Search results for: Layout form

Authors: Valentina Koliskina, Inta Volodko

Abstract:

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

Keywords: Transient eddy currents, Laplace transform, double conductor line.

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Authors: Andreas Savvides, Chloe Kadi

Abstract:

The objective of this study is to investigate how the planning and design of open parks within neighborhoods and communities can promote physical activity in order to enhance the health of the local population. A review of relevant literature was conducted for studies regarding the relationship between health and physical activity and the park characteristics that can promote physical activity among people. The findings of the literature review were then compared and analyzed, in order to identify the main characteristics of urban parks that can promote physical activity and enhance public health. In order to find out how the characteristics identified in the literature were applied in real life, an analysis of three existing parks in three different countries was conducted. The parks, apart from their geographical location, also vary in size and layout. The parks were chosen because they are urban open parks and they include facilities for physical activity.

Keywords: Urban planning, active living behavior, open parks, sustainable mobility.

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Authors: S. Yunus, A. Suratman, N. Mohamad Nor, M. Othman

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This paper presents the measurement and simulation results by Finite Element Method (FEM) for earth resistance (R_DC) for interconnected vertical ground rod configurations. The soil resistivity was measured using the Wenner four-pin Method, and R_DC was measured using the Fall of Potential (FOP) method, as outlined in the standard. Genetic Algorithm (GA) is employed to interpret the soil resistivity to that of a 2-layer soil model. The same soil resistivity data that were obtained by Wenner four-pin method were used in FEM for simulation. This paper compares the results of R_DC obtained by FEM simulation with the real measurement at field site. A good agreement was seen for R_DC obtained by measurements and FEM. This shows that FEM is a reliable software to be used for design of earthing systems. It is also found that the parallel rod system has a better performance compared to a similar setup using a grid layout.

Keywords: Earthing systems, earth electrodes, Finite Element Method, FEM, Genetic Algorithm, GA, earth resistances.

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Authors: Musthaya Patchanee

Abstract:

This research aimed to study form of traffic distribution and environmental factors of road that affect traffic accidents in Dusit District, only areas responsible of Samsen Police Station. Data used in this analysis is the secondary data of traffic accident case from year 2011. Observed area units are 15 traffic lines that are under responsible of Samsen Police Station. Technique and method used are the Cartographic Method, the Correlation Analysis, and the Multiple Regression Analysis. The results of form of traffic accidents show that, the Samsen Road area had most traffic accidents (24.29%), second was Rachvithi Road(18.10%), third was Sukhothai Road (15.71%), fourth was Rachasrima Road (12.38%), and fifth was Amnuaysongkram Road(7.62%). The result from Dusit District, onlyareasresponsibleofSamsen police station, has suggested that the scale of accidents have high positive correlation with statistic significant at level 0.05 and the frequency of travel (r=0.857). Traffic intersection point (r=0.763)and traffic control equipments (r=0.713) are relevant factors respectively. By using the Multiple Regression Analysis, travel frequency is the only one that has considerable influences on traffic accidents in Dusit district only Samsen Police Station area. Also, a factor in frequency of travel can explain the change in traffic accidents scale to 73.40 (R² = 0.734). By using the Multiple regression summation from analysis was Ŷ=-7.977+0.044X6

Keywords: Form of Traffic Distribution, Environmental Factors of road, Traffic Accidents, Dusit District.

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

Abstract:

In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Hana Maresova, Daniel Ecler, Miroslava Mensikova

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This article focuses on the use of 3D multi-user virtual environment in language teaching and presents the results of a four-year research at the Palacky University Olomouc Faculty of Education (Czech Republic). Language teaching was conducted in an experimental form in the 3D virtual worlds of Second Life and Kitely (experimental group) and, in parallel to this, there was also traditional teaching conducted on identical topics in the form of lectures using a textbook (control group). The didactic test, which was presented to both of the groups in an identical form before the start of teaching and after its implementation, verified the effect of teaching in the experimental group by comparing the achieved results of both groups. Out of the three components of mother tongue teaching (grammar, literature, composition and communication education) students achieved partial better results (in the case of points focused on the visualization of the subject matter, these were statistically significant) in literature. Students from the control group performed better in grammar and composition. Based on the achieved results, we can state that the most appropriate use of multi-user virtual environment (MUVE) can be seen in teaching those topics that have the possibility of dramatization, experiential learning and group cooperation.

Keywords: 3D virtual reality, multiuser environments, online education, language education.

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y₀, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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Authors: Hyeong-Geon Lee, Jae-Young Park, Suk-ki Lee, Jong-Tae Kim

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The LMS adaptive filter has several parameters which can affect their performance. From among these parameters, most papers handle the step size parameter for controlling the performance. In this paper, we approach three parameters: step-size, filter tap-size and filter form. The regression analysis is used for defining the relation between parameters and performance of LMS adaptive filter with using the system level simulation results. The results present that all parameters have performance trends in each own particular form, which can be estimated from equations drawn by regression analysis.

Keywords: System level model, adaptive LMS FIR filter, regression analysis, systemC.

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Authors: H. W. Corley

Abstract:

A scalar equilibrium (SE) is an alternative type of equilibrium in pure strategies for an n-person normal-form game G. It is defined using optimization techniques to obtain a pure strategy for each player of G by maximizing an appropriate utility function over the acceptable joint actions. The players’ actions are determined by the choice of the utility function. Such a utility function could be agreed upon by the players or chosen by an arbitrator. An SE is an equilibrium since no players of G can increase the value of this utility function by changing their strategies. SEs are formally defined, and examples are given. In a greedy SE, the goal is to assign actions to the players giving them the largest individual payoffs jointly possible. In a weighted SE, each player is assigned weights modeling the degree to which he helps every player, including himself, achieve as large a payoff as jointly possible. In a compromise SE, each player wants a fair payoff for a reasonable interpretation of fairness. In a parity SE, the players want their payoffs to be as nearly equal as jointly possible. Finally, a satisficing SE achieves a personal target payoff value for each player. The vector payoffs associated with each of these SEs are shown to be Pareto optimal among all such acceptable vectors, as well as computationally tractable.

Keywords: Compromise equilibrium, greedy equilibrium, normal-form game, parity equilibrium, pure strategies, satisficing equilibrium, scalar equilibria, utility function, weighted equilibrium.

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Authors: Olusheye Akinfenwa

Abstract:

We consider the development of an eight order Adam-s type method, with A-stability property discussed by expressing them as a one-step method in higher dimension. This makes it suitable for solving variety of initial-value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form reveals that it is highly competitive with existing methods in the literature.

Keywords: Block Adam's type Method; Periodic Ordinary Differential Equation; Stability.

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Authors: T. Balogh, L. G. Vigh

Abstract:

Seismic design may require non-conventional concept, due to the fact that the stiffness and layout of the structure have a great effect on the overall structural behaviour, on the seismic load intensity as well as on the internal force distribution. To find an economical and optimal structural configuration the key issue is the optimal design of the lateral load resisting system. This paper focuses on the optimal design of regular, concentric braced frame (CBF) multi-storey steel building structures. The optimal configurations are determined by a numerical method using genetic algorithm approach, developed by the authors. Aim is to find structural configurations with minimum structural cost. The design constraints of objective function are assigned in accordance with Eurocode 3 and Eurocode 8 guidelines. In this paper the results are presented for various building geometries, different seismic intensities, and levels of energy dissipation.

Keywords: Dissipative Structures, Genetic Algorithm, Seismic Effects, Structural Optimization.

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Authors: Hyunsang Kim, Younghun Kim, Younghee Kim, Sangku Lee

Abstract:

We investigated ecotoxicity and performed experiment for removing ZnO nanoparticles in water. Short term exposure of hatching test using fertilized eggs (O. latipes) showed deformity in 5ppm of ZnO nanoparticles solution. And in 10ppm ZnO nanoparticles solution delayed hatching was observed. Hereine, chemical precipitation method was suggested for removing ZnO nanoparticles in water. The precipitated ZnO nanoparticles showed the form of ZnS after addition of Na2S, and the form of Zn3(PO4)2 for Na2HPO4. The removal efficiency of ZnO nanoparticles in water was closed to 100% for two cases. In ecotoxicity evaluation of as-precipitated ZnS and Zn3(PO4)2, they did not cause any acute toxicity for D. magna. It is noted that this precipitation treatment of ZnO is effective to reduce the potential cytotoxicity.

Keywords: ZnO nanoparticles, ZnS, Zn3(PO4)2, ecotoxicity evaluation, chemical precipitation.

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Authors: Simeon Karafolas, Maciej Woźniak

Abstract:

Guarantee schemes have been introduced in the economic and financial system as response to difficulties of SMEs for the access to the banking credit. Guarantee companies first appeared at the 19e century. Last wave of the development of those schemes appeared at the decade of 1990’s in particular to the new countries members of the EU. Guarantee schemes are presented as public owned guarantee companies, private ones mainly through a mutual form, but also under a mixed form. The paper based on guarantee schemes of five countries tries to investigate the differences that can exist within different guarantee companies. This investigation is based on some indicators that are time of response to the demand of guarantee, threshold of guarantee, acceptance of applications for guarantee, jobs created or saved and bureaucratic issues. It appears that guarantee companies have not the same reaction to the demand of SMEs and some of them are much more active.

Keywords: DIFASS, Guarantees, Loans.

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Authors: Taechit Cheuypoung

Abstract:

The purpose of this research was to design costume by the inspiration from the configurations, colors and decorations of Thai Royal Barges. The researcher investigated the bibliographies and the important of the Thai Royal Water-Course Procession, configurations and decoration techniques of four Royal Barges history. Furthermore, the researcher combined the contemporary architecture which became part of the four costumes with four patterns in this research. The four costumes designed by applied the physical configuration of the Royal Barge with the fold techniques which create the geometry pattern that are part of the Royal Barge-s decoration and contemporary architecture. Therefore, the researcher united each identity color of the barges with each costume composed with the original patterns by adjusted new layout and resized. Lastly, the new attractive patterns appeared. Nevertheless, the beauty of Thai traditional still remain by using Thai painting figure with black and white color which are the prevalent colors for the contemporary architectures.

Keywords: Costume Design, Figurehead, Thai Royal Barges.

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Authors: Raid A. Al-Aomar

Abstract:

This paper presents an application of 5S lean technology to a production facility. Due to increased demand, high product variety, and a push production system, the plant has suffered from excessive wastes, unorganized workstations, and unhealthy work environment. This has translated into increased production cost, frequent delays, and low workers morale. Under such conditions, it has become difficult, if not impossible, to implement effective continuous improvement studies. Hence, the lean project is aimed at diagnosing the production process, streamlining the workflow, removing/reducing process waste, cleaning the production environment, improving plant layout, and organizing workstations. 5S lean technology is utilized for achieving project objectives. The work was a combination of both culture changes and tangible/physical changes on the shop floor. The project has drastically changed the plant and developed the infrastructure for a successful implementation of continuous improvement as well as other best practices and quality initiatives.

Keywords: 5S Technique, Continuous Improvement, Kaizen, Lean Technology, Work Methods, Work Standards

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Authors: T. J. Jamaleddine

Abstract:

Purge columns or degasser vessels are widely used in the polyolefin process for removing trapped hydrocarbons and in-excess catalyst residues from the polymer particles. A uniform distribution of purged gases coupled with a plug-flow characteristic inside the column system is desirable to obtain optimum desorption characteristics of trapped hydrocarbon and catalyst residues. Computational Fluid Dynamics (CFD) approach is a promising tool for design optimization of these vessels. The success of this approach is profoundly dependent on the solution strategy and the choice of geometrical layout at the vessel outlet. Filling the column with solids and initially solving for the solids flow minimized numerical diffusion substantially. Adopting a cylindrical configuration at the vessel outlet resulted in less numerical instability and resembled the hydrodynamics flow of solids in the hopper segment reasonably well.

Keywords: CFD, gas-solids flow, gas purging, species transport, purge column, degasser vessel.

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Authors: Kazuaki Maeda

Abstract:

This paper describes a code clone visualization method, called FC graph, and the implementation issues. Code clone detection tools usually show the results in a textual representation. If the results are large, it makes a problem to software maintainers with understanding them. One of the approaches to overcome the situation is visualization of code clone detection results. A scatter plot is a popular approach to the visualization. However, it represents only one-to-one correspondence and it is difficult to find correspondence of code clones over multiple files. FC graph represents correspondence among files, code clones and packages in Java. All nodes in FC graph are positioned using force-directed graph layout, which is dynami- cally calculated to adjust the distances of nodes until stabilizing them. We applied FC graph to some open source programs and visualized the results. In the author’s experience, FC graph is helpful to grasp correspondence of code clones over multiple files and also code clones with in a file.

Keywords: code clone detection, program comprehension, software maintenance, visualization

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Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: Channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow.

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Authors: Bhaskar M., Venkataramani B.

Abstract:

In the literature, surfing technique has been proposed for single ended wave-pipelined serial interconnects to increase the data transfer rate. In this paper a novel surfing technique is proposed for differential wave-pipelined serial interconnects, which uses a 'Controllable inverter pair' for surfing. To evaluate the efficiency of this technique, a transceiver with transmitter, receiver, delay locked loop (DLL) along with 40mm metal 4 interconnects using the proposed surfing technique is implemented in UMC 180nm technology and their performances are studied through post layout simulations. From the study, it is observed that the proposed scheme permits 1.875 times higher data transmission rate compared to the single ended scheme whose maximum data transfer rate is 1.33 GB/s. The proposed scheme has the ability to receive the correct data even with stuck-at-faults in the complementary line.

Keywords: Controllable inverter pair, differential interconnect, serial link, surfing, wave pipelining.

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Authors: Sabina Akter, Osiris Valdez Banda, Pentti Kujala, Jani Romanoff

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This paper examines the relationship between on-board environmental factors and customer overall satisfaction in the context of the cruise on-board experience. The on-board environmental factors considered are ambient, layout/design, social, product/service and on-board enjoyment factors. The study presents a data-driven framework and model for the on-board cruise experience. The data are collected from 893 respondents in an application of a self-administered online questionnaire of their cruise experience. This study reveals the cruise passengers’ on-board experience through the customer decision journey based on the publicly available data. Pearson correlation and regression analysis have been applied, and the results show a positive and a significant relationship between the environmental factors and on-board experience. These data help understand the cruise passengers’ on-board experience, which will be used for the ultimate decision-making process in cruise ship design.

Keywords: Cruise behavior, on-board environmental factors, on-board experience, user or customer satisfaction.

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Authors: W. Kiamouche, S. Lasmari, M. Benslama

Abstract:

In order to derive important parameters concerning mobile subscriber MS with ongoing calls in Low Earth Orbit Mobile Satellite Systems LEO MSSs, a positioning system had to be integrated into MSS in order to localize mobile subscribers MSs and track them during the connection. Such integration is regarded as a complex implementation. We propose in this paper a novel method based on advantages of mobility model of Low Earth Orbit Mobile Satellite System LEO MSS which allows the evaluation of instant of subsequent handover of a MS even if its location is unknown. This method is utilized to propose a Dynamic Channel Reservation DCRlike scheme based on the DCR scheme previously proposed in literature. Results presented show that DCR-like technique gives different QoS performance than DCR. Indeed, an improve in handover blocking probability and an increase in new call blocking probability are observed for the DCR-like technique.

Keywords: cellular layout, DCR, LEO mobile satellite system, mobility model, positioning system

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: Esra E. Aleisa

Abstract:

A local municipality has decided to build a sewage pit to receive residential sewage waste arriving by tank trucks. Daily accumulated waste are to be pumped to a nearby waste water treatment facility to be re-consumed for agricultural and construction projects. A discrete-event simulation model using Arena Software was constructed to assist in defining the capacity of the system in cubic meters, number of tank trucks to use the system, number of unload docks required, number of standby areas needed and manpower required for data collection at entrance checkpoint and truck tank load toxicity testing. The results of the model are statistically validated. Simulation turned out to be an excellent tool in the facility planning effort for the pit project, as it insured smooth flow lines of tank trucks load discharge and best utilization of facilities on site.

Keywords: Discrete-event simulation, Facilities Planning, Layout, Pit, Sewage management.

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Authors: Anselm L. Schüle, Thomas Rollmann, Reiner Anderl

Abstract:

Within the collaborative research center 666 a new product development approach and the innovative manufacturing method of linear flow splitting are being developed. So far the design process is supported by 3D-CAD models utilizing User Defined Features in standard CAD-Systems. This paper now presents new functions for generating 3D-models of integral sheet metal products with bifurcations using Siemens PLM NX 6. The emphasis is placed on design and semi-automated insertion of User Defined Features. Therefore User Defined Features for both, linear flow splitting and its derivative linear bend splitting, were developed. In order to facilitate the modeling process, an application was developed that guides through the insertion process. Its usability and dialog layout adapt known standard features. The work presented here has significant implications on the quality, accurateness and efficiency of the product generation process of sheet metal products with higher order bifurcations.

Keywords: Linear Flow Splitting, CRC 666, User Defined Features.

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Authors: Hezlina Mohd Hashim, Abdul Mutalib Embong, Zullina H. Shaari

Abstract:

This study analyses the perceptions of secondary school students about the accounting profession in Malaysia. Fifty five form three and form four students who are taking accounting/commerce subjects were met. Individual-s perception data were collected through questionnaires. The results at the secondary school level suggest that the stereotypical negative image of the accountant ends, with students expressing the positive view of the work of an accountant. There were also gender differences in perceiving the accounting profession. Overall, the results of the study suggest that we are now in line in projecting positive and accurate perceptions of the accounting profession to secondary school students.

Keywords: Perceptions, secondary school students, accounting profession, Malaysia.

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Authors: Z. Nougrara

Abstract:

In this paper we propose a novel methodology for extracting a road network and its nodes from satellite images of Algeria country. This developed technique is a progress of our previous research works. It is founded on the information theory and the mathematical morphology; the information theory and the mathematical morphology are combined together to extract and link the road segments to form a road network and its nodes. We therefore have to define objects as sets of pixels and to study the shape of these objects and the relations that exist between them. In this approach, geometric and radiometric features of roads are integrated by a cost function and a set of selected points of a crossing road. Its performances were tested on satellite images of Algeria country.

Keywords: Satellite image, road network, nodes.

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Authors: Syukri Himran, Rustan Taraka, Anto Duma

Abstract:

The aim of the study is to improve the understanding of latent and sensible thermal energy storage within a paraffin wax media by an array of cylindrical tubes arranged both in in-line and staggered layouts. An analytical and experimental study is carried out in a horizontal shell-and-tube type system during melting process. Pertamina paraffin-wax was used as a phase change material (PCM), while the tubes are embedded in the PCM. From analytical study we can obtain the useful information in designing a thermal energy storage such as: the motion of interface, amount of material melted at any time in the process, and the heat storage characteristic during melting. The use of staggered tubes is proposed compared to in-line layout in a heat exchanger as thermal storage. The experimental study is used to verify the validity of the analytical predictions. From the comparisons, the analytical and experimental data are in a good agreement.

Keywords: Latent, sensible, paraffin-wax, thermal energy storage, conduction, natural convection.

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Authors: Guo-Ming Sung, Naga Raju Naik R.

Abstract:

Paper presents a low power, high speed, sense-amplifier based flip-flop (SAFF). The flip-flop’s power con-sumption and delay are greatly reduced by employing a new conditionally precharge sense-amplifier stage and a single-ended latch stage. Glitch-free and contention-free latch operation is achieved by using a conditional cut-off strategy. The design uses fewer transistors, has a lower clock load, and has a simple structure, all of which contribute to a near-zero setup time. When compared to previous flip-flop structures proposed for similar input/output conditions, this design’s performance and overall PDP have improved. The post layout simulation of the circuit uses 2.91µW of power and has a delay of 65.82 ps. Overall, the power-delay product has seen some enhancements. Cadence Virtuoso Designing tool with CMOS 90nm technology are used for all designs.

Keywords: high-speed, low-power, flip-flop, sense-amplifier

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Authors: A.R. Aswatha, T. Basavaraju, S. Sandeep Kumar

Abstract:

Timing driven physical design, synthesis, and optimization tools need efficient closed-form delay models for estimating the delay associated with each net in an integrated circuit (IC) design. The total number of nets in a modern IC design has increased dramatically and exceeded millions. Therefore efficient modeling of interconnection is needed for high speed IC-s. This paper presents closed–form expressions for RC and RLC interconnection trees in current mode signaling, which can be implemented in VLSI design tool. These analytical model expressions can be used for accurate calculation of delay after the design clock tree has been laid out and the design is fully routed. Evaluation of these analytical models is several orders of magnitude faster than simulation using SPICE.

Keywords: IC design, RC/RLC Interconnection, VLSI Systems.

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

Abstract:

The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial or non-inertial reference frame.

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