Search results for: Cross Entropy Method

Authors: P. Ashok, G. M. Kadhar Nawaz

Abstract:

Rough set theory is used to handle uncertainty and incomplete information by applying two accurate sets, Lower approximation and Upper approximation. In this paper, the rough clustering algorithms are improved by adopting the Similarity, Dissimilarity–Similarity and Entropy based initial centroids selection method on three different clustering algorithms namely Entropy based Rough K-Means (ERKM), Similarity based Rough K-Means (SRKM) and Dissimilarity-Similarity based Rough K-Means (DSRKM) were developed and executed by yeast dataset. The rough clustering algorithms are validated by cluster validity indexes namely Rand and Adjusted Rand indexes. An experimental result shows that the ERKM clustering algorithm perform effectively and delivers better results than other clustering methods. Outlier detection is an important task in data mining and very much different from the rest of the objects in the clusters. Entropy based Rough Outlier Factor (EROF) method is seemly to detect outlier effectively for yeast dataset. In rough K-Means method, by tuning the epsilon (ᶓ) value from 0.8 to 1.08 can detect outliers on boundary region and the RKM algorithm delivers better results, when choosing the value of epsilon (ᶓ) in the specified range. An experimental result shows that the EROF method on clustering algorithm performed very well and suitable for detecting outlier effectively for all datasets. Further, experimental readings show that the ERKM clustering method outperformed the other methods.

Keywords: Clustering, Entropy, Outlier, Rough K-Means, validity index.

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Authors: Sheema Shuja Khattak, Gule Saman, Imran Khan, Abdus Salam

Abstract:

Image segmentation plays an important role in medical imaging applications. Therefore, accurate methods are needed for the successful segmentation of medical images for diagnosis and detection of various diseases. In this paper, we have used maximum entropy to achieve image segmentation. Maximum entropy has been calculated using Shannon, Renyi and Tsallis entropies. This work has novelty based on the detection of skin lesion caused by the bite of a parasite called Sand Fly causing the disease is called Cutaneous Leishmaniasis.

Keywords: Shannon, Maximum entropy, Renyi, Tsallis entropy.

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Authors: I. O. Nascimento, J. T. Manzi

Abstract:

The drying process is an important operation in the chemical industry and it is widely used in the food, grain industry and fertilizer industry. However, for demanding a considerable consumption of energy, such a process requires a deep energetic analysis in order to reduce operating costs. This paper deals with thermodynamic optimization applied to rotary dryers based on the entropy production minimization, aiming at to reduce the energy consumption. To do this, the mass, energy and entropy balance was used for developing a relationship that represents the rate of entropy production. The use of the Second Law of Thermodynamics is essential because it takes into account constraints of nature. Since the entropy production rate is minimized, optimals conditions of operations can be established and the process can obtain a substantial gain in energy saving. The minimization strategy had been led using classical methods such as Lagrange multipliers and implemented in the MATLAB platform. As expected, the preliminary results reveal a significant energy saving by the application of the optimal parameters found by the procedure of the entropy minimization It is important to say that this method has shown easy implementation and low cost.

Keywords: Drying, entropy minimization, modeling dryers, thermodynamic optimization.

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Authors: Young-Seok Choi

Abstract:

This work assesses the cortical and the sub-cortical neural activity recorded from rodents using entropy and mutual information based approaches to study how hypothermia affects neural activity. By applying the multi-scale entropy and Shannon entropy, we quantify the degree of the regularity embedded in the cortical and sub-cortical neurons and characterize the dependency of entropy of these regions on temperature. We study also the degree of the mutual information on thalamocortical pathway depending on temperature. The latter is most likely an indicator of coupling between these highly connected structures in response to temperature manipulation leading to arousal after global cerebral ischemia.

Keywords: Spiking activity, entropy, mutual information, temperature modulation.

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Authors: Anil Kumar, C. Nagaraja Kumar

Abstract:

The position and momentum space information entropies of hydrogen atom are exactly evaluated. Using isospectral Hamiltonian approach, a family of isospectral potentials is constructed having same energy eigenvalues as that of the original potential. The information entropy content is obtained in position space as well as in momentum space. It is shown that the information entropy content in each level can be re-arranged as a function of deformation parameter.

Keywords: Information Entropy, BBM inequality, Isospectral Potential.

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Authors: Francis Chinweuba Eboh, Peter Ahlström, Tobias Richards

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Entropy, as an outcome of the second law of thermodynamics, measures the level of irreversibility associated with any process. The identification and reduction of irreversibility in the energy conversion process helps to improve the efficiency of the system. The entropy of pure substances known as absolute entropy is determined at an absolute reference point and is useful in the thermodynamic analysis of chemical reactions; however, municipal solid waste (MSW) is a structurally complicated material with unknown absolute entropy. In this work, an empirical model to calculate the absolute entropy of MSW based on the content of carbon, hydrogen, oxygen, nitrogen, sulphur, and chlorine on a dry ash free basis (daf) is presented. The proposed model was derived from 117 relevant organic substances which represent the main constituents in MSW with known standard entropies using statistical analysis. The substances were divided into different waste fractions; namely, food, wood/paper, textiles/rubber and plastics waste and the standard entropies of each waste fraction and for the complete mixture were calculated. The correlation of the standard entropy of the complete waste mixture derived was found to be s^o_msw= 0.0101C + 0.0630H + 0.0106O + 0.0108N + 0.0155S + 0.0084Cl (kJ.K^-1.kg) and the present correlation can be used for estimating the absolute entropy of MSW by using the elemental compositions of the fuel within the range of 10.3% ≤ C ≤ 95.1%, 0.0% ≤ H ≤ 14.3%, 0.0% ≤ O ≤ 71.1%, 0.0 ≤ N ≤ 66.7%, 0.0% ≤ S ≤ 42.1%, 0.0% ≤ Cl ≤ 89.7%. The model is also applicable for the efficient modelling of a combustion system in a waste-to-energy plant.

Keywords: Absolute entropy, irreversibility, municipal solid waste, waste-to-energy.

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Authors: K.C. Deshmukh, P.G. Khot, Nikhil

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In the present communication, we have proposed some new generalized measure of fuzzy entropy based upon real parameters, discussed their and desirable properties, and presented these measures graphically. An important property, that is, monotonicity of the proposed measures has also been studied.

Keywords: Fuzzy numbers, Fuzzy entropy, Characteristicfunction, Crisp set, Monotonicity.

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Authors: Sheng-An Yang, Ren-Yi Hung, Ying-Yi Ho

Abstract:

This paper aims to perform the second law analysis of thermodynamics on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on an ellipsoid with variable wall temperature. The analysis provides us understanding how the geometric parameter- ellipticity and non-isothermal wall temperature variation amplitude “A." affect entropy generation during film-wise condensation heat transfer process. To understand of which irreversibility involved in this condensation process, we derived an expression for the entropy generation number in terms of ellipticity and A. The result indicates that entropy generation increases with ellipticity. Furthermore, the irreversibility due to finite temperature difference heat transfer dominates over that due to condensate film flow friction and the local entropy generation rate decreases with increasing A in the upper half of ellipsoid. Meanwhile, the local entropy generation rate enhances with A around the rear lower half of ellipsoid.

Keywords: Free convection; Non-isothermal; Thermodynamic second law; Entropy, Ellipsoid.

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Authors: Stoyan Nedeltchev, Markus Schubert

Abstract:

The gas holdup fluctuations in a bubble column (0.15 m in ID) have been recorded by means of a conductivity wire-mesh sensor in order to extract information about the main transition velocities. These parameters are very important for bubble column design, operation and scale-up. For this purpose, the classical definition of the Shannon entropy was modified and used to identify both the onset (at U_G=0.034 m/s) of the transition flow regime and the beginning (at U_G=0.089 m/s) of the churn-turbulent flow regime. The results were compared with the Kolmogorov entropy (KE) results. A slight discrepancy was found, namely the transition velocities identified by means of the KE were shifted to somewhat higher (0.045 and 0.101 m/s) superficial gas velocities U_G.

Keywords: Bubble column, gas holdup fluctuations, Modified Shannon entropy, Kolmogorov entropy.

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Authors: Vladimir K. Mukhomorov

Abstract:

Within the framework of a method of the information theory it is offered statistics and probabilistic model for definition of cause-and-effect relations in the coupled multicomponent subsystems. The quantitative parameter which is defined through conditional and unconditional entropy functions is introduced. The method is applied to the analysis of the experimental data on dynamics of change of the chemical elements composition of plants organs (roots, reproductive organs, leafs and stems). Experiment is directed on studying of temporal processes of primary soil formation and their connection with redistribution dynamics of chemical elements in plant organs. This statistics and probabilistic model allows also quantitatively and unambiguously to specify the directions of the information streams on plant organs.

Keywords: Chemical elements, entropy function, information, plants.

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Authors: S. Aouabdi, M. Taibi

Abstract:

This paper presents powerful techniques for the development of a new monitoring method based on multi-scale entropy (MSE) in order to characterize the behaviour of the concentrations of different gases present in the synthesis of Ammonia and soft-sensor based on Principal Component Analysis (PCA).

Keywords: Ammonia synthesis, concentrations of different gases, soft sensor, multi-scale entropy, multivariate statistics.

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Authors: Guomin Luo, Daming Zhang, Yong Kwee Koh, Kim Teck Ng, Helmi Kurniawan, Weng Hoe Leong

Abstract:

Partial discharge (PD) detection is an important method to evaluate the insulation condition of metal-clad apparatus. Non-intrusive sensors which are easy to install and have no interruptions on operation are preferred in onsite PD detection. However, it often lacks of accuracy due to the interferences in PD signals. In this paper a novel PD extraction method that uses frequency analysis and entropy based time-frequency (TF) analysis is introduced. The repetitive pulses from convertor are first removed via frequency analysis. Then, the relative entropy and relative peak-frequency of each pulse (i.e. time-indexed vector TF spectrum) are calculated and all pulses with similar parameters are grouped. According to the characteristics of non-intrusive sensor and the frequency distribution of PDs, the pulses of PD and interferences are separated. Finally the PD signal and interferences are recovered via inverse TF transform. The de-noised result of noisy PD data demonstrates that the combination of frequency and time-frequency techniques can discriminate PDs from interferences with various frequency distributions.

Keywords: Entropy, Fourier analysis, non-intrusive measurement, time-frequency analysis, partial discharge

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Authors: G.R. Ashari, N.Hedayat, S. Shalbaf, E.Hajidavalloo

Abstract:

In this paper a polymer electrolyte membrane (PEM) fuel cell power system including burner, steam reformer, heat exchanger and water heater has been considered to meet the electrical, heating, cooling and domestic hot water loads of residential building which in Tehran. The system uses natural gas as fuel and works in CHP mode. Design and operating conditions of a PEM fuel cell system is considered in this study. The energy requirements of residential building and the number of fuel cell stacks to meet them have been estimated. The method involved exergy analysis and entropy generation thorough the months of the year. Results show that all the energy needs of the building can be met with 12 fuel cell stacks at a nominal capacity of 8.5 kW. Exergy analysis of the CHP system shows that the increase in the ambient air temperature from 1oC to 40oC, will have an increase of entropy generation by 5.73%.Maximum entropy generates for 15 hour in 15th of June and 15th of July is estimated to amount at 12624 (kW/K). Entropy generation of this system through a year is estimated to amount to 1004.54 GJ/k.year.

Keywords: CHP mode, entropy, exergy, no of fuel cell stacks.

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Authors: R.K.Tuli

Abstract:

The objective of the present communication is to develop new genuine exponentiated mean codeword lengths and to study deeply the problem of correspondence between well known measures of entropy and mean codeword lengths. With the help of some standard measures of entropy, we have illustrated such a correspondence. In literature, we usually come across many inequalities which are frequently used in information theory. Keeping this idea in mind, we have developed such inequalities via coding theory approach.

Keywords: Codeword, Code alphabet, Uniquely decipherablecode, Mean codeword length, Uncertainty, Noiseless channel

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Authors: Z. Saidi, A.O. Boudraa, J.C. Cexus, S. Bourennane

Abstract:

In this paper, a new time-delay estimation technique based on the cross IB-energy operator [5] is introduced. This quadratic energy detector measures how much a signal is present in another one. The location of the peak of the energy operator, corresponding to the maximum of interaction between the two signals, is the estimate of the delay. The method is a fully data-driven approach. The discrete version of the continuous-time form of the cross IBenergy operator, for its implementation, is presented. The effectiveness of the proposed method is demonstrated on real underwater acoustic signals arriving from targets and the results compared to the cross-correlation method.

Keywords: Teager-Kaiser energy operator, Cross-energyoperator, Time-Delay, Underwater acoustic signals.

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Authors: Abdel-Rahman M. Jaradat, , Mansour I. Irshid, Talha T. Nassar

Abstract:

A novel file splitting technique for the reduction of the nth-order entropy of text files is proposed. The technique is based on mapping the original text file into a non-ASCII binary file using a new codeword assignment method and then the resulting binary file is split into several subfiles each contains one or more bits from each codeword of the mapped binary file. The statistical properties of the subfiles are studied and it is found that they reflect the statistical properties of the original text file which is not the case when the ASCII code is used as a mapper. The nth-order entropy of these subfiles are determined and it is found that the sum of their entropies is less than that of the original text file for the same values of extensions. These interesting statistical properties of the resulting subfiles can be used to achieve better compression ratios when conventional compression techniques are applied to these subfiles individually and on a bit-wise basis rather than on character-wise basis.

Keywords: Bit-wise compression, entropy, file splitting, source mapping.

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Authors: Om Parkash, C.P.Gandhi

Abstract:

In the literature of fuzzy measures, there exist many well known parametric and non-parametric measures, each with its own merits and limitations. But our main emphasis is on applications of these measures to a variety of disciplines. To extend the scope of applications of these fuzzy measures to geometry, we need some special fuzzy measures. In this communication, we have introduced two new fuzzy measures involving trigonometric functions and simultaneously provided their applications to obtain the basic results already existing in the literature of geometry.

Keywords: Entropy, Uncertainty, Fuzzy Entropy, Concavity, Symmetry.

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Authors: Young-Seok Choi

Abstract:

This paper presents a multiscale information measure of Electroencephalogram (EEG) for analysis with a short data length. A multiscale extension of permutation entropy (MPE) is capable of fully reflecting the dynamical characteristics of EEG across different temporal scales. However, MPE yields an imprecise estimation due to coarse-grained procedure at large scales. We present an improved MPE measure to estimate entropy more accurately with a short time series. By computing entropies of all coarse-grained time series and averaging those at each scale, it leads to the modified MPE (MMPE) which provides an enhanced accuracy as compared to MPE. Simulation and experimental studies confirmed that MMPE has proved its capability over MPE in terms of accuracy.

Keywords: Multiscale entropy, permutation entropy, EEG, seizure.

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Authors: R.Sukesh Kumar, Abhisek Verma, Jasprit Singh

Abstract:

In this work a novel approach for color image segmentation using higher order entropy as a textural feature for determination of thresholds over a two dimensional image histogram is discussed. A similar approach is applied to achieve multi-level thresholding in both grayscale and color images. The paper discusses two methods of color image segmentation using RGB space as the standard processing space. The threshold for segmentation is decided by the maximization of conditional entropy in the two dimensional histogram of the color image separated into three grayscale images of R, G and B. The features are first developed independently for the three ( R, G, B ) spaces, and combined to get different color component segmentation. By considering local maxima instead of the maximum of conditional entropy yields multiple thresholds for the same image which forms the basis for multilevel thresholding.

Keywords: conditional entropy, multi-level thresholding, segmentation, two dimensional image histogram

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Authors: A. Shaygani, R. Saifi, M. S. Saidi, M. Sani

Abstract:

Particle size distribution, the most important characteristics of aerosols, is obtained through electrical characterization techniques. The dynamics of charged nanoparticles under the influence of electric field in Electrical Mobility Spectrometer (EMS) reveals the size distribution of these particles. The accuracy of this measurement is influenced by flow conditions, geometry, electric field and particle charging process, therefore by the transfer function (transfer matrix) of the instrument. In this work, a wire-cylinder corona charger was designed and the combined fielddiffusion charging process of injected poly-disperse aerosol particles was numerically simulated as a prerequisite for the study of a multichannel EMS. The result, a cloud of particles with no uniform charge distribution, was introduced to the EMS. The flow pattern and electric field in the EMS were simulated using Computational Fluid Dynamics (CFD) to obtain particle trajectories in the device and therefore to calculate the reported signal by each electrometer. According to the output signals (resulted from bombardment of particles and transferring their charges as currents), we proposed a modification to the size of detecting rings (which are connected to electrometers) in order to evaluate particle size distributions more accurately. Based on the capability of the system to transfer information contents about size distribution of the injected particles, we proposed a benchmark for the assessment of optimality of the design. This method applies the concept of Von Neumann entropy and borrows the definition of entropy from information theory (Shannon entropy) to measure optimality. Entropy, according to the Shannon entropy, is the ''average amount of information contained in an event, sample or character extracted from a data stream''. Evaluating the responses (signals) which were obtained via various configurations of detecting rings, the best configuration which gave the best predictions about the size distributions of injected particles, was the modified configuration. It was also the one that had the maximum amount of entropy. A reasonable consistency was also observed between the accuracy of the predictions and the entropy content of each configuration. In this method, entropy is extracted from the transfer matrix of the instrument for each configuration. Ultimately, various clouds of particles were introduced to the simulations and predicted size distributions were compared to the exact size distributions.

Keywords: Aerosol Nano-Particle, CFD, Electrical Mobility Spectrometer, Von Neumann entropy.

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Authors: Samy Sadek, Ayoub Al-Hamadi, Axel Panning, Bernd Michaelis, Usama Sayed

Abstract:

In this paper, we propose a novel approach for image segmentation via fuzzification of Rènyi Entropy of Generalized Distributions (REGD). The fuzzy REGD is used to precisely measure the structural information of image and to locate the optimal threshold desired by segmentation. The proposed approach draws upon the postulation that the optimal threshold concurs with maximum information content of the distribution. The contributions in the paper are as follow: Initially, the fuzzy REGD as a measure of the spatial structure of image is introduced. Then, we propose an efficient entropic segmentation approach using fuzzy REGD. However the proposed approach belongs to entropic segmentation approaches (i.e. these approaches are commonly applied to grayscale images), it is adapted to be viable for segmenting color images. Lastly, diverse experiments on real images that show the superior performance of the proposed method are carried out.

Keywords: Entropy of generalized distributions, entropy fuzzification, entropic image segmentation.

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Authors: Alexander B. Bichkov, Valery V. Smirnov

Abstract:

Total cross section of helium atom photo-ionization by weak short pulse is calculated using the variant of trajectory method, developed in our earlier work. The method enables simple estimation of total ionization probability (or cross section) without integration of differential one.

Keywords: Evaluation of Photo-Ionization, Helium, Trajectory Method

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Authors: Amin Aghatabar Roodbary, Mohammad Hassan Bastani

Abstract:

One of the defects of stepped frequency radar systems is their sensitivity to target motion. In such systems, target motion causes range cell shift, false peaks, Signal to Noise Ratio (SNR) reduction and range profile spreading because of power spectrum interference of each range cell in adjacent range cells which induces distortion in High Resolution Range Profile (HRRP) and disrupt target recognition process. Thus Target Motion Parameters (TMPs) effects compensation should be employed. In this paper, such a method for estimating TMPs (velocity and acceleration) and consequently eliminating or suppressing the unwanted effects on HRRP based on entropy minimization has been proposed. This method is carried out in two major steps: in the first step, a discrete search method has been utilized over the whole acceleration-velocity lattice network, in a specific interval seeking to find a less-accurate minimum point of the entropy function. Then in the second step, a 1-D search over velocity is done in locus of the minimum for several constant acceleration lines, in order to enhance the accuracy of the minimum point found in the first step. The provided simulation results demonstrate the effectiveness of the proposed method.

Keywords: ATR, HRRP, motion compensation, SFW, TMP.

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Authors: Usman Qamar, Younus Javed

Abstract:

Frequent pattern mining is the process of finding a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set. It was proposed in the context of frequent itemsets and association rule mining. Frequent pattern mining is used to find inherent regularities in data. What products were often purchased together? Its applications include basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis. However, one of the bottlenecks of frequent itemset mining is that as the data increase the amount of time and resources required to mining the data increases at an exponential rate. In this investigation a new algorithm is proposed which can be uses as a pre-processor for frequent itemset mining. FASTER (FeAture SelecTion using Entropy and Rough sets) is a hybrid pre-processor algorithm which utilizes entropy and roughsets to carry out record reduction and feature (attribute) selection respectively. FASTER for frequent itemset mining can produce a speed up of 3.1 times when compared to original algorithm while maintaining an accuracy of 71%.

Keywords: Rough-sets, Classification, Feature Selection, Entropy, Outliers, Frequent itemset mining.

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Authors: Mehmet Hacibeyoglu, Ahmet Arslan, Sirzat Kahramanli

Abstract:

This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive Bayes, C4.5 and CN2 data mining classification algorithms. As the result the classification accuracies of the six datasets are improved averagely by 1.71% to 12.31%.

Keywords: Data mining classification algorithms, entropy-baseddiscretization method

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Authors: Rajkumar Verma, Bhu Dev Sharma

Abstract:

Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon’s entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon’s and those other entropy generalizations that involve logarithmic function for a probability distribution in general. In this paper, we introduce a measure of sample space, called ‘entropic measure of a sample space’, with respect to the underlying distribution. It is shown in both discrete and continuous cases that this new measure depends on the parameters of the distribution on the sample space - same sample space having different ‘entropic measures’ depending on the distributions defined on it. It was noted that Campbell’s idea applied for R`enyi’s parametric entropy of a given order also. Knowing that parameters play a role in providing suitable choices and extended applications, paper studies parametric entropic measures of sample spaces also. Exponential entropies related to Shannon’s and those generalizations that have logarithmic functions, i.e. are additive have been studies for wider understanding and applications. We propose and study exponential entropies corresponding to non additive entropies of type (α, β), which include Havard and Charvˆat entropy as a special case.

Keywords: Sample space, Probability distributions, Shannon’s entropy, R`enyi’s entropy, Non-additive entropies .

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Authors: Mohsen Torabi, Nader Karimi, Kaili Zhang

Abstract:

This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.

Keywords: Entropy generation, exothermicity, endothermicity, forced convection, local thermal non-equilibrium, analytical modeling.

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Authors: C. Ardil

Abstract:

Aircraft have different capabilities and specifications according to the required strategic goals and objectives in operations. With various types on the market with different aircraft characteristics, it becomes difficult to select a suitable aircraft for certain operations and requirements. The entropy weighting method (EWM) is a useful, highly consistent, and reliable method for obtaining the weights of the criteria and is worth integrating with the decision uncertainty distance (DUD) method, which is more applicable and requires less computation than other methods. An illustrative example is presented to demonstrate the validity and usability of the proposed methodology. Comparing the ranking results matches the distance-based approach, which is the technique for order preference by similarity to ideal solution (TOPSIS) method, which shows the robustness of the entropy DUD hybrid method. Validity analysis shows that the proposed hybrid multiple criteria decision-making analysis (MCDMA) methodology is quantitatively stable and reliable.

Keywords: aircraft selection, decision uncertainty distance (DUD), multiple criteria decision making analysis, MCDMA, TOPSIS

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Authors: R.K.Tuli

Abstract:

In the present communication, we have studied different variations in the entropy measures in the different states of queueing processes. In case of steady state queuing process, it has been shown that as the arrival rate increases, the uncertainty increases whereas in the case of non-steady birth-death process, it is shown that the uncertainty varies differently. In this pattern, it first increases and attains its maximum value and then with the passage of time, it decreases and attains its minimum value.

Keywords: Entropy, Birth-death process, M/G/1 system, G/M/1system, Steady state, Non-steady state

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Authors: E. Movahednejad, F. Ommi

Abstract:

Droplet size distributions in the cold spray of a fuel are important in observed combustion behavior. Specification of droplet size and velocity distributions in the immediate downstream of injectors is also essential as boundary conditions for advanced computational fluid dynamics (CFD) and two-phase spray transport calculations. This paper describes the development of a new model to be incorporated into maximum entropy principle (MEP) formalism for prediction of droplet size distribution in droplet formation region. The MEP approach can predict the most likely droplet size and velocity distributions under a set of constraints expressing the available information related to the distribution. In this article, by considering the mechanisms of turbulence generation inside the nozzle and wave growth on jet surface, it is attempted to provide a logical framework coupling the flow inside the nozzle to the resulting atomization process. The purpose of this paper is to describe the formulation of this new model and to incorporate it into the maximum entropy principle (MEP) by coupling sub-models together using source terms of momentum and energy. Comparison between the model prediction and experimental data for a gas turbine swirling nozzle and an annular spray indicate good agreement between model and experiment.

Keywords: Droplet, instability, Size Distribution, Turbulence, Maximum Entropy

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