Search results for: double oscillatory integral

Authors: Bingjie Wu, C. Q. Ru

Abstract:

The present work studies several reasonably expected candidate integral forms for self-attractive potential energy of a free monolayer graphene sheet. The admissibility of a specific integral form for ripple formation is verified, while all others most of the candidate integral forms are rejected based on the non-existence of stable periodic ripples. Based on the selected integral form of self-attractive potential energy, some mechanical behavior, including ripple formation and buckling, of a free monolayer grapheme sheet are discussed in details

Keywords: graphene, monolayer, ripples, van der Waals energy

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Serhat Tüzün, Tufan Demirel

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The objective of the present study is to select the most suitable location for a wind power plant station through Choquet integral method. The problem of selecting the location for a wind power station was considered as a multi-criteria decision-making problem. The essential and sub-criteria were specified and location selection was expressed in a hierarchic structure. Among the main criteria taken into account in this paper are wind potential, technical factors, social factors, transportation, and costs. The problem was solved by using different approaches of Choquet integral and the best location for a wind power station was determined. Then, the priority weights obtained from different Choquet integral approaches are compared and commented on.

Keywords: multi-criteria decision making, choquet integral, fuzzy sets, location of a wind power plant

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Authors: Ghulam Mustafa Peerzada, Shagufta Rashid, Nadeem Bashir

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These the influence of initial reagent concentrations on the Belousov-Zhabotinsky (BZ) system with Mn2+/Mn3+ as redox catalyst, inorganic bromate as oxidant and pyrogallol as organic substrate was studied. The reactions were monitored by potentiometery in oxidation reduction potential (ORP) mode. The aforesaid reagents were mixed with varying concentrations to evolve the optimal concentrations at which the reaction system exhibited better oscillations. The various oscillatory parameters such as induction period (tin), time period (tp), frequency (v), amplitude (A) and number of oscillations (n) were derived and the dependence of concentration of the reacting species on these oscillatory parameters was interpreted on the basis of the Field-Koros-Noyes mechanism. Ferroin based BZ system with pyrogallol as organic substrate was optimized under CSTR condition at temperature of 30±0.1oC Effect of molecules like monomer and polymer as additives to the system was checked and their interaction with the system was also studied. It has been observed that the monomer affects the time period, while the polymer has its effect on the amplitude of oscillations because of monomer’s interaction with the bromine and polymer’s with that of the Ferroin.

Keywords: Belousov Zhabotinsky reaction, oscillatory parameters, polymer, pyrogallol

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Authors: Hsiang-Wen Tang, Cheng-Ying Lo

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In this study, the static behavior of super elliptical Winkler plate is analyzed by applying the double side approach method. The lack of information about super elliptical Winkler plates is the motivation of this study and we use the double side approach method to solve this problem because of its superior ability on efficiently treating problems with complex boundary shape. The double side approach method has the advantages of high accuracy, easy calculation procedure and less calculation load required. Most important of all, it can give the error bound of the approximate solution. The numerical results not only show that the double side approach method works well on this problem but also provide us the knowledge of static behavior of super elliptical Winkler plate in practical use.

Keywords: super elliptical winkler plate, double side approach method, error bound, mechanic

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Authors: Abouzar Kaboudian, Ravi Chaithanya Mysa, Boo Cheong Khoo, Rajeev Kumar Jaiman

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Vortex induced vibrations can significantly affect the effectiveness of structures in aerospace as well as offshore marine industries. The oscillatory nature of the forces resulting from the vortex shedding around bluff bodies can result in undesirable effects such as increased loading, stresses, deflections, vibrations and noise in the structures, and also reduced fatigue life of the structures. To date, most studies concentrate on either the free oscillations or the prescribed motion of the bluff bodies. However, the structures in operation are usually subject to the external oscillatory forces (e.g. due to the platform motions in offshore industries). In this work, we present the effects of the external cross-flow forces on the vortex-induced vibrations of an oscillating cylinder. The effects of the amplitude, as well as the frequency of the external force on the fluid-forces on the oscillating cylinder are carefully studied and presented. Moreover, we present the transition of the response to be dominated by the vortex-induced-vibrations to the range where it is mostly dictated by the external oscillatory forces. Furthermore, we will discuss how the external forces can affect the flow structures around a cylinder. All results are compared against free oscillations of the cylinder.

Keywords: circular cylinder, external force, vortex-shedding, VIV

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Authors: Jamshaid Ul Rahman, Faiza Makhdoom, Dianchen Lu

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Activation functions play a decisive role in determining the capacity of Deep Neural Networks (DNNs) as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions primarily focused on the utility of monotonic or non-oscillatory functions, until Growing Cosine Unit (GCU) broke the taboo for a number of applications. In this paper, a Convolutional Neural Network (CNN) model named as ASU-CNN is proposed which utilizes recently designed activation function ASU across its layers. The effect of this non-monotonic and oscillatory function is inspected through feature map visualizations from different convolutional layers. The optimization of proposed network is offered by Adam with a fine-tuned adjustment of learning rate. The network achieved promising results on both training and testing data for the classification of CIFAR-10. The experimental results affirm the computational feasibility and efficacy of the proposed model for performing tasks related to the field of computer vision.

Keywords: amplifying sine unit, activation function, convolutional neural networks, oscillatory activation, image classification, CIFAR-10

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Authors: Artion Kashuri, Rozana Liko

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In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite-Hadamard's inequalities, Hölder's inequality, k-Riemann-Liouville fractional integral, special means

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: S. P. Sharma, Som Nath Saha

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This paper deals with the analytical investigation of thermal and thermohydraulic performance of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater has been presented, and a computer program in C⁺⁺ language is developed to estimate the outlet temperature of air for the evaluation of thermal and thermohydraulic efficiency by solving the governing equations numerically using relevant correlations for heat transfer coefficients. The results obtained from the mathematical model is compared with the available experimental results and it is found to be reasonably good. The results show that the double flow solar air heaters have higher efficiency than conventional solar air heater, although the double flow corrugated absorber is superior to that of flat plate double flow solar air heater. It is also observed that the thermal efficiency increases with increase in mass flow rate; however, thermohydraulic efficiency increases with increase in mass flow rate up to a certain limit, attains the maximum value, then thereafter decreases sharply.

Keywords: corrugated absorber, double flow, solar air heater, thermos-hydraulic efficiency

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Authors: Nadeem Bashir, Ghulam Mustafa Peerzada

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The present study pertains to the nonlinear behavior of acetaminophen based uncatalyzed Belousov-Zhabotinsky (BZ) oscillator and its dynamics in the presence of Ferroin as the catalyst. The role of free metal ions as catalysts was examined and the results compared with corresponding complexed catalysts. Free metal ions were found to be sluggish with respect to the evolution of the oscillatory regime as compared to complexed ones. Effect of change of the ligand moiety of the catalyst complex on the oscillatory parameters was monitored. Since ethanol potentiates the hepatotoxicity caused by acetaminophen in-vivo, it is thought to understand this interaction by virtue of causing perturbation of the acetaminophen based oscillator with different concentrations of the ethanol with and without ferroin as the catalyst. Another dimension to the ethanol effect was added by perturbation of the system with ethanol at different stages of the reaction so as to get an idea whether it is acetaminophen or some reactive intermediate generated in the reaction system which reacts with ethanol. Further, the ferroin-catalyzed oscillator is taken as a prototype inorganic model of the acetaminophen-ethanol syndrome, as ferroin and HOBr were inorganic replacements to Cyt P450 and NADPH in the alcohol metabolism.

Keywords: Belousov-Zhabotinsky reaction, ferroin, Paracetamol-Ethanol syndrome, kinetics

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Authors: S. P. Sharma, Som Nath Saha

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This paper presents the performance, based on exergy analysis of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater based on energy balance equations has been presented and the results obtained have been compared with that of a conventional flat-plate solar air heater. The double flow corrugated absorber solar air heater performs thermally better than the flat plate double flow and conventional flat-plate solar air heater under same operating conditions. However, the corrugated absorber leads to higher pressure drop thereby increasing pumping power. The results revealed that the energy and exergy efficiencies of double flow corrugated absorber solar air heater is much higher than conventional solar air heater with the concept involving of increase in heat transfer surface area and turbulence in air flow. The results indicate that the energy efficiency increases, however, exergy efficiency decreases with increase in mass flow rate.

Keywords: corrugated absorber, double flow, exergy efficiency, solar air heater

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Authors: Shai Sarussi

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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented.

Keywords: integral domains, Alexandroff topology, immediate neighbors, valuation domains

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Authors: Thana Ananacha

Abstract:

This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered namely 400 and 800 W.m-2 the corresponding initial condition temperatures were to 30.5 and 38.5 ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: thermal simulation, Double Glass Wall, velocity field, finite element method (FEM)

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Authors: Lila D. Sigdel, Chin J. Leo, Samanthika Liyanapathirana, Pan Hu, Minghao Lu

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Integral bridges are a class of bridges with integral or semi-integral abutments, designed without expansion joints in the bridge deck of the superstructure. Integral bridges are economical alternatives to conventional jointed bridges with lower maintenance costs and greater durability, thereby improving social and economic stability for the community. Integral bridges have also been proven to be effective in lowering the overall construction cost compared to the conventional type of bridges. However, there is significant uncertainty related to the design and analysis of integral bridges in response to cyclic thermal movements induced due to deck expansion and contraction. The cyclic thermal movements of the abutments increase the lateral earth pressures on the abutment and its foundation, leading to soil settlement and heaving of the backfill soil. Thus, the primary objective of this paper is to investigate the soil-abutment interaction under the cyclic translational movement of the abutment. Results from five experiments conducted to simulate different magnitudes of cyclic translational movements of abutments induced by thermal changes are presented, focusing on lateral earth pressure development at the abutment-soil interface. Test results show that the cycle number and magnitude of cyclic translational movements have significant effects on the escalation of lateral earth pressures. Experimentally observed earth pressure distributions behind the integral abutment were compared with the current design approaches, which shows that the most of the practices has under predicted the lateral earth pressure.

Keywords: integral bridge, cyclic thermal movement, lateral earth pressure, soil-structure interaction

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

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The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

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Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: double extreme ranked set sampling, extreme ranked set sampling, ranked set sampling, stratified double extreme ranked set sampling

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Authors: Abouzar Kaboudian, Ravi Chaithanya Mysa, Boo Cheong Khoo, Rajeev Kumar Jaiman

Abstract:

Vortex induced vibrations can significantly affect the effectiveness of structures in aerospace as well as offshore marine industries. The oscillatory nature of the forces resulting from the vortex shedding around bluff bodies can result in undesirable effects such as increased loading, stresses, deflections, vibrations and noise in the structures, and also reduced fatigue life of the structures. To date, most studies concentrate on either the free oscillations or the prescribed motion of the bluff bodies. However, the structures in operation are usually subject to the external oscillatory forces (e.g. due to the platform motions in offshore industries). Periodic forces can be considered as a combinations of sinusoids. In this work, we present the effects of sinusoidal external cross-flow forces on the vortex-induced vibrations of an oscillating cylinder. The effects of the amplitude, as well as the frequency of these sinusoidal external force on the fluid-forces on the oscillating cylinder are carefully studied and presented. Moreover, we present the transition of the response to be dominated by the vortex-induced-vibrations to the range where it is mostly dictated by the external oscillatory forces. Furthermore, we will discuss how the external forces can affect the flow structures around a cylinder. All results are compared against free oscillations of the cylinder.

Keywords: circular cylinder, external force, vortex-shedding, VIV

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Authors: Burak Yildirim, Muhsin Tunay Gencoglu

Abstract:

This publication shows the effects of Microgrid (MG) integration on the power systems oscillating stability. Generated MG model power systems were applied to the IEEE 14 bus test system which is widely used in stability studies. Stability studies were carried out with the help of eigenvalue analysis over linearized system models. In addition, Hopf bifurcation point detection was performed to show the effect of MGs on the system loadability margin. In the study results, it is seen that MGs affect system stability positively by increasing system loadability margin and has a damper effect on the critical modes of the system and the electromechanical local modes, but they make the damping amount of the electromechanical interarea modes reduce.

Keywords: Eigenvalue analysis, microgrid, Hopf bifurcation, oscillatory stability

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Authors: Jyh Jyh Chen, Fu H. Yang, Chen W. Wang, Yu M. Lin

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In this work, a reaction chamber is reciprocated among three temperature regions by using an oscillatory thermal cycling machine. Three cartridge heaters are collocated to heat three aluminum blocks in order to achieve PCR requirements in the reaction chamber. The effects of various chamber moving speeds among different temperature regions on the chamber temperature profiles are presented. To solve the evaporation effect of the sample in the PCR experiment, the mineral oil and the cover lid are used. The influences of various extension times on DNA amplification are also demonstrated. The target fragments of the amplification are 385-bp and 420-bp. The results show when the forward speed is set at 6 mm/s and the backward speed is 2.4 mm/s, the temperature required for the experiment can be achieved. It is successful to perform the amplification of DNA fragments in our device.

Keywords: oscillatory, polymerase chain reaction, reaction chamber, thermal cycling machine

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

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A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: M. Naji, A. R. Khalim, M. Naji

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Integral Abutment Bridges (IAB) are defined as simple or multiple span bridges in which the bridge deck is cast monolithically with the abutment walls. This kind of bridges are becoming very popular due to different aspects such as good response under seismic loading, low initial costs, elimination of bearings and less maintenance. However, the main issue related to the analysis of this type of structures is dealing with soil-structure interaction of the abutment walls and the supporting piles. A two-dimensional, non-linear finite element (FE) model of an integral abutment bridge has been developed to study the effect of lateral time history displacement loading on the soil system.

Keywords: integral abutment bridge, soil structure interaction, finite element modeling, soil-pile interaction

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Authors: C. W. Kwak, I. J. Park, D. I. Jang

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The importance of cost-wise effective application and construction is getting increase due to the surge of traffic volume in the metropolitan cities. Accordingly, the necessity of the tunnel has large section becomes more critical. Double deck tunnel can be one of the most appropriate solutions to the necessity. The dynamic stability of double deck tunnel is essential against seismic load since it has large section and connection between perimeter lining and interim slab. In this study, 3-dimensional dynamic numerical analysis was conducted based on the Finite Difference Method to investigate the seismic behavior of double deck tunnel. Seismic joint for dynamic stability and the mitigation of seismic impact on the lining was considered in the modeling and analysis. Consequently, the mitigation of acceleration, lining displacement and stress were verified successfully.

Keywords: double deck tunnel, interim slab, 3-dimensional dynamic numerical analysis, seismic joint

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Authors: Barenten Suciu, Akio Miyamura

Abstract:

In this paper, following the study-case of an inclined plane gravitational machine, efficiency of a double-cone gravitational motor and generator is evaluated. Two types of efficiency ratios, called translational efficiency and rotational efficiency, are defined relative to the intended duty of the gravitational machine, which can be either the production of translational kinetic energy, or rotational kinetic energy. One proved that, for pure rolling movement of the double- cone, in the absence of rolling friction, the total mechanical energy is conserved. In such circumstances, as the motion of the double-cone progresses along rails, the translational efficiency decreases and the rotational efficiency increases, in such way that sum of the rotational and translational efficiencies remains unchanged and equal to 1. Results obtained allow a comparison of the gravitational machine with other types of motor-generators, in terms of the achievable efficiency.

Keywords: efficiency, friction, gravitational motor and generator, rolling and sliding, truncated double-cone

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Authors: Naser Safdarian, Nader Jafarnia Dabanloo

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In this paper we used four features i.e. Q-wave integral, QRS complex integral, T-wave integral and total integral as extracted feature from normal and patient ECG signals to detection and localization of myocardial infarction (MI) in left ventricle of heart. In our research we focused on detection and localization of MI in standard ECG. We use the Q-wave integral and T-wave integral because this feature is important impression in detection of MI. We used some pattern recognition method such as Artificial Neural Network (ANN) to detect and localize the MI. Because these methods have good accuracy for classification of normal and abnormal signals. We used one type of Radial Basis Function (RBF) that called Probabilistic Neural Network (PNN) because of its nonlinearity property, and used other classifier such as k-Nearest Neighbors (KNN), Multilayer Perceptron (MLP) and Naive Bayes Classification. We used PhysioNet database as our training and test data. We reached over 80% for accuracy in test data for localization and over 95% for detection of MI. Main advantages of our method are simplicity and its good accuracy. Also we can improve accuracy of classification by adding more features in this method. A simple method based on using only four features which extracted from standard ECG is presented which has good accuracy in MI localization.

Keywords: ECG signal processing, myocardial infarction, features extraction, pattern recognition

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Authors: Jiwoo Park, Junseok Yoon, Jeong Kim, Beomsoo Kang

Abstract:

Multi-Point Stretch Forming (MPSF) process is suitable for flexible manufacturing, and it has several advantages including that it could be applied to various forming such as sheet metal forming, single curved surface forming and double curved one. In this study, a systematic numerical simulation was carried out for atypical double curved surface forming using the multiple die stretch forming process. In this simulation, urethane pads were defined based on hyper-elastic material model as a cushion for the smooth forming surface. The deformation behaviour on elastic recovery was also investigated to consider the exact result after the last forming process, and then the experiment was also carried out to confirm the formability of this forming process. By comparing the simulation and experiment results, the suitability of the multiple die stretch forming process for the atypical double curved surface was verified. Consequently, it is confirmed that the multi-point stretch forming process has the capability and feasibility of being used to manufacture the double curved surfaces of sheet metal.

Keywords: multi-point stretch forming, double curved surface, numerical simulation, manufacturing

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Authors: Babitha Elizabeth Philip

Abstract:

This paper aims to study in general about bridges without expansion joints. Integral Abutment Bridges (IAB) fall into this category of bridges. They are having a continuous deck and also the girders are integrated into the abutments. They are most cost effective system in terms of construction, maintenance, and longevity. The main advantage of IAB is that it is corrosion resistant since water is not allowed to pass through the structure. The other attractions of integral bridges are its simple and rapid construction, smooth and uninterrupted deck which provides a safe ride. Also damages to the abutments can be avoided to a great extent due to better load distribution at the bridge ends. Damages due to improper drainage are not seen in IAB because of its properly drained approach slabs thus eliminating the possibility of erosion of the abutment backfill and freeze and thaw damage resulting from saturated backfill.

Keywords: continuous bridge, integral abutment bridge, joint bridge, life cycle cost, soil interaction

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Authors: A. Calvin Antony, Sakthi Kumar Arul Prakash, V. R. Sanal Kumar

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In this paper a unique alpha-beta double piston 'stirling engine' is designed, manufactured and conducted laboratory test to ameliorate the efficiency of the stirling engine. The paper focuses on alpha and beta type engines, capturing their benefits and eradicating their short comings; along with the output observed from the flywheel. In this model alpha engine is kinematically with a piston cylinder arrangement which works quite like a beta engine. The piston of the new cylinder is so designed that it replicates a glued displacer and power piston as similar to that of beta engine. The bigger part of the piston is the power piston, which has a gap around it, while the smaller part of the piston is tightly fit in the cylinder and acts like the displacer piston. We observed that the alpha-beta double piston stirling engine produces 25% increase in power compare to a conventional alpha stirling engine. This working model is a pointer towards for the design and development of an alpha-beta double piston Stirling engine for industrial applications for producing electricity from the heat producing exhaust gases.

Keywords: alpha-beta double piston stirling engine , alpha stirling engine , beta double piston stirling engine , electricity from stirling engine

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Authors: K. K. Riabchenko, T. V Rybitskaya, A. A. Starostenko

Abstract:

Sper Charm-Tau Factory is a double ring e+e- collider to be operated in the center-of-mass energy range from 2 to 6 GeV, with a peak luminosity of about 1035 cm-2s-1 (Crab Waist collision) and with longitudinally polarized electrons at the IP (interaction point). One of the important elements of the cτ-factory is the superconducting two-aperture quadrupole of the final focus. It was decided to make a full-scale prototype quadrupole. The main objectives of our study included: 1) 3D modeling of the quadrupole in the Opera program, 2) Optimization of the geometry of the quadrupole lens, 3) Study of the influence of magnetic properties and geometry of a quadrupole on integral harmonics. In addition to this, the ways of producing unwanted harmonics have been studied. In the course of this work, a 3D model of a two-aperture iron superconducting quadrupole lens was created. A three-dimensional simulation of the magnetic field was performed, and the geometrical parameters of the lens were selected. Calculations helped to find sources of possible errors and methods for correcting unwanted harmonics. In addition to this, calculations show that there are no obstacles to the production of a prototype lens.

Keywords: super cτ-factory, final focus, twin aperture quadrupole lens, integral harmonics

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