Search results for: Nonlinear critical systems

Authors: Alexey V. Klyuev, Valery P. Samarin, Viktor F. Klyuev, Andrey V. Klyuev

Abstract:

A power measurement algorithm of the input mix components of the noise signal and pulse interference is considered. The algorithm efficiency analysis has been carried out for different interference-to-signal ratio. Algorithm performance features have been explored by numerical experiment results.

Keywords: Noise signal, pulse interference, signal power, spectrum width, detection.

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Authors: A. Shamsi, N. Choupani

Abstract:

Active vibration isolation systems are less commonly used than passive systems due to their associated cost and power requirements. In principle, semi-active isolation systems can deliver the versatility, adaptability and higher performance of fully active systems for a fraction of the power consumption. Various semi-active control algorithms have been suggested in the past. This paper studies the 4DOF model of semi-active suspension performance controlled by on–off and continuous skyhook damping control strategy. The frequency and transient responses of model are evaluated in terms of body acceleration, roll angle and tire deflection and are compared with that of a passive damper. The results show that the semi-active system controlled by skyhook strategy always provides better isolation than a conventional passively damped system except at tire natural frequencies.

Keywords: Semi-active suspension system, Skyhook, Vibration isolation, 4DOF model.

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Authors: Bhekisipho Twala, Mantepu Masetshaba, Ramapulana Nkoana

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Multiple classifier systems combine several individual classifiers to deliver a final classification decision. However, an increasingly controversial question is whether such systems can outperform the single best classifier, and if so, what form of multiple classifiers system yields the most significant benefit. Also, multi-target tracking detection using multiple sensors is an important research field in mobile techniques and military applications. In this paper, several multiple classifiers systems are evaluated in terms of their ability to predict a system’s failure or success for multi-sensor target tracking tasks. The Bristol Eden project dataset is utilised for this task. Experimental and simulation results show that the human activity identification system can fulfil requirements of target tracking due to improved sensors classification performances with multiple classifier systems constructed using boosting achieving higher accuracy rates.

Keywords: Single classifier, machine learning, ensemble learning, multi-sensor target tracking.

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Authors: Melissa C. LaDuke

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The use of new literacies within science classrooms needs to be balanced by teachers to both teach different forms of communication while assessing content area proficiency. Using new literacies such as Twitter and Facebook needs to be incorporated into science content area literacy studies in addition to continuing to use generally-accepted forms of scientific content area presentation which include scientific papers and textbooks. The research question this literature review seeks to answer is “What are some ways in which new forms of literacy are better suited to teach scientific content area literacy to 21st century learners?” The research question is addressed through a literature review that highlights methods currently being used to educate the next wave of learners in the world of science content area literacy. Both temporal discourse analysis (TDA) and critical discourse analysis (CDA) were used to determine the need to use new literacies to teach science content area literacy. Increased use of digital technologies and a change in science content area pedagogy were explored.

Keywords: Science content area literacy, new literacies, critical discourse analysis, temporal discourse analysis.

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Authors: Aleksander Nawrat, Karol Jędrasiak, Artur Ryt, Dawid Sobel

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The goal of the article is to present a novel Multimedia Firearms Training System. The system was developed in order to compensate for major problems of existing shooting training systems. The designed and implemented solution can be characterized by five major advantages: algorithm for automatic geometric calibration, algorithm of photometric recalibration, firearms hit point detection using thermal imaging camera, IR laser spot tracking algorithm for after action review analysis, and implementation of ballistics equations. The combination of the abovementioned advantages in a single multimedia firearms training system creates a comprehensive solution for detecting and tracking of the target point usable for shooting training systems and improving intervention tactics of uniformed services. The introduced algorithms of geometric and photometric recalibration allow the use of economically viable commercially available projectors for systems that require long and intensive use without most of the negative impacts on color mapping of existing multi-projector multimedia shooting range systems. The article presents the results of the developed algorithms and their application in real training systems.

Keywords: Firearms shot detection, geometric recalibration, photometric recalibration, IR tracking algorithm, thermography, ballistics.

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Authors: M.Paroncini, F.Corvaro, G.Nardini, S.Pistolesi

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The development of renewable energies - particularly energy from wind, water, solar power and biomass - is a central aim of the European Commission's energy policy. There are several reasons for this choice: renewable energies are sustainable, nonpolluting, widely available and clean. Increasing the share of renewable energy in the energy balance enhances sustainability. It also helps to improve the security of energy supply by reducing the Community's growing dependence on imported energy sources.In this paper it was studied the possibility to realize three photovoltaic systems in the Italian Natural Park “Gola della Rossa e di Frasassi". The first photovoltaic system is a grid-connected system for Services and Documentation Center of Castelletta with a nominal power of about 6 kWp. The second photovoltaic system is a grid-connected integrated system on the ticket office-s roof with a nominal power of about 4 kWp. The third project is set up by five grid-connected systems integrated on the roofs of the bungalows in Natural Park-s tourist camping with a nominal power of about 10 kWp. The electricity which is generated by all these plants is purchased according to the Italian program called “Conto Energia". Economical analysis and the amount of the avoided CO2 emissions are elaborated for these photovoltaic systems.

Keywords: CO2 emissions, conto energia, photovoltaic systems.

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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Authors: Chen-Chien Hsu, Chun-Hui Gao

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In this paper, a PSO-based approach is proposed to derive a digital controller for redesigned digital systems having an interval plant based on resemblance of the extremal gain/phase margins. By combining the interval plant and a controller as an interval system, extremal GM/PM associated with the loop transfer function can be obtained. The design problem is then formulated as an optimization problem of an aggregated error function revealing the deviation on the extremal GM/PM between the redesigned digital system and its continuous counterpart, and subsequently optimized by a proposed PSO to obtain an optimal set of parameters for the digital controller. Computer simulations have shown that frequency responses of the redesigned digital system having an interval plant bare a better resemblance to its continuous-time counter part by the incorporation of a PSO-derived digital controller in comparison to those obtained using existing open-loop discretization methods.

Keywords: Digital redesign, Extremal systems, Particle swarm optimization, Uncertain interval systems

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Authors: Helena Costa Oliveira, Carmem Oliveira, Rita Moutinho

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The Balanced Scorecard (BSC) is a continuous strategic monitoring model focused not only on financial issues but also on internal processes, patients/users, and learning and growth. Initially dedicated to business management, it currently serves organizations of other natures - such as hospitals. This paper presents a BSC designed for a Portuguese Acute Pain Unit (APU). This study is qualitative and based on the experience of collaborators at the APU. The management of APU is based on four perspectives – users, internal processes, learning and growth, and financial and legal. For each perspective, there were identified strategic objectives, critical factors, lead indicators and initiatives. The strategic map of the APU outlining sustained strategic relations among strategic objectives. This study contributes to the development of research in the health management area as it explores how organizational insufficiencies and inconsistencies in this particular case can be addressed, through the identification of critical factors, to clearly establish core outcomes and initiatives to set up.

Keywords: Acute pain unit, balanced scorecard, hospital management, organizational performance, Portugal.

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Authors: Jaehun Joo, Mie-jung Kim, Ismatilla Normatov, Lyunhwa Kim

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The purpose of this paper is to analyze determinants of information security affecting adoption of the Web-based integrated information systems (IIS). We introduced Web-based information systems which are designed to formulate strategic plans for Peruvian government. Theoretical model is proposed to test impact of organizational factors (deterrent efforts and severity; preventive efforts) and individual factors (information security threat; security awareness) on intentions to proactively use the Web-based IIS .Our empirical study results highlight that deterrent efforts and deterrent severity have no significant influence on the proactive use intentions of IIS, whereas, preventive efforts play an important role in proactive use intentions of IIS. Thus, we suggest that organizations need to do preventive efforts by introducing various information security solutions, and try to improve information security awareness while reducing the perceived information security threats.

Keywords: Information security, Deterrent efforts, deterrentseverity, preventive efforts, information security awareness, information security threats, integrated information systems

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Authors: R. Hajkova, J. Palecek, H. Malachova, A. Oulehlova

Abstract:

Ensuring of continuity of business is basic strategy of every company. Continuity of organization activities includes comprehensive procedures that help in solving unexpected situations of natural and anthropogenic character (for example flood, blaze, economic situations). Planning of continuity operations is a process that helps identify critical processes and implement plans for the security and recovery of key processes. The aim of this article is to demonstrate application of system approach to managing business continuity called business continuity management systems in military issues. This article describes the life cycle of business continuity management which is based on the established cycle PDCA (Plan- Do-Check-Act). After this is carried out by activities which are making by University of Defence during activation of forces and means of the integrated rescue system in case of emergencies - accidents at a nuclear power plant in Czech Republic. Activities of various stages of deployment earmarked forces and resources are managed and evaluated by using MCMS application (Military Continuity Management System).

Keywords: Business continuity management system, emergency management, military, nuclear safety.

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Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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Authors: Albert Albers, Pablo Enrique Leslabay

Abstract:

The Institute of Product Development is dealing with the development, design and dimensioning of micro components and systems as a member of the Collaborative Research Centre 499 “Design, Production and Quality Assurance of Molded micro components made of Metallic and Ceramic Materials". Because of technological restrictions in the miniaturization of conventional manufacturing techniques, shape and material deviations cannot be scaled down in the same proportion as the micro parts, rendering components with relatively wide tolerance fields. Systems that include such components should be designed with this particularity in mind, often requiring large clearance. On the end, the output of such systems results variable and prone to dynamical instability. To save production time and resources, every study of these effects should happen early in the product development process and base on computer simulation to avoid costly prototypes. A suitable method is proposed here and exemplary applied to a micro technology demonstrator developed by the CRC499. It consists of a one stage planetary gear train in a sun-planet-ring configuration, with input through the sun gear and output through the carrier. The simulation procedure relies on ordinary Multi Body Simulation methods and subsequently adds other techniques to further investigate details of the system-s behavior and to predict its response. The selection of the relevant parameters and output functions followed the engineering standards for regular sized gear trains. The first step is to quantify the variability and to reveal the most critical points of the system, performed through a whole-mechanism Sensitivity Analysis. Due to the lack of previous knowledge about the system-s behavior, different DOE methods involving small and large amount of experiments were selected to perform the SA. In this particular case the parameter space can be divided into two well defined groups, one of them containing the gear-s profile information and the other the components- spatial location. This has been exploited to explore the different DOE techniques more promptly. A reduced set of parameters is derived for further investigation and to feed the final optimization process, whether as optimization parameters or as external perturbation collective. The 10 most relevant perturbation factors and 4 to 6 prospective variable parameters are considered in a new, simplified model. All of the parameters are affected by the mentioned production variability. The objective functions of interest are based on scalar output-s variability measures, so the problem becomes an optimization under robustness and reliability constrains. The study shows an initial step on the development path of a method to design and optimize complex micro mechanisms composed of wide tolerated elements accounting for the robustness and reliability of the systems- output.

Keywords: Micro molded components, Optimization, Robustness und Reliability, Simulation

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Authors: Yucel Ugurlu

Abstract:

This paper explains a novel approach to human interactive e-learning systems using head posture images. Students- face and hair information are used to identify a human presence and estimate the gaze direction. We then define the human-computer interaction level and test the definition using ten students and seventy different posture images. The experimental results show that head posture images provide adequate information for increasing human-computer interaction in e-learning systems.

Keywords: E-learning, image segmentation, human-presence, gaze-direction, human-computer interaction, LabVIEW

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Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya

Abstract:

Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.

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Authors: Taher El-Bitar, Maha El-Meligy, Eman El-Shenawy, Almosilhy Almosilhy, Nader Dawood

Abstract:

The steel contains 0.3% C and 0.004% B, beside Mn, Cr, Mo, and Ni. The alloy was processed by using 20-ton capacity electric arc furnace (EAF), and then refined by ladle furnace (LF). Liquid steel was cast as rectangular ingots. Dilatation test showed the critical transformation temperatures Ac₁, Ac₃, M_s and M_f as 716, 835, 356, and 218 °C. The ingots were austenitized and soaked and then rough rolled to thin slabs with 80 mm thickness. The thin slabs were then reheated and soaked for finish rolling to 6.0 mm thickness plates. During the rough rolling, the roll force increases as a result of rolling at temperatures less than recrystallization temperature. However, during finish rolling, the steel reflects initially continuous static recrystallization after which it shows strain hardening due to fall of temperature. It was concluded that, the steel plates were successfully heat treated by quenching-tempering at 250 ºC for 20 min.

Keywords: Armor steel, austenitizing, critical transformation temperatures, dilatation curve, martensite, quenching, rough and finish rolling processes, soaking, tempering, thermo-mechanical processing.

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Authors: Benjapol Auprasert, Yachai Limpiyakorn

Abstract:

Measuring the complexity of software has been an insoluble problem in software engineering. Complexity measures can be used to predict critical information about testability, reliability, and maintainability of software systems from automatic analysis of the source code. During the past few years, many complexity measures have been invented based on the emerging Cognitive Informatics discipline. These software complexity measures, including cognitive functional size, lend themselves to the approach of the total cognitive weights of basic control structures such as loops and branches. This paper shows that the current existing calculation method can generate different results that are algebraically equivalence. However, analysis of the combinatorial meanings of this calculation method shows significant flaw of the measure, which also explains why it does not satisfy Weyuker's properties. Based on the findings, improvement directions, such as measures fusion, and cumulative variable counting scheme are suggested to enhance the effectiveness of cognitive complexity measures.

Keywords: Cognitive Complexity Measure, Cognitive Weight of Basic Control Structure, Counting Rules, Cumulative Variable Counting Scheme.

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Authors: Cenk Akbiyik, Gonul Altin Akbiyik

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The main purpose of the study was to determine whether students- interpretation achievement differed with the use of various multimedia presentation types. Four groups of students, text only (T), audio only (A), text and audio (TA), text and image (TI), were arranged and they were presented the same story via different types of multimedia presentations. Inference achievement was measured by a critical thinking inference test. Higher mean scores for the TA group compared to the other three groups were found. Also when compared pairwise, interpretation achievement of the TA group differed significantly from scores of the T and TI groups. These differences were interpreted with the increased cognitive load. Increased cognitive load for the TA group may have invited students to put more effort into comprehending the text, thus resulting in better test scores. Findings of the study can be seen as a sign of the importance of learning situations and learning outcomes in multimedia-supported learning environments and may have practical benefits for instructional designers.

Keywords: Multimedia, cognitive multimedia, dual coding, cognitive load, critical thinking.

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Authors: Mohsen Hayati, Yazdan Shirvany

Abstract:

In this paper, the application of neural networks to study the design of short-term load forecasting (STLF) Systems for Illam state located in west of Iran was explored. One important architecture of neural networks named Multi-Layer Perceptron (MLP) to model STLF systems was used. Our study based on MLP was trained and tested using three years (2004-2006) data. The results show that MLP network has the minimum forecasting error and can be considered as a good method to model the STLF systems.

Keywords: Artificial neural networks, Forecasting, Multi-layer perceptron.

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Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: Sheela Tiwari, R. Naresh, R. Jha

Abstract:

The paper presents an investigation in to the effect of neural network predictive control of UPFC on the transient stability performance of a multimachine power system. The proposed controller consists of a neural network model of the test system. This model is used to predict the future control inputs using the damped Gauss-Newton method which employs ‘backtracking’ as the line search method for step selection. The benchmark 2 area, 4 machine system that mimics the behavior of large power systems is taken as the test system for the study and is subjected to three phase short circuit faults at different locations over a wide range of operating conditions. The simulation results clearly establish the robustness of the proposed controller to the fault location, an increase in the critical clearing time for the circuit breakers, and an improved damping of the power oscillations as compared to the conventional PI controller.

Keywords: Identification, Neural networks, Predictive control, Transient stability, UPFC.

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Authors: Dina K. Badawy, Dina M. Ibrahim, Alsayed A. Sallam

Abstract:

Distributed database is a collection of logically related databases that cooperate in a transparent manner. Query processing uses a communication network for transmitting data between sites. It refers to one of the challenges in the database world. The development of sophisticated query optimization technology is the reason for the commercial success of database systems, which complexity and cost increase with increasing number of relations in the query. Mariposa, query trading and query trading with processing task-trading strategies developed for autonomous distributed database systems, but they cause high optimization cost because of involvement of all nodes in generating an optimal plan. In this paper, we proposed a modification on the autonomous strategy K-QTPT that make the seller’s nodes with the lowest cost have gradually high priorities to reduce the optimization time. We implement our proposed strategy and present the results and analysis based on those results.

Keywords: Autonomous strategies, distributed database systems, high priority, query optimization.

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Authors: Guy Rosman, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel

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We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.

Keywords: Dimensionality reduction, manifold learning, multidimensional scaling, geodesic distance, boundary detection.

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Authors: E. Asadzadeh, M. Alam

Abstract:

This study offers a comprehensive review of the research papers published in the field of cooling towers and gives an insight into the latest developments of the natural draught cooling towers. Different modeling, analysis and design techniques are summarized and the challenges are discussed. The 118 references included in this paper are mostly concentrated on the review of the published papers after 2005. The present paper represents a complete collection of the studies done for cooling towers and would give an updated material for the researchers and design engineers in the field of hyperbolic cooling towers.

Keywords: Hyperbolic cooling towers, earthquakes, wind, nonlinear behavior, buckling, collapse, interference.

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Authors: Amer A. Boushaala

Abstract:

The heuristic decision rules used for project scheduling will vary depending upon the project-s size, complexity, duration, personnel, and owner requirements. The concept of project complexity has received little detailed attention. The need to differentiate between easy and hard problem instances and the interest in isolating the fundamental factors that determine the computing effort required by these procedures inspired a number of researchers to develop various complexity measures. In this study, the most common measures of project complexity are presented. A new measure of project complexity is developed. The main privilege of the proposed measure is that, it considers size, shape and logic characteristics, time characteristics, resource demands and availability characteristics as well as number of critical activities and critical paths. The degree of sensitivity of the proposed measure for complexity of project networks has been tested and evaluated against the other measures of complexity of the considered fifty project networks under consideration in the current study. The developed measure showed more sensitivity to the changes in the network data and gives accurate quantified results when comparing the complexities of networks.

Keywords: Activity networks, Complexity index, Networkcomplexity measure, Network topology, Project Network.

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Authors: Kriangkrai Maneerat, Chutima Prommak

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This paper presents an analysis of the localization accuracy of indoor positioning systems using Cramer-s rule via IEEE 802.15.4 wireless sensor networks. The objective is to study the impact of the methods used to convert the received signal strength into the distance that is used to compute the object location in the wireless indoor positioning system. Various methods were tested and the localization accuracy was analyzed. The experimental results show that the method based on the empirical data measured in the non line-of-sight (NLOS) environment yield the highest localization accuracy; with the minimum error distance less than 3 m.

Keywords: Indoor positioning systems, localization accuracy, wireless networks, Cramer's rule.

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Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: Rotor dynamic analysis, Finite element method, shaft train, Campbell diagram.

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Authors: Samar Raffoul, Martin Heywood, Dimitrios Moutaftsis, Michael Rowell

Abstract:

This paper comprises an experimental investigation into the structural performance of cold formed steel (CFS) and timber board composite floor systems. The tests include a series of small-scale pushout tests and full-scale bending tests carried out using a refined loading system to simulate uniformly distributed constant load. The influence of connection details (screw spacing and adhesives) on floor performance was investigated. The results are then compared to predictions from relevant existing models for composite floor systems. The results of this research demonstrate the significant benefits of considering the composite action of the boards in floor design. Depending on connection detail, an increase in flexural stiffness of up to 40% was observed in the floor system, when compared to designing joists individually.

Keywords: Cold formed steel joists, composite action, flooring systems, shear connection.

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Authors: M. Cortés, E. Vera, O. Rojas

Abstract:

The research studies of the kinetics of the corrosion process that attacks concrete and occurs within sewerage systems agree on the amount of variables that interfere in the process. This study aims to check the impact of the pH levels of the corrosive environment and the concrete surface, the concentrations of chemical sulfuric acid, and in turn, measure the resistance of concrete to this attack under controlled laboratory conditions; it also aims to contribute to the development of further research related to the topic, in order to compare the impact of biogenic sulfuric acid and chemical sulfuric acid involvement on concrete structures, especially in scenarios such as sewerage systems.

Keywords: Acid Sulfuric, concrete, corrosion.

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Authors: Zachariah Sinkala

Abstract:

A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.

Keywords: Fokker-Plank equations, global attractor, stem cell.

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