Search results for: homogeneous model

Authors: Asok Adak, Debabrata Mazumder, Pratip Bandyopadhyay

Abstract:

Anaerobic Digestion has become a promising technology for biological transformation of organic fraction of the municipal solid wastes (MSW). In order to represent the kinetic behavior of such biological process and thereby to design a reactor system, development of a mathematical model is essential. Addressing this issue, a simplistic mathematical model has been developed for anaerobic digestion of MSW in a continuous flow reactor unit under homogeneous steady state condition. Upon simulated hydrolysis, the kinetics of biomass growth and substrate utilization rate are assumed to follow first order reaction kinetics. Simulation of this model has been conducted by studying sensitivity of various process variables. The model was simulated using typical kinetic data of anaerobic digestion MSW and typical MSW characteristics of Kolkata. The hydraulic retention time (HRT) and solid retention time (SRT) time were mainly estimated by varying different model parameters like efficiency of reactor, influent substrate concentration and biomass concentration. Consequently, design table and charts have also been prepared for ready use in the actual plant operation.

Keywords: Anaerobic digestion, municipal solid waste (MSW), process design model, simulation study, hydraulic retention time(HRT), solid retention time (SRT).

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Authors: A. R. Nezamabadi, M. Karami Khorramabadi

Abstract:

This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Dynamic stability, Homogeneous graded beam-Piezoelectric layer, Harmonic balance method.

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Authors: Paulo Gomes, Adelaide Figueiredo

Abstract:

We consider n individuals described by p standardized variables, represented by points of the surface of the unit hypersphere S_n-1. For a previous choice of n individuals we suppose that the set of observables variables comes from a mixture of bipolar Watson distribution defined on the hypersphere. EM and Dynamic Clusters algorithms are used for identification of such mixture. We obtain estimates of parameters for each Watson component and then a partition of the set of variables into homogeneous groups of variables. Additionally we will present a factor analysis model where unobservable factors are just the maximum likelihood estimators of Watson directional parameters, exactly the first principal component of data matrix associated to each group previously identified. Such alternative model it will yield us to directly interpretable solutions (simple structure), avoiding factors rotations.

Keywords: Dynamic Clusters algorithm, EM algorithm, Factor analysis model, Hierarchical Clustering, Watson distribution.

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Authors: Andrey D. Andreev, Ilona I. Iatcheva, Dimitar N. Karastoyanov, Rumena D. Stancheva

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A study of electromagnetic flow meter is presented in the paper. Comparison has been made between the analytical and the numerical results by the use of FEM numerical analysis (Quick Field 5.6) for determining polarization voltage through the circle cross section of the polarization transducer. Exciting and geometrical parameters increasing its effectiveness has been examined. The aim is to obtain maximal output signal. The investigations include different variants of the magnetic flux density distribution around the tube: homogeneous field of magnitude Bm, linear distribution with maximal value Bm and trapezium distribution conserving the same exciting magnetic energy as the homogeneous field.

Keywords: Effectiveness, electromagnetic flow meter, finite element method, polarization voltage.

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Authors: R. Saini, R. Lal

Abstract:

The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: Bilinear thickness, generalized differential quadrature (GDQ), non-homogeneous, Rectangular.

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Authors: Stoyan Nedeltchev, Markus Schubert

Abstract:

By means of the ultrafast X-ray tomography facility, data were obtained at different superficial gas velocities U_G in a bubble column (0.1 m in ID) operated with an air-deionized water system at ambient conditions. Raw reconstructed images were treated by both the information entropy (IE) and the reconstruction entropy (RE) algorithms in order to identify the main transition velocities in a bubble column. The IE values exhibited two well-pronounced minima at U_G=0.025 m/s and U_G=0.085 m/s identifying the boundaries of the homogeneous, transition and heterogeneous regimes. The RE extracted from the central region of the column’s cross-section exhibited only one characteristic peak at U_G=0.03 m/s, which was attributed to the transition from the homogeneous to the heterogeneous flow regime. This result implies that the transition regime is non-existent in the core of the column.

Keywords: Bubble column, ultrafast X-ray tomography, information entropy, reconstruction entropy.

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Authors: Seyed Hamed Mahdaviani, Davood Soudbar, Matin Parvari

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In the present research, the titanium-catalyzed ethylene dimerization and more specifically, the concomitant byproducts and polymer formation have been studied in the presence of 2,5-dimethoxytetrahydrofuran as an electron donor compound in the combination with triethylaluminium (TEA) as activator. Then, we added ethylene chlorobromide as a new efficient promoter to the relevant catalyst system. Finally, the behavior of novel homogeneous [Titanium tetrabutoxide (Ti(OC4H9)4)/2,5-dimethoxytetrahydrofuran/ TEA/ethylene chlorobromide] was investigated in the various operating conditions for the optimum production of 1-butene. In the optimum conditions, a very high ethylene conversion (almost 90.77 %), a relative high selectivity to 1-butene (79.00 %), yield of reaction equal to 71.70 % and a significant productivity (turnover frequency equal to 1370 h-1) were achieved.

Keywords: Ethylene dimerization, 2, 5-dimethoxytetrahydrofuran, ethylene chlorobromide, polymeric compounds

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: H. Wakily, M. Mehrali, H. S. C. Metselaar

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Homogeneous composites of alumina and zirconia with a small amount of MgO (<1 wt %) were prepared by colloidal filtration. The object of using ZrO2 (15wt %) was to provide zirconia toughened alumina (ZTA). Suspensions of alumina and Zirconia with various solid loadings and various concentrations of Dolapix CE64 as surfactant were studied. The stability of these suspensions was investigated using rheological measurements. The optimum amount of using Dolapix was 0.8wt% for ZTA containing MgO suspension which gave low apparent viscosity in basic area (100 mPa s at shear rate of 50 s-1). The satisfactory mixtures were made into sample pallets using colloidal filtration. The process was completed with pressureless sintering in suitable temperature. Phase, grain size and qualitative compositional analysis were done using X-ray diffraction (XRD) and scanning electron microscopy (SEM) images. ZTA containing 0.05 wt% MgO shows the lowest grain size for alumina around 0.5 μm. Densification studies show that near full densities (>99%) were obtained for ZTA ceramic containing 0.05 wt% MgO in 1500 °C.

Keywords: Colloidal filtration, Dolapix, MgO, Zirconiatoughened alumina.

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Authors: M. Staníčková

Abstract:

The paper deals with an application of quantitative analysis – the Data Envelopment Analysis (DEA) method to performance evaluation of the European Union Member States, in the reference years 2000 and 2011. The main aim of the paper is to measure efficiency changes over the reference years and to analyze a level of productivity in individual countries based on DEA method and to classify the EU Member States to homogeneous units (clusters) according to efficiency results. The theoretical part is devoted to the fundamental basis of performance theory and the methodology of DEA. The empirical part is aimed at measuring degree of productivity and level of efficiency changes of evaluated countries by basic DEA model – CCR CRS model, and specialized DEA approach – the Malmquist Index measuring the change of technical efficiency and the movement of production possibility frontier. Here, DEA method becomes a suitable tool for setting a competitive/uncompetitive position of each country because there is not only one factor evaluated, but a set of different factors that determine the degree of economic development.

Keywords: CCR CRS model, cluster analysis, DEA method, efficiency, EU, Malmquist index, performance.

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Authors: Habtu Alemayehu, G. Radhakrishnamacharya

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An analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid in the presence of magnetic field with both homogeneous and heterogeneous chemical reactions is presented. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average effective coefficient of dispersion have been studied. The average effective dispersion coefficient tends to decrease with magnetic field parameter, homogeneous chemical reaction rate parameter and amplitude ratio but tends to increase with heterogeneous chemical reaction rate parameter.

Keywords: Dispersion, Peristalsis, Couple stress fluid, Chemicalreaction, Magnetic field.

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Authors: Habtu Alemayehu, G. Radhakrishnamacharya

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The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a micropolar fluid in the presence of magnetic field and both homogeneous and heterogeneous chemical reactions. The average effective dispersion coefficient has been found using Taylor-s limiting condition under long wavelength approximation. The effects of various relevant parameters on the average coefficient of dispersion have been studied. The average effective dispersion coefficient increases with amplitude ratio, cross viscosity coefficient and heterogeneous chemical reaction rate parameter. But it decreases with magnetic field parameter and homogeneous chemical reaction rate parameter. It can be noted that the presence of peristalsis enhances dispersion of a solute.

Keywords: Peristalsis, Dispersion, Chemical reaction, Magneticfield, Micropolar fluid

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Authors: Yinchang Du, Yangfang Li

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In this work, we used the single Langmuir probe to measure the plasma density distribution in an geometrically asymmetric capacitive coupled plasma discharge system. Because of the frame structure of powered electrode, the plasma density was not homogeneous in the discharge volume. It was higher under the frame, but lower in the centre. Finite element simulation results showed a good agreement with the experiment results. To increase the electron density in the central volume and improve the homogeneity of the plasma, we added an auxiliary electrode, powered by DC voltage, in the simulation geometry. The simulation results showed that the auxiliary electrode could alter the potential distribution and improve the density homogeneity effectively.

Keywords: Capacitive coupled discharge, asymmetric discharge, homogeneous plasma.

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Authors: Daniel J. O. Ferreira, Juan H. Sosa-Arnao, Bruno C. Moreira, Leonardo P. Rangel, Song W. Park

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The comprehensive CFD models have been used to represent and study the heterogeneous combustion of biomass. In the present work, the operation of a global flue gas circuit in the sugarcane bagasse combustion, from wind boxes below primary air grate supply, passing by bagasse insertion in swirl burners and boiler furnace, to boiler bank outlet is simulated. It uses five different meshes representing each part of this system located in sequence: wind boxes and grate, boiler furnace, swirl burners, superheaters and boiler bank. The model considers turbulence using standard k-ε, combustion using EDM, radiation heat transfer using DTM with 16 ray directions and bagasse particle tracking represented by Schiller- Naumann model. The results showed good agreement with expected behavior found in literature and equipment design. The more detailed results view in separated parts of flue gas system allows observing some flow behaviors that cannot be represented by usual simplifications like bagasse supply under homogeneous axial and rotational vectors and others that can be represented using new considerations like the representation of 26 thousand grate orifices by 144 rectangular inlets.

Keywords: Comprehensive CFD model, sugar-cane bagasse combustion, sugar-cane bagasse grate boiler.

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Authors: Habtu Alemayehu, G. Radhakrishnamacharya

Abstract:

The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid through a porous medium with slip condition in the presence of both homogeneous and heterogeneous chemical reactions. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average coefficient of dispersion have been studied. The average effective dispersion coefficient tends to increase with permeability parameter but tends to decrease with homogeneous chemical reaction rate parameter, couple stress parameter, slip parameter and heterogeneous reaction rate parameter.

Keywords: Dispersion, Peristalsis, Couple stress fluid, Porousmedium, Chemical reaction, Slip condition.

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Authors: Eleftheria Tzamali, Panayiota Poirazi, Ioannis G. Tollis, Martin Reczko

Abstract:

Stable bacterial polymorphism on a single limiting resource may appear if between the evolved strains metabolic interactions take place that allow the exchange of essential nutrients [8]. Towards an attempt to predict the possible outcome of longrunning evolution experiments, a network based on the metabolic capabilities of homogeneous populations of every single gene knockout strain (nodes) of the bacterium E. coli is reconstructed. Potential metabolic interactions (edges) are allowed only between strains of different metabolic capabilities. Bacterial communities are determined by finding cliques in this network. Growth of the emerged hypothetical bacterial communities is simulated by extending the metabolic flux balance analysis model of Varma et al [2] to embody heterogeneous cell population growth in a mutual environment. Results from aerobic growth on 10 different carbon sources are presented. The upper bounds of the diversity that can emerge from single-cloned populations of E. coli such as the number of strains that appears to metabolically differ from most strains (highly connected nodes), the maximum clique size as well as the number of all the possible communities are determined. Certain single gene deletions are identified to consistently participate in our hypothetical bacterial communities under most environmental conditions implying a pattern of growth-condition- invariant strains with similar metabolic effects. Moreover, evaluation of all the hypothetical bacterial communities under growth on pyruvate reveals heterogeneous populations that can exhibit superior growth performance when compared to the performance of the homogeneous wild-type population.

Keywords: Bacterial polymorphism, clique identification, dynamic FBA, evolution, metabolic interactions.

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Authors: Ashish Thakur, Radhey Shyam Anand

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This paper presents the region based segmentation method for ultrasound images using local statistics. In this segmentation approach the homogeneous regions depends on the image granularity features, where the interested structures with dimensions comparable to the speckle size are to be extracted. This method uses a look up table comprising of the local statistics of every pixel, which are consisting of the homogeneity and similarity bounds according to the kernel size. The shape and size of the growing regions depend on this look up table entries. The algorithms are implemented by using connected seeded region growing procedure where each pixel is taken as seed point. The region merging after the region growing also suppresses the high frequency artifacts. The updated merged regions produce the output in formed of segmented image. This algorithm produces the results that are less sensitive to the pixel location and it also allows a segmentation of the accurate homogeneous regions.

Keywords: Local statistics, region growing, segmentation, ultrasound images.

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Authors: Jonghyun Park, Soonyoung Park, Sanggyun Kim, Wanhyun Cho, Sunworl Kim

Abstract:

In general, image-based 3D scenes can now be found in many popular vision systems, computer games and virtual reality tours. So, It is important to segment ROI (region of interest) from input scenes as a preprocessing step for geometric stricture detection in 3D scene. In this paper, we propose a method for segmenting ROI based on tensor voting and Dirichlet process mixture model. In particular, to estimate geometric structure information for 3D scene from a single outdoor image, we apply the tensor voting and Dirichlet process mixture model to a image segmentation. The tensor voting is used based on the fact that homogeneous region in an image are usually close together on a smooth region and therefore the tokens corresponding to centers of these regions have high saliency values. The proposed approach is a novel nonparametric Bayesian segmentation method using Gaussian Dirichlet process mixture model to automatically segment various natural scenes. Finally, our method can label regions of the input image into coarse categories: “ground", “sky", and “vertical" for 3D application. The experimental results show that our method successfully segments coarse regions in many complex natural scene images for 3D.

Keywords: Region segmentation, tensor voting, image-based 3D, geometric structure, Gaussian Dirichlet process mixture model

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Authors: Suthat Turapan, Cattareya Yotkamchornkun, Kamchai Nuithitikul

Abstract:

The production of biodiesel from crude palm oil with a homogeneous base catalyst is unlikely owing to considerable formation of soap. Free fatty acids (FFA) in crude palm oil need to be reduced, e.g. by esterification. This study investigated the activity of sulfated zirconia calcined at various temperatures for esterification of FFA in crude palm oil to biodiesel. It was found that under a proper reaction condition, sulfated zirconia well catalyzes esterification. FFA content can be reduced to an acceptable value for typical biodiesel production with a homogeneous base catalyst. Crystallinity and sulfate attachment of sulfated zirconia depend on calcination temperature during the catalyst preparation. Too low temperature of calcination gives amorphous sulfated zirconia which has low activity for esterification of FFA. In contrast, very high temperature of calcination removes sulfate group, consequently, conversion of FFA is reduced. The appropriate temperature range of calcination is 550-650 oC.

Keywords: Biodiesel, Esterification, Free fatty acids, Sulfatedzirconia.

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Authors: Neil Bar, Andrew Heweston

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Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

Keywords: Probability of failure, point estimate method, Monte-Carlo simulations, sensitivity analysis, slope stability.

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Authors: Cheng-Che Tsai, Huang-Ming Chuang

Abstract:

The purpose of this paper is to explore the role of cognitive decision effort in recommendation system, combined with indicators "information quality" and "service quality" from IS success model to exam the awareness of the user for the "recommended system performance". A total of 411 internet user answered a questionnaire assessing their attention of use and satisfaction of recommendation system in internet book store. Quantitative result indicates following research results. First, information quality of recommended system has obvious influence in consumer shopping decision-making process, and the attitude to use the system. Second, in the process of consumer's shopping decision-making, the recommendation system has no significant influence for consumers to pay lower cognitive decision-making effort. Third, e-commerce platform provides recommendations and information is necessary, but the quality of information on user needs must be considered, or they will be other competitors offer homogeneous services replaced.

Keywords: Recommender system, Cognitive decision-making efforts, IS success model, Internet bookstore.

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Authors: Junjie Chen, Deguang Xu

Abstract:

The high energy density of hydrocarbon fuels creates a great opportunity to develop catalytic combustion based micro-power generation systems to meet increasing demands for micro-scale devices. In this work, the recent technological development progress in fundamental understanding of the catalytic combustion at micro-scales are reviewed. The underlying fundamental mechanisms, flame stability, hetero-homogeneous interaction, catalytic ignition, and catalytic reforming are reviewed in catalytic micro-scale combustion systems. Catalytic combustion and its design, diagnosis, and modeling operation are highlighted for micro-combustion application purpose; these fundamental aspects are reviewed. Finally, an overview of future studies is made. The primary objective of this review is to present an overview of the development of micro-power generators by focusing more on the advances and challenges in the fundamental understanding of the catalytic combustion at micro-scales.

Keywords: Micro-combustion, catalytic combustion, flame stability, hetero-homogeneous interaction, catalytic ignition, catalytic reforming.

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Authors: Fatima Zohra Mahi, Luca Varani

Abstract:

We present an analytical model for the calculation of the sensitivity, the spectral current noise and the detective parameter for an optically illuminated In0.53Ga0.47As n+nn+ diode. The photocurrent due to the excess carrier is obtained by solving the continuity equation. Moreover, the current noise level is evaluated at room temperature and under a constant voltage applied between the diode terminals. The analytical calculation of the current noise in the n+nn+ structure is developed by considering the free carries fluctuations. The responsivity and the detection parameter are discussed as functions of the doping concentrations and the emitter layer thickness in one-dimensional homogeneous n+nn+ structure.

Keywords: Responsivity, detection parameter, photo-detectors, continuity equation, current noise.

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Authors: Junaid Rashid, Waqar Mehmood, Muhammad Wasif Nisar

Abstract:

This survey paper shows the recent state of model comparison as it’s applies to Model Driven engineering. In Model Driven Engineering to calculate the difference between the models is a very important and challenging task. There are number of tasks involved in model differencing that firstly starts with identifying and matching the elements of the model. In this paper, we discuss how model matching is accomplished, the strategies, techniques and the types of the model. We also discuss the future direction. We found out that many of the latest model comparison strategies are geared near enabling Meta model and similarity based matching. Therefore model versioning is the most dominant application of the model comparison. Recently to work on comparison for versioning has begun to deteriorate, giving way to different applications. Ultimately there is wide change among the tools in the measure of client exertion needed to perform model comparisons, as some require more push to encourage more sweeping statement and expressive force.

Keywords: Model comparison, model clone detection, model versioning, EMF Model, model diff.

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Authors: M. Venkatesan, N. Shenbaga Vinayaga Moorthi, R. Karthikeyan, A. Manivannan

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Homogeneous Charge Compression (HCCI) Ignition technology has been around for a long time, but has recently received renewed attention and enthusiasm. This paper deals with experimental investigations of HCCI engine using hydrous methanol as a primary fuel and Dimethyl Ether (DME) as an ignition improver. A regular diesel engine has been modified to work as HCCI engine for this investigation. The hydrous methanol is inducted and DME is injected into a single cylinder engine. Hence, hydrous methanol is used with 15% water content in HCCI engine and its performance and emission behavior is documented. The auto-ignition of Methanol is enabled by DME. The quantity of DME varies with respect to the load. In this study, the experiments are conducted independently and the effect of the hydrous methanol on the engine operating limit, heat release rate and exhaust emissions at different load conditions are investigated. The investigation also proves that the Hydrous Methanol with DME operation reduces the oxides of Nitrogen and smoke to an extreme low level which is not possible by the direct injection CI engine. Therefore, it is beneficial to use hydrous methanol-DME HCCI mode while using hydrous methanol in internal Combustion Engines.

Keywords: Hydrous Methanol, Dimethyl ether, Performance, Emission and Combustion.

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Authors: Faghihnia Torshizi Mostafa, Saitoh Masato

Abstract:

An efficient method is developed for the response of a group of vertical, cylindrical fixed-head, finite length piles embedded in a homogeneous elastic stratum, subjected to harmonic force atop the pile group cap. Pile to pile interaction is represented through simplified beam-on-dynamic-Winkler-foundation (BDWF) with realistic frequency-dependent springs and dashpots. Pile group effect is considered through interaction factors. New closed-form expressions for interaction factors and curvature ratios atop the pile are extended by considering different boundary conditions at the tip of the piles (fixed, hinged). In order to investigate the fundamental characteristics of inertial bending strains in pile groups, inertial bending strains at the head of each pile are expressed in terms of slenderness ratio. The results of parametric study give valuable insight in understanding the behavior of fixed head pile groups in fundamental natural frequency of soil stratum.

Keywords: Winkler-foundation, fundamental frequency of soil stratum, normalized inertial bending strain, harmonic excitation.

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Authors: Amir Hadi Ziaie

Abstract:

In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.

Keywords: Gravitational collapse, non-commutative geometry, spacetime singularity, black hole physics.

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Authors: Paola Lecca, Lorenzo Dematte, Corrado Priami

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The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work a mathematical treatment of diffusion that can be incorporated in a stochastic algorithm simulating the dynamics of a reaction-diffusion system is presented. The movement of a molecule A from a region i to a region j of the space is represented as a first order reaction Ai k- ! Aj , where the rate constant k depends on the diffusion coefficient. The diffusion coefficients are modeled as function of the local concentration of the solutes, their intrinsic viscosities, their frictional coefficients and the temperature of the system. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the intrinsic reaction kinetics and diffusion dynamics. To demonstrate the method the simulation results of the reaction-diffusion system of chaperoneassisted protein folding in cytoplasm are shown.

Keywords: Reaction-diffusion systems, diffusion coefficient, stochastic simulation algorithm.

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Authors: Chih-Ling Huang, Wen-Yi Lin, Kuo-Mo Hsiao

Abstract:

A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.

Keywords: Flapping vibration, Inclination angle, Natural frequency, Rotating beam.

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieh

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: Polynomial constitutive equation, solitary.

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