Search results for: vortex ring.

Authors: Zhipeng Feng, Huanhuan Qi, Pingchuan Shen, Fenggang Zang, Yixiong Zhang

Abstract:

Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×10⁴. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.

Keywords: Vortex induced vibration, limit cycle, CFD, FEM.

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Authors: M.R.Isvandzibaei, E.Bidokh, M.R.Alinaghizadeh, A.Nasirian, A.Moarrefzadeh

Abstract:

In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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Authors: Mohammad J. Almalkawi

Abstract:

A broadband wire monopole antenna loaded by inhomogeneous stack of annular dielectric ring resonators (DRRs) is proposed. The proposed antenna exhibits a broad impedance bandwidth from 3 to 30 GHz. This is achieved by adding an external step matching network at the antenna feed point. The matching network is comprised of three annular DRRs possessing different permittivity values and sharing the same axial over a finite ground plane. The antenna performance is characterized using full-wave EM simulation. Compared to previous-reported wire antennas with improved bandwidth achieved by DRRs, the proposed topology provides relatively compact realization and superior broadband performance.

Keywords: Broadband, dielectric ring resonator, wire monopole antenna.

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Authors: Hesamodin Ebnodin Hamidi, Mojtaba Rahimi

Abstract:

Along with increasing development of generation of supersonic planes especially fighters and request for increasing the performance and maneuverability scientists and engineers suggested the delta and double delta wing design. One of the areas which was necessary to be researched, was the Aerodynamic review of this type of wings in high angles of attack at low speeds that was very important in landing and takeoff the planes and maneuvers. Leading Edges of the wings,cause the separation flow from wing surface and then formation of powerful vortex with high rotational speed which studing the mechanism and location of formation and also the position of the vortex breakdown in high angles of attack is very important. In this research, a double delta wing with 76o/45o sweep angles at high angle of attack in steady state and incompressible flow were numerically analyzed with Fluent software. With analaysis of the numerical results, we arrived the most important characteristic of the double delta wings which is keeping of lift at high angles of attacks.

Keywords: Double delta wing, high angle of attack, vortex breakdown, incompressible flow.

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Authors: Kyoungwoo Park, Chol-Ho Hong, Ji-Won Han, Byeong-Sam Kim, Cha-Sik Park, Oh Kyung Kwon

Abstract:

Numerical analysis of flow characteristics and separation efficiency in a high-efficiency cyclone has been performed. Several models based on the experimental observation for a design purpose were proposed. However, the model is only estimated the cyclone's performance under the limited environments; it is difficult to obtain a general model for all types of cyclones. The purpose of this study is to find out the flow characteristics and separation efficiency numerically. The Reynolds stress model (RSM) was employed instead of a standard k-ε or a k-ω model which was suitable for isotropic turbulence and it could predict the pressure drop and the Rankine vortex very well. For small particles, there were three significant components (entrance of vortex finder, cone, and dust collector) for the particle separation. In the present work, the particle re-entraining phenomenon from the dust collector to the cyclone body was observed after considerable time. This re-entrainment degraded the separation efficiency and was one of the significant factors for the separation efficiency of the cyclone.

Keywords: CFD, High-efficiency cyclone, Pressure drop, Rankine vortex, Reynolds stress model (RSM), Separation efficiency.

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Authors: Deepak R. Bhat, Netra P. Bhandery, Ryuichi Yatabe

Abstract:

Strength recovery effect from the residual-state of shear is not well address in scientific literature. Torsional ring shear strength recovery tests on kaolin clay using rest periods up to 30 days are performed at the effective normal stress 100kN/m2. Test results shows that recovered strength measured in the laboratory is slightly noticeable after rest period of 3 days, but recovered strength lost after very small shear displacement. This paper mainly focused on the strength recovery phenomenon from the residual strength of kaolin clay based on torsional ring shear test results. Mechanisms of recovered strength are also discussed.

Keywords: Kaolin clay, Residual strength, Strength recovery, Torsional ring shear test.

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Authors: Thanut Kallaka, Ching-Jong Wang

Abstract:

High level and high velocity flood flows are potentially harmful to bridge piers as evidenced in many toppled piers, and among them the single-column piers were considered as the most vulnerable. The flood flow characteristic parameters including drag coefficient, scouring and vortex shedding are built into a pier-flood interaction model to investigate structural safety against flood hazards considering the effects of local scouring, hydrodynamic forces, and vortex induced resonance vibrations. By extracting the pier-flood simulation results embedded in a neural networks code, two cases of pier toppling occurred in typhoon days were reexamined: (1) a bridge overcome by flash flood near a mountain side; (2) a bridge washed off in flood across a wide channel near the estuary. The modeling procedures and simulations are capable of identifying the probable causes for the tumbled bridge piers during heavy floods, which include the excessive pier bending moments and resonance in structural vibrations.

Keywords: Bridge piers, Neural networks, Scour depth, Structural safety, Vortex shedding

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Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

Abstract:

In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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Authors: Suleyman Ciftci, Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that some collineations of M(A) preserve cross-ratio.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio.

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Authors: Arash Taheri

Abstract:

In this paper, effects of the ventral body planform of a swimming whale shark on the formation of ‘reverse von-Kármán vortex street’ behind the aquatic animal are studied using Fluid-Structure Interaction (FSI) approach. In this regard, incompressible Navier-Stokes equations around the whale shark’s body with a prescribed deflection dynamics are solved with the aid of Boundary Data Immersion Method (BDIM) and Implicit Large Eddy Simulation (ILES) turbulence treatment by WaterLily.jl solver; fully-written in Julia programming language. The whale shark flow simulations here are performed at high Reynolds number, i.e. 1.4 107 corresponding to the swimming of a 10 meter-whale shark at an average speed of 5 km/h. For comparison purposes, vortical flow generation behind a silky shark with a streamlined forehead eidonomy is also simulated at high Reynolds number, Re = 2 106, corresponding to the swimming of a 2 meter-silky shark at an average speed of 3.6 km/h. The results depict formation of distinct wake topologies behind the swimming sharks depending on the travelling wave oscillating amplitudes.

Keywords: Whale shark, vortex street, BDIM, FSI, functional eidonomy, bionics.

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Authors: M. Nageswara Rao, V. S. N. K. Chaitanya, P. Pratyusha

Abstract:

High voltage insulator has to withstand sever electrical stresses. Higher electrical stresses lead to erosion of the insulator surface. Degradation of insulating properties leads to flashover and in some extreme cases it may cause to puncture. For analyzing these electrical stresses and implement necessary actions to diminish the electrical stresses, numerical methods are best. By minimizing the electrical stresses, reliability of the power system will improve. In this paper electric field intensity at critical regions of 400 kV silicone composite insulator is analyzed using finite element method. Insulator is designed using FEMM-2D software package. Electric Field Analysis (EFA) results are analyzed for five cases i.e., only insulator, insulator with two sides arcing horn, High Voltage (HV) end grading ring, grading ring-arcing horn arrangement and two sides grading ring. These EFA results recommended that two sides grading ring is better for minimization of electrical stresses and improving life span of insulator.

Keywords: Polymer insulator, electric field analysis, numerical methods, finite element method, FEMM-2D.

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Authors: D. Yilmaz, M.R. Usal

Abstract:

Nozzle is the main part of various spinning systems such as air-jet and Murata air vortex systems. Recently, many researchers worked on the usage of the nozzle on different spinning systems such as conventional ring and compact spinning systems. In these applications, primary purpose is to improve the yarn quality. In present study, it was produced the yarns with two different nozzle types and determined the changes in yarn properties. In order to explain the effect of the nozzle, airflow structure in the nozzle was modelled and airflow variables were determined. In numerical simulation, ANSYS 12.1 package program and Fluid Flow (CFX) analysis method was used. As distinct from the literature, Shear Stress Turbulent (SST) model is preferred. And also air pressure at the nozzle inlet was measured by electronic mass flow meter and these values were used for the simulation of the airflow. At last, the yarn was modelled and the area from where the yarn is passing was included to the numerical analysis.

Keywords: Nozzle, compressed air, swirling airflow, yarn properties.

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Authors: Hailu Dessalegn, T. Srinivas

Abstract:

We propose new multiple-channel piezoelectric (PZT) actuated tunable optical filter based on racetrack multi-ring resonators for wavelength de-multiplexing network applications. We design tunable eight-channel wavelength de-multiplexer consisting of eight cascaded PZT actuated tunable multi-ring resonator filter with a channel spacing of 1.6nm. The filter for each channel is basically structured on a suspended beam, sandwiched with piezoelectric material and built in integrated ring resonators which are placed on the middle of the beam to gain uniform stress and linearly varying longitudinal strain. A reference single mode serially coupled multi stage racetrack ring resonator with the same radii and coupling length is designed with a line width of 0.8974nm with a flat top pass band at 1dB of 0.5205nm and free spectral range of about 14.9nm. In each channel, a small change in the perimeter of the rings is introduced to establish the shift in resonance wavelength as per the defined channel spacing. As a result, when a DC voltage is applied, the beams will elongate, which involves mechanical deformation of the ring resonators that induces a stress and a strain, which brings a change in refractive index and perimeter of the rings leading to change in the output spectrum shift providing the tunability of central wavelength in each channel. Simultaneous wave length shift as high as 45.54pm/

Keywords: Optical MEMS, piezoelectric (PZT) actuation, tunable optical filter, wavelength de-multiplexer.

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Authors: Beibei Han, Yong-Jin Yoon, Muhammad Hamidullah, Angel Tsu-Hui Lin, Woo-Tae Park

Abstract:

This paper presents the design of a ring-shaped tri-axial fore sensor that can be incorporated into the tip of a guidewire for use in minimally invasive surgery (MIS). The designed sensor comprises a ring-shaped structure located at the center of four cantilever beams. The ringdesign allows surgical tools to be easily passed through which largely simplified the integration process. Silicon nanowires (SiNWs) are used aspiezoresistive sensing elementsembeddedon the four cantilevers of the sensor to detect the resistance change caused by the applied load.An integration scheme with new designed guidewire tip structure having two coils at the distal end is presented. Finite element modeling has been employed in the sensor design to find the maximum stress location in order to put the SiNWs at the high stress regions to obtain maximum output. A maximum applicable force of 5 mN is found from modeling. The interaction mechanism between the designed sensor and a steel wire has been modeled by FEM. A linear relationship between the applied load on the steel wire and the induced stress on the SiNWs were observed.

Keywords: Triaxial MEMS force sensor, Ring shape, Silicon Nanowire, Minimally invasive surgery.

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Authors: Atilla Akpinar, Basri Celik, Suleyman Ciftci

Abstract:

In this paper, we carry over some of the results which are valid on a certain class of Moufang-Klingenberg planes M(A) coordinatized by an local alternative ring A := A(ε) = A+Aε of dual numbers to finite projective Klingenberg plane M(A) obtained by taking local ring Zq (where prime power q = pk) instead of A. So, we show that the collineation group of M(A) acts transitively on 4-gons, and that any 6-figure corresponds to only one inversible m ∈ A.

Keywords: finite Klingenberg plane, projective collineation, 4-transitivity, 6-figures.

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Authors: Jessie Yiying Quah, Vivian Netto, Jack Sheng Kee, Eric Mouchel La Fosse, Mi Kyoung Park

Abstract:

We present a dextran modified silicon microring resonator sensor for high density antibody immobilization. An array of sensors consisting of three sensor rings and a reference ring was fabricated and its surface sensitivity and the limit of detection were obtained using polyelectrolyte multilayers. The mass sensitivity and the limit of detection of the fabricated sensor ring are 0.35 nm/ng mm-2 and 42.8 pg/mm2 in air, respectively. Dextran modified sensor surface was successfully prepared by covalent grafting of oxidized dextran on 3-aminopropyltriethoxysilane (APTES) modified silicon sensor surface. The antibody immobilization on hydrogel dextran matrix improves 40% compared to traditional antibody immobilization method via APTES and glutaraldehyde linkage.

Keywords: Antibody immobilization, Dextran, Immunosensor, Label-free detection, Silicon micro-ring resonator

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Authors: Peristera A. Baziana

Abstract:

The idea of the asynchronous transmission in wavelength division multiplexing (WDM) ring MANs is studied in this paper. Especially, we present an efficient access technique to coordinate the collisions-free transmission of the variable sizes of IP traffic in WDM ring core networks. Each node is equipped with a tunable transmitter and a tunable receiver. In this way, all the wavelengths are exploited for both transmission and reception. In order to evaluate the performance measures of average throughput, queuing delay and packet dropping probability at the buffers, a simulation model that assumes symmetric access rights among the nodes is developed based on Poisson statistics. Extensive numerical results show that the proposed protocol achieves apart from high bandwidth exploitation for a wide range of offered load, fairness of queuing delay and dropping events among the different packets size categories.

Keywords: Asynchronous transmission, collision avoidance, wavelength division multiplexing.

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Authors: Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that a collineation of M(A) preserve cross-ratio. Also, we obtain some results about harmonic points.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonic points.

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Authors: Pierre-Louis Cayrel, Sidi Mohamed El Yousfi Alaoui

Abstract:

In this paper, we propose a dual version of the first threshold ring signature scheme based on error-correcting code proposed by Aguilar et. al in [1]. Our scheme uses an improvement of Véron zero-knowledge identification scheme, which provide smaller public and private key sizes and better computation complexity than the Stern one. This scheme is secure in the random oracle model.

Keywords: Stern algorithm, Véron algorithm, threshold ring signature, post-quantum cryptography.

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Authors: Satya P. Dubey, Hrushikesh A. Abhyankar, Veronica Marchante, James L. Brighton, Björn Bergmann

Abstract:

PLA emerged as a promising polymer because of its property as a compostable, biodegradable thermoplastic made from renewable sources. PLA can be polymerized from monomers (Lactide or Lactic acid) obtained by fermentation processes from renewable sources such as corn starch or sugarcane. For PLA synthesis, ring opening polymerization (ROP) of Lactide monomer is one of the preferred methods. In the literature, the technique mainly developed for ROP of PLA is based on metal/bimetallic catalyst (Sn, Zn and Al) or other organic catalysts in suitable solvent. However, the PLA synthesized using such catalysts may contain trace elements of the catalyst which may cause toxicity. This work estimated the usefulness and drawbacks of using different catalysts as well as effect of alternative energies and future aspects for PLA production.

Keywords: Alternative energy, bio-degradable, metal catalyst, poly lactic acid (PLA), ring opening polymerization (ROP).

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Authors: C. Elavarasi, T. Shanmuganantham

Abstract:

A coplanar waveguide (CPW) feed is presented, and comprising a split ring resonator (SRR) loaded fractal with water lily shape is used for multi band applications. The impedance matching of the antenna is determined by the number of Koch curve fractal unit cells. The antenna is designed on a FR4 substrate with a permittivity of ε_{r =} 4.4 and size of 14 x 16 x 1.6 mm³ to generate multi resonant mode at 3.8 GHz covering S band, 8.68 GHz at X band, 13.96 GHz at Ku band, and 19.74 GHz at K band with reflection coefficient better than -10 dB. Simulation results show that the antenna exhibits the desired voltage standing wave ratio (VSWR) level and radiation patterns across the wide frequency range. The fundamental parameters of the antenna such as return loss, VSWR, good radiation pattern with reasonable gain across the operating bands are obtained.

Keywords: Monopole antenna, fractal, metamaterial, waterlily shape, split ring resonator, multiband.

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Authors: Khaled M. Nabil

Abstract:

This paper introduces the Nested Vortexes conception of the universe structure and interprets all the physical phenomena according this conception. The paper first reviews recent physics theories, either in microscopic scale or macroscopic scale, to collect evidence that the space is not empty. But, these theories describe the property of the space medium without determining its structure. Determining the structure of space medium is essential to understand the mechanism that leads to its properties. Without determining the space medium structure, many phenomena; such as electric and magnetic fields, gravity, or wave-particle duality remain uninterpreted. Thus, this paper introduces a conception about the structure of the universe. It assumes that the universe is a medium of ultra-tiny homogeneous particles which are still undiscovered. Like any medium with certain movements, possibly because of a great asymmetric explosion, vortexes have occurred. A vortex condenses the ultra-tiny particles in its center forming a bigger particle, the bigger particles, in turn, could be trapped in a bigger vortex and condense in its center forming a much bigger particle and so on. This conception describes galaxies, stars, protons as particles at different levels. Existing of the particle’s vortexes make the consistency of the speed of light postulate is not true. This conception shows that the vortex motion dynamic agrees with the motion of all the universe particles at any level. An experiment has been carried out to detect the orbiting effect of aggregated vortexes of aligned atoms of a permanent magnet. Based on the described particle’s structure, the gravity force of a particle and attraction between particles as well as charge, electric and magnetic fields and quantum mechanics characteristics are interpreted. All augmented physics phenomena are solved.

Keywords: Astrophysics, cosmology, particles’ structure model, particles’ forces, vortex dynamics.

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Authors: Hung-Wei Wu, Yung-Wei Chen, Yu-Fu Chen, Cheng-Yuan Hung

Abstract:

This paper presents a new ultra-wideband (UWB) bandpass filter (BPF) with sharp roll-off and dual-notched bands. The filter consists of a triangle ring multi-mode resonator (MMR) with the stub-loaded resonator (SLR) for controlling the two transmission zeros at 2.8 / 11 GHz, the embedded open-circuited stub and the asymmetric tight coupled input/output (I/O) lines for introducing the dual notched bands at 5.2 / 6.8 GHz. The attenuation slope in the lower and higher passband edges of the proposed filter show 160- and 153-dB/GHz, respectively. This study mainly provides a simple method to design a UWB bandpass filter with high passband selectivity and dual-notched bands for satisfying the Federal Communications Commission (FCC-defined) indoor UWB specification

Keywords: steeply slopes transition band, bandpass filter, ultra-wideband (UWB), triangle-ring, multi-mode resonator, stub-loaded resonator.

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Authors: Mohammed A. Aziz, Ibrahim A. M. Gad, El Shahat F. A. Mohammed, Ramy H. Mohammed

Abstract:

This paper investigates experimental and numerical study of the airflow characteristics for vortex, round and square ceiling diffusers and its effect on the thermal comfort in a ventilated room. Three different thermal comfort criteria namely; Mean Age of the Air (MAA), ventilation effectiveness (E), and Effective Draft Temperature (EDT) have been used to predict the thermal comfort zone inside the room. In experimental work, a sub-scale room is set-up to measure the temperature field in the room. In numerical analysis, unstructured grids have been used to discretize the numerical domain. Conservation equations are solved using FLUENT commercial flow solver. The code is validated by comparing the numerical results obtained from three different turbulence models with the available experimental data. The comparison between the various numerical models shows that the standard k-ε turbulence model can be used to simulate these cases successfully. After validation of the code, effect of supply air velocity on the flow and thermal field could be investigated and hence the thermal comfort. The results show that the pressure coefficient created by the square diffuser is 1.5 times greater than that created by the vortex diffuser. The velocity decay coefficient is nearly the same for square and round diffusers and is 2.6 times greater than that for the vortex diffuser.

Keywords: Ceiling diffuser, Thermal Comfort, MAA, EDT, Fluent, Turbulence model.

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Authors: Subal Kar, Madhuja Ghosh, Amitesh Kumar, Arijit Majumder

Abstract:

Complementary split-ring resonator (CSRR) loaded microstrip square patch antenna has been optimally designed with the help of high frequency structure simulator (HFSS). The antenna has been fabricated on the basis of the simulation design data and experimentally tested in anechoic chamber to evaluate its gain, bandwidth, efficiency and polarization characteristics. The CSRR loaded microstrip patch antenna has been found to realize significant size miniaturization (to the extent of 24%) compared to the conventional-type microstrip patch antenna both operating at the same frequency (5.2 GHz). The fabricated antenna could realize a maximum gain of 4.17 dB, 10 dB impedance bandwidth of 34 MHz, efficiency 50.73% and with maximum cross-pol of 10.56 dB down at the operating frequency. This practically designed antenna with its miniaturized size is expected to be useful for airborne and space borne applications at microwave frequency.

Keywords: Split ring resonator, metamaterial, CSRR loaded patch antenna, microstrip patch antenna, LC resonator.

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Authors: Jianmin Xing

Abstract:

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ =  T M D 0 U N 0 0 V .

Keywords: Generalized module homomorphism, ring homomorphism, isomorphisms, triangular matrix rings.

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Authors: Shaoquan Sun, Chunxiang Liu

Abstract:

In this paper, we extend the fuzzy subrings with operators to the (λ, μ)-fuzzy subrings with operators. And the concepts of the (λ, μ)-fuzzy subring with operators and (λ, μ)-fuzzy quotient ring with operators are gived, while their elementary properties are discussed.

Keywords: Fuzzy subring with operators, (λ, μ)-fuzzy subring with operators, (λ, μ)-fuzzy quotient ring with operators.

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Authors: M. Azadbakht, Y. Fadakar

Abstract:

Since fuel must be injected with appropriate pressure and time for accurate performance of diesel engines, then proper function of engine is influenced by accurate function of injector pump. At first total pump was designed by SolidWorks 2012 software. Then the total relationship of rotor, roller, internal cam ring, pole shoe and plunger in injector pump in MF285 tractor and their performance was shown. During suction state rollers connect with dents in internal cam ring and in pressure course pole shoes have drawer move in rotor and perform tappet action between rollers and plungers. The maximum stress was obtained by using analysis of finite element method. The maximum stress in contact surface of roller and internal cam ring and on roller surface. The maximum amount of this stress is 288.12 MPa. According to conducted analyses, the minimum value for safety factor is related to roller surface and it equals to 2.0477.

Keywords: Rotary injector pump, MF285 tractor, finite element, stress.

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Authors: Sreedevi P. Chakyar, Jolly Andrews, V. P. Joseph

Abstract:

A compact method for measuring the relative permittivity of a dielectric material at different temperatures using a single circular Split Ring Resonator (SRR) metamaterial unit working as a test probe is presented in this paper. The dielectric constant of a material is dependent upon its temperature and the LC resonance of the SRR depends on its dielectric environment. Hence, the temperature of the dielectric material in contact with the resonator influences its resonant frequency. A single SRR placed between transmitting and receiving probes connected to a Vector Network Analyser (VNA) is used as a test probe. The dependence of temperature between 30 ^oC and 60 ^oC on resonant frequency of SRR is analysed. Relative permittivities ‘ε’ of test samples for different temperatures are extracted from a calibration graph drawn between the relative permittivity of samples of known dielectric constant and their corresponding resonant frequencies. This method is found to be an easy and efficient technique for analysing the temperature dependent permittivity of different materials.

Keywords: Metamaterials, negative permeability, permittivity measurement techniques, split ring resonators, temperature dependent dielectric constant.

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Authors: Troy L. Story

Abstract:

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.

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