Search results for: Mass entrainment

Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

Abstract:

Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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Authors: N. Zaki Alamdari, M. Banihashemi, A. Mirghasemi

Abstract:

To estimate the risks of dam failure phenomenon, it is necessary to understand this phenomenon and the involved governing factors. Overtopping and piping are the two main reasons of earthdam failures. In the piping context, the piping is determined as a phenomenon which is occurred between two phases, the water liquid and the solid soil. In this investigation, the onset of piping and its development, as well as the movement of water in soil, are numerically approached. In this regard, a one-dimensional numerical model based on the mass-conserving finite-volume method is developed and applied in order to simulate the piping phenomenon in a continuous circular tunnel of given initial length and radius, located between upstream and downstream. The simulation result includes the time-variations of radius along the tunnel until the radius value reaches its critical and the piping phenomenon converts to overtopping.

Keywords: Earth dam, dam break, piping, internal erosion

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Authors: A. Naceri, M. Chikouche Hamina, P. Grosseau

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The effect of artificial pozzolan (waste brick) on the physico-chemical properties of cement manufactured was investigated. The waste brick is generated by the manufacture of bricks. It was used in the proportions of 0%, 5%, 10%, 15% and 20% by mass of cement to study its effect on the physico-chemical properties of cement incorporating artificial pozzolan. The physicochemical properties of cement at anhydrous state and the hydrated state (chemical composition, specific weight, fineness, consistency of the cement paste and setting times) were studied. The experimental results obtained show that the quantity of pozzolanic admixture (waste brick) of cement manufactured is the principal parameter who influences on the variation of the physico-chemical properties of the cement tested.

Keywords: Artificial pozzolan, waste brick, cement, physicochemicalcharacteristics.

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Authors: Antônio P. de Araújo Neto, Ruy D. A. da Silva Neto, Juliana R. de Souza, Salete K. P. de Medeiros, João T. N. de Medeiros

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The tribological test with Pin-On-Disc configuration measures friction and wear properties in dry or lubricated sliding surfaces of a variety of materials and coatings. Polymeric matrix composites loaded with mineral filler were used, 1%, 3%, 10%, 30%, and 50% mass percentage of filler, to reduce the material cost by using mineral tailings. Using a pin-on-disc tribometer to quantify coefficient of friction and wear resistance of the specimens. The parameters known to performing the test were 300 rpm rotation, normal load of 16N and duration of 33.5 minutes. The composite with 10% mineral filler performed better, considering that the wear resistance was good when compared to the other compositions and an average low coefficient of friction, in the order of μ ≤ 0.15.

Keywords: Microcomposites, microparticles tailings of scheelite, PTFE, tribology.

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Authors: Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin

Abstract:

This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

Keywords: Finite element method, free convection, Hartmann number, square cavity.

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Authors: Y. L. Yung, Kong Mun Lo

Abstract:

In this study, solid phase micro-extraction (SPME) was optimized to improve the sensitivity and accuracy in formaldehyde determination for plywood panels. Further work has been carried out to compare the newly developed technique with existing method which reacts formaldehyde collected in desiccators with acetyl acetone reagent (DC-AA). In SPME, formaldehyde was first derivatized with O-(2,3,4,5,6 pentafluorobenzyl)-hydroxylamine hydrochloride (PFBHA) and analysis was then performed by gas chromatography in combination with mass spectrometry (GC-MS). SPME data subjected to various wood species gave satisfactory results, with relative standard deviations (RSDs) obtained in the range of 3.1-10.3%. It was also well correlated with DC values, giving a correlation coefficient, RSQ, of 0.959. The quantitative analysis of formaldehyde by SPME was an alternative in wood industry with great potential

Keywords: Formaldehyde, GCMS, Plywood and SPME

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Authors: A. Almuwallad

Abstract:

The magnetoplasmadynamic (MPD) thruster is classified as an electric propulsion system and consists of two metal electrodes separated by an insulator. A high-current electric arc is driven between electrodes to ionize the injected propellant between electrodes for plasma creation. At the same time, a magnetic field is generated by the electric current returning to the power supply. This magnetic field interacts with the electric current flowing through the plasma to produce thrust. This paper compares the performance of MPD thrusters when using three different propellants (methane, nitrogen, and propane) at varying input mass flow rates. Methane provided the best performance, and nitrogen performed better than propane. In addition, when using the same parameters, the thruster with a divergent nozzle performed better than the thruster with a constant nozzle.

Keywords: Magnetoplasmadynamic thruster, electric propulsion, propellant, plasma.

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Authors: Bo Yang, Christopher Monterola

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Urban intersection control without the use of the traffic light has the potential to vastly improve the efficiency of the urban traffic flow. For most proposals in the literature, such lightless intersection control depends on the mass market commercialization of highly intelligent autonomous vehicles (AV), which limits the prospects of near future implementation. We present an efficient lightless intersection traffic control scheme that only requires Level 1 AV as defined by NHTSA. The technological barriers of such lightless intersection control are thus very low. Our algorithm can also accommodate a mixture of AVs and conventional vehicles. We also carry out large scale numerical analysis to illustrate the feasibility, safety and robustness, comfort level, and control efficiency of our intersection control scheme.

Keywords: Intersection control, autonomous vehicles, traffic modelling, intelligent transport system.

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Authors: K. Yılmaz, B. Birol, M. N. Sarıdede, E. Yiğit

Abstract:

A bauxite ore can be utilized in Bayer Process, if the mass ratio of Al2O3 to SiO2 is greater than 10. Otherwise, its FexOy and SiO2 content should be removed. On the other hand, removal of TiO2 from the bauxite ore would be beneficial because of both lowering the red mud residue and obtaining a valuable raw material containing TiO2 mineral. In this study, the low grade diasporic bauxite ore of Yalvaç, Isparta, Turkey was roasted under reducing atmosphere and subjected to magnetic separation. According to the experimental results, 800°C for reduction temperature and 20000 Gauss of magnetic intensity were found to be the optimum parameters for removal of iron oxide and rutile from the nonmagnetic ore. On the other hand, 600°C and 5000 Gauss were determined to be the optimum parameters for removal of silica from the non-magnetic ore.

Keywords: Low grade diasporic bauxite, magnetic separation, reduction roasting, separation index.

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Authors: Azam Marjani, Saeed Shirazian

Abstract:

In this study is presented a general methodology to predict the performance of a continuous near-critical fluid extraction process to remove compounds from aqueous solutions using hollow fiber membrane contactors. A comprehensive 2D mathematical model was developed to study Porocritical extraction process. The system studied in this work is a membrane based extractor of ethanol and acetone from aqueous solutions using near-critical CO2. Predictions of extraction percentages obtained by simulations have been compared to the experimental values reported by Bothun et al. [5]. Simulations of extraction percentage of ethanol and acetone show an average difference of 9.3% and 6.5% with the experimental data, respectively. More accurate predictions of the extraction of acetone could be explained by a better estimation of the transport properties in the aqueous phase that controls the extraction of this solute.

Keywords: Solvent extraction, Membrane, Mass transfer, Densegas, Modeling

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Authors: Yan Rongxin, Sun Wei, Li Weidan

Abstract:

Based on the acoustics cascade sound theory, the mechanism of air leak sound producing, transmitting and signal detecting has been analyzed. A formula of the sound power, leak size and air pressure in the spacecraft has been built, and the relationship between leak sound pressure and receiving direction and distance has been studied. The center frequency in millimeter diameter leak is more than 20 kHz. The situation of air leaking from spacecraft to space has been simulated and an experiment of different leak size and testing distance and direction has been done. The sound pressure is in direct proportion to the cosine of the angle of leak to sensor. The portable ultrasonic leak detector has been developed, whose minimal leak rate is 10^-1 Pa·m³/s, the testing radius is longer than 20 mm, the mass is less than 1.0 kg, and the electric power is less than 2.2 W.

Keywords: Leak detection, manned spacecraft, ultrasonic, sound transmitting.

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Authors: H. Al-Baghli

Abstract:

In this investigation, rubberized HMA technology was examined to address the most critical forms of pavement distresses in the State of Kuwait, namely, high temperature rutting, and moisture induced raveling. PelletPAVE™ additive was selected as the preferred technology, since it offered a convenient method of directly modifying the exiting local HMA recipe without having to polymer modify the bitumen. Experimental work, using various Pelletpave contents was carried out at Kuwait Institute for Scientific Research (KISR) to design an optimum rubberized HMA formulation prior to conducting a pilot-scale road trial. With the aid of a gyratory compactor, the compaction and volumetric properties of HMAs containing 2.5% and 3.0% Pelletpave additive were investigated at a range of bitumen contents, all by mass of total mix.

Keywords: Modified bitumen, rubberized hot mix asphalt, gyratory compaction, volumetric properties.

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Authors: FiroozBakhtiari-Nejad, Hamidreza Rostami, MeysamMirzaee, Mona Zandbaf

Abstract:

Dynamic tests are an important step of the design of engineering structures, because the accuracy of predictions of theoretical–numerical procedures can be assessed. In experimental test of moving loads that is one of the major research topics, the load is modeled as a simple moving mass or a small vehicle. This paper deals with the applicability of Non-contact Moving Load (NML) for vibration analysis. For this purpose, an experimental set-up is designed to generate the different types of NML including constant and harmonic. The proposed method relies on pressurized air which is useful, especially when dealing with fragile or sensitive structures. To demonstrate the performance of this system, the set-up is employedfor a modal analysis of a beam and detecting crack of the beam.The obtained results indicate that the experimental set-up for NML can be an attractive alternative to the moving load problems.

Keywords: Experimental analysis, Moving load, Non-contact excitation.

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Authors: M. Ayazi, R. Karami, B. Kamkari

Abstract:

Solid oxide fuel cells have been considered in the last years as one of the most promising technologies for very highefficiency electric energy generation from hydrogen or other hydrocarbons, both with simple fuel cell plants and with integrated gas turbine-fuel cell systems. In the present study, a detailed thermodynamic analysis has been carried out. Mass and exergy balances are performed not only for the whole plant but also for each component in order to evaluate the thermal efficiency of combined cycle. Moreover, different sources of irreversibilities within the SOFC stack have been discussed and a parametric study conducted to evaluate the effect of temperature as well as pressure on SOFC irreversibilities and its performance. In this investigation methane and hydrogen have been used for fueling the SOFC stack and combustion chamber.

Keywords: SOFC, Energy, Power turbine, Irreversibility.

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Authors: Mehran Pourgholi , Amin Lotfi Eghlim

Abstract:

These Nowadays the explosion of bombs or explosive materials such as gas and oil near or inside the buildings cause some losses in installations and building components. This has made the engineers to make the buildings and their components resistance against the effects of explosion. These activities lead to provide regulations and different methods. The above regulations are mostly focused on the explosion effects resulting from the vehicles around the buildings. Therefore, the explosion resulting from the vehicles outside the buildings will be studied in this research. In the present study, the main goals are to investigate the explosion load effects on the structures located on the piles with the specific quantity of plasticity and observing the permissible response of these structures. The concentrated mass system and the spring with two degree of freedom will be used to study the structural system.

Keywords: Concrete-Framework Building, Explosion Load, piles.

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Authors: Kyoung Hoon Kim

Abstract:

The absorption power generation cycle based on the ammonia-water mixture has attracted much attention for efficient recovery of low-grade energy sources. In this paper a thermodynamic performance analysis is carried out for a Kalina cycle using ammonia-water mixture as a working fluid for efficient conversion of low-temperature heat source in the form of sensible energy. The effects of the source temperature on the system performance are extensively investigated by using the thermodynamic models. The results show that the source temperature as well as the ammonia mass fraction affects greatly on the thermodynamic performance of the cycle.

Keywords: Ammonia-water mixture, Kalina cycle, low-grade heat source, source temperature.

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Authors: Mixed Frequency Excitation of an Electrostatically Actuated Resonator

Abstract:

We investigate experimentally and theoretically the dynamics of a capacitive resonator under mixed frequency excitation of two AC harmonic signals. The resonator is composed of a proof mass suspended by two cantilever beams. Experimental measurements are conducted using a laser Doppler Vibrometer to reveal the interesting dynamics of the system when subjected to twosource excitation. A nonlinear single-degree-of-freedom model is used for the theoretical investigation. The results reveal combination resonances of additive and subtractive type, which are shown to be promising to increase the bandwidth of the resonator near primary resonance frequency. Our results also demonstrate the ability to shift the combination resonances to much lower or much higher frequency ranges. We also demonstrate the dynamic pull-in instability under mixed frequency excitation.

Keywords: Nonlinear electrostatically actuated resonator.

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Authors: Martin Kendra, Jaroslav Mašek, Juraj Čamaj, Matej Babin

Abstract:

The railway transport is considered as a one of the most environmentally friendly mode of transport. With future prediction of increasing of freight transport there are lines facing problems with demanded capacity. Increase of the track capacity could be achieved by infrastructure constructive adjustments. The contribution shows how the travel time can be minimized and the track capacity increased by changing some of the basic infrastructure and operation parameters, for example, the minimal curve radius of the track, the number of tracks, or the usable track length at stations. Calculation of the necessary parameter changes is based on the fundamental physical laws applied to the train movement, and calculation of the occupation time is dependent on the changes of controlling the traffic between the stations.

Keywords: Curve radius, maximum curve speed, track mass capacity, reconstruction.

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Authors: Saleem Z. Ramadan

Abstract:

The material selection problem is concerned with the determination of the right material for a certain product to optimize certain performance indices in that product such as mass, energy density, and power-to-weight ratio. This paper is concerned about optimizing the selection of the manufacturing process along with the material used in the product under performance indices and availability constraints. In this paper, the material selection problem is formulated using binary programming and solved by genetic algorithm. The objective function of the model is to minimize the total manufacturing cost under performance indices and material and manufacturing process availability constraints.

Keywords: Optimization, Material selection, Process selection, Genetic algorithm.

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Authors: Ji-il Park, Donghan Koo, Hyungtae Seo, Jihyuk Park, Heewon Park, Sukyung Park, Kyung-Soo Kim, and Soohyun Kim

Abstract:

In the paper, the energetic features of the loaded gait are newly analyzed depending on the trunk flexion change. To investigate the loaded gait, walking experiments are performed for five subjects and, the ground reaction forces and kinematic data are measured. Based on these information, we compute the impulse, momentum and mechanical works done on the center of body mass, through the trunk flexion change. As a result, it is shown that the trunk flexion change does not affect the impulses and momentums during the step-to-step transition as well. However, the direction of the pre-collision momentum does change depending on the trunk flexion change, which is degenerated just after (or during) the collision period.

Keywords: Loaded gait, collision, impulse, gravity, heel strike, push-off, gait analysis.

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Authors: M. Adamski, J. Cwiklak

Abstract:

The contemporary battlefield creates a demand for more costly and highly advanced munitions. Training personnel responsible for operations as well as immediate execution of combat tasks which engage real asset is unrealistic and economically not feasible. Owing to a wide array of exploited simulators and various types of imitators, it is possible to reduce the costs. One of the effective elements of training, which can be applied in the training of all service branches, is imitator of aerial targets. This research serves as an introduction to the commencement of design analysis over a real aerial target imitator. Within the project, the basic aerodynamic calculations were made, which enabled to determine its geometry, design layout, performance as well as mass balance of individual components. The conducted calculations of the parameters of flight characteristics come closer to the real performance of such Unmanned Aerial Vehicles.

Keywords: Aerial target, aerodynamics, imitator, performance.

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Authors: H. Aminfar, M. Mohammadpourfard, K. Khajeh

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This paper has focused on the most important parameters in the LSC uptake; inlet Re number and Sc number in the presence of non-uniform magnetic field. The magnetic field is arising from the thin wire with electric current placed vertically to the arterial blood vessel. According to the results of this study, applying magnetic field can be a treatment for atherosclerosis by reducing LSC along the vessel wall. Homogeneous porous layer as a arterial wall has been regarded. Blood flow has been considered laminar and incompressible containing Ferro fluid (blood and 4 % vol. Fe₃O₄) under steady state conditions. Numerical solution of governing equations was obtained by using the single-phase model and control volume technique for flow field.

Keywords: LDL Surface Concentration (LSC), Magnetic field, Computational fluid dynamics, Porous wall.

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Authors: Buntheng Chhorn, WooYoung Jung

Abstract:

Large-scale swing has been used in entertainment and performance, especially in circus, for a very long time. To increase the safety of this type of structure, a thorough analysis for displacement and bearing stress was performed for an extreme condition where a full cycle swing occurs. Different masses, ranging from 40 kg to 220 kg, and velocities were applied on the swing. Then, based on the solution of differential dynamics equation, swing velocity response to harmonic force was obtained. Moreover, the resistance capacity was estimated based on ACI steel structure design guide. Subsequently, numerical analysis was performed in ABAQUS to obtain the stress on each frame of the swing. Finally, the analysis shows that the expansion of swing structure frame section was required for mass bigger than 150kg.

Keywords: Swing structure, displacement, bearing stress, dynamic loads response, finite element analysis.

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Authors: A. M. Maqableh

Abstract:

Modelling techniques for a fluid coupling taken from published literature have been extended to include the effects of the filling and emptying of the coupling with oil and the variation in losses when the coupling is partially full. In the model, the fluid flow inside the coupling is considered to have two principal velocity components; one circumferentially about the coupling axis (centrifugal head) and the other representing the secondary vortex within the coupling itself (vortex head). The calculation of liquid mass flow rate circulating between the two halves of the coupling is based on: the assumption of a linear velocity variation in the circulating vortex flow; the head differential in the fluid due to the speed difference between the two shafts; and the losses in the circulating vortex flow as a result of the impingement of the flow with the blades in the coupling and friction within the passages between the blades.

Keywords: Fluid Coupling, Mathematical Modelling, partially filled.

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Authors: Somi Nah, Timothy Yoonsuk Lee, Jinhwan Yu

Abstract:

In films, visual effects have played the role of expressing realities more realistically or describing imaginations as if they are real. Such images are immediated images representing realism, and the logic of immediation for the reality of images has been perceived dominant in visual effects. In order for immediation to have an identity as immediation, there should be the opposite concept hypermediation. In the mid 2000s, hypermediated images were settled as a code of mass culture in Asia. Thus, among Asian films highly popular in those days, this study selected five displaying hypermediated images – 2 Korean, 2 Japanese, and 1 Thailand movies – and examined the semiotic meanings of such images using Roland Barthes- directional and implicated meaning analysis and Metz-s paradigmatic analysis method, focusing on how hypermediated images work in the general context of the films, how they are associated with spaces, and what meanings they try to carry.

Keywords: Asian Films, Hypermediated Images, Semiotics, Visual Effects

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Authors: V. Prasannavenkadesan, A. Elango, S. Chockalingam

Abstract:

During machining process, chatter is an unavoidable phenomenon. Boring bars possess the cantilever shape and due to this, it is subjected to chatter. The adverse effect of chatter includes the increase in temperature which will leads to excess tool wear. To overcome these problems, in this investigation, Cartridge brass (Cu – 70% and Zn – 30%) is passively fixed on the boring bar and also clearance is provided in order to reduce the displacement, tool wear and cutting temperature. A conventional all geared lathe is attached with vibrometer and pyrometer is used to measure the displacement and temperature. The influence of input parameters such as cutting speed, depth of cut and clearance on temperature, tool wear and displacement are investigated for various cutting conditions. From the result, the optimum conditions to obtain better damping in boring process for chatter reduction is identified.

Keywords: Boring, chatter, mass damping, passive damping.

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Authors: Swati Tomar, Sunil Kumar Gupta

Abstract:

Anammox is a novel and promising technology that has changed the traditional concept of biological nitrogen removal. The process facilitates direct oxidation of ammonical nitrogen under anaerobic conditions with nitrite as an electron acceptor without addition of external carbon sources. The present study investigated the feasibility of Anammox Hybrid Reactor (AHR) combining the dual advantages of suspended and attached growth media for biodegradation of ammonical nitrogen in wastewater. Experimental unit consisted of 4 nos. of 5L capacity AHR inoculated with mixed seed culture containing anoxic and activated sludge (1:1). The process was established by feeding the reactors with synthetic wastewater containing NH4-H and NO2-N in the ratio 1:1 at HRT (hydraulic retention time) of 1 day. The reactors were gradually acclimated to higher ammonium concentration till it attained pseudo steady state removal at a total nitrogen concentration of 1200 mg/l. During this period, the performance of the AHR was monitored at twelve different HRTs varying from 0.25-3.0 d with increasing NLR from 0.4 to 4.8 kg N/m3d. AHR demonstrated significantly higher nitrogen removal (95.1%) at optimal HRT of 1 day. Filter media in AHR contributed an additional 27.2% ammonium removal in addition to 72% reduction in the sludge washout rate. This may be attributed to the functional mechanism of filter media which acts as a mechanical sieve and reduces the sludge washout rate many folds. This enhances the biomass retention capacity of the reactor by 25%, which is the key parameter for successful operation of high rate bioreactors. The effluent nitrate concentration, which is one of the bottlenecks of anammox process was also minimised significantly (42.3-52.3 mg/L). Process kinetics was evaluated using first order and Grau-second order models. The first-order substrate removal rate constant was found as 13.0 d-1. Model validation revealed that Grau second order model was more precise and predicted effluent nitrogen concentration with least error (1.84±10%). A new mathematical model based on mass balance was developed to predict N2 gas in AHR. The mass balance model derived from total nitrogen dictated significantly higher correlation (R2=0.986) and predicted N2 gas with least error of precision (0.12±8.49%). SEM study of biomass indicated the presence of heterogeneous population of cocci and rod shaped bacteria of average diameter varying from 1.2-1.5 mm. Owing to enhanced NRE coupled with meagre production of effluent nitrate and its ability to retain high biomass, AHR proved to be the most competitive reactor configuration for dealing with nitrogen laden wastewater.

Keywords: Anammox, filter media, kinetics, nitrogen removal.

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

Abstract:

Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: Design of experiments, regression analysis, SI Engine, statistical modeling.

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Authors: D. Wrzecionkowska

Abstract:

Mass media campaigns against obesity are often designed to impact large audiences. This usually means that their audience is defined based on general demographic characteristics like age, gender, occupation etc., not taking into account psychographics like behavior, motivations, wants, etc. Using psychographics, as the base for the audience segmentation, is a common practice in case of successful campaigns, as it allows developing more relevant messages. It also serves a purpose of identifying key segments, those that generate the best return on investment. For a health campaign, that would be segments that have the best chance of being converted into healthy lifestyle at the lowest cost. This paper presents the limitations of the demographic targeting, based on the findings from the reception study of IMSS (Mexican Social Security Institute) antiobesity TV commercials and proposes mothers as the first level of segmentation, in the process of identifying the key segment for these campaigns.

Keywords: Anti-obesity campaigns, mothers, segmentation, targeting.

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Authors: Tawiwat V., Phermsak S., Noppasit C.

Abstract:

This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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