Search results for: Density functional theory

Authors: Yusuke Uchiyama, Hidetoshi Konno

Abstract:

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.

Keywords: sub-Poisson statistics, hyper gamma distribution, fractional Poisson configuration.

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: Munehiro Iwami

Abstract:

A property is called persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property. In this paper,we show that termination is persistent for non-overlapping term rewriting systems and we give the example as application of this result. Furthermore we obtain that completeness is persistent for non-overlapping term rewriting systems.

Keywords: Theory of computing, Model-based reasoning, termrewriting system, termination

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Authors: Tadeusz Pieczonka, Jan Kazior

Abstract:

The influence of SiC powder addition on densification of Al-SiC compacts during sintering in different atmospheres was investigated. It was performed in a dilatometer in flowing nitrogen, nitrogen/hydrogen (95/5 by volume) and argon. Fine, F500 grade of SiC powder was used. Mixtures containing 10 and 30 vol.% of SiC reinforcement were prepared in a Turbula mixer. Green compacts of about 82% of theoretical density were made of each mixture. For comparison, compacts made of pure aluminum powder were also investigated. It was shown that nitrogen is the best sintering atmosphere because only in this atmosphere did shrinkage take place. Its amount is lowered by ceramic powder addition, i.e. the more SiC the less densification occurs. Additionally, the formation of clusters, enhanced in compacts containing 30 vol.% SiC, is also responsible for limiting the shrinkage. Microstructural examinations of sintered composites revealed that sintering of compacts occurs in the presence of the liquid phase exclusively in nitrogen.

Keywords: Al-SiC composites, densification, sintering atmosphere.

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Authors: V. Kabeer, N.K.Narayanan

Abstract:

This paper reports a new pattern recognition approach for face recognition. The biological model of light receptors - cones and rods in human eyes and the way they are associated with pattern vision in human vision forms the basis of this approach. The functional model is simulated using CWD and WPD. The paper also discusses the experiments performed for face recognition using the features extracted from images in the AT & T face database. Artificial Neural Network and k- Nearest Neighbour classifier algorithms are employed for the recognition purpose. A feature vector is formed for each of the face images in the database and recognition accuracies are computed and compared using the classifiers. Simulation results show that the proposed method outperforms traditional way of feature extraction methods prevailing for pattern recognition in terms of recognition accuracy for face images with pose and illumination variations.

Keywords: Face recognition, Image analysis, Wavelet feature extraction, Pattern recognition, Classifier algorithms

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Authors: R. S. Giraddi, C. M. Poleshi

Abstract:

Organic cultivation of crops is gaining importance consumer awareness towards pesticide residue free foodstuffs is increasing globally. This is also because of high costs of synthetic fertilizers and pesticides, making the conventional farming non-remunerative. In India, organic manures (such as vermicompost) are an important input in organic agriculture.  Though vermicompost obtained through earthworm and microbe-mediated processes is known to comprise most of the crop nutrients, but they are in small amounts thus necessitating enrichment of nutrients so that crop nourishment is complete. Another characteristic of organic manures is that the pest infestations are kept under check due to induced resistance put up by the crop plants. In the present investigation, deoiled neem cake containing azadirachtin, copper ore tailings (COT), a source of micro-nutrients and microbial consortia were added for enrichment of vermicompost. Neem cake is a by-product obtained during the process of oil extraction from neem plant seeds. Three enriched vermicompost blends were prepared using vermicompost (at 70, 65 and 60%), deoiled neem cake (25, 30 and 35%), microbial consortia and COTwastes (5%). Enriched vermicompost was thoroughly mixed, moistened (25+5%), packed and incubated for 15 days at room temperature. In the crop response studies, the field trials on chili (Capsicum annum var. longum) and soybean, (Glycine max cv JS 335) were conducted during Kharif 2015 at the Main Agricultural Research Station, UAS, Dharwad-Karnataka, India. The vermicompost blend enriched with neem cake (known to possess higher amounts of nutrients) and vermicompost were applied to the crops and at two dosages and at two intervals of crop cycle (at sowing and 30 days after sowing) as per the treatment plan along with 50% recommended dose of fertilizer (RDF). 10 plants selected randomly in each plot were studied for pest density and plant damage. At maturity, crops were harvested, and the yields were recorded as per the treatments, and the data were analyzed using appropriate statistical tools and procedures. In the crops, chili and soybean, crop nourishment with neem enriched vermicompost reduced insect density and plant damage significantly compared to other treatments. These treatments registered as much yield (16.7 to 19.9 q/ha) as that realized in conventional chemical control (18.2 q/ha) in soybean, while 72 to 77 q/ha of green chili was harvested in the same treatments, being comparable to the chemical control (74 q/ha). The yield superiority of the treatments was of the order neem enriched vermicompost>conventional chemical control>neem cake>vermicompost>untreated control.  The significant features of the result are that it reduces use of inorganic manures by 50% and synthetic chemical insecticides by 100%.

Keywords: Humic acid, azadirachtin, vermicompost, insect-pest.

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Authors: A. Ersan, A. S. Kipcak, M. Yildirim, A. M. Erayvaz, E. M. Derun, N. Tugrul, S. Piskin

Abstract:

Zinc borates are used as a multi-functional flame retardant additive for its high dehydration temperature. In this study, the method of ultrasonic mixing was used in the synthesis of zinc borates. The reactants of zinc oxide (ZnO) and boric acid (H3BO3) were used at the constant reaction parameters of 90°C reaction temperature and 55 min of reaction time. Several molar ratios of ZnO:H3BO3 (1:1, 1:2, 1:3, 1:4 and 1:5) were conducted for the determination of the optimum reaction ratio. Prior to synthesis the characterization of the synthesized zinc borates were made by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). From the results Zinc Oxide Borate Hydrate [Zn3B6O12.3.5H2O], were synthesized optimum at the molar ratio of 1:3, with a reaction efficiency of 95.2%.

Keywords: Zinc borates, ultrasonic mixing, XRD, FT-IR, reaction efficiency.

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Authors: Md. Sharif Imam Ibne Amir, M. Shah Alam Khan, Mohammad Masud Kamal Khan, Mohammad Golam Rasul, Fatema Akram

Abstract:

The problems of severe drainage congestion and water logging in the southwestern Bangladesh have been solved by an innovative concept, Tidal River Management (TRM). TRM involves the uniform raising of the land inside a tidal basin (beel) while simultaneously maintaining the proper drainage capacity in the river. The present practice of TRM is to link the river with the selected beel by constructing a link canal at the entrance of which most of the sedimentation takes place. This localized sedimentation also creates drainage congestion and water logging making it unattractive to landowners who participate in the program. In this paper a functional sediment management plan is presented to get rid of this problem

Keywords: Beel, embankment, MIKE 21 Flow Model FM, Tidal River Management.

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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: H. Ettouney, A. AL-Haddad, S. Saqer

Abstract:

This paper focuses on assessment of air pollution in Umm-Alhyman, Kuwait, which is located south to oil refineries, power station, oil field, and highways. The measurements were made over a period of four days in March and July in 2001, 2004, and 2008. The measured pollutants included methanated and nonmethanated hydrocarbons (MHC, NMHC), CO, CO2, SO2, NOX, O3, and PM10. Also, meteorological parameters were measured, which includes temperature, wind speed and direction, and solar radiation. Over the study period, data analysis showed increase in measured SO2, NOX and CO by factors of 1.2, 5.5 and 2, respectively. This is explained in terms of increase in industrial activities, motor vehicle density, and power generation. Predictions of the measured data were made by the ISC-AERMOD software package and by using the ISCST3 model option. Finally, comparison was made between measured data against international standards.

Keywords: Air pollution, Emission inventory, ISCST3 model, Modeling

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Authors: Romel N. Georgees, Rayya A Hassan, Robert P. Evans, Piratheepan Jegatheesan

Abstract:

Among other traditional and non-traditional additives, polymers have shown an efficient performance in the field and improved sustainability. Polyacrylamide (PAM) is one such additive that has demonstrated many advantages including a reduction in permeability, an increase in durability and the provision of strength characteristics. However, information about its effect on the improved geotechnical characteristics is very limited to the field performance monitoring. Therefore, a laboratory investigation was carried out to examine the basic and engineering behaviors of three types of soils treated with a PAM additive. The results showed an increase in dry density and unconfined compressive strength for all the soils. The results further demonstrated an increase in unsoaked CBR and a reduction in permeability for all stabilized samples.

Keywords: CBR, Hydraulic conductivity, PAM, Unconfined compressive strength.

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Authors: M. Rezvani, M. Ahangari, F. Zaefarian

Abstract:

In a field experiment, growth parameters of soybean cultivars in different weeding regimes was investigated. The trial was split plot in a randomized complete block design. The four cultivars and two lines of soybean (Glycine max L.) including: Sahar, Hill, Sari, Telar, 032 and 033 in main plot and weeding regime consist of no weeding (control), one weeding (35 days after planting) and two weeding (35+20 days after planting) were randomized in sub plot. The results showed that during the growth season 033 had the highest dry matter in two weeding. In two weeding regime the dry matter decreased. ). In all weeding regimes 033 had the highest CGR (Figs. 3a, 3b and 3c), which cleared this cultivar ability compare to the others. This cultivar by increasing its leaf area could do more photosynthesis, so, have a higher CGR.

Keywords: Crop growth rate, Density, Leaf area index

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Authors: E. Barkanov, E. Skukis, M. Wesolowski, A. Chate

Abstract:

New nondestructive technique, namely an inverse technique based on vibration tests, to characterize nonlinear mechanical properties of adhesive layers in sandwich composites is developed. An adhesive layer is described as a viscoelastic isotropic material with storage and loss moduli which are both frequency dependent values in wide frequency range. An optimization based on the planning of experiments and response surface technique to minimize the error functional is applied to decrease considerably the computational expenses. The developed identification technique has been tested on aluminum panels and successfully applied to characterize viscoelastic material properties of 3M damping polymer ISD-112 used as a core material in sandwich panels.

Keywords: Adhesive layer, finite element method, inverse technique, sandwich panel, vibration test, viscoelastic material properties.

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Authors: Khaled Harrar, Rachid Jennane

Abstract:

The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an agematched control group of 28 women using texture analysis based on fractals. Two pre-processing approaches are applied on radiographic images; these techniques are compared to highlight the choice of the pre-processing method. Furthermore, the values of the fractal dimension are compared to those of the fractal signature in terms of the classification of the two populations. In a second analysis, the BMD measure at proximal femur was compared to the fractal analysis, the latter, which is a non-invasive technique, allowed a better discrimination; the results confirm that the fractal analysis of texture on calcaneus radiographs is able to discriminate osteoporotic patients with femoral fracture from controls. This discrimination was efficient compared to that obtained by BMD alone. It was also present in comparing subgroups with overlapping values of BMD.

Keywords: Osteoporosis, fractal dimension, fractal signature, bone mineral density.

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Authors: Chimin Tsai

Abstract:

This work consists of three parts. First, the alias-free condition for the conventional two-channel quadrature mirror filter bank is analyzed using complex arithmetic. Second, the approach developed in the first part is applied to the complex quadrature mirror filter bank. Accordingly, the structure is simplified and the theory is easier to follow. Finally, a new class of complex quadrature mirror filter banks is proposed. Interesting properties of this new structure are also discussed.

Keywords: Aliasing cancellation, complex signal processing, polyphase realization, quadrature mirror filter banks.

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Authors: N. Tugrul, A. S. Kipcak, N. Baran Acarali, E. Moroydor Derun, S. Piskin

Abstract:

Magnesium borate(MB) istechnical ceramic for high heat-resisting, corrosion-resisting, super mechanical strength, superinsulation, light weight, high strength, and high coefficient of elasticity. Zinc borate (ZB) can be used as multi-functional synergistic additives with flame retardant additives in polymers. The most important properties are low solubility in water and high dehydration temperature. ZB dehydrates above 290°C and anhydrous ZB has thermal resistance about 400°C. In this study, the raw materials of ZnO, MgO and H₃BO₃ were used with mole ratio of 1:1:9. With the starting materials hydrothermal method was applied at a temperature of 100^oC. The reaction time was determined as 30, 60, 90 and 120 minutes after some preliminary experiments. After the synthesis, the crystal structure and the morphology of the products were examined by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). As a result, the forms of Zinc Oxide Borate Hydrate [Zn₃B₆O₁₂.3.5H₂O], Admontite [MgO(B₂O₃)₃.7(H₂O)] and Mcallisterite [Mg₂(B₆O₇(OH)₆)₂.9(H₂O)] were synthesized.

Keywords: Magnesium borate, zinc borate, XRD, FT-IR.

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Xiaoquan Ding, Jianmin Hao, Changwen Liu

Abstract:

This paper is devoted to a delayed periodic predatorprey system with non-monotonic numerical response on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.

Keywords: Predator-prey system, periodic solution, time scale, delay, coincidence degree.

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Authors: Costin Pribeanu

Abstract:

The model-based approach to user interface design relies on developing separate models that are capturing various aspects about users, tasks, application domain, presentation and dialog representations. This paper presents a task modeling approach for user interface design and aims at exploring the mappings between task, domain and presentation models. The basic idea of our approach is to identify typical configurations in task and domain models and to investigate how they relate each other. A special emphasis is put on application-specific functions and mappings between domain objects and operational task structures. In this respect, we will distinguish between three layers in the task decomposition: a functional layer, a planning layer, and an operational layer.

Keywords: task modeling, user interface design, unit tasks, basic tasks, operational task model

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Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

Abstract:

In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: Segmentation, color-texture, neural networks, fractal, watershed.

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Authors: Shankar Subramanian Iyer

Abstract:

The vocational education, enhanced by technology and Recognition of Prior Learning (RPL) is going to be the main ingredient of the future of education. This is coming from the various issues of the current educational system like cost, time, type of course, type of curriculum, unemployment, to name the major reasons. Most millennials like to perform and learn rather than learning how to perform. This is the essence of vocational education be it any field from cooking, painting, plumbing to modern technologies using computers. Even a more theoretical course like entrepreneurship can be taught as to be an entrepreneur and learn about its nuances. The best way to learn accountancy is actually keeping accounts for a small business or grocer and learn the ropes of accountancy and finance. The purpose of this study is to investigate the relationship between vocational skills, RPL and new technologies with future employability. This study implies that individual's knowledge and skills are essential aspects to be emphasized in future education and to give credit for prior experience for future employability. Virtual reality can be used to stimulate workplace situations for vocational learning for fields like hospitality, medical emergencies, healthcare, draughtsman ship, building inspection, quantity surveying, estimation, to name a few. All disruptions in future education, especially vocational education, are going to be technology driven with the advent of AI, ML, IoT, VR, VI etc. Vocational education not only helps institutes cut costs drastically, but allows all students to have hands-on experiences, rather than to be observers. The earlier experiential learning theory and the recent theory of knowledge and skills-based learning modified and applied to the vocational education and development of skills is the proposed contribution of this paper. Apart from secondary research study on major scholarly articles, books, primary research using interviews, questionnaire surveys have been used to validate and test the reliability of the suggested model using Partial Least Square- Structural Equation Method (PLS-SEM), the factors being assimilated using an existing literature review. Major findings have been that there exists high relationship between the vocational skills, RPL, new technology to the future employability through mediation of future employability skills.

Keywords: Vocational education, vocational skills, competencies, modern technologies, Recognition of Prior Learning, RPL.

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Authors: R. Uthayakumar, G. Arockia Prabakar

Abstract:

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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Authors: G. A. Florides, E. Theofanous, I. Iosif-Stylianou, P. Christodoulides, S. Kalogirou, V. Messarites, Z. Zomeni, E. Tsiolakis, P. D. Pouloupatis, G. P. Panayiotou

Abstract:

Ground Coupled Heat Pumps (GCHPs) exploit effectively the heat capacity of the ground, with the use of Ground Heat Exchangers (GHE). Depending on the mode of operation of the GCHPs, GHEs dissipate or absorb heat from the ground. For sizing the GHE the thermal properties of the ground need to be known. This paper gives information about the density, thermal conductivity, specific heat and thermal diffusivity of various lithologies encountered in Cyprus with various relations between these properties being examined through comparison and modeling. The results show that the most important correlation is the one encountered between thermal conductivity and thermal diffusivity with both properties showing similar response to the inlet and outlet flow temperature of vertical and horizontal heat exchangers.

Keywords: Ground heat exchangers, ground thermal conductivity, ground thermal diffusivity, ground thermal properties.

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Authors: Essam Al-Daoud

Abstract:

A potentially serious problem with current payment systems is that their underlying hard problems from number theory may be solved by either a quantum computer or unanticipated future advances in algorithms and hardware. A new quantum payment system is proposed in this paper. The suggested system makes use of fundamental principles of quantum mechanics to ensure the unconditional security without prior arrangements between customers and vendors. More specifically, the new system uses Greenberger-Home-Zeilinger (GHZ) states and Quantum Key Distribution to authenticate the vendors and guarantee the transaction integrity.

Keywords: Bell state, GHZ state, Quantum key distribution, Quantum payment system.

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Authors: Youssou Faye, Ibrahima Niang, Thomas Noel

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Access control is a critical security service in Wire- less Sensor Networks (WSNs). To prevent malicious nodes from joining the sensor network, access control is required. On one hand, WSN must be able to authorize and grant users the right to access to the network. On the other hand, WSN must organize data collected by sensors in such a way that an unauthorized entity (the adversary) cannot make arbitrary queries. This restricts the network access only to eligible users and sensor nodes, while queries from outsiders will not be answered or forwarded by nodes. In this paper we presentee different access control schemes so as to ?nd out their objectives, provision, communication complexity, limits, etc. Using the node density parameter, we also provide a comparison of these proposed access control algorithms based on the network topology which can be flat or hierarchical.

Keywords: Access Control, Authentication, Key Management, Wireless Sensor Networks.

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Authors: Rishabh Sharma, Renu Vig, Neeraj Sharma

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The main design parameter of WSN (wireless sensor network) is the energy consumption. To compensate this parameter, hierarchical clustering is a technique that assists in extending duration of the networks life by efficiently consuming the energy. This paper focuses on dealing with the WSNs and the FIS (fuzzy interface system) which are deployed to enhance the BEENISH protocol. The node energy, mobility, pause time and density are considered for the selection of CH (cluster head). The simulation outcomes exhibited that the projected system outperforms the traditional system with regard to the energy utilization and number of packets transmitted to sink.

Keywords: Wireless sensor network, sink, sensor node, routing protocol, fuzzy rule, fuzzy inference system.

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Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: P. Tueku, P. Supnithi, R. Wongsathan

Abstract:

Heat-Assisted Magnetic Recording (HAMR) is one of the leading technologies identified to enable areal density beyond 1 Tb/in² of magnetic recording systems. A key challenge to HAMR designing is accuracy of positioning, timing of the firing laser, power of the laser, thermo-magnetic head, head-disk interface and cooling system. We study the effect of HAMR parameters on transition center and transition width. The HAMR is model using Thermal Williams-Comstock (TWC) and microtrack model. The target and equalizer are designed by the minimum mean square error (MMSE). The result shows that the unit energy constraint outperforms other constraints.

Keywords: Heat-Assisted Magnetic Recording, Thermal Williams-Comstock equation, Microtrack model, Equalizer.

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Authors: H. Noun, C. Urban-Seelmann, M. Abdelfattah, G. Zeller, G. Rajesh, I. Mozgova, R. Lachmayer

Abstract:

Several modules in automotive are usually modified and adapted for various project-specific applications. Due to a standardized safety concept a high reusability is accessible. A safety element out of context (SEooC) according to ISO 26262 can be a suitable approach. Based on the same safety concept and analysis, common modules can reach high reusability. For developing according to a module out of context, an appropriate and detailed development approach is required. This paper shows how to deduce this development processes for platform modules. Therefore, the detailed approach of the SEooC is derived. The aim is to create a detailed workflow for all phases of the development and integration of any kind of system modules. As an application example, an automotive project for an actuator control module is considered.

Keywords: Functional Safety, Safety Element out of Context, System Engineering, Hardware Engineering.

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Authors: Chunming Xu

Abstract:

In this paper, the finite-time symplectic synchronization between two different chaotic systems is investigated. Based on the finite-time stability theory, a simple adaptive feedback scheme is proposed to realize finite-time symplectic synchronization for the Lorenz and L¨u systems. Numerical examples are provided to show the effectiveness of the proposed method.

Keywords: Chaotic systems, symplectic synchronization, finite-time synchronization, adaptive controller.

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