Search results for: Mechanical Properties

Authors: Siwar Fadhel, Imen Bahri, Man Zhang

Abstract:

The switched reluctance machine (SRM) has undeniable qualities in terms of low cost and mechanical robustness. However, its highly nonlinear character and its uncertain parameters justify the development of complicated controls. In this paper, authors present the design of a robust H-infinity current controller for an 8/6 SRM with taking into account the nonlinearity of the SRM and with rejection of disturbances. The electromagnetic torque is indirectly regulated through the current controller. To show the performances of this control, a robustness analysis is performed by comparing the H-infinity and PI controller simulation results. This comparison demonstrates better performances for the presented controller. The effectiveness and robustness of the presented controller are also demonstrated by experimental tests.

Keywords: Current regulation, experimentation, robust H-infinity control, switched reluctance machine.

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Authors: F. Yilmaz, Y. Saylan, A. Derazshamshir, S. Atay, A. Denizli

Abstract:

A quartz crystal microbalance (QCM) nanosensor was developed to detect lysozyme enzyme by functionalizing its gold surface with the attachment of poly(methacroyl-L-phenylalanine) (PMAPA) nanoparticles. PMAPA was chosen as a hydrophobic matrix. The hydrophobic nanoparticles were synthesized by micro-emulsion polymerization method. Hydrophobic QCM nanosensor was tested for real time detection of lysozyme enzyme from aqueous solution. The kinetic and affinity studies were determined by using lysozyme solutions with different concentrations. The responses related with mass (Δm) and frequency (Δf) shifts were used to evaluate adsorption properties. 

 

Keywords: HIC, lysozyme, nanosensor, QCM.

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Authors: Afshin Ahmadi Nadooshan

Abstract:

In this article, various models of surface tension force (CSF, CSS and PCIL) for interfacial flows have been applied to dynamic case and the results were compared. We studied the Kelvin- Helmholtz instabilities, which are produced by shear at the interface between two fluids with different physical properties. The velocity inlet is defined as a sinusoidal perturbation. When gravity and surface tension are taking into account, we observe the development of the Instability for a critic value of the difference of velocity of the both fluids. The VOF Model enables to simulate Kelvin-Helmholtz Instability as dynamic case.

Keywords: Interfacial flow, Incompressible flow, surface tension, Volume-Of-Fluid, Kelvin-Helmholtz.

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Authors: Neeraj K. Chasta

Abstract:

This paper presents an idea for analog current comparison which compares input signal and reference currents with high speed and accuracy. Proposed circuit utilizes amplification properties of common gate configuration, where voltage variations of input current are amplified and a compared output voltage is developed. Cascaded inverter stages are used to generate final CMOS compatible output voltage. Power consumption of circuit can be controlled by the applied gate bias voltage. The comparator is designed and studied at 180nm CMOS process technology for a supply voltage of 3V.

Keywords: Current Mode, Comparator, High Resolution, High Speed.

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Authors: Anamaria Bechir, Rodica Sirbu, Minodora Leca, Maria Maris, Dan Artenie Maris, Emilia Mihaela Cadar, Marius Maris

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This paper aims at presenting the biotechnology used to obtain collagen-based gels from shark (Squalus acanthias) and brill skin, marine fish growing in the Black Sea. Due to the structure of its micro-fibres, collagen can be considered a nanomaterial; in order to use collagen-based matrixes as biomaterial, rheological studies must be performed first, to state whether they are stable or not. For the triple-helix structure to remain stable within these gels at room or human body temperature, they must be stabilized by reticulation.

Keywords: Collagen, biotechnology, reticulation.

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Authors: Adedokun D. A., Ndambuki J. M., Salim R. W.

Abstract:

Due to urbanization, trees and plants which covered a great land mass of the earth and are an excellent carbon dioxide (CO2) absorber through photosynthesis are being replaced by several concrete based structures. It is therefore important to have these cement based structures absorb the large volume of carbon dioxide which the trees would have removed from the atmosphere during their useful lifespan. Hence the need for these cement based structures to be designed to serve other useful purposes in addition to shelter. This paper reviews the properties of Sodium carbonate and sugar as admixtures in concrete with respect to improving carbon sequestration in concrete.

Keywords: Carbon sequestration, Sodium carbonate, Sugar, concrete, Carbon dioxide.

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Authors: C. Perez, O. Reinoso, N. Garcia, J. M. Sabater, L. Gracia

Abstract:

For high-speed control of robots, a good knowledge of system modelling is necessary to obtain the desired bandwidth. In this paper, we present a cartesian robot with a pan/tilt unit in end-effector (5 dof). This robot is implemented with powerful direct drive AC induction machines. The dynamic model, parameter identification and model validation of the robot are studied (including actuators). This work considers the cartesian robot coupled and non linear (contrary to normal considerations for this type of robots). The mechanical and control architecture proposed in this paper is efficient for industrial and research application in which high speed, well known model and very high accuracy are required.

Keywords: Robot modelling, parameter identification and validation, AC servo-motors.

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Authors: Tetsuya Furukawa, Masahiro Kuzunishi

Abstract:

Collected data must be organized to be utilized efficiently, and hierarchical classification of data is efficient approach to organize data. When data is classified to multiple categories or annotated with a set of labels, users request multi-labeled data by giving a set of labels. There are several interpretations of the data expressed by a set of labels. This paper discusses which data is expressed by a set of labels by introducing orders for sets of labels and shows that there are four types of orders, which are characterized by whether the labels of expressed data includes every label of the given set of labels within the range of the set. Desirable properties of the orders, data is also expressed by the higher set of labels and different sets of labels express different data, are discussed for the orders.

Keywords: Classification Hierarchies, Multi-labeled Data, Multiple Classificaiton, Orders of Sets of Labels

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Authors: Weng Ian Ho, Seng Fat Wong

Abstract:

In recent years, Radio Frequency Identification (RFID) is followed with interest by many researches, especially for the purpose of indoor positioning as the innate properties of RFID are profitable for achieving it. A lot of algorithms or schemes are proposed to be used in the RFID-based positioning system, but most of them are lack of environmental consideration and it induces inaccuracy of application. In this research, a lot of algorithms and schemes of RFID indoor positioning are discussed to see whether effective or not on application, and some rules are summarized for achieving accurate positioning. On the other hand, a new term “Noise Factor" is involved to describe the signal loss between the target and the obstacle. As a result, experimental data can be obtained but not only simulation; and the performance of the positioning system can be expressed substantially.

Keywords: Indoor positioning, LANDMARC, noise factors, RFID.

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Authors: H. M. Nanjundaswamy, S. K. Nath, S. Ray

Abstract:

TiO₂ particles have been added in molten aluminium to result in aluminium based cast Al/Al₃Ti-Al₂O₃ composite, which has been added then to molten magnesium to synthesize magnesium based cast Mg-Al/Al₃Ti-Al₂O₃ composite. The nominal compositions in terms of Mg, Al, and TiO₂ contents in the magnesium based composites are Mg-9Al-0.6TiO₂, Mg-9Al-0.8TiO₂, Mg-9Al-1.0TiO₂ and Mg-9Al-1.2TiO₂ designated respectively as MA6T, MA8T, MA10T and MA12T. The microstructure of the cast magnesium based composite shows grayish rods of intermetallics Al₃Ti, inherited from aluminium based composite but these rods, on hot forging, breaks into smaller lengths decreasing the average aspect ratio (length to diameter) from 7.5 to 3.0. There are also cavities in between the broken segments of rods. β-phase in cast microstructure, Mg₁₇Al₁₂, dissolves during heating prior to forging and re-precipitates as relatively finer particles on cooling. The amount of β-phase also decreases on forging as segregation is removed. In both the cast and forged composite, the Brinell hardness increases rapidly with increasing addition of TiO₂ but the hardness is higher in forged composites by about 80 BHN. With addition of higher level of TiO₂ in magnesium based cast composite, yield strength decreases progressively but there is marginal increase in yield strength over that of the cast Mg-9 wt. pct. Al, designated as MA alloy. But the ultimate tensile strength (UTS) in the cast composites decreases with the increasing particle content indicating possibly an early initiation of crack in the brittle inter-dendritic region and their easy propagation through the interfaces of the particles. In forged composites, there is a significant improvement in both yield strength and UTS with increasing TiO₂ addition and also, over those observed in their cast counterpart, but at higher addition it decreases. It may also be noted that as in forged MA alloy, incomplete recovery of forging strain increases the strength of the matrix in the composites and the ductility decreases both in the forged alloy and the composites. Initiation fracture toughness, J_IC, decreases drastically in cast composites compared to that in MA alloy due to the presence of intermetallic Al₃Ti and Al₂O₃ particles in the composite. There is drastic reduction of J_IC on forging both in the alloy and the composites, possibly due to incomplete recovery of forging strain in both as well as breaking of Al₃Ti rods and the voids between the broken segments of Al₃Ti rods in composites. The ratio of tearing modulus to elastic modulus in cast composites show higher ratio, which increases with the increasing TiO₂ addition. The ratio decreases comparatively more on forging of cast MA alloy than those in forged composites.

Keywords: Composite, fracture toughness, forging, tensile properties.

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Authors: Nneka Osuchukwu, Leonid Shpanin

Abstract:

The concept of converting the kinetic energy of quadcopter propellers into electrical energy is considered in this contribution following the feasibility study of the propeller vibrations, theoretical energy conversion, and simulation techniques. Analysis of the propeller vibration performance is presented via graphical representation of calculated and simulated parameters, in order to demonstrate the possibility of recovering the harvested energy from the propeller vibrations of the quadcopter while the quadcopter is in operation. Consideration of using piezoelectric materials in such concept, converting the mechanical energy of the propeller into the electrical energy, is given. Photographic evidence of the propeller in operation is presented and discussed together with experimental results to validate the theoretical concept.

Keywords: Unmanned aerial vehicle, energy harvesting, piezoelectric material, propeller vibration.

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Authors: D. Liu, D. M. Donskoy

Abstract:

The vibroacoustic modulation method is based on the modulation effect of high-frequency ultrasonic wave (carrier) by low-frequency vibration in the presence of various defects, primarily contact-type such as cracks, delamination, etc. The presence and severity of the defect are measured by the ratio of the spectral sidebands and the carrier in the spectrum of the modulated signal. This approach, however, does not differentiate between amplitude and frequency modulations, AM and FM, respectfully. This paper is an attempt to explain the generation mechanisms of FM and its correlation with the flaw properties. Here we proposed two possible mechanisms leading to FM modulation based on nonlinear local defect resonance and dynamic acoustoelastic models.

Keywords: Non-destructive testing, nonlinear acoustics, structural health monitoring, acoustoelasticity, local defect resonance.

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Authors: M.Lanez, M.N.Oudjit, A.Bali

Abstract:

Reactive powder concretes (RPC) are characterized by particle diameter not exceeding 600 μm and having very high compressive and tensile strengths. This paper describes a new generation of micro concrete, which has an initial, as well as a final, high physicomechanical performance. To achieve this, we replaced the Portland cement (15% by weight) by materials rich in Silica (Slag and Dune Sand). The results obtained from tests carried out on RPC show that compressive and tensile strengths increase when adding the additions, thus improving the compactness of mixtures via filler and pozzolanic effect. With a reduction of the aggregate phase in the RPC and the abundance of dune sand (south Algeria) and slag (industrial byproduct of blast furnace), the use of the RPC will allow Algeria to fulfil economical as well as ecological requirements.

Keywords: High mechanical strength, Reactive Powder Concrete, rheology, superplasticizer, workability

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Authors: R. Uthayakumar, D. Easwaramoorthy

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The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

Keywords: Contraction, Iterated Function System, Hutchinson- Barnsley Operator, Intuitionistic Fuzzy Metric Space, Hausdorff Intuitionistic Fuzzy Metric.

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Authors: M. Ertas, A. C. Onel, G. Ekinci, B. Toydemir, S. Durdu, M. Usta, L. Colakerol Arslan

Abstract:

To develop AZ91D magnesium alloys with improved properties, we have applied TiN and VN/TiN multilayer coatings using DC magnetron sputter technique. Coating structure, surface morphology, chemical bonding and corrosion resistance of coatings were analyzed by x-ray diffraction (XRD), scanning electron microscope (SEM), x-ray photoelectron spectroscopy (XPS), and tafel extrapolation method, respectively. XPS analysis reveal that VN overlayer reacts with oxygen at the VN/TiN interface and forms more stable TiN layer. Morphological investigations and the corrosion results show that VN/TiN multilayer thin film coatings are quite effective to optimize the corrosion resistance of Mg alloys.

Keywords: AZ91D Mg alloys, High corrosion resistance, Transition metal nitride coatings, Magnetron sputter.

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Authors: George M. Nyori, Peter K’Obonyo

Abstract:

Over the past few decades, manufacturing has evolved from a more labor-intensive set of mechanical processes to a sophisticated set of information based technology processes. With the existence of various advanced manufacturing technologies (AMTs), more and more functions or jobs are performed by these machines instead of human labour. This study was undertaken in order to research the extent of AMTs adoption in manufacturing companies in Kenya. In order to investigate a survey was conducted via questionnaires that were sent to 183 selected AMT manufacturing companies in Kenya. 92 companies responded positively. All the surveyed companies were found to have a measure of investment in at least two of the 14 types of AMTs investigated. In general the company surveyed showed that the level of AMT adoption in Kenya is very low with investments levels at a mean of 2.057 and integration levels at a mean of 1.639 in a scale of 1-5.

Keywords: AMT adoption, AMT investments, AMT integration, companies in Kenya.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: Zeinab Jokar, Mohammad Reza Moslemi

Abstract:

In this work, we study the behavior of introducing atomic size vacancy in a graphene nanoribbon superlattice. Our investigations are based on the density functional theory (DFT) with the Local Density Approximation in Atomistix Toolkit (ATK). We show that, in addition to its shape, the position of vacancy has a major impact on the electrical properties of a graphene nanoribbon superlattice. We show that the band gap of an armchair graphene nanoribbon may be tuned by introducing an appropriate periodic pattern of vacancies. The band gap changes in a zig-zag manner similar to the variation of band gap of a graphene nanoribbon by changing its width.

Keywords: Antidot, Atomistix ToolKit, Superlattice, Vacancy.

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Authors: A. Sedky, E. El-Suheel

Abstract:

We report here structural, mechanical and I-V characteristics of Zn1-xMxO ceramic samples with various x and M. It is found that the considered dopants does not influence the wellknown peaks related to wurtzite structure of ZnO ceramics, while the shape and size of grains are clearly affected. Average crystalline diameters, deduced from XRD are between 42 nm and 54 nm, which are 70 times lower than those obtained from SEM micrographs. Interestingly, the potential barrier could be formed by adding Cu up to 0.20, and it is completely deformed by 0.025 Ni additions. The breakdown field could be enhanced up to 4138 V/cm by 0.025 Cu additions, followed by a decrease with further increase of Cu . On the other hand a gradual decrease in VHN is reported for both dopants and their values are higher in Ni samples as compared to Cu samples. The electrical conductivity is generally improved by Ni, while addition of Cu improved it only in the over doped region (≥ 0.10). These results are discussed in terms of the difference of valency and ferromagnetic ordering for both dopants as compared to undoped sample.

Keywords: Semiconductors, Chemical Synthesis, Impurities and Electronic Transport

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Authors: Zubair Ahmad, M. H. Sayyad, M. Yaseen, M. Ali

Abstract:

In this work, an organic compound 5,10,15,20- Tetrakis(3,5-di-tertbutylphenyl)porphyrinatocopper(II) (TDTBPPCu) is studied as an active material for thin film electronic devices. To investigate the electrical properties of TDTBPPCu, junction of TDTBPPCu with heavily doped n-Si and Al is fabricated. TDTBPPCu film was sandwiched between Al and n-Si electrodes. Various electrical parameters of TDTBPPCu are determined. The current-voltage characteristics of the junction are nonlinear, asymmetric and show rectification behavior, which gives the clue of formation of depletion region. This behavior indicates the potential of TDTBPPCu for electronics applications. The current-voltage and capacitance-voltage techniques are used to find the different electronic parameters.

Keywords: P-type, organic semiconductor, Electricalcharacteristics

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Authors: M. Bobojanov, D. Rismukhamedov, F. Tuychiev, Kh. Shamsutdinov

Abstract:

The article presents the results of experimental study of a two-speed asynchronous motor 4A80B6/4U3 with pole-changing winding on a fan drive VSUN 160x74-0.55-4 in static and dynamic modes. A prototype of a pole-changing Motor was made based on the results of the calculation and the performance and mechanical characteristics of the Motor were removed at the experimental stand, and useful capacities and other parameters from both poles were determined. In dynamic mode, the curves of changes of torque and current of the stator were removed by direct start, constant speed operation, by switching of speeds and stopping.

Keywords: Pole-changing winding, two speed asynchronous machine, basic scheme, winding factor, differential leakage factor.

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Authors: S. Desouky, A. Al sabagh , M. Betiha, A. Badawi, A. Ghanem, S. Khalil

Abstract:

Two Amphiphilic catalysts, iron (III) dodecylbenzene sulfonate and nickel (II) dodecylbenzene sulfonate, were synthesized and used in the catalytic aquathermolysis of heavy crude oil to reduce its viscosity. The prepared catalysts exhibited good performance in the aquathermolysis and the viscosity is reduced by ~ 78.9 % for Egyptian heavy crude oil. The chemical and physical properties of heavy oil both before and after reaction were investigated by FT-IR, dynamic viscosity, molecular weight and SARA analysis. The results indicated that the content of resin, asphaltene, average molecular weight and sulfur content of heavy oil is reduced after the catalytic aquathermolysis.

Keywords: Amphiphilic catalyst, Aquathermolysis, Heavy oil, Viscosity reduction.

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Authors: Seyed Abbas Tabatabaei

Abstract:

One of the important factors of cracks on the asphalt pavements is bitumen aging that associated with the loss of volatile components and oxidation of asphalt binder. This paper is about effect of Styrene-Butadiene-Styrene (SBS) polymer on asphalt aging In order to decrease asphalt aging effects. For this purpose samples of base bitumen and SBS modified bitumen aged according to the rolling thin film oven test (RTFOT) and pressure aging vessel (PAV), respectively. Properties of each sample were evaluated using Fourier Transform Infrared (FTIR) spectroscopy, n-heptane precipitation, viscosity test, softening point test and penetration test. FT-IR Analysis, showed lower oxidation of SBS modified bitumen than base bitumen, after aging.

Keywords: SBS, Asphalt aging, modified bitumen.

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Authors: A. Shishkin, A. Korjakins, V. Mironovs

Abstract:

Present paper describes method of obtaining clay ceramic foam (CCF) and foam concrete (FC), by direct foaming with high speed mixer-disperser (HSMD). Three foaming agents (FA) are compared for the FC and CCF production: SCHÄUMUNGSMITTEL W 53 FLÜSSIG (Zschimmer & Schwarz Gmbh, Germany), SCF- 1245 (Sika, test sample, Latvia) and FAB-12 (Elade, Latvija). CCF were obtained at 950, 1000°C, 1150°C and 1150°C firing temperature and have mechanical compressive strength 1.2, 2.55 and 4.3 MPa and porosity 79.4, 75.1, 71.6%, respectively. Obtained FC has 6-14 MPa compressive strength and porosity 44-55%. The goal of this work was development of a sustainable and durable ceramic cellular structures using HSMD.

Keywords: Ceramic foam, foam concrete, clay foam, open cell, close cell, direct foaming.

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Authors: O. Eisa, M. Shuhaimi

Abstract:

This paper presents a study on the thermodynamics and transport properties of hot potassium carbonate aqueous system (HPC) using electrolyte non-random two liquid, (ELECNRTL) model. The operation conditions are varied to determine the system liquid phase stability range at the standard and critical conditions. A case study involving 30 wt% K2CO3, H2O standard system at pressure of 1 bar and temperature range from 280.15 to 366.15 K has been studied. The estimated solubility index, viscosity, water activity, and density which obtained from the simulation showed a good agreement with the experimental work. Furthermore, the saturation temperature of the solution has been estimated.

Keywords: Viscosity, Saturation index, Activity coefficient, Density.

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Authors: B. G. Sampath, K. C. R. Perera, W. A. S. I. Wijesuriya, V. P. C. Dassanayake

Abstract:

In this paper the design, development and testing of a stabilizer control system for a Quad-rotor is presented which is focused on the maneuverability. The mechanical design is performed along with the design of the controlling algorithm which is devised using fuzzy logic controller. The inputs for the system are the angular positions and angular rates of the Quad-rotor relative to three axes. Then the output data is filtered from an accelerometer and a gyroscope through a Kalman filter. In the development of the stability controlling system Mandani fuzzy model is incorporated. The results prove that the fuzzy based stabilizer control system is superior in high dynamic disturbances compared to the traditional systems which use PID integrated stabilizer control systems.

Keywords: Fuzzy stabilizer, maneuverability, PID, Quad-rotor.

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Authors: Zhazgul Kelgenbaeva, Emil Omurzak, Saadat Sulaimankulova, Tsutomu Mashimo

Abstract:

Spherical shaped magnetite (Fe3O4) and Au@Fe3O4 nanoparticles were successfully synthesized from Fe electrodes immersed in water with CTAB surfactant and HAuCl4 solution using simple method-pulsed plasma in liquid, without the use of dopants or special conditions for stabilization. Vibrating sample magnetometer indicated ferromagnetic behavior of particles at room temperature with coercivity and saturation magnetization of (Hc=105 Oe, Ms=6.83 emu/g) for Fe3O4 and (Hc=175, Ms=3.56emu/g) for Au@Fe3O4 nanoparticles. Structure and morphology of nanoparticles were characterized by X-ray Diffraction analysis and HR-TEM measurements. The cytotoxicity of nanoparticles was indicated using a XTT assay to be very low (cell viability: 98-89% with Fe3O4 and 99-91% for Au@Fe3O4 NPs).

Keywords: Magnetite, Gold coated magnetite, Nanoparticles, Pulsed Plasma in Liquid, Cytotoxicity.

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Authors: A. Nuric, S. Nuric, L. Kricak, I. Lapandic, R. Husagic

Abstract:

This paper describes topic of computer simulation with regard to the ground movement above an underground mine. Simulation made with software package ADINA for nonlinear elastic-plastic analysis with finite elements method. The one of representative profiles from Mine 'Stara Jama' in Zenica has been investigated. A collection and selection of both geo-mechanical data and geometric parameters of the mine was necessary for performing these simulations. Results of estimation have been compared with measured values (vertical displacement of surface), and then simulation performed with assumed dynamic and dimensions of excavation, over a period of time. Results are presented with bitmaps and charts.

Keywords: Computer, finite element method, mine, nonlinear analysis, numerical modeling, simulation, subsidence.

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

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This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: Chaos, chaotic trajectories, differential mobile robot, Henons map, Khepera III robot, patrolling applications.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

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In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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