Search results for: Rajesh Kumar Gautam

Authors: Surjit Angra, Gajanan Rane, Vinod Kumar, Sushma Rani

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This paper presents metallurgical investigation of failed helical gear of diesel engine gear box used in a car. The failure had occurred near the bottomland of the tooth spacing. The failed surface was studied under Scanning Electron Microscope (SEM) and also visually investigated. The images produced through SEM at various magnifications were studied. Detailed metallurgical study indicates that failure was due to foreign material inclusion which is a casting defect. Further study also revealed pitting, spalling and inter-granular fracture as the causes of gear failure.

Keywords: helical gear, scanning electron microscope, casting defect, pitting

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Authors: D. Satish Kumar, T. K. V. Iyengar

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In this paper, we study the Brinkman flow, under Stokesian assumption, past an impervious prolate spheroid and obtain the expressions for the velocity and pressure fields in terms of Legendre functions, Associated Legendre functions, prolate radial and angular spheroidal wave functions. We further obtain an expression for the drag experienced by the spheroid and numerically study its variation with respect to the flow parameters and display the results through graphs.

Keywords: prolate spheoid, porous medium, stokesian assumption, brinkman model, velocity, pressure, drag

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%.

Keywords: ADALINE, neural network, gradient decent, process mining, resource behaviour, polynomial regression model

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Authors: Niyti, Aman Deep, Rajesh Kharab, Sahila Chopra, Raj. K. Gupta

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Relatively long-lived transactinide elements (i.e., elements with atomic number Z≥104) up to Z = 108 have been produced in nuclear reactions between low Z projectiles (C to Al) and actinide targets. Cross sections have been observed to decrease steeply with increasing Z. Recently, production cross sections of several picobarns have been reported for comparatively neutron-rich nuclides of 112 through 118 produced via hot fusion reactions with 48Ca and actinide targets. Some of those heavy nuclides are reported to have lifetimes on the order of seconds or longer. The relatively high cross sections in these hot fusion reactions are not fully understood and this has renewed interest in systematic studies of heavy-ion reactions with actinide targets. The main aim of this work is to understand the dynamics hot fusion reactions 18O+ 248Cm and 22Ne+244Pu (carried out at RIKEN and TASCA respectively) using the collective clusterization technique, carried out by undertaking the decay of the compound nucleus 266Rf∗ into 4n, 5n and 6n neutron evaporation channels. Here we extend our earlier study of the excitation functions (EFs) of 266Rf∗, formed in fusion reaction 18O+248Cm, based on Dynamical Cluster-decay Model (DCM) using the pocket formula for nuclear proximity potential, to the use of other nuclear interaction potentials derived from Skyrme energy density formalism (SEDF) based on semiclassical extended Thomas Fermi (ETF) approach and also study entrance channel effects by considering the synthesis of 266Rf* in 22Ne+244Pu reaction. The Skyrme forces used are the old force SIII, and new forces GSkI and KDE0(v1). Here, the EFs for the production of 260Rf, 261Rf and 262Rf isotope via 6n, 5n and 4n decay channel from the 266Rf∗ compound nucleus are studied at Elab = 88.2 to 125 MeV, including quadrupole deformations β2i and ‘hot-optimum’ orientations θi. The calculations are made within the DCM where the neck-length ∆R is the only parameter representing the relative separation distance between two fragments and/or clusters Ai which assimilates the neck formation effects.

Keywords: entrance channel effects, fusion reactions, skyrme force, superheavy nucleus

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Authors: Neeraj Kumar Verma

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Lanthanum hydroxide and manganese oxide nanocomposite are synthesized by chemical routes. Physical characterization is done by TEM to look at the size and dispersion of the nanoparticles in the composite. Chemical characterization is done by X-ray diffraction technique and FTIR to ascertain the attachment of the functionalities and bond stretching. Further thermal analysis is done by thermogravimetric analysis to find the tendency of the thermal decomposition in the elevated temperature range of 0-1000°C. Proper analysis and correlation of the various results obtained suggested the controlled growth of crystalline without agglomeration and good stability in the various temperature ranges of the composite.

Keywords: nanoparticles, XRD, TEM, lanthanum hydroxide, manganese oxide

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Authors: Ajay Pratap Singh Lodhi, Deepak Kumar

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Vegetable oil-based environmentally friendly metalworking fluids (MWFs) are formulated. The tribological performance, cytotoxicity, and corrosion resistance of the formulated fluids (FFs) are evaluated and benchmarked with commercial mineral oil-based MWFs (CF). Results show that FFs exhibited better machining characteristics (roughness, cutting forces, and surface morphology) during machining than CF. MTT assay and Live dead cell assay confirm the cytocompatibility nature of the FFs relative to the toxic CF. Electrochemical analysis shows that FFs and CF exhibited comparable corrosion current density.

Keywords: corrosion inhibitors, cytotoxicity, machining, MTT assay, Taguchi method, vegetable oil

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Authors: Ritesh Kumar, Rajendra Pamula

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In this paper, we present our contribution for book recommendation. In our experiment, we combine the results of Sequential Dependence Model (SDM) and exploitation of book information such as reviews, tags and ratings. This social information is assigned by users. For this, we used CLEF-2016 Social Book Search Track Suggestion task. Finally, our proposed method extensively evaluated on CLEF -2015 Social Book Search datasets, and has better performance (nDCG@10) compared to other state-of-the-art systems. Recently we got the good performance in CLEF-2016.

Keywords: sequential dependence model, social information, social book search, query expansion

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Authors: Vimal Kumar Dewangan, T. S. Sampath Kumar, Mukesh Doble, Viju Daniel Varghese

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The apatite-based, i.e., calcium-deficient hydroxyapatite (CDHAp) bone cement is well-known potential bone graft/substitute in orthopaedics due to its similar chemical composition with natural bone minerals. Therefore, an easy approach was attempted to fabricate the apatite-based (CDHAp) bone cement with improved injectability, bioresorbability, and macroporosity. In this study, the desired bone cement was developed by mixing the solid phase (consisting of wet chemically synthesized nanocrystalline hydroxyapatite and commercially available (synthetic) tricalcium phosphate) and the liquid phase (consisting of cement binding accelerator with few biopolymers in a dilute acidic solution) along with a liquid porogen as polysorbate or a solid porogen as mannitol (for comparison) in an optimized liquid-to-powder ratio. The fabricated cement sets within clinically preferred setting time (≤20 minutes) are better injectable (>70%) and also stable at ~7.3-7.4 (physiological pH). The CDHAp phased bone cement was resulted by immersing the fabricated after-set cement in phosphate buffer solution and other similar artificial body fluids and incubated at physiological conditions for seven days, confirmed through the X-ray diffraction and Fourier transform-infrared spectroscopy analyses. The so-formed synthetic apatite-based bone cement holds the acceptable compressive strength (within the range of trabecular bone) with average interconnected pores size falls in a macropores range (~50-200μm) inside the cement, verified by scanning electron microscopy (SEM), mercury intrusion porosimetry and micro-CT analysis techniques. Also, it is biodegradable (degrades ~19-22% within 10-12 weeks) when incubated in artificial body fluids under physiological conditions. The biocompatibility study of the bone cement, when incubated with MG63 cells, shows a significant increase in the cell viability after 3rd day of incubation compared with the control, and the cells were well-attached and spread completely on the surface of the bone cement, confirmed through SEM and fluorescence microscopy analyses. With this all, we can conclude that the developed synthetic macroporous apatite-based bone cement may have the potential to become promising material used as a trabecular bone substitute.

Keywords: calcium deficient hydroxyapatite, synthetic apatite-based bone cement, injectability, macroporosity, trabecular bone substitute

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Authors: Guo Haonan, Chen Peiyu, Zhao Hanyu, Burra Venkata Durga Kumar

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Unix and Unix-like operating systems are widely used due to their high stability but are limited by the parent-child process structure, and the child process depends on the parent process, so the crash of a single process may cause the entire process group or even the entire system to fail. Another possibility of unexpected process termination is that the system administrator inadvertently closed the terminal or pseudo-terminal where the application was launched, causing the application process to terminate unexpectedly. This paper mainly analyzes the reasons for the problems and proposes two solutions.

Keywords: process management, daemon, login-bash and non-login bash, process group

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: S. Siddharth, Saravana Kumar

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All Metros across the world tend to have a large number of bridges and there have been concerns about the safety of these bridges. As the traffic in most cities in India is heterogeneous, Trucks and Heavy vehicles traverse on our roads on an everyday basis this will lead to structural damage on the long run. All bridges are designed with a maximum Load limit and this limit is seldom checked. We have hence come up with an idea to check the load of all the vehicles entering the bridge and block the bridge with barricades if the vehicle surpasses the maximum load , this is done to catch hold of the perpetrators. By doing this we can avoid further structural damage and also provide an effective way to enforce the law. If our solution is put in place structural damage and accidents would be reduced to a great deal and it would also make the law enforcement job easier.

Keywords: heterogeneous, structural, load, law, heavy, vehicles

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Authors: Chander Shekhar, Manoj Kumar

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Present paper deal with the discovery of the stupa’s relics which belongs to the Kushana period. These remains were found during the scientific clearance work at a mound near Brahma-SarovarThanesar, Kurukshetra. This archaeological work was done by Department of Archaeology & Museums Haryana Government. The relics of stupa show that it would have been similar to Assandh and Damekhstupa. As per-Buddhist literature, GoutamBudhha reached Thanesar. In memory of Buddh’s Journey, King Ashoka built a big Stupa at Thanesar on the bank of Sarasvati River. Chinese pilgrim Yuan Chuang also referred a Monastery and stupa near Aujas-ghatof Brahma-sarovar. It may be part of that settlement which was mentioned by Yuan Chuang.

Keywords: archaeology, stupa, buddhism, excavtoin

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: R. Vishnu, K. S. Reddy, Amrendra Kumar

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The present guideline for the construction of flexible pavement in India, IRC 37: 2012 recommends to use viscous grade VG 40 bitumen in both wearing and binder bituminous layers. However, most of the bitumen production plants in India are unable to produce the air-blown VG40 grade bitumen. This requires plant’s air-blowing technique modification, and often the manufactures finds it as uneconomical. In this context, stiffer grade bitumen can be produced if bitumen is modified. Gilsonite, which is naturally occurring asphalt have been found to be used for increasing the stiffness of binders. The present study evaluates the physical, rheological characteristics of Gilsonite modified binders and the performance characteristics of these binders when used in the mix.

Keywords: bitumen, gilsonite, stiffness, laboratory evaluation

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Authors: Sai Siddharth S., Prasanna Kumar G. M., Alagarsamy R.

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This research introduces an alternative approach to urban road maintenance by utilizing Blended Wing Body (BWB) design and Vertical Takeoff and Landing (VTOL) drones. The integration of this aerospace innovation, combining blended wing efficiency with VTOL maneuverability, aims to optimize fuel consumption and explore versatile applications in solving urban problems. A few problems are discussed along with optimization of the design and comparative study with other drone configurations.

Keywords: design optimization, CFD, CAD, VTOL, blended wing body

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Authors: Prateeksha Sharma, V. Dinesh Kumar

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Performances of cylindrical multilayer hybrid plasmonic waveguides have been investigated in detail considering their structural and material aspects. Characteristics of hybrid metal insulator metal (HMIM) and hybrid insulator metal insulator (HIMI) waveguides have been compared on the basis of propagation length and confinement factor. Necessity of this study is to understand newer kind of waveguides that overcome the limitations of conventional waveguides. Investigation reveals that sub wavelength confinement can be obtained in two low dielectric spacer layers. This study provides gateway for many applications such as nano lasers, interconnects, bio sensors and optical trapping etc.

Keywords: hybrid insulator metal insulator, hybrid metal insulator metal, nano laser, surface plasmon polariton

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Authors: Vinesh Thiruchelvam, Umar Mumtaz Chowdry, Sathish Kumar Selvaperumal

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The prime purpose of the project is to provide a sophisticated system for surveillance specialized for the Port Authorities in the Maritime Industry. The current aerial surveillance does not have a wide dimensioning view. The channels of communication is shared and not exclusive allowing for communications errors or disturbance mainly due to traffic. The scope is to analyze the various aspects as real-time aerial and marine surveillance is one of the most important methods which could ensure the domain security of the sailors. The system will improve real time data as obtained for the controller base station. The key implementation will be based on camera speed, angle and adherence to a sustainable power utilization module.

Keywords: SMS, real time, GUI, maritime industry

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Authors: Vandana Deopanée Tomar, Gurpreet Kaur Sidhu, Panchsheela Nogia, Rajesh Mehrotra, Sandhya Mehrotra

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The cyanobacterial CO₂ concentrating mechanism (CCM) operates to raise the levels of CO₂ in the vicinity of the main carboxylation enzyme Rubisco which is encapsulated in protein micro compartments called carboxysomes. Thus, due to the presence of CCM, cyanobacterial cells are able to work with high photosynthetic efficiency even at low Ci conditions and can accumulate 1000 folds high internal concentrations of Ci than external environment. Engineering of some useful CCM components into higher plants is one of the plausible approaches to improve their photosynthetic performance. The first step and the simplest approach for attaining this objective would be the transfer of cyanobacterial bicarbonate transporter such as SbtA to inner chloroplast envelope of C₃ plants. For this, SbtA transporter gene from Synechococcus elongatus PCC 7942 was fused to a transit peptide element to generate chimeric constructs in order to direct it to chloroplast inner envelope. Two transit peptides namely, TnaXTP (transit peptide from AT3G56160) and TMDTP (transit peptide from AT2G02590) were shortlisted from Arabidopsis thaliana genome and cloned in plant expression vector pCAMBIA1302 having mgfp5 as a reporter gene. Plant transformation was done by agro infiltration and Agrobacterium mediated co-culture. DNA, RNA, and protein were isolated from the leaves four days post infiltration, and the presence of transgene was confirmed by gene specific PCR (Polymerase Chain Reaction) analysis and by RT-PCR (Reverse Transcription Polymerase Chain Reaction). The expression was confirmed at the protein level by western blotting using anti-GFP primary antibody and horseradish peroxidase (HRP) conjugated secondary antibody. The localization of the protein was detected by confocal microscopy of isolated protoplasts. We observed chloroplastic expression for both the fusion constructs which suggest that the transit peptide sequences are capable of taking the cargo protein to the chloroplasts. These constructs are now being used to generate stable transgenic plants by Agrobacterium mediated transformation. The stability of transgene expression will be analyzed from T₀ to T₂ generation.

Keywords: agro infiltration, bicarbonate transporter, carbon concentrating mechanisms, cyanobacteria, SbtA

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Authors: Tulasi Rayasa, Phani Kumar Pullela

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A systematic review is a research method that involves collecting and evaluating the information on a specific topic in order to provide a comprehensive and unbiased review. This type of review aims to improve the software development process by ensuring that the research is thorough and accurate. To ensure objectivity, it is important to follow systematic guidelines and consider multiple sources, such as literature reviews, interviews, and surveys. The evaluation process should also be streamlined by incorporating research from journals and other sources, such as grey literature. The main goal of a systematic review is to identify the consistency of current models in the field of computer application and software engineering.

Keywords: computer application, software engineering, process research, data science

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Authors: Abhishek Kumar

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X70 pipeline steel was electrochemically charged with hydrogen for different durations in order to find crack nucleation and propagation sites. After 3 hours charging, suitable regions for crack initiation and propagation were found. These regions were studied by OM, SEM, EDS and later Vicker hardness test was done. The results brought out that HIC cracks nucleated from regions rich of inclusions and further propagated through the segregation area of some elements, such as manganese, carbon, silicon and sulfur. It is worth-mentioning that all these potential sites for crack nucleation and propagation appeared at the centre of cross section of the specimens. Additionally, cracked area has harder phase than the non-cracked area which was confirmed by hardness test.

Keywords: X70 steel, morphology of inclusions, SEM/EDS/OM, simulation, statistical data

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Authors: Ananya G., B. Varshitha, Shwetha S., Kavitha S. N., Praveen Kumar Gupta

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Teleportation is the ability to travel by just reappearing at some other spot. Though teleportation has never been achieved, quantum teleportation is possible. Quantum teleportation is a process of transferring the quantum state of a particle onto another particle, under the circumstance that one does not get to know any information about the state in the process of transformation. This paper presents a brief overview of quantum teleportation, discussing the topics like Entanglement, EPR Paradox, Bell's Theorem, Qubits, elements for a successful teleport, some examples of advanced teleportation systems (also covers few ongoing experiments), applications (that includes quantum cryptography), and the current hurdles for future scientists interested in this field. Finally, major advantages and limitations to the existing teleportation theory are discussed.

Keywords: teleportation, quantum teleportation, quantum entanglement, qubits, EPR paradox, bell states, quantum particles, spooky action at a distance

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Authors: Lata Kiran Dey, Rajendra Kumar, Biren Karmakar

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Web Real Time Communications is a collection of standards, protocols, which provides real-time communications capabilities between web browsers and devices. This paper outlines the design and further implementation of web real-time communications on secure web applications having audio and video call capabilities. This proposed application may put up a system that will be able to work over both desktops as well as the mobile browser. Though, WebRTC also gives a set of JavaScript standard RTC APIs, which primarily works over the real-time communication framework. This helps to build a suitable communication application, which enables the audio, video, and message transfer in between the today’s modern browsers having WebRTC support.

Keywords: WebRTC, SIP, RTC, JavaScript, SRTP, secure web sockets, browser

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Authors: Parag Nihawan, Ravinder Singh Bhatia, Dinesh Kumar Jain

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Industrial drives are source of serious power quality problems. In this, two typical industrial drives have been dealt with, namely, FOC induction motor drives and DTC induction motor drive. The Z-source inverter is an emerging topology of power electronic converters which is capable of buck boost characteristics. The performances of different control methods based Z-source inverters feeding these industrial drives have been investigated, in this work. The test systems have been modeled and simulated in MATLAB/SIMULINK. The results obtained after carrying out these simulations have been used to draw the conclusions.

Keywords: Z-source inverter, total harmonic distortion, direct torque control, field orientation control

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Authors: Shougi Suliman Abosuliman, Arun Kumar, Firoz Alam

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Disaster preparedness is a key success factor for any effective disaster management practices. This paper evaluates the disaster preparedness and management in Saudi Arabia using an empirical investigation approach. It presents the results of the survey conducted by interviewing representatives of the Saudi decision-makers and administrators responsible for disaster control in Jeddah before, during and after flooding in 2009 and 2010. First, demographics of the respondents are presented, followed by quantitative analysis of their views and experiences regarding the Kingdom’s readiness before and after each flood. This is shown as a series of dependent and independent variables. Following this is a list of respondents’ priorities for disaster preparation in the Kingdom.

Keywords: disaster response policy, crisis management, effective service delivery, Jeddah

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Authors: Anshul Jain, P. Deepak Kumar, P. K. S. Dikshit

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To stabilize the riverbanks in the curved reaches of alluvial channels due to erosion and to stop sediment transportation, many models and theories have been put forth. One among such methods is to install flat vanes on the channel bed in predetermined manner. In practical, a relatively small no of vanes can produce bend flows which are practically uniform across the channel. The objective of the present study is to measure the drag and lift on such submerged vanes in open channels. Experiments were performed and the data collected have been presented and analyzed. Using the data collected herein, predictors for the coefficients of drag and lift have been developed. Such predictors yield the value of these coefficients for the known fluid properties and flow characteristic of the channel.

Keywords: drag, lift, vanes, open channel

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Authors: Abhishek Srivastava, Jeevesh Nandan, Manish Kumar

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The study was taken to analyse the alternative source of traffic system for effective and more convenient traffic flow by reducing points of conflicts as well as angle of conflict and keeping in view to minimize the problem of unnecessarily long waiting time, delays, congestion, traffic jam and geometric delays due to intersection between circular and straight lanes. It is a twin kidney-spine type structure system with special allowance for Highway users for quicker passes. Thus reduction in number and intensity of accidents, significance reduction in traffic jam, conservation of valuable time.

Keywords: traffic system, collision reduction of vehicles, smooth flow of vehicles, traffic jam

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Authors: Rajesh Karki, Safal Bhattarai, Saket Adhikari

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Reliable and economic operation of power systems are becoming extremely challenging with large scale integration of renewable energy sources due to the intermittency and uncertainty associated with renewable power generation. It is, therefore, important to make a quantitative risk assessment and explore the potential resources to mitigate such risks. Probabilistic models for different energy storage systems (ESS), such as the flywheel energy storage system (FESS) and the compressed air energy storage (CAES) incorporating specific charge/discharge performance and failure characteristics suitable for probabilistic risk assessment in power system operation and planning are presented in this paper. The proposed methodology used in FESS modelling offers flexibility to accommodate different configurations of plant topology. It is perceived that CAES has a high potential for grid-scale application, and a hybrid approach is proposed, which embeds a Monte-Carlo simulation (MCS) method in an analytical technique to develop a suitable reliability model of the CAES. The proposed ESS models are applied to a test system to investigate the economic and reliability benefits of the energy storage technologies in system operation and planning, as well as to assess their contributions in facilitating wind integration during different operating scenarios. A comparative study considering various storage system topologies are also presented. The impacts of failure rates of the critical components of ESS on the expected state of charge (SOC) and the performance of the different types of ESS during operation are illustrated with selected studies on the test system. The paper also applies the proposed models on the test system to investigate the economic and reliability benefits of the different ESS technologies and to evaluate their contributions in facilitating wind integration during different operating scenarios and system configurations. The conclusions drawn from the study results provide valuable information to help policymakers, system planners, and operators in arriving at effective and efficient policies, investment decisions, and operating strategies for planning and operation of power systems with large penetrations of renewable energy sources.

Keywords: flywheel energy storage, compressed air energy storage, power system reliability, renewable energy, system planning, system operation

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Authors: Yousef Abu Nahleh, Arun Kumar, Fugen Daver, Reham Al-Hindawi

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Despite the availability of natural disaster related time series data for last 110 years, there is no forecasting tool available to humanitarian relief organizations to determine forecasts for emergency logistics planning. This study develops a forecasting tool based on identifying probability of disaster for each country in the world by using decision tree modeling. Further, the determination of aggregate forecasts leads to efficient pre-disaster planning. Based on the research findings, the relief agencies can optimize the various resources allocation in emergency logistics planning.

Keywords: decision tree modeling, forecasting, humanitarian relief, emergency supply chain

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Authors: Ravi Kumar, Dhrubajit Barman, Nomi Baruah

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Software Cloning has grown an active area in software engineering research community yielding numerous techniques, various tools and other methods for clone detection and removal. The copying, modifying a block of code is identified as cloning as it is the most basic means of software reuse. Agile Software Development is an approach which is currently being used in various software projects, so that it helps to respond the unpredictability of building software through incremental, iterative, work cadences. Software Cloning has been introduced to Agile Environment and many Agile Software Development approaches are using the concept of Software Cloning. This paper discusses the various Agile Software Development approaches. It also discusses the degree to which the Software Cloning concept is being introduced in the Agile Software Development approaches.

Keywords: agile environment, refactoring, reuse, software cloning

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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