Search results for: Average Run Length.

Authors: Zakir Husain, Neem Sagar, Neeraj Gupta

Abstract:

Due to the increased penetration of renewable energy resources in the distribution system, the system is no longer passive in nature. In this paper, a steady state analysis of the distribution system has been done with the inclusion of wind generation. The modeling of wind turbine generator system and wind generator has been made to obtain the average active and the reactive power injection into the system. The study has been conducted on a IEEE-33 bus system with two wind generators. The present research work is useful not only to utilities but also to customers.

Keywords: Distributed generation, distribution network, radial network, wind turbine generating system.

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Authors: Chien-Cheng Kuo

Abstract:

We design and discuss metal-dielectric antireflection coating on metallic substrates for Solar Selective Absorbers of Concentrating Solar Power Systems. The average reflectance is 8.5% at 400-3000nm and 84.4% at 3000nm-10000nm of the metal-dielectric structure.

Keywords: Concentrating solar power systems, solar thermal, solar selective absorber, absorptance, emittance.

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Authors: Emanuela Paranhos Lima, Vitaly Félix Rodríguez Esquerre

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In this work, efficient directional coupler composed of dielectric waveguides and metallic film has been analyzed in details by simulations using finite element method (FEM). The structure consists of a step-index fiber with dielectric core, silica cladding, and a metal nanowire parallel to the core. The results show that an efficient conversion of optical dielectric modes to long range plasmonic is possible. Low insertion losses in conjunction with short coupling length and a broadband operation can be achieved under certain conditions. This kind of couplers has potential applications for the design of photonic integrated circuits for signal routing between dielectric/plasmonic waveguides, sensing, lithography, and optical storage systems. A high efficient focusing of light in a very small region can be obtained.

Keywords: Directional coupler, finite element method, metallic nanowire, plasmonic, surface plasmon polariton.

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Authors: Meshkati M. E., Dehghani A. A., Naser G., E mamgholizadeh S., Mosaedi A.

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Sedimentation in reservoirs and the corresponding loss of storage capacity is one of the most serious problems in dam engineering. Pressurized flushing, a way to remove sediments from the reservoir, is flushing under a pressurized flow condition and nearly constant water level. Pressurized flushing has only local effects around the outlet. Sediment in the vicinity of the outlet openings is scoured and a funnel shaped crater is created. In this study, the temporal development of flushing cone under various hydraulic conditions was studied experimentally. Time variations of parameters such as maximum length and width of flushing and also depth of scouring cone was measured. Results indicated that an increase in flow velocity (and consequently in Froude number) established new hydraulically conditions for flushing mechanism and so a sudden growth was observed in the amount of sediment released and also scouring dimenssions. In addition, a set of nondimensional relationships were identified for temporal variations of flushing scour dimenssions, which can eventuallt be used to estimate the development of flushing cone.

Keywords: Pressure Flushing, Dam, Sediment, Scouring.

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Authors: T. K. Sriram, Joydip Dhar

Abstract:

Models based on stage structure have found varied applications in population models. This paper proposes a stage structured model to study the trends in the computer and video game playing population of US. The game paying population is divided into three compartments based on their age group. After simulating the mathematical model, a forecast of the number of game players in each stage as well as an approximation of the average age of game players in future has been made.

Keywords: Age structure, Forecasting, Mathematical modeling, Stage structure.

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Authors: Md Abdullah Al Faruque

Abstract:

A very large percentage of bridge failures are attributed to scouring around bridge piers and this directly influences public safety. Experiments are carried out in a 12-m long rectangular open channel flume made of transparent tempered glass. A 300 mm thick bed made up of sand particles is leveled horizontally to create the test bed and a 50 mm hollow plastic cylinder is used as a model bridge pier. Tests are carried out with varying flow depths and velocities. Data points of various scour parameters such as scour depth, width, and length are collected based on different flow conditions and visual observations of changes in the stream bed downstream the bridge pier are also made as the scour progresses. Result shows that all three major flow characteristics (flow depth, Froude number and densimetric Froude number) have one way or other affect the scour profile.

Keywords: Bridge pier scour, densimetric Froude number, flow depth, Froude Number, sand.

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Authors: A. Jawahar

Abstract:

In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).

Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.

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Authors: S. GhaffariTooran, H. Abolghasemi, H. Bahmanyar, M. Esmaeili, A. Safari

Abstract:

Using plug flow model in conjunction with experimental solute concentration profiles, overall volumetric mass transfer coefficient based on continuous phase (Koca), in a packed liquid-liquid extraction column has been optimized. Number of 12 experiments has been done using standard system of water/acid acetic/toluene in a 6 cm diameter, 120 cm height column. Thorough consideration of influencing parameters we intended to correlate dimensionless parameters in term of overall Sherwood number which has an acceptable average error of about 15.8%.

Keywords: Packed column, mass transfer coefficient, solvent extraction, Sherwood number.

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Authors: Se Kyung Oh, Ary Bachtiar Krishna Putra, Soo Whan Ahn

Abstract:

A numerical study on the turbulent flow and heat transfer characteristics in the rectangular channel with different types of baffles is carried out. The inclined baffles have the width of 19.8 cm, the square diamond type hole having one side length of 2.55 cm, and the inclination angle of 5o. Reynolds number is varied between 23,000 and 57,000. The SST turbulence model is applied in the calculation. The validity of the numerical results is examined by the experimental data. The numerical results of the flow field depict that the flow patterns around the different baffle type are entirely different and these significantly affect the local heat transfer characteristics. The heat transfer and friction factor characteristics are significantly affected by the perforation density of the baffle plate. It is found that the heat transfer enhancement of baffle type II (3 hole baffle) has the best values.

Keywords: Turbulent flow, rectangular channel, inclined baffle, heat transfer, friction factor.

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Authors: M. Kamal M. Shah, Noorhifiantylaily Ahmad, O. Irma Wani, J. Sahari

Abstract:

This paper presents the computationally mechanics analysis of energy absorption for cylindrical and square thin wall tubed structure by using ABAQUS/explicit. The crashworthiness behavior of AISI 1020 mild steel thin-walled tube under axial loading has been studied. The influence effects of different model’s cross-section, as well as model length on the crashworthiness behavior of thin-walled tube, are investigated. The model was placed on loading platform under axial loading with impact velocity of 5 m/s to obtain the deformation results of each model under quasi-static loading. The results showed that model undergoes different deformation mode exhibits different energy absorption performance.

Keywords: Axial loading, energy absorption performance, computational mechanics, crashworthiness behavior, deformation mode, thin-walled tubes.

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Authors: M.J. Park, K.H. Kim, O.M. Kwon

Abstract:

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.

Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

This paper presents the effect of stiffeners on the behavior of slender steel I-beams. Nonlinear three dimensional finite element models are developed to represent the stiffened steel I-beams. The well established finite element (ANSYS 13.0) program is used to simulate the geometric and material nonlinear nature of the problem. Verification is achieved by comparing the obtained numerical results with the results of previous published experimental work. The parameters considered in the analysis are the horizontal stiffener's position and the horizontal stiffener's dimensions as well as the number of vertical stiffeners. The studied dimensions of the horizontal stiffeners include the stiffener width, the stiffener thickness and the stiffener length. The results of the achieved numerical parametric study for slender steel I-beams show the significant effect of stiffeners on the beam behavior and its failure load.

Keywords: Steel I-beams, local buckling, slender, stiffener, thin walled section.

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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: Raheleh Khademian, Roghayeh Aminian

Abstract:

For the study of salinity stress on Vicia villosa and calcium effect for modulation of that, an experiment was conducted under hydroponic condition, and some important morphological and physiological characteristics were evaluated. This experiment was conducted as a factorial based on randomized complete design with three replications. The treatments include salinity stress in three levels (0, 50, and 100 mM NaCl) and calcium in two levels (content in Hoagland solution and double content). The results showed that all morphological and physiological traits include root and shoot length, root and shoot wet and dry weight, leaf area, leaf chlorophyll content, RWC, CMS, and biological yield was significantly different from the control and is affected by the salinity stress severely. But, calcium effect on them was not significant despite of decreasing salinity effect.

Keywords: Vicia villossa, salinity stress, calcium, hydroponic.

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Authors: Aurora Cerri, Niko Pullojani

Abstract:

Long-term differential settlement between the bridge structure and the bridge embankment typically results in an abrupt grade change, causing driver discomfort, impairing driver safety, and exerting a potentially excessive impact traffic loading on the abutment. This paper has analysed a case of study showing the effect of an approaching slab realized in a bridge constructed at Tirane-Elbasan Motorway. The layer thickness under the slab is modeled as homogenous, the slab is a reinforced concrete structure and over that the asphaltic layers take place. Analysis indicates that reinforced concrete approaching slab distributes the stresses quite uniformly into the road fill layers and settlements varies in a range less than 2.50 cm in the total slab length of 6.00 m with a maximum slope of 1/240. Results taken from analytical analysis are compared with topographic measurements done on field and they carry great similarities.

Keywords: Approach slab, bridge, road pavement, differential settlement.

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Authors: Paul O'Leary, Matthew Harker

Abstract:

This paper presents unified theory for local (Savitzky- Golay) and global polynomial smoothing. The algebraic framework can represent any polynomial approximation and is seamless from low degree local, to high degree global approximations. The representation of the smoothing operator as a projection onto orthonormal basis functions enables the computation of: the covariance matrix for noise propagation through the filter; the noise gain and; the frequency response of the polynomial filters. A virtually perfect Gram polynomial basis is synthesized, whereby polynomials of degree d = 1000 can be synthesized without significant errors. The perfect basis ensures that the filters are strictly polynomial preserving. Given n points and a support length ls = 2m + 1 then the smoothing operator is strictly linear phase for the points xi, i = m+1. . . n-m. The method is demonstrated on geometric surfaces data lying on an invariant 2D lattice.

Keywords: Gram polynomials, Savitzky-Golay Smoothing, Discrete Polynomial Moments

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Authors: M. Yoneda

Abstract:

In this paper, a lateral walking design force per person is proposed and compared with Imperial College test results. Numerical simulations considering the proposed walking design force which is incorporated into the neural-oscillator model are carried out placing much emphasis on the synchronization (the lock-in phenomenon) for a pedestrian bridge model with the span length of 50 m. Numerical analyses are also conducted for an existing pedestrian suspension bridge. As compared with full scale measurements for this suspension bridge, it is confirmed that the analytical method based on the neural-oscillator model might be one of the useful ways to explain the synchronization (the lock-in phenomenon) of pedestrians being on the bridge.

Keywords: Pedestrian bridge, human-induced lateral vibration, neural-oscillator, full scale measurement, dynamic response analysis.

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Authors: Boualem Chetti

Abstract:

In this paper, the dynamic characteristics of a threelobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory .The finite difference technique has been used to determine the solution of the modified Reynolds equation. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show that the three-lobe bearing lubricated with micropolar fluid exhibits better stability compared with that lubricated with Newtonian fluid. According to the results obtained, the effect of the parameter micropolar fluid is remarkable on the dynamic characteristics and stability of the three-lobe bearing.

Keywords: Three-lobe bearings, Micropolar fluid, Dynamic characteristics, Stability analysis.

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Authors: Sajith Sajeev, Brenton McLaury, Siamack Shirazi

Abstract:

In the petroleum industry, solid particles are often present along with the produced fluids. It is imperative to keep particles from accumulating in flow lines. In this study, various experiments are conducted to study sand particle transport, where critical velocity is defined as the average fluid velocity to keep particles continuously moving. Many parameters related to the fluid, particles and pipe affect the transport process. Experimental results are presented varying the particle concentration. Additionally, CFD simulations using a discrete element modeling (DEM) approach are presented to compare with experimental result.

Keywords: Particle transport, critical velocity, CFD, DEM.

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Authors: Sanjay Kumar Srivastava, Anu Rani Sharma, Kamna Sachdeva

Abstract:

Every year, fog formation over the Indo-Gangetic Plains (IGPs) of Indian region during the winter months of December and January is believed to create numerous hazards, inconvenience, and economic loss to the inhabitants of this densely populated region of Indian subcontinent. The aim of the paper is to analyze the spatial and temporal variability of winter fog over IGPs. Long term ground observations of visibility and other meteorological parameters (1971-2010) have been analyzed to understand the formation of fog phenomena and its relevance during the peak winter months of January and December over IGP of India. In order to examine the temporal variability, time series and trend analysis were carried out by using the Mann-Kendall Statistical test. Trend analysis performed by using the Mann-Kendall test, accepts the alternate hypothesis with 95% confidence level indicating that there exists a trend. Kendall tau’s statistics showed that there exists a positive correlation between time series and fog frequency. Further, the Theil and Sen’s median slope estimate showed that the magnitude of trend is positive. Magnitude is higher during January compared to December for the entire IGP except in December when it is high over the western IGP. Decade wise time series analysis revealed that there has been continuous increase in fog days. The net overall increase of 99 % was observed over IGP in last four decades. Diurnal variability and average daily persistence were computed by using descriptive statistical techniques. Geo-statistical analysis of fog was carried out to understand the spatial variability of fog. Geo-statistical analysis of fog revealed that IGP is a high fog prone zone with fog occurrence frequency of more than 66% days during the study period. Diurnal variability indicates the peak occurrence of fog is between 06:00 and 10:00 local time and average daily fog persistence extends to 5 to 7 hours during the peak winter season. The results would offer a new perspective to take proactive measures in reducing the irreparable damage that could be caused due to changing trends of fog.

Keywords: Fog, climatology, Mann-Kendall test, trend analysis, spatial variability, temporal variability, visibility.

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Authors: S. Moghaddaszadeh-Ahrabi, S. Farajnia, Gh. Rahimi-Mianji, A. Nejati-Javaremi

Abstract:

In recent years, there has been an increasing interest toward the use of bovine genotyped embryos for commercial embryo transfer programs. Biopsy of a few cells in morulla stage is essential for preimplantation genetic diagnosis (PGD). Low amount of DNA have limited performing the several molecular analyses within PGD analyses. Whole genome amplification (WGA) promises to eliminate this problem. We evaluated the possibility and performance of an improved primer extension preamplification (I-PEP) method with a range of starting bovine genomic DNA from 1-8 cells into the WGA reaction. We optimized a short and simple I-PEP (ssI-PEP) procedure (~3h). This optimized WGA method was assessed by 6 loci specific polymerase chain reactions (PCRs), included restriction fragments length polymorphism (RFLP). Optimized WGA procedure possesses enough sensitivity for molecular genetic analyses through the few input cells. This is a new era for generating characterized bovine embryos in preimplantation stage.

Keywords: Whole genome amplification (WGA), Genotyping, Bovine, Preimplantation genetic diagnosis (PGD)

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Authors: Pavel Psota, Vít Lédl, Jan Václavík, Roman Doleček, Pavel Mokrý, Petr Vojtíšek

Abstract:

This paper presents advanced time average digital holography by means of frequency shift and phase modulation. This technique can measure amplitudes of vibrations at ultimate dynamic range while the amplitude distribution evaluation is done independently in every pixel. The main focus of the paper is to gain insight into behavior of the method at low amplitudes of vibrations. In order to reach that, a set of experiments was performed. Results of the experiments together with novel noise suppression show the limit of the method to be below 0.1 nm.

Keywords: Acousto-optical modulator, digital holography, low amplitudes, vibrometry.

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Authors: Shuhana Shamsuddin, Nur Rasyiqah Abu Hassan, Ahmad Bashri Sulaiman

Abstract:

Liveable city is referred to as the quality of life in an area that contributes towards a safe, healthy and enjoyable place. This paper discusses the role of the streets- activities in making Kuala Lumpur a liveable city and the happiness level of the residents towards the city-s street activities. The study was conducted using the residents of Kuala Lumpur. A mixed method technique is used with the quantitative data as a main data and supported by the qualitative data. Data were collected using questionnaires, observation and also an interview session with a sample of residents of Kuala Lumpur. The sampling technique is based on multistage cluster data sampling. The findings revealed that, there is still no significant relationship between the length of stay of the resident in Kuala Lumpur with the happiness level towards the street activities that occurred in the city.

Keywords: Liveable city, activities, urban design quality, quality of life, happiness level.

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Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

Abstract:

Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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Authors: A. Benmerkhi, A. Bounouioua, M. Bouchemat, T. Bouchemat

Abstract:

In this paper, we present a numerical optical properties of a triangular periodic lattice of elliptical air holes. We report the influence of the ratio (semi-major axis length of elliptical hole to the filling ratio) on the photonic band gap. Then by using the finite difference time domain (FDTD) algorithm, the resonant wavelength of the point defect microcavities in a two-dimensional photonic crystal (PC) shifts towards the low wavelengths with significantly increased filing ratio. It can be noted that the Q factor is gradually changed to higher when the filling ratio increases. It is due to an increase in reflectivity of the PC mirror. Also we theoretically investigate the H1 cavity, where the value of semi-major axis (Rx) of the six holes surrounding the cavity are fixed at 0.5a and the Rx of the two edge air holes are fixed at the optimum value of 0.52a. The highest Q factor of 4.1359 × 10⁶ is achieved at the resonant mode located at λ = 1.4970 µm.

Keywords: Photonic crystal, microcavity, filling ratio, elliptical holes.

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Authors: D. Salari, A. Niaei, P. Chitsaz Yazdi, M. Derakhshani, S. R. Nabavi

Abstract:

This work aims to test the application of computational fluid dynamics (CFD) modeling to fixed bed catalytic cracking reactors. Studies of CFD with a fixed bed design commonly use a regular packing with N=2 to define bed geometry. CFD allows us to obtain a more accurate view of the fluid flow and heat transfer mechanisms present in fixed bed equipment. Naphtha was used as feedstock and the reactor length was 80cm. It is divided in three sections that catalyst bed packed in the middle section of the reactor. The reaction scheme was involved one primary reaction and 24 secondary reactions. Because of high CPU times in these simulations, parallel processing have been used. In this study the coke formation process in fixed bed and empty tube reactor was simulated and coke in these reactors are compared. In addition, the effect of steam ratio and feed flow rate on coke formation was investigated.

Keywords: Coke Formation, CFD Simulation, Fixed Bed, Catalyitic Cracking.

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Authors: N. Azadi-Tinat, H. Oraizi

Abstract:

Design of compact UWB multilayered microstrip filter with E-shape resonator is presented, which provides wide stopband up to 20 GHz and arbitrary impedance matching. The design procedure is developed based on the method of least squares and theory of N-coupled transmission lines. The dimensions of designed filter are about 11 mm × 11 mm and the three E-shape resonators are placed among four dielectric layers. The average insertion loss in the passband is less than 1 dB and in the stopband is about 30 dB up to 20 GHz. Its group delay in the UWB region is about 0.5 ns. The performance of the optimized filter design perfectly agrees with the microwave simulation softwares.

Keywords: Ultra-wideband, method of least square, multilayer microstrip filter, n-coupled transmission lines.

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Authors: Y. Obikane , M.Kaneko, K.Kakioka, K.Ogura

Abstract:

The fine structure of supercavitation in the wake of a symmetrical cylinder is studied with high-speed video cameras. The flow is observed in a cavitation tunnel at the speed of 8m/sec when the sidewall and the wake are partially filled with the massive cavitation bubbles. The present experiment observed that a two-dimensional ripple wave with a wave length of 0.3mm is propagated in a downstream direction, and then abruptly increases to a thicker three-dimensional layer. IR-photography recorded that the wakes originated from the horseshoe vortexes alongside the cylinder. The wake was developed to inside the dead water zone, which absorbed the bubbly wake propelled from the separated vortices at the center of the cylinder. A remote sensing classification technique (maximum most likelihood) determined that the surface porosity was 0.2, and the mean speed in the mixed wake was 7m/sec. To confirm the existence of two-dimensional wave motions in the interface, the experiments were conducted at a very low frequency, and showed similar gravity waves in both the upper and lower interfaces.

Keywords: Supercavitation, density gradient correlation

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Authors: Avantika Verma

Abstract:

In industrialized nations, corneal lacerations are one of the most common reason for hospitalization. This study was designed to study visual and clinical outcome in patients presenting with full thickness corneal lacerations in Indian population and to ascertain the impact of various preoperative and operative factors influencing prognosis after repair of corneal lacerations. Males in third decade with injuries at work with metallic objects were common. Lens damage, hyphema, vitreous hemorrhage, retinal detachment and endophthalmitis were seen. All the patients underwent primary repair within first 24 hours of presentation. At 3 months, 74.3% had a good visual outcome. About 5.7% of patients had no perception of light.In conclusion, various demographic and preoperative factors like age, time of presentation, vision at presentation, length of corneal wound, involvement of visual axis, associated ocular features like hyphaema, lenticular changes, vitreous haemorrhage and retinal detachment are significant prognostic indicators for final visual outcome.

Keywords: Cornea, laceration, visual outcome, wound repair.

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Authors: Jing-Gang Xie

Abstract:

The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: General relativity theory, particles, photons, quantum gravity model, gravitational frequency shift.

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