. The presently most efficient attacks against the KLJN scheme are thereby completely nullified. Full article
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Article
A Further Indication of the Self-Ordering Capacity of Water Via the Droplet Evaporation Method
Entropy 2014, 16(10), 5211-5222; https://doi.org/10.3390/e16105211 - 07 Oct 2014
Cited by 2 | Viewed by 2748
Abstract
The droplet evaporation method (DEM) is increasingly used for assessing various characteristics of water. In our research we tried to use DEM to detect a possible self-ordering capability of (spring) water that would be similar to the already found and described autothixotropic phenomenon, [...] Read more.
The droplet evaporation method (DEM) is increasingly used for assessing various characteristics of water. In our research we tried to use DEM to detect a possible self-ordering capability of (spring) water that would be similar to the already found and described autothixotropic phenomenon, namely increasing order of non-distilled water subject to aging. The output of DEM is a droplet remnant pattern (DRP). For analysis of DRP images we used a specially developed computer program that does the frequency distribution analysis of certain parameters of the images. The results of experiments demonstrated statistically significant differences in both aging of water as well as in the glass exposed surface/volume ratio of the aged water. The most important result supporting the self-ordering character of water was found in an increasing dependence between two analyzed parameters: distance and frequency, at the peak frequency. As the result concerns mostly aging and shows increasing order it further corroborates other findings concerning increasing order by aging. Such further confirmation of self-ordering capacity of water is not important only for physical chemistry, but also for biology. Full article
(This article belongs to the Special Issue Entropy and EZ-Water)
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Article
Exact Probability Distribution versus Entropy
Entropy 2014, 16(10), 5198-5210; https://doi.org/10.3390/e16105198 - 07 Oct 2014
Viewed by 3085
Abstract
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a natural language are considered. The guessing strategy [...] Read more.
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a natural language are considered. The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, approximations are necessary in order to estimate the number of guesses. Several kinds of approximations are discussed demonstrating moderate requirements regarding both memory and central processing unit (CPU) time. When considering realistic sizes of alphabets and words (100), the number of guesses can be estimated within minutes with reasonable accuracy (a few percent) and may therefore constitute an alternative to, e.g., various entropy expressions. For many probability distributions, the density of the logarithm of probability products is close to a normal distribution. For those cases, it is possible to derive an analytical expression for the average number of guesses. The proportion of guesses needed on average compared to the total number decreases almost exponentially with the word length. The leading term in an asymptotic expansion can be used to estimate the number of guesses for large word lengths. Comparisons with analytical lower bounds and entropy expressions are also provided. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Article
Entropy Generation in Flow of Highly Concentrated Non-Newtonian Emulsions in Smooth Tubes
Entropy 2014, 16(10), 5178-5197; https://doi.org/10.3390/e16105178 - 07 Oct 2014
Cited by 3 | Viewed by 2790
Abstract
Entropy generation in adiabatic flow of highly concentrated non-Newtonian emulsions in smooth tubes of five different diameters (7.15–26.54 mm) was investigated experimentally. The emulsions were of oil-in-water type with dispersed-phase concentration (Φ) ranging from 59.61–72.21% vol. The emulsions exhibited shear-thinning behavior [...] Read more.
Entropy generation in adiabatic flow of highly concentrated non-Newtonian emulsions in smooth tubes of five different diameters (7.15–26.54 mm) was investigated experimentally. The emulsions were of oil-in-water type with dispersed-phase concentration (Φ) ranging from 59.61–72.21% vol. The emulsions exhibited shear-thinning behavior in that the viscosity decreased with the increase in shear rate. The shear-stress (τ) versus shear rate (˙γ) data of emulsions could be described well by the power-law model: τ=K˙γn. The flow behavior index n was less than 1 and it decreased sharply with the increase in Φ whereas the consistency index K increased rapidly with the increase in Φ . For a given emulsion and tube diameter, the entropy generation rate per unit tube length increased linearly with the increase in the generalized Reynolds number ( Re_n ) on a log-log scale. For emulsions with Φ ≤65.15 % vol., the entropy generation rate decreased with the increase in tube diameter. A reverse trend in diameter-dependence was observed for the emulsion with Φ of 72.21% vol. New models are developed for the prediction of entropy generation rate in flow of power-law emulsions in smooth tubes. The experimental data shows good agreement with the proposed models. Full article
(This article belongs to the Section Thermodynamics)
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Article
Progress in the Prediction of Entropy Generation in Turbulent Reacting Flows Using Large Eddy Simulation
Entropy 2014, 16(10), 5159-5177; https://doi.org/10.3390/e16105159 - 26 Sep 2014
Cited by 15 | Viewed by 4128
Abstract
An overview is presented of the recent developments in the application of large eddy simulation (LES) for prediction and analysis of local entropy generation in turbulent reacting flows. A challenging issue in such LES is subgrid-scale (SGS) modeling of filtered entropy generation terms. [...] Read more.
An overview is presented of the recent developments in the application of large eddy simulation (LES) for prediction and analysis of local entropy generation in turbulent reacting flows. A challenging issue in such LES is subgrid-scale (SGS) modeling of filtered entropy generation terms. An effective closure strategy, recently developed, is based on the filtered density function (FDF) methodology with inclusion of entropy variations. This methodology, titled entropy FDF (En-FDF), is the main focus of this article. The En-FDF has been introduced as the joint velocity-scalar-turbulent frequency-entropy FDF and the marginal scalar-entropy FDF. Both formulations contain the chemical reaction and its entropy generation effects in closed forms. The former constitutes the most comprehensive form of the En-FDF and provides closure for all of the unclosed terms in LES transport equations. The latter is the marginal En-FDF and accounts for entropy generation effects, as well as scalar-entropy statistics. The En-FDF methodologies are described, and some of their recent predictions of entropy statistics and entropy generation in turbulent shear flows are presented. Full article
(This article belongs to the Special Issue Exergy: Analysis and Applications)
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