Search results for: hybrid cements

Authors: Z. Abdollahnejad, P. Torgal, J. Barroso Aguiar

Abstract:

Publications on the field of alkali-activated binders, state that this new material is likely to have high potential to become an alternative to Portland cement. Classical alkali-activated cements could be made more eco-efficient if the use of sodium silicate is avoided. Besides, most alkali-activated cements suffer from severe efflorescence originated by the fact that alkaline and/or soluble silicates that are added during processing cannot be totally consumed. This paper presents experimental results on hybrid alkaline cements. Compressive strength results and efflorescence’s observations show that the new mixes already analyzed are promising. SEM results show that no traditional porous ITZ was detected in these binders.

Keywords: Hybrid alkaline cements, Compressive strength, Efflorescence, SEM, ITZ.

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Authors: Z. Abdollahnejad, M. Kheradmand, F. Pacheco Torgal

Abstract:

The workability of hybrid alkaline cements is a field of knowledge that still needs further research efforts. This paper reports experimental results of 32 hybrid cement mixes regarding the joint effect of sodium hydroxide concentration, the use of a commercial superplasticizer and a biopolymer on the flow and compressive strength performance. The results show that the use of commercial admixtures led to a slightly increase in the flow of mortars with lower sodium hydroxide concentration.

Keywords: Waste reuse, fly ash, waste glass, hybrid cement, biopolymer, polycarboxylate, flow.

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Authors: Z. Abdollahnejad, M. Mastali, F. Pacheco-Torgal

Abstract:

Waste reuse is crucial in a context of circular economy and zero waste sustainable needs. Some wastes deserve further studies by the scientific community not only because they are generated in high amount but also because they have a low reuse rate. This paper reports results of 32 hybrid cement mortars based on fly ash and waste glass. They allow to explore the influence of mix design on the cost and on the embodied carbon of the hybrid cement mortars. The embodied carbon data for all constituents were taken from the database Ecoinvent. This study led to the development of a mixture with just 70 kg CO2e.

Keywords: Waste reuse, fly ash, waste glass, hybrid cements, cost, embodied carbon.

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Authors: Zhuomin Zou, Thijs Van Landeghem, Elke Gruyaert

Abstract:

Using supplementary cementitious materials, such as ground granulated blast-furnace slag (GGBFS) and limestone to replace Portland cement (PC) is a promising method to reduce the carbon emissions from cement production. To efficiently use GGBFS and limestone, it is necessary to carefully select the particle size distribution (PSD) of the binders. This study investigated the effects of the PSD of binders on the performance of slag-limestone ternary cement. Based on the PSD parameters of the binders, three types of ternary cements with a similar overall PSD were designed, i.e., No.1 fine GGBFS, medium PC, and coarse limestone; No.2 fine limestone, medium PC, and coarse GGBFS; No.3. fine PC, medium GGBFS, and coarse limestone. The binder contents in the ternary cements were 50% PC, 40% slag, and 10% limestone. The mortar performance of the three ternary cements was investigated in terms of flow table value, strength at 28 days, carbonation resistance and non-steady state chloride migration resistance at 28 days. Results show that ternary cement with fine limestone (No.2) has the weakest performance among the three ternary cements. Ternary cements with fine slag (No.1) show an overall comparable performance to ternary cement with fine PC (No.3). Moreover, the chloride migration coefficient of ternary cements with fine slag (No.1) is significantly lower than the other two ternary cements.

Keywords: Limestone, particle size distribution, slag, ternary cement.

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Authors: Areej Almalkawi, Sameer Hamadna, Parviz Soroushian, Nalin Darsana

Abstract:

The work on indigenous binders in this paper focused on the following indigenous raw materials: red clay, red lava and pumice (as primary aluminosilicate precursors), wood ash and gypsum (as supplementary minerals), and sodium sulfate and lime (as alkali activators). The experimental methods used for evaluation of these indigenous raw materials included laser granulometry, x-ray fluorescence (XRF) spectroscopy, and chemical reactivity. Formulations were devised for transforming these raw materials into alkali aluminosilicate-based hydraulic cements. These formulations were processed into hydraulic cements via simple heating and milling actions to render thermal activation, mechanochemical and size reduction effects. The resulting hydraulic cements were subjected to laser granulometry, heat of hydration and reactivity tests. These cements were also used to prepare mortar mixtures, which were evaluated via performance of compressive strength tests. The measured values of strength were correlated with the reactivity, size distribution and microstructural features of raw materials. Some of the indigenous hydraulic cements produced in this reporting period yielded viable levels of compressive strength. The correlation trends established in this work are being evaluated for development of simple and thorough methods of qualifying indigenous raw materials for use in production of indigenous hydraulic cements.

Keywords: One-part geopolymer cement, aluminosilicate precursors, thermal activation, mechanochemical.

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Authors: M. Zielina, W. Dabrowski, E. Radziszewska-Zielina

Abstract:

Several different cements have been tested to evaluate their potential to leach calcium, chromium and aluminum ions in soft water environment. The research allows comparing some different cements in order to the potential risk of water contamination. This can be done only in the same environment. To reach the results in reasonable short time intervals and to make heavy metals measurements with high accuracy, demineralized water was used. In this case the conditions of experiments are far away from the water supply practice, but short time experiments and measurably high concentrations of elements in the water solution are an important advantage. Moreover leaching mechanisms can be recognized, our experiments reported here refer to this kind of cements evaluation.

Keywords: Concrete corrosion, hydrogen sulfide, odors, reinforced concrete sewers, sewerage.

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Authors: Samantha E. Booth, Andrew D. Deacon, Nichola J. Coleman

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A study has been carried out to determine the effect of coating two commercial glass-ionomer cements in either petroleum jelly or wax. After coating, specimens were stored in water for 24 or 168 hours, then the coating removed and the surface examined. Coating in wax was found to increase the surface hardness significantly compared with the uncoated control, whereas coating the specimens in petroleum jelly led to only a slight increase in surface hardness. Coating in wax led to no detectable ion release after either 24 or 168 hours, though there was some ion release after the coating had been removed and the specimens exposed to water for a further 24 hours. This shows that soluble species remained in these specimens. Overall, this study confirms the idea that immature glass-ionomers should be protected from early exposure to moisture, and that the protection offered by petroleum jelly is only modest.

Keywords: Coating, Glass-Ionomer Cements, Ion Release, Surface Hardness, Wax.

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Authors: W. K. Yap, V. Karri

Abstract:

This paper presents a hybrid electric scooter model developed and simulated using Matlab/Simulink. This hybrid scooter modeled has a parallel hybrid structure. The main propulsion units consist of a two stroke internal combustion engine and a hub motor attached to the front wheel of the scooter. The methodology used to optimize the energy and fuel consumption of the hybrid electric scooter is the multi-mode approach. Various case studies were presented to check the model and were compared to the literatures. Results shown that the model developed was feasible and valuable.

Keywords: Hybrid electric scooters, modeling and simulation, hybrid scooter energy management.

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Authors: S. O. Adeosun, L. O. Osoba, O. O. Taiwo

Abstract:

Aluminum hybrid reinforcement technology is a response to the dynamic ever increasing service requirements of such industries as transportation, aerospace, automobile, marine, etc. It is unique in that it offers a platform of almost unending combinations of materials to produce various hybrid composites. This article reviews the studies carried out on various combinations of aluminum hybrid composite and the effects on mechanical, physical and chemical properties. It is observed that the extent of enhancement of these properties of hybrid composites is strongly dependent on the nature of the reinforcement, its hardness, particle size, volume fraction, uniformity of dispersion within the matrix and the method of hybrid production.

Keywords: Aluminum alloy, hybrid composites, properties, reinforcements.

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Authors: Jaechun No

Abstract:

This paper focuses on I/O optimizations of N-hybrid (New-Form of hybrid), which provides a hybrid file system space constructed on SSD and HDD. Although the promising potentials of SSD, such as the absence of mechanical moving overhead and high random I/O throughput, have drawn a lot of attentions from IT enterprises, its high ratio of cost/capacity makes it less desirable to build a large-scale data storage subsystem composed of only SSDs. In this paper, we present N-hybrid that attempts to integrate the strengths of SSD and HDD, to offer a single, large hybrid file system space. Several experiments were conducted to verify the performance of N-hybrid.

Keywords: SSD, data section, I/O optimizations.

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Authors: Suresh Palla, Suresh Vanguri, Anitha, B. N. Mohapatra

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This paper presents the results of the study on the estimation of fly ash, slag and cement contents in blended and composite cements by selective dissolution method. Types of cement samples investigated include Ordinary Portland Cement (OPC) with fly ash as performance improver, OPC with slag as performance improver, Portland Pozzolana Cement (PPC), Portland Slag Cement (PSC) and composite cement confirming to respective Indian Standards. Slag and OPC contents in PSC were estimated by selectively dissolving OPC in stage 1 and selectively dissolving slag in stage 2. In the case of composite cement sample, the percentage of cement, slag and fly ash were estimated systematically by selective dissolution of cement, slag and fly ash in three stages. In the first stage, cement is dissolved and separated by leaving the residue of slag and fly ash, designated as R1. The second stage involves gravimetric estimation of fractions of OPC, residue and selective dissolution of fly ash and slag contents. Fly ash content, R2 was estimated through gravimetric analysis. Thereafter, the difference between the R1 and R2 is considered as slag content. The obtained results of cement, fly ash and slag using selective dissolution method showed 10% of standard deviation with the corresponding percentage of respective constituents. The results suggest that this selective dissolution method can be successfully used for estimation of OPC and Supplementary Cementitious material (SCM) contents in different types of cements.

Keywords: Selective dissolution method, fly ash, Ground Granulated blast furnace slag, EDTA.

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Authors: W. Thepsuwan, N. Monmaturapoj

Abstract:

Calcium phosphate cement (CPC) is one of the most attractive bioceramics due to its moldable and shape ability to fill complicated bony cavities or small dental defect positions. In this study, CPC was produced by using mixture of tetracalcium phosphate (TTCP, Ca4O(PO4)2) and dicalcium phosphate anhydrous (DCPA, CaHPO4) in equimolar ratio (1/1) with aqueous solutions of acetic acid (C2H4O2) and disodium hydrogen phosphate dehydrate (Na2HPO4.2H2O) in combination with sodium alginate in order to improve theirs moldable characteristic. The concentration of the aqueous solutions and sodium alginate were varied to investigate the effect of different aqueous solutions and alginate on properties of the cements. The cement paste was prepared by mixing cement powder (P) with aqueous solution (L) in a P/L ratio of 1.0g/0.35ml. X-ray diffraction (XRD) was used to analyses phase formation of the cements. Setting time and compressive strength of the set CPCs were measured using the Gilmore apparatus and Universal testing machine, respectively. The results showed that CPCs could be produced by using both basic (Na2HPO4.2H2O) and acidic (C2H4O2) solutions. XRD results show the precipitation of hydroxyapatite in all cement samples. No change in phase formation among cements using difference concentrations of Na2HPO4.2H2O solutions. With increasing concentration of acidic solutions, samples obtained less hydroxyapatite with a high dicalcium phosphate dehydrate leaded to a shorter setting time. Samples with sodium alginate exhibited higher crystallization of hydroxyapatite than that of without alginate as a result of shorten setting time in a basic solution but a longer setting time in an acidic solution. The stronger cement was attained from samples using the acidic solution with sodium alginate; however the strength was lower than that of using the basic solution.

Keywords: Calcium phosphate cements, TTCP, DCPA, hydroxyapatite, properties.

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Authors: Uma Thanganathan

Abstract:

The hybrid membranes containing inorganic materials in polymer matrix are identified as a remarkable family of proton conducting hybrid electrolytes. In this work, the proton conducting inorganic/organic hybrid membranes for proton exchange membrane fuel cells (PEMFCs) were prepared using polyvinyl alcohol (PVA), tetraethoxyorthosilane (TEOS) and heteropolyacid (HPA). The synthesized hybrid membranes were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction spectroscopy (XRD), Scanning electron microscopy (SEM) and Thermogravimetry analysis (TGA). The effects of heteropolyacid incorporation on membrane properties, including morphology and thermal stability were extensively investigated.

Keywords: PEMFC, Hybrid membrane, FTIR, TGA, Phosphomolybdic acid

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Authors: Hechmi Saidi, Noureddine Hamdi

Abstract:

The performance of hybrid amplify and forward - decode and forward (AF-DF) hybrid radio frequency/free space optical (RF/FSO) communication system, that adopts M-ary pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived. The random variations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the gamma-gamma (GG) statistical distribution. A closed-form expression for the probability density function (PDF) is derived for the whole above system is obtained. Thanks to the use of hybrid AF-DF hybrid RF/FSO configuration and MPPM, the effects of atmospheric turbulence is mitigated; hence the capacity of combating atmospheric turbulence and the transmissitted signal quality are improved.

Keywords: FSO, RF, hybrid, AF, DF, SER, SNR, GG channel.

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Authors: M. Mourad, K. Mahmoud

Abstract:

Recently hybrid vehicles have become a major concern as one alternative vehicles. This type of hybrid vehicle contributes greatly to reducing pollution. Therefore, this work studies the influence of electrification phase of hybrid electric vehicle on emission of vehicle at different road conditions. To accomplish this investigation, a simulation model was used to evaluate the external characteristics of the hybrid electric vehicle according to variant conditions of road resistances. Therefore, this paper reports a methodology to decrease the vehicle emission especially greenhouse gas emission inside cities. The results show the effect of electrification on vehicle performance characteristics. The results show that CO₂ emission of vehicle decreases up to 50.6% according to an urban driving cycle due to applying the electrification strategy for hybrid electric vehicle.

Keywords: Electrification strategy, hybrid electric vehicle, CO2 emission.

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Authors: Adriana Estokova, Lenka Palascakova, Martina Kovalcikova

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Cement is a basic material used for building construction. Chromium as an indelible non-volatile trace element of raw materials occurs in cement clinker in the trivalent or hexavalent form. Hexavalent form of chromium is harmful and allergenic having very high water solubility and thus can easily come into contact with the human skin. The paper is aimed at analyzing the content of total chromium in Portland cements and leaching rate of hexavalent chromium in various leachants: Deionized water, Britton-Robinson buffer, used to simulate the natural environment, and hydrochloric acid (HCl). The concentration of total chromium in Portland cement samples was in a range from 173.2 to 218.5 mg/kg. The content of dissolved hexavalent chromium ranged 0.23-3.19, 2.0-5.78 and 8.88-16.25 mg/kg in deionized water, Britton-Robinson solution and hydrochloric acid, respectively. The calculated leachable fraction of Cr(VI) from cement samples was observed in the range 0.1--7.58 %.

Keywords: Cement, hexavalent chromium, leaching, total chromium.

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Authors: Tetsuya Yabuki, Yasunori Arizumi, Tetsuhiro Shimozato, Samy Guezouli, Hiroaki Matsusita, Masayuki Tai

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The main object of this paper is to present the research results of the development of a hybrid stainless steel girder system for bridge construction undertaken at University of Ryukyu. In order to prevent the corrosion damage and reduce the fabrication costs, a hybrid stainless steel girder in bridge construction is developed, the stainless steel girder of which is stiffened and braced by structural carbon steel materials. It is verified analytically and experimentally that the ultimate strength of the hybrid stainless steel girder is equal to or greater than that of conventional carbon steel girder. The benefit of the life-cycle cost of the hybrid stainless steel girder is also shown.

Keywords: Smart structure, hybrid stainless steel members, ultimate strength, steel bridge, corrosion prevention.

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Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

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In the past decade, because of wide applications of hybrid systems, many researchers have considered modeling and control of these systems. Since switching systems constitute an important class of hybrid systems, in this paper a method for optimal control of linear switching systems is described. The method is also applied on the two-tank system which is a much appropriate system to analyze different modeling and control techniques of hybrid systems. Simulation results show that, in this method, the goals of control and also problem constraints can be satisfied by an appropriate selection of cost function.

Keywords: Hybrid systems, optimal control, switched systems, two-tank system

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Authors: Moudar H. A. Zgoul, Amin Al Zamer

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Adhesive materials and adhesion have been the focal point of multiple research works related to numerous applications, particularly, aerospace, and aviation industries. To enhance the properties of conventional adhesive materials, additives have been introduced to the mix in order to enhance their mechanical and physical properties by creating a hybrid adhesive material. The evaluation of the mechanical properties of such hybrid adhesive materials is thus of an essential requirement for the purpose of properly modeling their behavior accurately. This paper presents an approach/tool to simulate the behavior such hybrid adhesives in a way that will allow researchers to better understand their behavior while in service.

Keywords: Adhesive materials, analysis, hybrid adhesives, mechanical properties, simulation.

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Authors: A. Meydanlioglu, F. Arikan

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In recent years, thanks to the development of information and communication technologies, the computer and internet have been used widely in higher education. Internet-based education is impacting traditional higher education as online components increasingly become integrated into face- to- face (FTF) courses. The goal of combined internet-based and traditional education is to take full advantage of the benefits of each platform in order to provide an educational opportunity that can promote student learning better than can either platform alone. Research results show that the use of hybrid learning is more effective than online or FTF models in higher education. Due to the potential benefits, an increasing number of institutions are interested in developing hybrid courses, programs, and degrees. Future research should evaluate the effectiveness of hybrid learning. This paper is designed to determine the impact of hybrid learning on higher education.

Keywords: E-learning, higher education, hybrid learning, online education.

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Authors: Atul K. Desai, Hemal J. Shah

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The tall windmill towers are designed as monopole tower or lattice tower. In the present research, a 125-meter high hybrid tower which is a combination of lattice and monopole type is proposed. The response of hybrid tower is compared with conventional monopole tower. The towers were analyzed in finite element method software considering nonlinear seismic time history load. The synthetic seismic time history for different soil is derived using the SeismoARTIF software. From the present research, it is concluded that, in the hybrid tower, we are not getting resonance condition. The base shear is less in hybrid tower compared to monopole tower for different soil conditions.

Keywords: Dynamic analysis, hybrid wind mill tower, resonance condition, synthetic time history.

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Authors: Yu-Ta Shen, Yean-Ren Hwang

Abstract:

Although electrical motors are still the main devices used in vehicular exhaust comprises more than 95 percent of the air pollution in Taiwan's largest city, Taipei. On average, all commuters in Taipei travel 13.6 km daily, while motorcycle commuters travel 12.2 km. The convenience and mobility of motorcycles makes them irreplaceable in Taiwan city traffic but they add significantly to air pollution problems. In order to improve air pollution conditions, some new types of vehicles have been proposed, such as fuel cell driven and hybrid energy vehicles. In this study, we develop a model pneumatic hybrid motorcycle system and simulate its acceleration and mileage (km/L) performance. The results show that the pneumatic hybrid motorcycle can improve efficiency.

Keywords: vehicular, exhaust, air pollution, pneumatic, hybrid, motorcycle

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Authors: Kandarpa Kumar Sarma

Abstract:

The key to the continued success of ANN depends, considerably, on the use of hybrid structures implemented on cooperative frame-works. Hybrid architectures provide the ability to the ANN to validate heterogeneous learning paradigms. This work describes the implementation of a set of Distributed and Hybrid ANN models for Character Recognition applied to Anglo-Assamese scripts. The objective is to describe the effectiveness of Hybrid ANN setups as innovative means of neural learning for an application like multilingual handwritten character and numeral recognition.

Keywords: Assamese, Feature, Recurrent.

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Authors: Aurobi Das, V. Balakrishnan

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This paper focuses on the integration of hybrid renewable energy resources available in remote isolated islands of Sundarban-24 Parganas-South of Eastern part of India to National Grid of conventional power supply to give a Smart-Grid scenario. Before grid-integration, feasibility of optimization of hybrid renewable energy system is monitored through an Intelligent Controller proposed to be installed at Moushuni Island of Sundarban. The objective is to ensure the reliability and efficiency of the system to optimize the utilization of the hybrid renewable energy sources and also a proposition of how theses isolated Hybrid Renewable Energy Systems at remote islands can be grid-connected is analyzed towards vision of green smart-grid.

Keywords: Intelligent controller, hybrid renewable, solar photo voltaic, smart-grid.

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Authors: Rohitash Chandra, Christian W. Omlin

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We present a hybrid architecture of recurrent neural networks (RNNs) inspired by hidden Markov models (HMMs). We train the hybrid architecture using genetic algorithms to learn and represent dynamical systems. We train the hybrid architecture on a set of deterministic finite-state automata strings and observe the generalization performance of the hybrid architecture when presented with a new set of strings which were not present in the training data set. In this way, we show that the hybrid system of HMM and RNN can learn and represent deterministic finite-state automata. We ran experiments with different sets of population sizes in the genetic algorithm; we also ran experiments to find out which weight initializations were best for training the hybrid architecture. The results show that the hybrid architecture of recurrent neural networks inspired by hidden Markov models can train and represent dynamical systems. The best training and generalization performance is achieved when the hybrid architecture is initialized with random real weight values of range -15 to 15.

Keywords: Deterministic finite-state automata, genetic algorithm, hidden Markov models, hybrid systems and recurrent neural networks.

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Authors: K. Kusakana

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A hybrid energy system is a combination of renewable energy sources with back up, as well as a storage system used to respond to given load energy requirements. Given that the electrical output of each renewable source is fluctuating with changes in weather conditions, and since the load demand also varies with time; one of the main attributes of hybrid systems is to be able to respond to the load demand at any time by optimally controlling each energy source, storage and back-up system. The induced optimization problem is to compute the optimal operation control of the system with the aim of minimizing operation costs while efficiently and reliably responding to the load energy requirement. Current optimization research and development on hybrid systems are mainly focusing on the sizing aspect. Thus, the aim of this paper is to report on the state-of-the-art of optimal operation control of hybrid renewable energy systems. This paper also discusses different challenges encountered, as well as future developments that can help in improving the optimal operation control of hybrid renewable energy systems.

Keywords: Renewable energies, hybrid systems, optimization, operation control.

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Authors: Hassan El Maia, Ahmed Hammouch, Driss Aboutajdine

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This work presents an approach for the construction of a hybrid color-texture space by using mutual information. Feature extraction is done by the Laws filter with SVM (Support Vectors Machine) as a classifier. The classification is applied on the VisTex database and a SPOT HRV (XS) image representing two forest areas in the region of Rabat in Morocco. The result of classification obtained in the hybrid space is compared with the one obtained in the RGB color space.

Keywords: Color, texture, laws filter, mutual information, SVM, hybrid space.

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Authors: Z. Abdollahnejad, M. Kheradmand, F. Pacheco-Torgal

Abstract:

The use of bio-based admixtures on construction materials is a recent trend that is gaining momentum. However, to our knowledge, no studies have been reported concerning the use of biopolymers on hybrid cement based mortars. This paper reports experimental results regarding the study of the influence of mix design of 43 hybrid cement mortars containing two different biopolymers on its mechanical performance. The results show that the use of the biopolymer carrageenan is much more effective than the biopolymer xanthan concerning the increase in compressive strength. An optimum biopolymer content was found.

Keywords: Waste reuse, fly ash, waste glass, hybrid cement, biopolymers, mechanical strength.

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Authors: L. G. Karancsi, K. Máriás

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We examined the crop yield results of hybrids in 2012. We found out that in the control treatments the lowest yield was reached with the hybrid PR37M81: 10,012 kg ha^-1. The highest yield was in case of hybrid P37N01: 11,581 kg ha^-1. As we raised the nutrient doses the lowest yield of all examined nutrient levels was in case of hybrid PR37M81. We measured at N₆₀+PK nutrient level 12,517 kg ha^-1, at N₁₂₀+PK nutrient level 12,760 kg ha^-1, and at N₁₅₀+PK nutrient level 12,535 kg ha^-1 yield results. At N₆₀+PK and N₁₂₀+PK nutrient level the highest yield was reached with the hybrid P9494 (N₆₀+PK: 13,970 kg ha^-1, N₁₂₀+PK: 13,871 kg ha^-1). In case of the N₁₅₀+PK fertilization treatment the hybrid P37N01 gave the highest yield results (13,962 kg ha^-1).

Keywords: Hybrids, maize, nutrient levels, SPAD and LAI values.

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Authors: Ellysa Nursanti, Anas Ma'ruf, Tota Simatupang, Bermawi P. Iskandar

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This study proposes a hybrid minimal repair policy which combines periodic maintenance policy with age-based maintenance policy for a serial production system. Parameters of such policy are defined as
and  which indicate as hybrid minimal repair time and planned preventive maintenance time respectively  . Under this hybrid policy, the system is repaired minimally if it fails during ,
. A perfect repair is conducted on the first failure after
at any machines. At the same time, we take opportunity to advance the preventive maintenance of other machines simultaneously. If the system is still operating properly up to , then the preventive maintenance is carried out as its predetermined schedule. For a given , we obtain the optimal value
which minimizes the expected cost per time unit. Numerical example is presented to illustrate the properties of the optimal solution.

Keywords: Hybrid minimal repair, opportunistic maintenance, preventive maintenance, series system

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