Next Issue
Previous Issue

E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Table of Contents

Entropy, Volume 18, Issue 4 (April 2016)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
View options order results:
result details:
Displaying articles 1-53
Export citation of selected articles as:
Open AccessArticle Logical Entropy of Fuzzy Dynamical Systems
Entropy 2016, 18(4), 157; https://doi.org/10.3390/e18040157
Received: 23 February 2016 / Revised: 23 March 2016 / Accepted: 12 April 2016 / Published: 23 April 2016
Cited by 9 | PDF Full-text (249 KB) | HTML Full-text | XML Full-text
Abstract
Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and
[...] Read more.
Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and for logical mutual information of fuzzy partitions are established. Using the concept of logical entropy of fuzzy partition we define the logical entropy of fuzzy dynamical systems. Finally, it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamical systems. Full article
(This article belongs to the Section Complexity)
Open AccessArticle Analyses of the Instabilities in the Discretized Diffusion Equations via Information Theory
Entropy 2016, 18(4), 155; https://doi.org/10.3390/e18040155
Received: 26 October 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 21 April 2016
PDF Full-text (4372 KB) | HTML Full-text | XML Full-text
Abstract
In a previous investigation (Bigerelle and Iost, 2004), the authors have proposed a physical interpretation of the instability λ = Δtx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained
[...] Read more.
In a previous investigation (Bigerelle and Iost, 2004), the authors have proposed a physical interpretation of the instability λ = Δtx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained using integration techniques based on erf functions meaning that no statistical fluctuation was introduced in the mathematical background. In this paper, we showed that the diffusive system can be divided into sub-systems onto which a Brownian motion is applied. Monte Carlo simulations are carried out to reproduce the macroscopic diffusive system. It is shown that the amount of information characterized by the compression ratio of information of the system is pertinent to quantify the entropy of the system according to some concepts introduced by the authors (Bigerelle and Iost, 2007). Thanks to this mesoscopic discretization, it is proved that information on each sub-cell of the diffusion map decreases with time before the unstable equality λ = 1/2 and increases after this threshold involving an increase in negentropy, i.e., a decrease in entropy contrarily to the second principle of thermodynamics. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Figures

Figure 1

Open AccessArticle Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects
Entropy 2016, 18(4), 153; https://doi.org/10.3390/e18040153
Received: 21 January 2016 / Revised: 7 April 2016 / Accepted: 15 April 2016 / Published: 21 April 2016
Cited by 2 | PDF Full-text (2236 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the
[...] Read more.
Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the functional change of cardiovascular system which is accepted to occur at the subclinical stage of CAD. In addition, systolic time interval (STI) and diastolic time interval (DTI) also show potential. There may be coupling in these electromechanical time series due to their physiological connection. However, to the best of our knowledge no publication has systematically investigated how can the coupling be measured and how it changes in CAD patients. In this study, we enrolled 39 CAD patients and 36 healthy subjects and for each subject the electrocardiogram (ECG) and photoplethysmography (PPG) signals were recorded simultaneously for 5 min. The RRI series, STI series, and DTI series were constructed, respectively. We used linear cross correlation (CC), coherence function (CF), as well as nonlinear mutual information (MI), cross conditional entropy (XCE), cross sample entropy (XSampEn), and cross fuzzy entropy (XFuzzyEn) to analyse the bivariate RRI-DTI coupling, RRI-STI coupling, and STI-DTI coupling, respectively. Our results suggest that the linear CC and CF generally have no significant difference between the two groups for all three types of bivariate coupling. The MI only shows weak change in RRI-DTI coupling. By comparison, the three entropy-based coupling measurements show significantly decreased coupling in CAD patients except XSampEn for RRI-DTI coupling (less significant) and XCE for STI-DTI and RRI-STI coupling (not significant). Additionally, the XFuzzyEn performs best as it was still significant if we further applied the Bonferroni correction in our statistical analysis. Our study indicates that the intrinsic electromechanical coupling is most probably nonlinear and can better be measured by nonlinear entropy-based measurements especially the XFuzzyEn. Besides, CAD patients are accompanied by a loss of electromechanical coupling. Our results suggest that cardiac electromechanical coupling may potentially serve as a noninvasive diagnostic tool for CAD. Full article
Figures

Figure 1

Open AccessArticle Heat Transfer Enhancement and Entropy Generation of Nanofluids Laminar Convection in Microchannels with Flow Control Devices
Entropy 2016, 18(4), 134; https://doi.org/10.3390/e18040134
Received: 15 February 2016 / Revised: 31 March 2016 / Accepted: 7 April 2016 / Published: 21 April 2016
Cited by 13 | PDF Full-text (4193 KB) | HTML Full-text | XML Full-text
Abstract
The heat transfer enhancement and entropy generation of Al2O3-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel,
[...] Read more.
The heat transfer enhancement and entropy generation of Al2O3-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel, nanofluids concentration φ(0%–3%), and Reynolds number Re (50–300) were comparatively studied by means of performance parameters, as well as the limiting streamlines and temperature contours on the modified heated surfaces. The results reveal that the relative Fanning frictional factor f/f0 of the microchannel with rectangle and protrusion devices are much larger and smaller than others, respectively. As the nanofluids concentration increases, f/f0 increases accordingly. For the microchannel with rectangle ribs, there is a transition Re for obtaining the largest heat transfer. The relative Nusselt number Nu/Nu0 of the cases with larger nanofluids concentration are greater. The microchannels with cylinder and v-groove profiles have better heat transfer performance, especially at larger Re cases, while, the microchannel with the protrusion devices is better from an entropy generation minimization perspective. Furthermore, the variation of the relative entropy generation S′/S′0 are influenced by not only the change of Nu/Nu0 and f/f0, but also the physical parameters of working substances. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Figures

Figure 1

Open AccessArticle Energetic and Exergetic Analysis of a Heat Exchanger Integrated in a Solid Biomass-Fuelled Micro-CHP System with an Ericsson Engine
Entropy 2016, 18(4), 154; https://doi.org/10.3390/e18040154
Received: 22 October 2015 / Revised: 2 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
Cited by 1 | PDF Full-text (2929 KB) | HTML Full-text | XML Full-text
Abstract
A specific heat exchanger has been developed to transfer heat from flue gas to the working fluid (hot air) of the Ericsson engine of a solid biomass-fuelled micro combined heat and power (CHP). In this paper, the theoretical and experimental energetic analyses of
[...] Read more.
A specific heat exchanger has been developed to transfer heat from flue gas to the working fluid (hot air) of the Ericsson engine of a solid biomass-fuelled micro combined heat and power (CHP). In this paper, the theoretical and experimental energetic analyses of this heat exchanger are compared. The experimental performances are described considering energetic and exergetic parameters, in particular the effectiveness on both hot and cold sides. A new exergetic parameter called the exergetic effectiveness is introduced, which allows a comparison between the real and the ideal heat exchanger considering the Second Law of Thermodynamics. A global analysis of exergetic fluxes in the whole micro-CHP system is presented, showing the repartition of the exergy destruction among the components. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Figures

Figure 1

Open AccessArticle An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization
Entropy 2016, 18(4), 152; https://doi.org/10.3390/e18040152
Received: 20 November 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
Cited by 5 | PDF Full-text (1372 KB) | HTML Full-text | XML Full-text
Abstract
Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail,
[...] Read more.
Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail, the self-organization process by which a population of individuals coordinates into a given behavior. Real socio-economic scenarios, however, often involve the interaction between multiple co-evolving sectors, with specific options of their own, that call for generalized and more sophisticated mathematical frameworks. In this paper, we explore a general EGT approach to deal with coordination dynamics in which individuals from multiple sectors interact. Starting from a two-sector, consumer/producer scenario, we investigate the effects of including a third co-evolving sector that we call public. We explore the changes in the self-organization process of all sectors, given the feedback that this new sector imparts on the other two. Full article
(This article belongs to the Special Issue Information and Self-Organization)
Figures

Figure 1

Open AccessArticle Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network
Entropy 2016, 18(4), 151; https://doi.org/10.3390/e18040151
Received: 20 February 2016 / Revised: 8 April 2016 / Accepted: 12 April 2016 / Published: 19 April 2016
Cited by 8 | PDF Full-text (2378 KB) | HTML Full-text | XML Full-text
Abstract
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential
[...] Read more.
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM. Full article
Figures

Figure 1

Open AccessArticle On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators
Entropy 2016, 18(4), 150; https://doi.org/10.3390/e18040150
Received: 5 March 2016 / Revised: 5 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 10 | PDF Full-text (225 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are
[...] Read more.
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods. Full article
(This article belongs to the Section Complexity)
Open AccessArticle Interference Energy Spectrum of the Infinite Square Well
Entropy 2016, 18(4), 149; https://doi.org/10.3390/e18040149
Received: 26 February 2016 / Revised: 7 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
PDF Full-text (819 KB) | HTML Full-text | XML Full-text
Abstract
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros,
[...] Read more.
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction Ψ ( x , t ) with N known zeros located at points s i = ( x i , t i ) . Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle’s quantum state is examined. Full article
Figures

Figure 1

Open AccessArticle Entropy Generation and Heat Transfer Performances of Al2O3-Water Nanofluid Transitional Flow in Rectangular Channels with Dimples and Protrusions
Entropy 2016, 18(4), 148; https://doi.org/10.3390/e18040148
Received: 25 February 2016 / Revised: 8 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 5 | PDF Full-text (4032 KB) | HTML Full-text | XML Full-text
Abstract
Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al2O3-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this
[...] Read more.
Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al2O3-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this study. Four different volume fractions are considered and the boundary condition with a constant heat flux is adopted. The flow Reynolds number covers laminar flow, transitional flow and turbulent flow. The influences of the flow regime and nanofluid volume fraction are examined. Furthermore, dimples and protrusions are employed, and the impacts on heat transfer characteristic and entropy generation are acquired. It is found that the average heat transfer entropy generation rate descends and the average friction entropy generation rate rises with an increasing nanofluid volume fraction. The effect of nanofluid on average heat transfer entropy generation rate declines when Reynolds number ascends, which is inverse for average friction entropy generation rate. The average wall temperature and temperature uniformity both drop accompanied with increasing pumping power with the growth in nanofluid volume fraction. The employment of dimples and protrusions significantly decreases the average entropy generation rate and improve the heat transfer performance. The effect of dimple-case shows great difference with that of protrusion-case. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Figures

Figure 1

Open AccessArticle Numerical Simulation of Williamson Combined Natural and Forced Convective Fluid Flow between Parallel Vertical Walls with Slip Effects and Radiative Heat Transfer in a Porous Medium
Entropy 2016, 18(4), 147; https://doi.org/10.3390/e18040147
Received: 29 February 2016 / Revised: 5 April 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 7 | PDF Full-text (2831 KB) | HTML Full-text | XML Full-text | Correction
Abstract
Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are
[...] Read more.
Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are considered at both boundary conditions. Radiative highly absorbing medium is modeled by the Rosseland approximation. The non-dimensional governing Navier–Stokes and energy coupled partial differential equations formed a boundary problem are solved numerically using the fourth order Runge–Kutta algorithm by means of a shooting method. Numerical outcomes for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number were presented even as the velocity and temperature profiles illustrated graphically and analyzed. The effects of the temperature number, Grashof number, thermal radiation parameter, Reynolds number, velocity slip length, Darcy number, and temperature jump, on the flow field and temperature field and their effects on the boundaries are presented and discussed. Full article
(This article belongs to the Section Thermodynamics)
Figures

Figure 1

Open AccessArticle A Quantum Query Expansion Approach for Session Search
Entropy 2016, 18(4), 146; https://doi.org/10.3390/e18040146
Received: 30 January 2016 / Revised: 9 April 2016 / Accepted: 11 April 2016 / Published: 18 April 2016
Cited by 5 | PDF Full-text (1097 KB) | HTML Full-text | XML Full-text
Abstract
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking
[...] Read more.
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking and query expansion. In this paper, we aim to further extend this work by constructing a new superposed state of each document in the information need space, based on which we can incorporate the quantum interference idea in query expansion. We then apply the new quantum query expansion model to session search, which is a typical Web search task. Empirical evaluation on the large-scale Clueweb12 dataset has shown that the proposed model is effective in the session search tasks, demonstrating the potential of developing novel and effective IR models based on intuitions and formalisms of QT. Full article
Figures

Figure 1

Open AccessArticle Training Concept, Evolution Time, and the Maximum Entropy Production Principle
Entropy 2016, 18(4), 145; https://doi.org/10.3390/e18040145
Received: 15 December 2015 / Revised: 17 March 2016 / Accepted: 7 April 2016 / Published: 18 April 2016
Cited by 1 | PDF Full-text (1893 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity
[...] Read more.
The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity of the MEPP and to test the scope of its applicability, it is necessary to conduct experiments in which the entropy produced per unit time is measured with a high precision. Thus we study electric-field-induced self-assembly in suspensions of carbon nanotubes and realize precise measurements of the entropy production rate (EPR). As a strong voltage is applied the suspended nanotubes merge together into a conducting cloud which produces Joule heat and, correspondingly, produces entropy. We introduce two types of EPR, which have qualitatively different significance: global EPR (g-EPR) and the entropy production rate of the dissipative cloud itself (DC-EPR). The following results are obtained: (1) As the system reaches the maximum of the DC-EPR, it becomes stable because the applied voltage acts as a stabilizing thermodynamic potential; (2) We discover metastable states characterized by high, near-maximum values of the DC-EPR. Under certain conditions, such efficient entropy-producing regimes can only be achieved if the system is allowed to initially evolve under mildly non-equilibrium conditions, namely at a reduced voltage; (3) Without such a “training” period the system typically is not able to reach the allowed maximum of the DC-EPR if the bias is high; (4) We observe that the DC-EPR maximum is achieved within a time, Te, the evolution time, which scales as a power-law function of the applied voltage; (5) Finally, we present a clear example in which the g-EPR theoretical maximum can never be achieved. Yet, under a wide range of conditions, the system can self-organize and achieve a dissipative regime in which the DC-EPR equals its theoretical maximum. Full article
Figures

Figure 1

Open AccessArticle Exploration of Quantum Interference in Document Relevance Judgement Discrepancy
Entropy 2016, 18(4), 144; https://doi.org/10.3390/e18040144
Received: 30 January 2016 / Revised: 28 March 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 5 | PDF Full-text (863 KB) | HTML Full-text | XML Full-text
Abstract
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While
[...] Read more.
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While a series of quantum-inspired IR models has been proposed, limited effort has been devoted to verify the existence of the quantum-like phenomenon in real users’ information retrieval processes, from a real user study perspective. In this paper, we aim to explore and model the quantum interference in users’ relevance judgement about documents, caused by the presentation order of documents. A user study in the context of IR tasks have been carried out. The existence of the quantum interference is tested by the violation of the law of total probability and the validity of the order effect. Our main findings are: (1) there is an apparent judging discrepancy across different users and document presentation orders, and empirical data have violated the law of total probability; (2) most search trials recorded in the user study show the existence of the order effect, and the incompatible decision perspectives in the quantum question (QQ) model are valid in some trials. We further explain the judgement discrepancy in more depth, in terms of four effects (comparison, unfamiliarity, attraction and repulsion) and also analyse the dynamics of document relevance judgement in terms of the evolution of the information need subspace. Full article
Figures

Figure 1

Open AccessFeature PaperArticle Mixed Diffusive-Convective Relaxation of a Warm Beam of Energetic Particles in Cold Plasma
Entropy 2016, 18(4), 143; https://doi.org/10.3390/e18040143
Received: 9 December 2015 / Revised: 29 February 2016 / Accepted: 11 April 2016 / Published: 16 April 2016
Cited by 2 | PDF Full-text (4120 KB) | HTML Full-text | XML Full-text
Abstract
This work addresses the features of fast particle transport in the bump-on-tail problem for varying the width of the fluctuation spectrum, in the view of possible applications to studies of energetic particle transport in fusion plasmas. Our analysis is built around the idea
[...] Read more.
This work addresses the features of fast particle transport in the bump-on-tail problem for varying the width of the fluctuation spectrum, in the view of possible applications to studies of energetic particle transport in fusion plasmas. Our analysis is built around the idea that strongly-shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are convective (ballistic-like). We cast this idea in the form of a self-consistent nonlinear dynamical model, which extends the classic equations of the quasi-linear theory to “broad” beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport essentially depending on nonlinear wave-particle interactions and phase-space structures. Taking into account the modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution function and the fluctuation intensity spectrum. Full article
Figures

Figure 1

Back to Top