Open AccessArticle
Spatio-Temporal Variability of Soil Water Content under Different Crop Covers in Irrigation Districts of Northwest China
Entropy 2017, 19(8), 410; doi:10.3390/e19080410 (registering DOI) -
Abstract
The relationship between soil water content (SWC) and vegetation, topography, and climatic conditions is critical for developing effective agricultural water management practices and improving agricultural water use efficiency in arid areas. The purpose of this study was to determine how crop cover influenced
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The relationship between soil water content (SWC) and vegetation, topography, and climatic conditions is critical for developing effective agricultural water management practices and improving agricultural water use efficiency in arid areas. The purpose of this study was to determine how crop cover influenced spatial and temporal variation of soil water. During a study, SWC was measured under maize and wheat for two years in northwest China. Statistical methods and entropy analysis were applied to investigate the spatio-temporal variability of SWC and the interaction between SWC and its influencing factors. The SWC variability changed within the field plot, with the standard deviation reaching a maximum value under intermediate mean SWC in different layers under various conditions (climatic conditions, soil conditions, crop type conditions). The spatial-temporal-distribution of the SWC reflects the variability of precipitation and potential evapotranspiration (ET0) under different crop covers. The mutual entropy values between SWC and precipitation were similar in two years under wheat cover but were different under maize cover. However, the mutual entropy values at different depths were different under different crop covers. The entropy values changed with SWC following an exponential trend. The informational correlation coefficient (R0) between the SWC and the precipitation was higher than that between SWC and other factors at different soil depths. Precipitation was the dominant factor controlling the SWC variability, and the crop efficient was the second dominant factor. This study highlights the precipitation is a paramount factor for investigating the spatio-temporal variability of soil water content in Northwest China. Full article
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Open AccessArticle
Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study
Entropy 2017, 19(8), 279; doi:10.3390/e19080279 (registering DOI) -
Abstract
This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) CF(β/tβ) and Atangana–Baleanu (AB) AB(α/tα
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This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) CF(β/tβ) and Atangana–Baleanu (AB) AB(α/tα) fractional derivatives. For this purpose, second grade fluids flow with combined gradients of mass concentration and temperature distribution over a vertical flat plate is considered. The problem is first written in non-dimensional form and then based on AB and CF fractional derivatives, it is developed in fractional form, and then using the Laplace transform technique, exact solutions are established for both cases of AB and CF derivatives. They are then expressed in terms of newly defined M-function Mqp(z) and generalized Hyper-geometric function pΨq(z). The obtained exact solutions are plotted graphically for several pertinent parameters and an interesting comparison is made between AB and CF derivatives results with various similarities and differences. Full article
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Open AccessArticle
Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes
Entropy 2017, 19(8), 417; doi:10.3390/e19080417 (registering DOI) -
Abstract
We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors
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We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations. Full article
Open AccessArticle
Thermal and Exergetic Analysis of the Goswami Cycle Integrated with Mid-Grade Heat Sources
Entropy 2017, 19(8), 416; doi:10.3390/e19080416 (registering DOI) -
Abstract
This paper presents a theoretical investigation of a combined Power and Cooling Cycle that employs an Ammonia-Water mixture. The cycle combines a Rankine and an absorption refrigeration cycle. The Goswami cycle can be used in a wide range of applications including recovering waste
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This paper presents a theoretical investigation of a combined Power and Cooling Cycle that employs an Ammonia-Water mixture. The cycle combines a Rankine and an absorption refrigeration cycle. The Goswami cycle can be used in a wide range of applications including recovering waste heat as a bottoming cycle or generating power from non-conventional sources like solar radiation or geothermal energy. A thermodynamic study of power and cooling co-generation is presented for heat source temperatures between 100 to 350 °C. A comprehensive analysis of the effect of several operation and configuration parameters, including the number of turbine stages and different superheating configurations, on the power output and the thermal and exergy efficiencies was conducted. Results showed the Goswami cycle can operate at an effective exergy efficiency of 60–80% with thermal efficiencies between 25 to 31%. The investigation also showed that multiple stage turbines had a better performance than single stage turbines when heat source temperatures remain above 200 °C in terms of power, thermal and exergy efficiencies. However, the effect of turbine stages is almost the same when heat source temperatures were below 175 °C. For multiple turbine stages, the use of partial superheating with Single or Double Reheat stream showed a better performance in terms of efficiency. It also showed an increase in exergy destruction when heat source temperature was increased. Full article
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Open AccessDiscussion
Quality Systems. A Thermodynamics-Related Interpretive Model
Entropy 2017, 19(8), 418; doi:10.3390/e19080418 (registering DOI) -
Abstract
In the present paper, a Quality Systems Theory is presented. Certifiable Quality Systems are treated and interpreted in accordance with a Thermodynamics-based approach. Analysis is also conducted on the relationship between Quality Management Systems (QMSs) and systems theories. A measure of entropy is
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In the present paper, a Quality Systems Theory is presented. Certifiable Quality Systems are treated and interpreted in accordance with a Thermodynamics-based approach. Analysis is also conducted on the relationship between Quality Management Systems (QMSs) and systems theories. A measure of entropy is proposed for QMSs, including a virtual document entropy and an entropy linked to processes and organisation. QMSs are also interpreted in light of Cybernetics, and interrelations between Information Theory and quality are also highlighted. A measure for the information content of quality documents is proposed. Such parameters can be used as adequacy indices for QMSs. From the discussed approach, suggestions for organising QMSs are also derived. Further interpretive thermodynamic-based criteria for QMSs are also proposed. The work represents the first attempt to treat quality organisational systems according to a thermodynamics-related approach. At this stage, no data are available to compare statements in the paper. Full article
Open AccessArticle
The Emergence of Hyperchaos and Synchronization in Networks with Discrete Periodic Oscillators
Entropy 2017, 19(8), 413; doi:10.3390/e19080413 -
Abstract
In this paper, the emergence of hyperchaos in a network with two very simple discrete periodic oscillators is presented. Uncoupled periodic oscillators may represent, in the crudest and simplest form, periodic oscillators in nature, for example fireflies, crickets, menstrual cycles of women, among
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In this paper, the emergence of hyperchaos in a network with two very simple discrete periodic oscillators is presented. Uncoupled periodic oscillators may represent, in the crudest and simplest form, periodic oscillators in nature, for example fireflies, crickets, menstrual cycles of women, among others. Nevertheless, the emergence of hyperchaos in this kind of real-life network has not been proven. In particular, we focus this study on the emergence of hyperchaotic dynamics, considering that these can be mainly used in engineering applications such as cryptography, secure communications, biometric systems, telemedicine, among others. In order to corroborate that the emerging dynamics are hyperchaotic, some chaos and hyperchaos verification tests are conducted. In addition, the presented hyperchaotic coupled system synchronizes, based on the proposed coupling scheme. Full article
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Open AccessArticle
Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders
Entropy 2017, 19(8), 415; doi:10.3390/e19080415 -
Abstract
We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person–situation debate. We relate the person
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We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person–situation debate. We relate the person approach with the quenched disorder and the situation approach with the annealed disorder, and investigate how these two approaches influence order–disorder phase transitions observed in the q-voter model with noise. We show that under a quenched disorder, differences between models with independence and anticonformity are weaker and only quantitative. In contrast, annealing has a much more profound impact on the system and leads to qualitative differences between models on a macroscopic level. Furthermore, only under an annealed disorder may the discontinuous phase transitions appear. It seems that freezing the agents’ behavior at the beginning of simulation—introducing quenched disorder—supports second-order phase transitions, whereas allowing agents to reverse their attitude in time—incorporating annealed disorder—supports discontinuous ones. We show that anticonformity is insensitive to the type of disorder, and in all cases it gives the same result. We precede our study with a short insight from statistical physics into annealed vs. quenched disorder and a brief review of these two approaches in models of opinion dynamics. Full article
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Open AccessArticle
Effect of Slip Conditions and Entropy Generation Analysis with an Effective Prandtl Number Model on a Nanofluid Flow through a Stretching Sheet
Entropy 2017, 19(8), 414; doi:10.3390/e19080414 -
Abstract
This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum
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This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum boundary layers. For this purpose, we have considered a model for effective Prandtl number which is borrowed by means of experimental analysis on a nano boundary layer, steady, two-dimensional incompressible flow through a stretching sheet. We have considered γAl2O3-H2O andAl2O3-C2H6O2 nanoparticles for the governing flow problem. An entropy generation analysis is also presented with the help of the second law of thermodynamics. A numerical technique known as Successive Taylor Series Linearization Method (STSLM) is used to solve the obtained governing nonlinear boundary layer equations. The numerical and graphical results are discussed for two cases i.e., (i) effective Prandtl number and (ii) without effective Prandtl number. From graphical results, it is observed that the velocity profile and temperature profile increases in the absence of effective Prandtl number while both expressions become larger in the presence of Prandtl number. Further, numerical comparison has been presented with previously published results to validate the current methodology and results. Full article
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Open AccessArticle
Solutions to the Cosmic Initial Entropy Problem without Equilibrium Initial Conditions
Entropy 2017, 19(8), 411; doi:10.3390/e19080411 -
Abstract
The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem
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The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1) Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2) Dissatisfied with explaining a low gravitational entropy as the product of a ‘special’ scalar field, some theorists argue (following Boltzmann) for a “more natural” initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background. The initial conditions of inflationary models are as natural as the equilibrium background favored by many theorists. Full article
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Open AccessArticle
Relationship between Entropy, Corporate Entrepreneurship and Organizational Capabilities in Romanian Medium Sized Enterprises
Entropy 2017, 19(8), 412; doi:10.3390/e19080412 -
Abstract
This paper analyses the relations between entropy, organizational capabilities and corporate entrepreneurship. The results indicate strong links between strategy and corporate entrepreneurship, moderated by the organizational capabilities. We find that companies with strong organizational capabilities, using a systematic strategic approach, widely use corporate
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This paper analyses the relations between entropy, organizational capabilities and corporate entrepreneurship. The results indicate strong links between strategy and corporate entrepreneurship, moderated by the organizational capabilities. We find that companies with strong organizational capabilities, using a systematic strategic approach, widely use corporate entrepreneurship as an instrument to fulfil their objectives. Our study contributes to the limited amount of empirical research on entropy in an organization setting by highlighting the boundary conditions of the impact by examining the moderating effect of firms’ organizational capabilities and also to the development of Econophysics as a fast growing area of interdisciplinary sciences. Full article
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Open AccessReview
A View of Information-Estimation Relations in Gaussian Networks
Entropy 2017, 19(8), 409; doi:10.3390/e19080409 -
Abstract
Relations between estimation and information measures have received considerable attention from the information theory community. One of the most notable such relationships is the I-MMSE identity of Guo, Shamai and Verdú that connects the mutual information and the minimum mean square error (MMSE).
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Relations between estimation and information measures have received considerable attention from the information theory community. One of the most notable such relationships is the I-MMSE identity of Guo, Shamai and Verdú that connects the mutual information and the minimum mean square error (MMSE). This paper reviews several applications of the I-MMSE relationship to information theoretic problems arising in connection with multi-user channel coding. The goal of this paper is to review the different techniques used on such problems, as well as to emphasize the added-value obtained from the information-estimation point of view. Full article
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Open AccessFeature PaperArticle
Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes
Entropy 2017, 19(8), 408; doi:10.3390/e19080408 -
Abstract
Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information
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Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by prevalently redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone. Full article
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Open AccessArticle
Generalized Maxwell Relations in Thermodynamics with Metric Derivatives
Entropy 2017, 19(8), 407; doi:10.3390/e19080407 -
Abstract
In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also
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In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α-total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe. Full article
Open AccessArticle
Statistical Process Control for Unimodal Distribution Based on Maximum Entropy Distribution Approximation
Entropy 2017, 19(8), 406; doi:10.3390/e19080406 -
Abstract
In statistical process control, the control chart utilizing the idea of maximum entropy distribution density level sets has been proven to perform well for monitoring the quantity with multimodal distribution. However, it is too complicated to implement for the quantity with unimodal distribution.
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In statistical process control, the control chart utilizing the idea of maximum entropy distribution density level sets has been proven to perform well for monitoring the quantity with multimodal distribution. However, it is too complicated to implement for the quantity with unimodal distribution. This article proposes a simplified method based on maximum entropy for the control chart design when the quantity being monitored is unimodal distribution. First, we use the maximum entropy distribution to approximate the unknown distribution of the monitored quantity. Then we directly take the value of the quantity as the monitoring statistic. Finally, the Lebesgue measure is applied to estimate the acceptance regions and the one with minimum volume is chosen as the optimal in-control region of the monitored quantity. The results from two cases show that the proposed method in this article has a higher detection capability than the conventional control chart techniques when the monitored quantity is asymmetric unimodal distribution. Full article
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Open AccessArticle
Intrinsic Losses Based on Information Geometry and Their Applications
Entropy 2017, 19(8), 405; doi:10.3390/e19080405 -
Abstract
One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the
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One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence). For an exponential family endowed with the Fisher metric and α-connections, the two loss functions are uniformly described as the energy difference along an α-geodesic path, for some α{1,0,1}. Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle. Full article
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Open AccessArticle
Thermal Transport and Entropy Production Mechanisms in a Turbulent Round Jet at Supercritical Thermodynamic Conditions
Entropy 2017, 19(8), 404; doi:10.3390/e19080404 -
Abstract
In the present paper, thermal transport and entropy production mechanisms in a turbulent round jet of compressed nitrogen at supercritical thermodynamic conditions are investigated using a direct numerical simulation. First, thermal transport and its contribution to the mixture formation along with the anisotropy
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In the present paper, thermal transport and entropy production mechanisms in a turbulent round jet of compressed nitrogen at supercritical thermodynamic conditions are investigated using a direct numerical simulation. First, thermal transport and its contribution to the mixture formation along with the anisotropy of heat fluxes and temperature scales are examined. Secondly, the entropy production rates during thermofluid processes evolving in the supercritical flow are investigated in order to identify the causes of irreversibilities and to display advantageous locations of handling along with the process regimes favorable to mixing. Thereby, it turned out that (1) the jet disintegration process consists of four main stages under supercritical conditions (potential core, separation, pseudo-boiling, turbulent mixing), (2) causes of irreversibilities are primarily due to heat transport and thermodynamic effects rather than turbulence dynamics and (3) heat fluxes and temperature scales appear anisotropic even at the smallest scales, which implies that anisotropic thermal diffusivity models might be appropriate in the context of both Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) approaches while numerically modeling supercritical fluid flows. Full article
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Open AccessArticle
Optimal Belief Approximation
Entropy 2017, 19(8), 402; doi:10.3390/e19080402 -
Abstract
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how “embarrassing” it is to communicate a given approximation. We reproduce and discuss
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In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how “embarrassing” it is to communicate a given approximation. We reproduce and discuss an old proof showing that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. The loss function that is obtained in the derivation is equal to the Kullback-Leibler divergence when normalized. This loss function is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments—the approximated and non-approximated beliefs—should be used. The correct order ensures that the recipient of a communication is only deprived of the minimal amount of information. We hope that the elementary derivation settles the apparent confusion. For example when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many suggested computational schemes. Full article
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Open AccessEditorial
Complexity, Criticality and Computation
Entropy 2017, 19(8), 403; doi:10.3390/e19080403 -
Open AccessArticle
On the Modelling and Control of a Laboratory Prototype of a Hydraulic Canal Based on a TITO Fractional-Order Model
Entropy 2017, 19(8), 401; doi:10.3390/e19080401 -
Abstract
In this paper a two-input, two-output (TITO) fractional order mathematical model of a laboratory prototype of a hydraulic canal is proposed. This canal is made up of two pools that have a strong interaction between them. The inputs of the TITO model are
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In this paper a two-input, two-output (TITO) fractional order mathematical model of a laboratory prototype of a hydraulic canal is proposed. This canal is made up of two pools that have a strong interaction between them. The inputs of the TITO model are the pump flow and the opening of an intermediate gate, and the two outputs are the water levels in the two pools. Based on the experiments developed in a laboratory prototype the parameters of the mathematical models have been identified. Then, considering the TITO model, a first control loop of the pump is closed to reproduce real-world conditions in which the water level of the first pool is not dependent on the opening of the upstream gate, thus leading to an equivalent single input, single output (SISO) system. The comparison of the resulting system with the classical first order systems typically utilized to model hydraulic canals shows that the proposed model has significantly lower error: about 50%, and, therefore, higher accuracy in capturing the canal dynamics. This model has also been utilized to optimize the design of the controller of the pump of the canal, thus achieving a faster response to step commands and thus minimizing the interaction between the two pools of the experimental platform. Full article
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Open AccessArticle
Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons
Entropy 2017, 19(8), 399; doi:10.3390/e19080399 -
Abstract
Networks of stochastic spiking neurons are interesting models in the area of theoretical neuroscience, presenting both continuous and discontinuous phase transitions. Here, we study fully-connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge
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Networks of stochastic spiking neurons are interesting models in the area of theoretical neuroscience, presenting both continuous and discontinuous phase transitions. Here, we study fully-connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality (SOSC)) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and Dragon-king avalanches. We also find that neuronal gains can produce collective oscillations that coexist with neuronal avalanches. Full article
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