Search results for: Differential Quadrature Method

Authors: S. Tupsie, A. Isaramongkolrak, P. Pao-la-or

Abstract:

This paper presents the mathematical model of electric field and magnetic field in transmission system, which performs in second-order partial differential equation. This research has conducted analyzing the electromagnetic field radiating to atmosphere around the transmission line, when there is the transmission line transposition in case of long distance distribution. The six types of 500 kV transposed HV transmission line with double circuit will be considered. The computer simulation is applied finite element method that is developed by MATLAB program. The problem is considered to two dimensions, which is time harmonic system with the graphical performance of electric field and magnetic field. The impact from simulation of six types long distance distributing transposition will not effect changing of electric field and magnetic field which surround the transmission line.

Keywords: Transposition, Electromagnetic Field, Finite Element Method (FEM), Transmission Line, Computer Simulation

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: Majed Omar Al-Dwairi

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This paper evaluate the multilevel modulation for different techniques such as amplitude shift keying (M-ASK), MASK, differential phase shift keying (M-ASK-Bipolar), Quaternary Amplitude Shift Keying (QASK) and Quaternary Polarization-ASK (QPol-ASK) at a total bit rate of 107 Gbps. The aim is to find a costeffective very high speed transport solution. Numerical investigation was performed using Monte Carlo simulations. The obtained results indicate that some modulation formats can be operated at 100Gbps in optical communication systems with low implementation effort and high spectral efficiency.

Keywords: Optical communication, multilevel amplitude shift keying (M-ASK), Differential phase shift keying (DPSK), Quaternary Amplitude Shift Keying (QASK), Quaternary Polarization-ASK (QPol-ASK).

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Authors: Magdy G. Asaad

Abstract:

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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Authors: Sara Bilal, Abdi Omar Shuriye, Raihan Othman

Abstract:

Numerical Methods is a course that can be conducted using workshops and group discussion. This study has been implemented on undergraduate students of level two at the Faculty of Engineering, International Islamic University Malaysia. The Numerical Method course has been delivered to two Sections 1 and 2 with 44 and 22 students in each section, respectively. Systematic steps have been followed to apply the student centered learning approach in teaching Numerical Method course. Initially, the instructor has chosen the topic which was Euler’s Method to solve Ordinary Differential Equations (ODE) to be learned. The students were then divided into groups with five members in each group. Initial instructions have been given to the group members to prepare their subtopics before meeting members from other groups to discuss the subtopics in an expert group inside the classroom. For the time assigned for the classroom discussion, the setting of the classroom was rearranged to accommodate the student centered learning approach. Teacher strength was by monitoring the process of learning inside and outside the class. The students have been assessed during the migrating to the expert groups, recording of a video explanation outside the classroom and during the final examination. Euler’s Method to solve the ODE was set as part of Question 3(b) in the final exam. It is observed that none of the students from both sections obtained a zero grade in Q3(b), compared to Q3(a) and Q3(c). Also, for Section 1(44 students), 29 students obtained the full mark of 7/7, while only 10 obtained 7/7 for Q3(a) and no students obtained 6/6 for Q3(c). Finally, we can recommend that the Numerical Method course be moved toward more student-centered Learning classrooms where the students will be engaged in group discussion rather than having a teacher one man show.

Keywords: Teacher centered learning, student centered learning, mathematic, numerical methods.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: C. Panya-Isara, T. Kulworawanichpong, P. Pao-La-Or

Abstract:

Piezoelectric transformers are electronic devices made from piezoelectric materials. The piezoelectric transformers as the name implied are used for changing voltage signals from one level to another. Electrical energy carried with signals is transferred by means of mechanical vibration. Characterizing in both electrical and mechanical properties leads to extensively use and efficiency enhancement of piezoelectric transformers in various applications. In this paper, study and analysis of electrical and mechanical properties of multi-layer piezoelectric transformers in forms of potential and displacement distribution throughout the volume, respectively. This paper proposes a set of quasi-static mathematical model of electromechanical coupling for piezoelectric transformer by using a set of partial differential equations. Computer-based simulation utilizing the three-dimensional finite element method (3-D FEM) is exploited as a tool for visualizing potentials and displacements distribution within the multi-layer piezoelectric transformer. This simulation was conducted by varying a number of layers. In this paper 3, 5 and 7 of the circular ring type were used. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Multi-layer Piezoelectric Transformer, 3-D Finite Element Method (3-D FEM), Electro-mechanical Coupling, Mechanical Vibration

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Authors: V. Sandeep Kumar, S. Anuradha

Abstract:

The high Peak to Average Power Ratio (PAR) in Filter Bank Multicarrier with Offset Quadrature Amplitude Modulation (FBMC-OQAM) can significantly reduce power efficiency and performance. In this paper, we address the problem of PAPR reduction for FBMC-OQAM systems using Tone Reservation (TR) technique. Due to the overlapping structure of FBMCOQAM signals, directly applying TR schemes of OFDM systems to FBMC-OQAM systems is not effective. We improve the tone reservation (TR) technique by employing sliding window with Active Constellation Extension for the PAPR reduction of FBMC-OQAM signals, called sliding window tone reservation Active Constellation Extension (SW-TRACE) technique. The proposed SW-TRACE technique uses the peak reduction tones (PRTs) of several consecutive data blocks to cancel the peaks of the FBMC-OQAM signal inside a window, with dynamically extending outer constellation points in active(data-carrying) channels, within margin-preserving constraints, in order to minimize the peak magnitude. Analysis and simulation results compared to the existing Tone Reservation (TR) technique for FBMC/OQAM system. The proposed method SW-TRACE has better PAPR performance and lower computational complexity.

Keywords: FBMC-OQAM, peak-to-average power ratio, sliding window, tone reservation Active Constellation Extension.

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Authors: Joon Ho Kim, Tae Kwon Ha

Abstract:

Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by differential speed rolling (DSR) process were studied by electron back scattered diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100^oC with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400^oC for 30 to 120min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: Aluminum/Copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction.

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Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

Abstract:

This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: Finite element method, heat transfer, moisture transfer, porous materials, wood.

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

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A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: Alpana Agarwal, Akhil Sharma

Abstract:

This work presents a fully differential CMOS amplifier consisting of two self-biased gain boosted inverter stages, that provides an alternative to the power hungry operational amplifier. The self-biasing avoids the use of external biasing circuitry, thus reduces the die area, design efforts, and power consumption. In the present work, regulated cascode technique has been employed for gain boosting. The Miller compensation is also applied to enhance the phase margin. The circuit has been designed and simulated in 1.8 V 0.18 µm CMOS technology. The simulation results show a high DC gain of 100.7 dB, Unity-Gain Bandwidth of 107.8 MHz, and Phase Margin of 66.7^o with a power dissipation of 286 μW and makes it suitable candidate for the high resolution pipelined ADCs.

Keywords: CMOS amplifier, gain boosting, inverter-based amplifier, self-biased inverter.

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

Abstract:

This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: Differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control.

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Authors: Jer-Rong Chang

Abstract:

The flexible follower response of a translating cam with four different profiles for rise-dwell-fall-dwell (RDFD) motion is investigated. The cycloidal displacement motion, the modified sinusoidal acceleration motion, the modified trapezoidal acceleration motion, and the 3-4-5 polynomial motion are employed to describe the rise and the fall motions of the follower and the associated four kinds of cam profiles are studied. Since the follower flexibility is considered, the contact point of the roller and the cam is an unknown. Two geometric constraints formulated to restrain the unknown position are substituted into Hamilton-s principle with Lagrange multipliers. Applying the assumed mode method, one can obtain the governing equations of motion as non-linear differential-algebraic equations. The equations are solved using Runge-Kutta method. Then, the responses of the flexible follower undergoing the four different motions are investigated in time domain and in frequency domain.

Keywords: translating cam, flexible follower, rise-dwell-falldwell, response

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Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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Authors: Supayotin Na Songkla, Winai Jaikla

Abstract:

This article presents a resistorless current-mode firstorder allpass filter based on second generation current controlled current conveyors (CCCIIs). The features of the circuit are that: the pole frequency can be electronically controlled via the input bias current: the circuit description is very simple, consisting of 2 CCCIIs and single grounded capacitor, without any external resistors and component matching requirements. Consequently, the proposed circuit is very appropriate to further develop into an integrated circuit. Low input and high output impedances of the proposed configuration enable the circuit to be cascaded in current-mode without additional current buffers. The PSpice simulation results are depicted. The given results agree well with the theoretical anticipation. The application example as a current-mode quadrature oscillator is included.

Keywords: First-order all pass filter, current-mode, CCCII.

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Authors: Edina Koch, Péter Hudacsek

Abstract:

In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: Culvert, dynamic load, HS small model, railway transition zone.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

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The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Rampal Singh, S. Balasundaram

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In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: N. Yuvaraj, V. B. Prakash, D. Venkatraj

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This paper may be considered as combination of both pervasive computing and Differential GPS (global positioning satellite) which relates to control automatic traffic signals in such a way as to pre-empt normal signal operation and permit lifesaving vehicles. Before knowing the arrival of the lifesaving vehicles from the signal there is a chance of clearing the traffic. Traffic signal preemption system includes a vehicle equipped with onboard computer system capable of capturing diagnostic information and estimated location of the lifesaving vehicle using the information provided by GPS receiver connected to the onboard computer system and transmitting the information-s using a wireless transmitter via a wireless network. The fleet management system connected to a wireless receiver is capable of receiving the information transmitted by the lifesaving vehicle .A computer is also located at the intersection uses corrected vehicle position, speed & direction measurements, in conjunction with previously recorded data defining approach routes to the intersection, to determine the optimum time to switch a traffic light controller to preemption mode so that lifesaving vehicles can pass safely. In case when the ambulance need to take a “U" turn in a heavy traffic area we suggest a solution. Now we are going to make use of computerized median which uses LINKED BLOCKS (removable) to solve the above problem.

Keywords: Ubiquitous computing, differential GPS, fleet management system, wireless transmitter and receiver computerized median i.e. linked blocks (removable).

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: R. Srinivasa Rao

Abstract:

This paper presents a new method which applies an artificial bee colony algorithm (ABC) for capacitor placement in distribution systems with an objective of improving the voltage profile and reduction of power loss. The ABC algorithm is a new population based meta heuristic approach inspired by intelligent foraging behavior of honeybee swarm. The advantage of ABC algorithm is that it does not require external parameters such as cross over rate and mutation rate as in case of genetic algorithm and differential evolution and it is hard to determine these parameters in prior. The other advantage is that the global search ability in the algorithm is implemented by introducing neighborhood source production mechanism which is a similar to mutation process. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 69-bus system and compared the results with the other approach available in the literature. The proposed method has outperformed the other methods in terms of the quality of solution and computational efficiency.

Keywords: Distribution system, Capacitor Placement, Loss reduction, Artificial Bee Colony Algorithm.

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Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: Nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock.

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Authors: Tan Wee Choon, Abdul Saad Salleh, Saifulnizan Jamian, Mohd. Imran Ghazali

Abstract:

Phase transformation temperature is one of the most important parameters for the shape memory alloys (SMAs). The most popular method to determine these phase transformation temperatures is the Differential Scanning Calorimeter (DSC), but due to the limitation of the DSC testing itself, it made it difficult for the finished product which is not in the powder form. A novel method which uses the Universal Testing Machine has been conducted to determine the phase transformation temperatures. The Flexinol wire was applied with force and maintained throughout the experiment and at the same time it was heated up slowly until a temperature of approximately 1000C with direct current. The direct current was then slowly decreased to cool down the temperature of the Flexinol wire. All the phase transformation temperatures for Flexinol wire were obtained. The austenite start at 52.540C and austenite finish at 60.900C, while martensite start at 44.780C and martensite finish at 32.840C.

Keywords: Phase transformation temperature, Robotic, Shapememory alloy, Universal Testing Machine.

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Authors: Arpita Soni, Sapna Mittal

Abstract:

Austenite and Martensite indicate the phases of solids undergoing phase transformation which we usually associate with materials and not with living organisms. This article provides an overview of bacterial proteins and structures that are undergoing phase transformation and suggests its probable effect on mechanical behavior. The context is mainly within the role of phase transformations occurring in the flagellum of bacteria. The current knowledge of molecular mechanism leading to phase variation in living organisms is reviewed. Since in bacteria, each flagellum is driven by a separate motor, similarity to a Differential drive in case of four-wheeled vehicles is suggested. It also suggests the application of the mechanism in which bacteria changes its direction of movement to facilitate single point turning of a multi-wheeled vehicle. Finally, examples are presented to illustrate that the motion due to phase transformation of flagella in bacteria can start a whole new research on motion mechanisms.

Keywords: Flagella, Phase Transformation, Nanobots, Differential Drive, Single point turn, Biomimetics

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Authors: Arup K. George, Wai Pan Chan, Zhi Hui Kong, Minkyu Je

Abstract:

This paper describes a low-power second-order filter for a continuous-time chopper stabilized capacitive sensor interface, integrated with a fully differential post-CMOS surface-micromachined MEMS pressure sensor. The circuit uses a single-ended folded-cascode operational amplifier and two GM-C filters connected in cascade. The circuit is realized in a 0.18 μm CMOS process and offers differential to single-ended conversion. The novelty of the scheme is the cascade of two GM-C filters to achieve a second-order filter while minimizing power dissipation. The simulated filter cutoff frequency is 1.14 kHz at common-mode voltage 1.65 V, operating from a 3.3 V supply while dissipating 172μW of power. The filter achieves an operating range of 1V for an output load of 1MOhm and 10pF.

Keywords: Chopper Stabilization, MEMS, Pressure Sensors, Low Pass Filter

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Authors: Ravi V. Joat, Pravin S. Bodke, Shradha S. Binani, S. S. Wasnik

Abstract:

A phase diagram of the Ag₂SO₄ - CaSO₄ (Silver sulphate – Calcium Sulphate) binaries system using conductivity, XRD (X-Ray Diffraction Technique) and DTA (Differential Thermal Analysis) data is constructed. The eutectic reaction (liquid -» a-Ag₂SO₄ + CaSO₄) is observed at 10 mole% CaSO₄ and 645°C. Room temperature solid solubility limit up to 5.27 mole % of Ca ²⁺ in Ag₂SO₄ is set using X-ray powder diffraction and scanning electron microscopy results. All compositions beyond this limit are two-phase mixtures below and above the transition temperature (≈ 416°C). The bulk conductivity, obtained following complex impedance spectroscopy, is found decreasing with increase in CaSO₄ content. Amongst other binary compositions, the 80AgSO₄-20CaSO₄ gave improved sinterability/packing density.

Keywords: Ag2SO4-CaSO4 (Silver sulphate–Calcium Sulphate) binaries system, XRD (X-Ray Diffraction Technique) and DTA (Differential Thermal Analysis).

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Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

Abstract:

The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Non-isothermal wedge, thermal radiation, nanofluid, magnetic field, Soret and Dufour effects.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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