Search results for: Linear model

Authors: Ali Ameur Haj Salah, Tarek Garna, Hassani Messaoud

Abstract:

This paper attempts to define the validity domain of LSDP (Loop Shaping Design Procedure) controller system, by determining the suitable uncertainty region, so that linear system be stable. Indeed the LSDP controller cannot provide stability for any perturbed system. For this, we will use the gap metric tool that is introduced into the control literature for studying robustness properties of feedback systems with uncertainty. A 2nd order electric linear system example is given to define the validity domain of LSDP controller and effectiveness gap metric.

Keywords: LSDP, Gap metric, Robust Control.

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Authors: Muhibul Haque Bhuyan, Farseem Mannan Mohammedy, Quazi Deen Mohd Khosru

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This paper presents the doping profile measurement and characterization technique for the pocket implanted nano scale n-MOSFET. Scanning capacitance microscopy and atomic force microscopy have been used to image the extent of lateral dopant diffusion in MOS structures. The data are capacitance vs. voltage measurements made on a nano scale device. The technique is nondestructive when imaging uncleaved samples. Experimental data from the published literature are presented here on actual, cleaved device structures which clearly indicate the two-dimensional dopant profile in terms of a spatially varying modulated capacitance signal. Firstorder deconvolution indicates the technique has much promise for the quantitative characterization of lateral dopant profiles. The pocket profile is modeled assuming the linear pocket profiles at the source and drain edges. From the model, the effective doping concentration is found to use in modeling and simulation results of the various parameters of the pocket implanted nano scale n-MOSFET. The potential of the technique to characterize important device related phenomena on a local scale is also discussed.

Keywords: Linear Pocket Profile, Pocket Implanted n-MOSFET, Scanning Capacitance Microscope, Atomic Force Microscope.

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Authors: Jaswinder Kaur, Satwinder Singh, Karanjeet Singh Kahlon

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Accurate software cost estimates are critical to both developers and customers. They can be used for generating request for proposals, contract negotiations, scheduling, monitoring and control. The exact relationship between the attributes of the effort estimation is difficult to establish. A neural network is good at discovering relationships and pattern in the data. So, in this paper a comparative analysis among existing Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model and Neural Network Based Model is performed. Neural Network has outperformed the other considered models. Hence, we proposed Neural Network system as a soft computing approach to model the effort estimation of the software systems.

Keywords: Effort Estimation, Neural Network, Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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This paper presents a model predictive control (MPC) of a utility interactive three phase inverter (TPI) for a photovoltaic (PV) system at commercial level. The proposed model uses phase locked loop (PLL) to synchronize the TPI with the power electric grid (PEG) and performs MPC control in a dq reference frame. TPI model consists of a boost converter (BC), maximum power point tracking (MPPT) control, and a three-leg voltage source inverter (VSI). The operational model of VSI is used to synthesize the sinusoidal current and track the reference. The model is validated using a 35.7 kW PV system in Matlab/Simulink. Implementation results show simplicity and accuracy, as well as reliability of the model.

Keywords: Model predictive control, three phase voltage source inverter, PV system, Matlab/Simulink.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Ondruska Marek, Matustik Ondrej

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The main goal of the article is to present new model of application architecture of banking IT solution providing the Internet Banking services that is particularly outsourced. At first, we propose business rationale and a SWOT analysis to explain the reasons for the model in the article. The most important factor for our model is nowadays- big boom around smart phones and tablet devices. As next, we focus on IT architecture viewpoint where we design application, integration and security model. Finally, we propose a generic governance model that serves as a basis for the specialized governance model. The specialized instance of governance model is designed to ensure that the development and the maintenance of different parts of the IT solution are well governed in time.

Keywords: governance model, front-end application, Internet Banking, smart phones

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

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Sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: Sampled-data control, Sector bound, Solid oxide fuel cell, Time-delay.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

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This paper proposes an efficient method for the design of two channel quadrature mirror filter (QMF) bank. To achieve minimum value of reconstruction error near to perfect reconstruction, a linear optimization process has been proposed. Prototype low pass filter has been designed using Kaiser window function. The modified algorithm has been developed to optimize the reconstruction error using linear objective function through iteration method. The result obtained, show that the performance of the proposed algorithm is better than that of the already exists methods.

Keywords: Filterbank, near perfect reconstruction, Kaiserwindow, QMF.

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Authors: Byung-Joo Oh

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This paper describes a method to improve the robustness of a face recognition system based on the combination of two compensating classifiers. The face images are preprocessed by the appearance-based statistical approaches such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). LDA features of the face image are taken as the input of the Radial Basis Function Network (RBFN). The proposed approach has been tested on the ORL database. The experimental results show that the LDA+RBFN algorithm has achieved a recognition rate of 93.5%

Keywords: Face recognition, linear discriminant analysis, radial basis function network.

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Authors: K. Sandjak, B. Tiliouine

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Structural analysis of flexible pavements has been and still is currently performed using multi-layer elastic theory. However, for thinly surfaced pavements subjected to low to medium volumes of traffics, the importance of non-linear stress-strain behavior of unbound granular materials (UGM) requires the use of more sophisticated numerical models for structural design and performance of such pavements. In the present work, nonlinear unbound aggregates constitutive model is implemented within an axisymmetric finite element code developed to simulate the nonlinear behavior of pavement structures including two local aggregates of different mineralogical nature, typically used in Algerian pavements. The performance of the mechanical model is examined about its capability of representing adequately, under various conditions, the granular material non-linearity in pavement analysis. In addition, deflection data collected by Falling Weight Deflectometer (FWD) are incorporated into the analysis in order to assess the sensitivity of critical pavement design criteria and pavement design life to the constitutive model. Finally, conclusions of engineering significance are formulated. 

Keywords: Nonlinear resilient behavior, unbound granular materials, RLT test results, FWD backcalculations, finite element simulations, pavement response and performance.

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Authors: Le Kang

Abstract:

According to the nature of the university, as a free and responsible academic community, USR is based on a different foundation —academic responsibility, so the Pyramid and the IC Model of CSR could not fully explain the most distinguished feature of USR. This paper sought to put forward a new model— Ferris Wheel Model, to illustrate the nature of USR and the process of achievement. The Ferris Wheel Model of USR shows the university creates a balanced, fairness and neutrality systemic structure to afford social responsibilities; that makes the organization could obtain a synergistic effect to achieve more extensive interests of stakeholders and wider social responsibilities.

Keywords: USR, Achievement model, Ferris wheel model.

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Authors: A. Johannet, B. Vayssade, D. Bertin

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Neural networks are well known for their ability to model non linear functions, but as statistical methods usually does, they use a no parametric approach thus, a priori knowledge is not obvious to be taken into account no more than the a posteriori knowledge. In order to deal with these problematics, an original way to encode the knowledge inside the architecture is proposed. This method is applied to the problem of the evapotranspiration inside karstic aquifer which is a problem of huge utility in order to deal with water resource.

Keywords: Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.

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Authors: R. Sahraian, A. Karampour Haghighi, E. Ghasemi

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Process planning and production scheduling play important roles in manufacturing systems. In this paper a multiobjective mixed integer linear programming model is presented for the integrated planning and scheduling of multi-product. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimization problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for it, a PSO-based algorithm is proposed by fully utilizing the capability of the exploration search and fast convergence. To fit the continuous PSO in the discrete modeled problem, a solution representation is used in the algorithm. The numerical experiments have been performed to demonstrate the effectiveness of the proposed algorithm.

Keywords: Integrated process planning and scheduling, multi objective, MILP, Particle swarm optimization

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: All-or-none, computational modelling, mathematical model, transmembrane voltage, action potential.

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Authors: Joonas Pääkkönen

Abstract:

In sports, individuals and teams are typically interested in final rankings. Final results, such as times or distances, dictate these rankings, also known as places. Places can be further associated with ordered random variables, commonly referred to as order statistics. In this work, we introduce a simple, yet accurate order statistical ordinal regression function that predicts relay race places with changeover-times. We call this function the Fenton-Wilkinson Order Statistics model. This model is built on the following educated assumption: individual leg-times follow log-normal distributions. Moreover, our key idea is to utilize Fenton-Wilkinson approximations of changeover-times alongside an estimator for the total number of teams as in the notorious German tank problem. This original place regression function is sigmoidal and thus correctly predicts the existence of a small number of elite teams that significantly outperform the rest of the teams. Our model also describes how place increases linearly with changeover-time at the inflection point of the log-normal distribution function. With real-world data from Jukola 2019, a massive orienteering relay race, the model is shown to be highly accurate even when the size of the training set is only 5% of the whole data set. Numerical results also show that our model exhibits smaller place prediction root-mean-square-errors than linear regression, mord regression and Gaussian process regression.

Keywords: Fenton-Wilkinson approximation, German tank problem, log-normal distribution, order statistics, ordinal regression, orienteering, sports analytics, sports modeling.

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Authors: M. Massour El Aoud, M. Franceschi, M. Maher

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The approach proposed here is oriented in the direction of fuzzy system for the analysis and the synthesis of intelligent climate controllers, the simulation of the internal climate of the greenhouse is achieved by a linear model whose coefficients are obtained by identification. The use of fuzzy logic controllers for the regulation of climate variables represents a powerful way to minimize the energy cost. Strategies of reduction and optimization are adopted to facilitate the tuning and to reduce the complexity of the controller.

Keywords: Greenhouse, fuzzy logic, optimization, gradient descent.

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Authors: Elena Ezhova, Vadim Mottl, Olga Krasotkina

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The problem of estimating time-varying regression is inevitably concerned with the necessity to choose the appropriate level of model volatility - ranging from the full stationarity of instant regression models to their absolute independence of each other. In the stationary case the number of regression coefficients to be estimated equals that of regressors, whereas the absence of any smoothness assumptions augments the dimension of the unknown vector by the factor of the time-series length. The Akaike Information Criterion is a commonly adopted means of adjusting a model to the given data set within a succession of nested parametric model classes, but its crucial restriction is that the classes are rigidly defined by the growing integer-valued dimension of the unknown vector. To make the Kullback information maximization principle underlying the classical AIC applicable to the problem of time-varying regression estimation, we extend it onto a wider class of data models in which the dimension of the parameter is fixed, but the freedom of its values is softly constrained by a family of continuously nested a priori probability distributions.

Keywords: Time varying regression, time-volatility of regression coefficients, Akaike Information Criterion (AIC), Kullback information maximization principle.

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Authors: Y. N. Phang, E. F. Loh

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The zero truncated model is usually used in modeling count data without zero. It is the opposite of zero inflated model. Zero truncated Poisson and zero truncated negative binomial models are discussed and used by some researchers in analyzing the abundance of rare species and hospital stay. Zero truncated models are used as the base in developing hurdle models. In this study, we developed a new model, the zero truncated strict arcsine model, which can be used as an alternative model in modeling count data without zero and with extra variation. Two simulated and one real life data sets are used and fitted into this developed model. The results show that the model provides a good fit to the data. Maximum likelihood estimation method is used in estimating the parameters.

Keywords: Hurdle models, maximum likelihood estimation method, positive count data.

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Authors: M. Kovac

Abstract:

This article describes design of the 8-bit asynchronous microcontroller simulation model in VHDL. The model is created in ISE Foundation design tool and simulated in Modelsim tool. This model is a simple application example of asynchronous systems designed in synchronous design tools. The design process of creating asynchronous system with 4-phase bundled-data protocol and with matching delays is described in the article. The model is described in gate-level abstraction. The simulation waveform of the functional construction is the result of this article. Described construction covers only the simulation model. The next step would be creating synthesizable model to FPGA.

Keywords: Asynchronous, Microcontroller, VHDL, FPGA.

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Authors: Jiashan Tang

Abstract:

In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the proposed criteria is weaker than that in the literature which requires that the channel matrix is irreducible/invertible or reversible.

Keywords: Blind source separable, FIR-MIMO system, Binary input, Bezout equality.

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Authors: GuoQiang Peng, Yi Sun

Abstract:

In this paper, based on the work in [1], we further give a general model for acquiring knowledge, which first focuses on the research of how and when things involved in problems are made then describes the goals, the energy and the time to give an optimum model to decide how many related things are supposed to be involved in. Finally, we acquire knowledge from this model in which there are the attributes, actions and connections of the things involved at the time when they are born and the time in their life. This model not only improves AI theories, but also surely brings the effectiveness and accuracy for AI system because systems are given more knowledge when reasoning or computing is used to bring about results.

Keywords: Time, knowledge, model.

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Authors: Jooho Hwang, Chang-Kyu Song, Chun-Hong Park

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This paper describes a method to measure and compensate a 4 axes ultra-precision machine tool that generates micro patterns on the large surfaces. The grooving machine is usually used for making a micro mold for many electrical parts such as a light guide plate for LCD and fuel cells. The ultra precision machine tool has three linear axes and one rotational table. Shaping is usually used to generate micro patterns. In the case of 50 μm pitch and 25 μm height pyramid pattern machining with a 90° wedge angle bite, one of linear axis is used for long stroke motion for high cutting speed and other linear axis are used for feeding. The triangular patterns can be generated with many times of long stroke of one axis. Then 90° rotation of work piece is needed to make pyramid patterns with superposition of machined two triangular patterns. To make a two dimensional positioning error, straightness of two axes in out of plane, squareness between the each axis are important. Positioning errors, straightness and squarness were measured by laser interferometer system. Those were compensated and confirmed by ISO230-6. One of difficult problem to measure the error motions is squareness or parallelism of axis between the rotational table and linear axis. It was investigated by simultaneous moving of rotary table and XY axes. This compensation method is introduced in this paper.

Keywords: Ultra-precision machine tool, muti-axis errors, squraness, positioning errors.

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Authors: Yogesh Aggarwal

Abstract:

The paper discusses the results obtained to predict reinforcement in singly reinforced beam using Neural Net (NN), Support Vector Machines (SVM-s) and Tree Based Models. Major advantage of SVM-s over NN is of minimizing a bound on the generalization error of model rather than minimizing a bound on mean square error over the data set as done in NN. Tree Based approach divides the problem into a small number of sub problems to reach at a conclusion. Number of data was created for different parameters of beam to calculate the reinforcement using limit state method for creation of models and validation. The results from this study suggest a remarkably good performance of tree based and SVM-s models. Further, this study found that these two techniques work well and even better than Neural Network methods. A comparison of predicted values with actual values suggests a very good correlation coefficient with all four techniques.

Keywords: Linear Regression, M5 Model Tree, Neural Network, Support Vector Machines.

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Authors: Neeta Awasthy, J.P.Saini, D.S.Chauhan

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ICA which is generally used for blind source separation problem has been tested for feature extraction in Speech recognition system to replace the phoneme based approach of MFCC. Applying the Cepstral coefficients generated to ICA as preprocessing has developed a new signal processing approach. This gives much better results against MFCC and ICA separately, both for word and speaker recognition. The mixing matrix A is different before and after MFCC as expected. As Mel is a nonlinear scale. However, cepstrals generated from Linear Predictive Coefficient being independent prove to be the right candidate for ICA. Matlab is the tool used for all comparisons. The database used is samples of ISOLET.

Keywords: Cepstral Coefficient, Distance measures, Independent Component Analysis, Linear Predictive Coefficients.

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.

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Authors: A. Zaidi, F. Khelifi, R. Masmoudi, M. Bouhicha

Abstract:

5

In order to eradicate the degradation of reinforced concrete structures due to the steel corrosion, professionals in constructions suggest using fiber reinforced polymers (FRP) for their excellent properties. Nevertheless, high temperatures may affect the bond between FRP bar and concrete, and consequently the serviceability of FRP-reinforced concrete structures. This paper presents a nonlinear numerical investigation using ADINA software to investigate the effect of the spacing between glass FRP (GFRP) bars embedded in concrete on circumferential thermal deformations and the distribution of radial thermal cracks in reinforced concrete beams submitted to high temperature variations up to 60 °C for asymmetrical problems. The thermal deformations predicted from nonlinear finite elements model, at the FRP bar/concrete interface and at the external surface of concrete cover, were established as a function of the ratio of concrete cover thickness to FRP bar diameter (c/d_b) and the ratio of spacing between FRP bars in concrete to FRP bar diameter (e/d_b). Numerical results show that the circumferential thermal deformations at the external surface of concrete cover are linear until cracking thermal load varied from 32 to 55 °C corresponding to the ratio of e/d_b varied from 1.3 to 2.3, respectively. However, for ratios e/d_b >2.3 and c/d_b >1.6, the thermal deformations at the external surface of concrete cover exhibit linear behavior without any cracks observed on the specified surface. The numerical results are compared to those obtained from analytical models validated by experimental tests.

Keywords: Concrete beam, FRP bars, spacing effect, thermal deformation.

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Authors: A. Gürses, Z. Eroğlu, E. Şahin, K. Güneş, Ç. Doğar

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In recent years, polymer/clay nanocomposites have generated great interest in the polymer industry as a new type of composite material because of their superior properties, which includes high heat deflection temperature, gas barrier performance, dimensional stability, enhanced mechanical properties, optical clarity and flame retardancy when compared with the pure polymer or conventional composites. The investigation of change of the tensile properties of organoclay/linear low density polyethylene (LLDPE) nanocomposites with the use of Dioctyl terephthalate (DOTP) (as plasticizer) and calcite (as filler) has been aimed. The composites and organoclay synthesized were characterized using the techniques such as XRD, HRTEM and FTIR techniques. The spectroscopic results indicate that platelets of organoclay were well dispersed within the polymeric matrix. The tensile properties of the composites were compared considering the stress-strain curve drawn for each composite and pure polymer. It was observed that the composites prepared by adding the plasticizer at different ratios and a certain amount of calcite exhibited different tensile behaviors compared to pure polymer.

Keywords: Linear low density polyethylene, nanocomposite, organoclay, plasticizer.

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Authors: M. Rozanek, K. Roubik

Abstract:

The article deals with development, design and implementation of a mathematical model of the human respiratory system. The model is designed in order to simulate distribution of important intrapulmonary parameters along the bronchial tree such as pressure amplitude, tidal volume and effect of regional mechanical lung properties upon the efficiency of various ventilatory techniques. Therefore exact agreement of the model structure with the lung anatomical structure is required. The model is based on the lung morphology and electro-acoustic analogy is used to design the model.

Keywords: Model of the respiratory system, total lung impedance, intrapulmonary parameters.

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Authors: Zia R. Tahir, P. Mandal

Abstract:

This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0^o/+45^o/-45^o/0^o] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

Keywords: CFRP Composite Cylindrical Shell, Asymmetric Meshing Technique, Primary Buckling, Secondary Buckling, Linear Eigenvalue Analysis, Non-linear Riks Analysis.

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Authors: A. M. El Ansary, A. A. El Damatty, A. O. Nassef

Abstract:

The aim of the current study is to develop a numerical tool that is capable of achieving an optimum shape and design of hyperbolic cooling towers based on coupling a non-linear finite element model developed in-house and a genetic algorithm optimization technique. The objective function is set to be the minimum weight of the tower. The geometric modeling of the tower is represented by means of B-spline curves. The finite element method is applied to model the elastic buckling behaviour of a tower subjected to wind pressure and dead load. The study is divided into two main parts. The first part investigates the optimum shape of the tower corresponding to minimum weight assuming constant thickness. The study is extended in the second part by introducing the shell thickness as one of the design variables in order to achieve an optimum shape and design. Design, functionality and practicality constraints are applied.

Keywords: B-splines, Cooling towers, Finite element, Genetic algorithm, Optimization

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