Search results for: analytical.

Authors: Hadi Farhadian, Homayoon Katibeh

Abstract:

In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occured in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: Water Seepage, Amirkabir Tunnel, Analytical Method, DEM, SGR.

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Authors: Jamal Amani Rad, Kourosh Parand

Abstract:

In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which have previously been applied. The results of homotopy perturbation method are of high accuracy and the method is very effective and succinct.

Keywords: Unsteady gas equation, Homotopy perturbation method(HPM), Porous medium, Nonlinear ODE

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Authors: Tao Nie, Weiqiang Liu

Abstract:

In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.

Keywords: variable separation method, analytical solution, rib, heat transfer

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Authors: M. Pasbani Khiavi, M. A. Ghorbani

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This paper presents an analytical solution to get a reliable estimation of the hydrodynamic pressure on gravity dams induced by vertical component earthquake when solving the fluid and dam interaction problem. Presented analytical technique is presented for calculation of earthquake-induced hydrodynamic pressure in the reservoir of gravity dams allowing for water compressibility and wave absorption at the reservoir bottom. This new analytical solution can take into account the effect of bottom material on seismic response of gravity dams. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.

Keywords: Dam, Reservoir, Analytical solution, Vertical component, Earthquake

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Authors: F. Djeffal, N. Lakhdar, T. Bendib

Abstract:

The study of the transport coefficients in electronic devices is currently carried out by analytical and empirical models. This study requires several simplifying assumptions, generally necessary to lead to analytical expressions in order to study the different characteristics of the electronic silicon-based devices. Further progress in the development, design and optimization of Silicon-based devices necessarily requires new theory and modeling tools. In our study, we use the PSO (Particle Swarm Optimization) technique as a computational tool to develop analytical approaches in order to study the transport phenomenon of the electron in crystalline silicon as function of temperature and doping concentration. Good agreement between our results and measured data has been found. The optimized analytical models can also be incorporated into the circuits simulators to study Si-based devices without impact on the computational time and data storage.

Keywords: Particle Swarm, electron mobility, Si-based devices, Optimization.

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Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

A camera in the building site is exposed to different weather conditions. Differences between images of the same scene captured with the same camera arise also due to temperature variations. The influence of temperature changes on camera parameters were modelled and integrated into existing analytical camera model. Modified camera model enables quantitatively assessing the influence of temperature variations.

Keywords: camera calibration, analytical model, intrinsic parameters, extrinsic parameters, temperature variations.

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Authors: Abuzar.Abazari, Saeed. Ziaei-Rad, Hoseein. Dalayeli

Abstract:

Collision is considered as a time-depended nonlinear dynamic phenomenon. The majority of researchers have focused on deriving the resultant damage of the ship collisions via analytical, experimental, and finite element methods.In this paper, first, the force-penetration curve of a head collision on a container ship with rigid barrier based on Yang and Pedersen-s methods for internal mechanic section is studied. Next, the obtained results from different analytical methods are compared with each others. Then, through a simulation of the container ship collision in Ansys Ls-Dyna, results from finite element approach are compared with analytical methods and the source of errors is discussed. Finally, the effects of parameters such as velocity, and angle of collision on the forcepenetration curve are investigated.

Keywords: Ship collision, Force-penetration curve, Damage

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Authors: Xiaoshu Lu, Martti Viljanen

Abstract:

A new analytical model is developed which provides close-formed solutions for both transient indoor and envelope temperature changes in buildings. Time-dependent boundary temperature is presented as Fourier series which can approximate real weather conditions. The final close-formed solutions are simple, concise, and comprehensive. The model was compared with numerical results and good accuracy was obtained. The model can be used as design and control guidelines in engineering applications for analysing mechanical heat transfer properties for buildings.

Keywords: Analytical model, heat transfer, whole building.

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Authors: Yin-Yann Chen

Abstract:

As the gradual increase of the enterprise scale, the firms may possess many manufacturing plants located in different places geographically. This change will result in the multi-site production planning problems under the environment of multiple plants or production resources. Our research proposes the structural framework to analyze the multi-site planning problems. The analytical framework is composed of six elements: multi-site conceptual model, product structure (bill of manufacturing), production strategy, manufacturing capability and characteristics, production planning constraints, and key performance indicators. As well as the discussion of these six ingredients, we also review related literatures in this paper to match our analytical framework. Finally we take a real-world practical example of a TFT-LCD manufacturer in Taiwan to explain our proposed analytical framework for the multi-site production planning problems.

Keywords: Multi-Site, Production Planning, Supply Chain, TFT-LCD.

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Authors: Mahesh Chudasama, Harit Raval

Abstract:

Conical sections and shells of metal plates manufactured by 3-roller conical bending process are widely used in the industries. The process is completed by first bending the metal plates statically and then dynamic roller bending sequentially. It is required to have an analytical model to get maximum bending force, for optimum design of the machine, for static bending stage. Analytical models assuming various stress conditions are considered and these analytical models are compared considering various parameters and reported in this paper. It is concluded from the study that for higher bottom roller inclination, the shear stress affects greatly to the static bending force whereas for lower bottom roller inclination it can be neglected.

Keywords: Roller-bending, static-bending, stress-conditions, analytical-modeling.

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Authors: Takao Sakakura, Kazunori Fujimoto

Abstract:

This paper proposes an analytical method for the dynamics of generating firms- alliance networks along with business phases. Dynamics in network developments have previously been discussed in the research areas of organizational strategy rather than in the areas of regional cluster, where the static properties of the networks are often discussed. The analytical method introduces the concept of business phases into innovation processes and uses relationships called prior experiences; this idea was developed in organizational strategy to investigate the state of networks from the viewpoints of tradeoffs between link stabilization and node exploration. This paper also discusses the results of the analytical method using five cases of the network developments of firms. The idea of Embeddedness helps interpret the backgrounds of the analytical results. The analytical method is useful for policymakers of regional clusters to establish concrete evaluation targets and a viewpoint for comparisons of policy programs.

Keywords: Regional Clusters, Alliance Networks, Innovation Processes, Prior Experiences, Embeddedness.

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Authors: M. Abouelatta, A. Shaker, M. El-Banna, G. T. Sayah, C. Gontrand, A. Zekry

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In this paper, a methodology for physically modeling the intrinsic MOS part and the drift region of the n-channel Laterally Double-diffused MOSFET (LDMOS) is presented. The basic physical effects like velocity saturation, mobility reduction, and nonuniform impurity concentration in the channel are taken into consideration. The analytical model is implemented using MATLAB. A comparison of the simulations from technology computer aided design (TCAD) and that from the proposed analytical model, at room temperature, shows a satisfactory accuracy which is less than 5% for the whole voltage domain.

Keywords: LDMOS, MATLAB, RESURF, modeling, TCAD.

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

Abstract:

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: Bonded rubber, quasi-static test, shape factor, apparent Young’s modulus.

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Authors: Adel Bettayeb, Robert Kaczmarek, Jean-Claude Vannier

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In this paper, we analyze the rotor eddy currents losses provoqued by the stator slot harmonics developed in the permanent magnets or pole pieces of synchronous machines. An analytical approach is presented to evaluate the effect of slot ripples on rotor field and losses calculation. This analysis is then tested on a model by 2D/3D finite element (FE) calculation. The results show a good agreement on loss calculations when skin effect is negligible and the magnet is considered.

Keywords: Analytical modeling, Eddy-currents, Finite-elementmethods, Power losses, Slot harmonics effect.

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Authors: Thassanant Unnanantn, Suttipong Boonphadung

Abstract:

This research study aimed to survey and analyze the attitudes of pre-service teachers’ the analytical thinking development based on Miller’s Model. The informants of this study were 22 third year teacher students majoring in Thai. The course where the instruction was conducted was English for Academic Purposes in Thai Language 2. The instrument of this research was an open-ended questionnaire with two dimensions of questions: academic and satisfaction dimensions. The investigation revealed the positive attitudes. In the academic dimension, the majority of 12 (54.54%), the highest percentage, reflected that the method of teaching analytical thinking and language simultaneously was their new knowledge and the similar percentage also belonged to text cohesion in writing. For the satisfaction, the highest frequency count was from 17 of them (77.27%) and this majority favored the openness or friendliness of the teacher.

Keywords: Analytical thinking development, Attitudes, Miller’s Model, Pre-service teachers.

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Authors: S. Daneshmand, C. Aghanajafi, A. Bahrami

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In this paper the supersonic ejectors are experimentally and analytically studied. Ejector is a device that uses the energy of a fluid to move another fluid. This device works like a vacuum pump without usage of piston, rotor or any other moving component. An ejector contains an active nozzle, a passive nozzle, a mixing chamber and a diffuser. Since the fluid viscosity is large, and the flow is turbulent and three dimensional in the mixing chamber, the numerical methods consume long time and high cost to analyze the flow in ejectors. Therefore this paper presents a simple analytical method that is based on the precise governing equations in fluid mechanics. According to achieved analytical relations, a computer code has been prepared to analyze the flow in different components of the ejector. An experiment has been performed in supersonic regime 1.5Keywords: Ejector, Wind Tunnel, Supersonic, Diffuser, Machnumber, Mixing Chamber

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Authors: T. Zitoun, M. Bouhadef

Abstract:

When a partially or completely immersed solid moves in a liquid such as water, it undergoes a force called hydrodynamic drag. Reducing this force has always been the objective of hydrodynamic engineers to make water slide better on submerged bodies. This paper deals with the examination of the different terms composing the analytical solution of the flow over an obstacle embedded at the bottom of a hydraulic channel. We have chosen to use a linear method to study a two-dimensional flow over an obstacle, in order to understand the evolution of the drag. We set the following assumptions: incompressible inviscid fluid, irrotational flow, low obstacle height compared to the water height. Those assumptions allow overcoming the difficulties associated with modelling these waves. We will mathematically formulate the equations that allow the determination of the stream function, and then the free surface equation. A similar method is used to determine the exact analytical solution for an obstacle in the shape of a sinusoidal arch.

Keywords: Free-surface wave, inviscid fluid, analytical solution, hydraulic channel.

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Authors: Syukri Himran, Rustan Taraka, Anto Duma

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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: Mahesh Chudasama, Harit Raval

Abstract:

Conical sections and shells made from metal plates are widely used in various industrial applications. 3-roller conical bending process is preferably used to produce such conical sections and shells. Bending mechanics involved in the process is complex and little work is done in this area. In the present paper an analytical model is developed to predict bending force which will be acting during 3-roller conical bending process. To verify the developed model, conical bending experiments are performed. Analytical results and experimental results were compared. Force predicted by analytical model is in close proximity of the experimental results. The error in the prediction is ±10%. Hence the model gives quite satisfactory results. Present model is also compared with the previously published bending force prediction model and it is found that the present model gives better results. The developed model can be used to estimate the bending force during 3-roller bending process and can be useful to the designers for designing the 3-roller conical bending machine.

Keywords: Bending-force, Experimental-verification, Internal-moment, Roll-bending.

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Authors: Priyanka Malik A, Rishu Chaujar B, Mridula Gupta C, R.S. Gupta D

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In this paper, for the first time, a two-dimensional (2D) analytical drain current model for sub-100 nm multi-layered gate material engineered trapezoidal recessed channel (MLGMETRC) MOSFET: a novel design is presented and investigated using ATLAS and DEVEDIT device simulators, to mitigate the large gate leakages and increased standby power consumption that arise due to continued scaling of SiO2-based gate dielectrics. The twodimensional (2D) analytical model based on solution of Poisson-s equation in cylindrical coordinates, utilizing the cylindrical approximation, has been developed which evaluate the surface potential, electric field, drain current, switching metric: ION/IOFF ratio and transconductance for the proposed design. A good agreement between the model predictions and device simulation results is obtained, verifying the accuracy of the proposed analytical model.

Keywords: ATLAS, DEVEDIT, NJD, MLGME- TRCMOSFET.

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Authors: Loke Kean Koay, Horizon Gitano-Briggs, Mani Maran Ratnam

Abstract:

Today air-core coils (ACC) are a viable alternative to ferrite-core coils in a range of applications due to their low induction effect. An analytical study was carried out and the results were used as a guide to understand the relationship between the magnet-coil distance and the resulting attractive magnetic force. Four different ACC models were fabricated for experimental study. The variation in the models included the dimensions, the number of coil turns and the current supply to the coil. Comparison between the analytical and experimental results for all the models shows an average discrepancy of less than 10%. An optimized ACC design was selected for the scanner which can provide maximum magnetic force.

Keywords: Air-Core Coils, Electromagnetic, Linear Optical Scanner

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Authors: Mahesh K. Chudasama, Harit K. Raval

Abstract:

3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: Analytical modeling, cone frustum, dynamic bending, static bending.

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Authors: Ashwani K. Rana, Narottam Chand, Vinod Kapoor

Abstract:

This paper presents a new compact analytical model of the gate leakage current in high-k based nano scale MOSFET by assuming a two-step inelastic trap-assisted tunneling (ITAT) process as the conduction mechanism. This model is based on an inelastic trap-assisted tunneling (ITAT) mechanism combined with a semiempirical gate leakage current formulation in the BSIM 4 model. The gate tunneling currents have been calculated as a function of gate voltage for different gate dielectrics structures such as HfO2, Al2O3 and Si3N4 with EOT (equivalent oxide thickness) of 1.0 nm. The proposed model is compared and contrasted with santaurus simulation results to verify the accuracy of the model and excellent agreement is found between the analytical and simulated data. It is observed that proposed analytical model is suitable for different highk gate dielectrics simply by adjusting two fitting parameters. It was also shown that gate leakages reduced with the introduction of high-k gate dielectric in place of SiO2.

Keywords: Analytical model, High-k gate dielectrics, inelastic trap assisted tunneling, metal–oxide–semiconductor (MOS) devices.

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Authors: R. Noori, F. Feizi, M.R. Jafari

Abstract:

Khatunabad area is situated geologically in Urmieh- Dokhtar magmatic belt in NW of Iran. In this research, studied area has been investigated in order to recognize the potential copper and molybdenum-bearing target areas. The survey layers include the lithologic units, alteration, geochemical result, tectonics and copper and molybdenum occurrence. As an accurate decision can have a considerable effect on exploration plans, so in this efforts have been made to make use of new combination method. For this purpose, the analytical hierarchy process was used and revealed highly potential copper and molybdenum mineralization areas. Based on achieved results, geological perspective in north of studied area is appropriate for advance stage, especially for subsurface exploration in future.

Keywords: Analytical hierarchy process, Potential targets, Khatunabad, Iran

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

Abstract:

This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: Analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges.

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Authors: Abolfazl Hosseinkhani, Sepehr Sanaye

Abstract:

Different approaches have been used to predict the performance of the vertical axis wind turbines (VAWT), such as experimental, computational fluid dynamics (CFD), and analytical methods. Analytical methods, such as momentum models that use streamtubes, have low computational cost and sufficient accuracy. The double multiple streamtube (DMST) is one of the most commonly used of momentum models, which divide the rotor plane of VAWT into upwind and downwind. In fact, results from the DMST method have shown some discrepancy compared with experiment results; that is because the Darrieus turbine is a complex and aerodynamically unsteady configuration. In this study, analytical-experimental-based corrections, including dynamic stall, streamtube expansion, and finite blade length correction are used to improve the DMST method. Results indicated that using these corrections for a SANDIA 17-m VAWT will lead to improving the results of DMST.

Keywords: Vertical axis wind turbine, analytical, double multiple streamtube, streamtube expansion model, dynamic stall model, finite blade length correction.

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Authors: M. Tohidi, J. Yang, C. Baniotopoulos

Abstract:

Progressive collapse of buildings typically occurs  when abnormal loading conditions cause local damages, which leads  to a chain reaction of failure and ultimately catastrophic collapse. The  tie force (TF) method is one of the main design approaches for  progressive collapse. As the TF method is a simplified method, further  investigations on the reliability of the method is necessary. This study  aims to develop an improved TF method to design the cross wall  structures for progressive collapse. To this end, the pullout behavior of  strands in grout was firstly analyzed; and then, by considering the tie  force-slip relationship in the friction stage together with the catenary  action mechanism, a comprehensive analytical method was developed.  The reliability of this approach is verified by the experimental results  of concrete block pullout tests and full scale floor-to-floor joints tests  undertaken by Portland Cement Association (PCA). Discrepancies in  the tie force between the analytical results and codified specifications  have suggested the deficiency of TF method, hence an improved  model based on the analytical results has been proposed to address this  concern.

 

Keywords: Cross wall, progressive collapse, ties force method, catenary, analytical.

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Authors: P. Phenpun, S. Wareewan

Abstract:

This qualitative study aimed to describe the opinions in relation to humanized care emerging from the volunteer activities of nursing students at Boromarajonani College of Nursing, Chonburi, Thailand. One hundred and twenty-seven second-year nursing students participated in this study. The volunteer activity model was composed of preparation, implementation, and evaluation through a learning log, in which students were encouraged to write their daily activities after completing practical training at the healthcare center. The preparation content included three main categories: service minded, analytical thinking, and client participation. The preparation process took over three days that accumulates up to 20 hours only. The implementation process was held over 10 days, but with a total of 70 hours only, with participants taking part in volunteer work activities at a healthcare center. A learning log was used for evaluation and data were analyzed using content analysis. The findings were as follows. With service minded, there were two subcategories that emerged from volunteer activities, which were service minded towards patients and within themselves. There were three categories under service minded towards patients, which were rapport, compassion, and empathy service behaviors, and there were four categories under service minded within themselves, which were self-esteem, self-value, management potential, and preparedness in providing good healthcare services. In line with analytical thinking, there were two components of analytical thinking, which were analytical skill for their works and analytical thinking for themselves. There were four subcategories under analytical thinking for their works, which were evidence based thinking, real situational thinking, cause analysis thinking, and systematic thinking, respectively. There were four subcategories under analytical thinking for themselves, which were comparative between themselves, towards their clients that leads to the changing of their service behaviors, open-minded thinking, modernized thinking, and verifying both verbal and non-verbal cues. Lastly, there were three categories under participation, which were mutual rapport relationship; reconsidering client’s needs services and providing useful health care information.

Keywords: Humanized care service, volunteer activity, nursing student, and learning log.

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Authors: Omar D. Mohammed, Matti Rantatalo, Uday Kumar

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In this paper an analytical crack propagation scenario is proposed which assumes that a crack propagates in the tooth root in both the crack depth direction and the tooth width direction, and which is more reasonable and realistic for non-uniform load distribution cases than the other presented scenarios. An analytical approach is used for quantifying the loss of time-varying gear mesh stiffness with the presence of crack propagation in the gear tooth root. The proposed crack propagation scenario can be applied for crack propagation modelling and monitoring simulation, but further research is required for comparison and evaluation of all the presented crack propagation scenarios from the condition monitoring point of view.

Keywords: Crack propagation, Gear tooth crack, Time varying gear mesh stiffness.

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Authors: Mark Watson, J.-F. Bousquet, Adam Forget

Abstract:

A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell’s equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coils may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.

Keywords: Magnetic Induction, FDTD, Underwater Communication, Sommerfeld.

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