Search results for: Integral equations

Authors: Aliakbar Sayadi, Thomas R. Neitzert, G. Charles Clifton, Min Cheol Han

Abstract:

The present study aims to assess the performance of vermiculite concrete containing poly-lactic acid beads as an eco-friendly aggregate. Vermiculite aggregate was replaced by poly-lactic acid in percentages of 0%, 20%, 40%, 60% and 80%. Mechanical and thermal properties of concrete were investigated. Test results indicated that the inclusion of poly-lactic acid decreased the PH value of concrete and all the poly-lactic acid particles were dissolved due to the formation of sodium lactide and lactide oligomers when subjected to the high alkaline environment of concrete. In addition, an increase in thermal conductivity value of concrete was observed as the ratio of poly-lactic acid increased. Moreover, a set of equations was proposed to estimate the water-cement ratio, cement content and water absorption ratio of concrete.

Keywords: Poly-lactic acid, PLA, vermiculite, concrete, eco-friendly, mechanical properties.

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Authors: M. Behbahani-Nejad, A. Bagheri

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An efficient transient flow simulation for gas pipelines and networks is presented. The proposed transient flow simulation is based on the transfer function models and MATLABSimulink. The equivalent transfer functions of the nonlinear governing equations are derived for different types of the boundary conditions. Next, a MATLAB-Simulink library is developed and proposed considering any boundary condition type. To verify the accuracy and the computational efficiency of the proposed simulation, the results obtained are compared with those of the conventional finite difference schemes (such as TVD, method of lines, and other finite difference implicit and explicit schemes). The effects of the flow inertia and the pipeline inclination are incorporated in this simulation. It is shown that the proposed simulation has a sufficient accuracy and it is computationally more efficient than the other methods.

Keywords: Gas network, MATLAB-Simulink, transfer functions, transient flow.

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Authors: Vasiliki Vlachou, Christos Kontzinos, Ourania Markaki, Panagiotis Kokkinakos, Vagelis Karakolis, John Psarras

Abstract:

Higher Education is resisting the pull of technology, especially as this concerns the issuance and verification of degrees and certificates. It is widely known that education certificates are largely produced in paper form making them vulnerable to damage while holders of such certificates are dependent on the universities and other issuing organisations. QualiChain is an EU Horizon 2020 (H2020) research project aiming to transform and revolutionise the domain of public education and its ties with the job market by leveraging blockchain, analytics and decision support to develop a platform for the verification and sharing of education certificates. Blockchain plays an integral part in the QualiChain solution in providing a trustworthy environment to store, share and manage such accreditations. Under the context of this paper, three prominent blockchain platforms (Ethereum, Hyperledger Fabric, Hyperledger Iroha) were considered as a means of experimentation for creating a system with the basic functionalities that will be needed for trustworthy degree verification. The methodology and respective system developed and presented in this paper used Hyperledger Iroha and proved that this specific platform can be used to easily develop decentralize applications. Future papers will attempt to further experiment with other blockchain platforms and assess which has the best potential.

Keywords: Blockchain, degree verification, higher education certificates, Hyperledger Iroha.

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Authors: A. Chaudhuri, C. Guha, T. K. Dutta

Abstract:

Pressure driven microscale gas flow-separation has been investigated by solving the compressible Navier-Stokes (NS) system of equations. A two dimensional explicit finite volume (FV) compressible flow solver has been developed using modified advection upwind splitting methods (AUSM+) with no-slip/first order Maxwell-s velocity slip conditions to predict the flowseparation behavior in microdimensions. The effects of scale-factor of the flow geometry and gas species on the microscale gas flowseparation have been studied in this work. The intensity of flowseparation gets reduced with the decrease in scale of the flow geometry. In reduced dimension, flow-separation may not at all be present under similar flow conditions compared to the larger flow geometry. The flow-separation patterns greatly depend on the properties of the medium under similar flow conditions.

Keywords: AUSM+, FVM, Flow-separation, Microflow.

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Authors: Hilmi Kuscu, Ahmet Cihan, Kamil Kahveci, Ugur Akyol

Abstract:

In this study, a software has been developed to predict the optimum conditions for drying of cotton based yarn bobbins in a hot air dryer. For this purpose, firstly, a suitable drying model has been specified using experimental drying behavior for different values of drying parameters. Drying parameters in the experiments were drying temperature, drying pressure, and volumetric flow rate of drying air. After obtaining a suitable drying model, additional curve fittings have been performed to obtain equations for drying time and energy consumption taking into account the effects of drying parameters. Then, a software has been developed using Visual Basic programming language to predict the optimum drying conditions for drying time and energy consumption.

Keywords: Drying, bobbin, cotton, PLC control, Visual Basic.

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Authors: Marcin Sowa

Abstract:

The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: Numerical method, SubIval, fractional calculus, numerical solver, circuit analysis.

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Authors: S.A. Alqallaf, S.A. Al-Mawsawi, A. Haider

Abstract:

In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, Decoupled model, Load flow.

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Authors: A. M. Fudhail, N. A. C. Sidik, M. Z. M. Rody, H. M. Zahir, M.T. Musthafah

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In this paper, fluid flow patterns of steady incompressible flow inside shear driven cavity are studied. The numerical simulations are conducted by using lattice Boltzmann method (LBM) for different Reynolds numbers. In order to simulate the flow, derivation of macroscopic hydrodynamics equations from the continuous Boltzmann equation need to be performed. Then, the numerical results of shear-driven flow inside square and triangular cavity are compared with results found in literature review. Present study found that flow patterns are affected by the geometry of the cavity and the Reynolds numbers used.

Keywords: Lattice Boltzmann method, shear driven cavity, square cavity, triangular cavity.

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Authors: Alexandros Leontitsis, Archana P. Sangole

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This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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Authors: Aman Agarwal, Georg Klepp

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Impinging jets are used in various industrial areas as a cooling and drying technique. The current research is concerned with the means of improving the heat transfer for configurations with a minimum distance of the nozzle to the impingement surface. The impingement heat transfer is described using numerical methods over a wide range of parameters for an array of planar jets. These parameters include varying jet flow speed, width of nozzle, distance of nozzle, angle of the jet flow, velocity and geometry of the impingement surface. Normal pressure and shear stress are computed as additional parameters. Using dimensionless characteristic numbers the parameters and the results are correlated to gain generalized equations. The results demonstrate the effect of the investigated parameters on the flow.

Keywords: Heat Transfer Coefficient, Minimum distance jet impingement, Numerical simulation, Dimensionless coefficients.

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Authors: Oday Al-Mamoori, J. Enrique Martinez-Rueda

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'C' shape yielding devices (C-devices) are effective tools for introducing supplemental sources of energy dissipation by hysteresis. Studies have shown that C-devices made of mild steel can be successfully applied as integral parts of seismic retrofitting schemes. However, explicit modelling of these devices can become cumbersome, expensive and time consuming. The device under study in this article has been previously used in non-invasive dissipative bracing for seismic retrofitting. The device is cut from a mild steel plate and has an overall shape that resembles that of a rectangular portal frame with circular interior corner transitions to avoid stress concentration and to control the extension of the dissipative region of the device. A number of inelastic finite element (FE) analyses using either inelastic 2D plane stress elements or inelastic fibre frame elements are reported and used to calibrate a 1D equivalent inelastic spring model that effectively reproduces the cyclic response of the device. The more elaborate FE model accounts for the frictional forces developed between the steel plate and the bolts used to connect the C-device to structural members. FE results also allow the visualization of the inelastic regions of the device where energy dissipation is expected to occur. FE analysis results are in a good agreement with experimental observations.

Keywords: C-device, equivalent nonlinear spring, FE analyses, reversed cyclic tests.

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Authors: Muhammad Tahir, Muhammad H. Sayyad, Dil N. Khan, Fazal Wahab

Abstract:

Herein, the organic semiconductor methyl orange (MO), is investigated for the first time for its electronic applications. For this purpose, Al/MO/n-Si heterojunction is fabricated through economical cheap and simple “drop casting” technique. The currentvoltage (I-V) measurements of the device are made at room temperature under dark conditions. The I-V characteristics of Al/MO/n-Si junction exhibits asymmetrical and rectifying behavior that confirms the formation of diode. The diode parameters such as rectification ratio (RR), turn on voltage (Vturn on), reverse saturation current (I0), ideality factor (n), barrier height ( b f ), series resistance (Rs) and shunt resistance (Rsh) are determined from I-V curves using Schottky equations. These values of these parameters are also extracted and verified by applying Cheung’s functions. The conduction mechanisms are explained from the forward bias I-V characteristics using the power law.

Keywords: Electrical properties, Organic/inorganic heterojunction diode, Methyl Orange, Cheungs Functions

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Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

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Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Grigoris Giannarakis, Despina Galani, Charitoudi Georgia, Nikolaos Litinas

Abstract:

The Corporate Social Responsibility (CSR) performance has garnered significant interest during the last two decades as numerous methodologies are proposed by Social Responsible Investment (SRI) indexes. The weight of each indicator is a crucial component of the CSR measurement procedures. Based on a previous study, the appropriate weight of each proposed indicator for the Greek telecommunication sector is specified using the rank reciprocal weighting. The Kendall-s Coefficient of Concordance and Spearman Correlation Coefficient non-parametric tests are adopted to determine the level of consensus among the experts concerning the importance rank of indicators. The results show that there is no consensus regarding the rank of indicators in most of stakeholders- domains. The equal weight for all indicators could be proposed as a solution for the lack of consensus among the experts. The study recommends three different equations concerning the adopted weight approach.

Keywords: Corporate Social Responsibility, Indicator, Weight.

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

Abstract:

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: Indentation, contact problem, stress distribution, coating materials, layer-substrate body.

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Authors: M. Alauddin, M. M. Hossain, M. N. Uddin, M. E. Haque

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An optimal design of a spur is the first requirement to make it sustainable and function properly. In view of that, a thorough understanding to the hydro- and morpho-dynamics due to spurs is essential. This paper presents a literature review on the effect of spurs to obtain the most recent design criteria. Perpendicular and upstream aligned impermeable spurs have large disturbances to flow and less stability because of strong vortices and associated scour. Downstream aligned spurs minimize scour holes, but there is a chance of strong return current which could be controlled allowing flow through them. A series arrangement of spurs is important to have the desired results with a special care for the first one. Several equations have been presented in the paper for predicting the scour depth. But, they have to be used carefully. Different flow environments developed by spurs are favorable for various aquatic species. However, it is important to maintain almost a stable flow condition providing stable spurs.

Keywords: Bed topography, flow pattern, scour, spur.

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Authors: Dalila Hamami, Baghdad Atmani

Abstract:

Modelling is a widely used tool to facilitate the evaluation of disease management. The interest of epidemiological models lies in their ability to explore hypothetical scenarios and provide decision makers with evidence to anticipate the consequences of disease incursion and impact of intervention strategies.

All models are, by nature, simplification of more complex systems. Models that involve diseases can be classified into different categories depending on how they treat the variability, time, space, and structure of the population. Approaches may be different from simple deterministic mathematical models, to complex stochastic simulations spatially explicit.

Thus, epidemiological modelling is now a necessity for epidemiological investigations, surveillance, testing hypotheses and generating follow-up activities necessary to perform complete and appropriate analysis.

The state of the art presented in the following, allows us to position itself to the most appropriate approaches in the epidemiological study.

Keywords: Bio-PEPA, Cellular automata, Epidemiological modelling, multi agent system, ordinary differential equations, PEPA, Process Algebra, Tuberculosis.

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Authors: Nhon Do, Tam Pham

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Knowledge bases are basic components of expert systems or intelligent computational programs. Knowledge bases provide knowledge, events that serve deduction activity, computation and control. Therefore, researching and developing of models for knowledge representation play an important role in computer science, especially in Artificial Intelligence Science and intelligent educational software. In this paper, the extensive deduction computational model is proposed to design knowledge bases whose attributes are able to be real values or functional values. The system can also solve problems based on knowledge bases. Moreover, the models and algorithms are applied to produce the educational software for solving alternating current problems or solving set of equations automatically.

Keywords: Educational software, artificial intelligence, knowledge base systems, knowledge representation.

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Authors: Mehrdad Nouri Khajavi, Sajjad Ahoui Ghazvin, Ghader Rezazadeh, Mohammad Fathalilou

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In this paper static and dynamic response of a varactor of a micro-phase shifter to DC, step DC and AC voltages have been studied. By presenting a mathematical modeling Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. Then the frequency response and phase diagram of the system has been studied. It has been shown that applying the DC voltage shifts down the phase diagram and frequency response. Also increasing the damping ratio shifts up the phase diagram.

Keywords: MEMS, Phase Shifter, Pull-in Voltage, PhaseDiagram

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Authors: Roslinda Nazar, Anuar Ishak, Ioan Pop

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Unsteady boundary layer flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane is studied in this paper. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in a micropolar fluid. The transformed unsteady boundary layer equations are solved numerically using the Keller-box method for the whole transient from the initial state to final steady-state flow. Numerical results are obtained for the velocity and microrotation distributions as well as the skin friction coefficient for various values of the material parameter K. It is found that there is a smooth transition from the small-time solution to the large-time solution.

Keywords: Boundary layer, micropolar fluid, stretching surface, unsteady flow.

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Authors: O. F. Elkommos

Abstract:

Teaching English as a Second Language (TESL) has become a very rich area of research. Practitioners or teachers of English as a foreign or a second language are now promoting both collaborative learning and collaborative teaching. Students learning a language collaboratively and cooperatively are learning in a better environment of team work where they learn from each other. Further, teaching English collaboratively also creates an enriching environment that is also very enriching to students’ and teachers’ experiences of learning and teaching. Moreover, action research stems from actual teacher concerns and students’ needs. Reflection in turn, on the experience of the material taught and the delivery of material is becoming an integral part of the teaching and learning experience self- evaluation and self-development. In this case, the concern of the research field in the area of TESL will be the development of teaching delivery, material and quality of learning. In the present research, the TESL module taught to year two students in the Faculty of Arts and Humanities, British University in Egypt (BUE) will be evaluated reflexively by the students and teachers. The module was taught to students in two different specialisms. It was taught and delivered through collaborative teaching and was evaluated by both teachers and students as very successful and enjoyable. The reflections of both teachers and students as well as student results confirm that it was a success.

Keywords: Action research, addressing differentiation, collaborative teaching, reflective teaching and learning, reflexive learning, reflexive teaching, self-development, self-evaluation, TESL.

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Authors: Charles P. Mukumba, Kahilu K. Shakantu

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Achieving the Sustainable Development Goals (SDGs) is critical to achieving transformational results that support Zambia's developmental agenda. Public procurement is integral to the government's mission to deliver goods and services in a timely and economical manner beyond the value of money spent. This study explores the link between sustainable public procurement and the SDGs in Zambia. To validate the established links with public sector procurement in Zambia, the study employed qualitative research using semi-structured interviews with 12 public procurement officials. The collected data were analysed using thematic analysis. The findings indicate that public procurement plays a fundamental role in achieving the SDGs by helping deliver core public services that support SDGs and systematizing and co-delivering added value along the way. The study further established the importance of sustainable public procurement within the development context. The interviews were limited to mainstream public sector procurement entities in Lusaka, Zambia. Sustainable public procurement actions have the potential to impact SDGs. Promoting sustainable public procurement will enhance sustainable development and significantly improve the supply chain, benefiting the economy, society and environment. Findings will inform policy-makers how to strategically design sustainable public procurement policy by attuning it to procuring entities' objectives and priorities to contribute to attaining SDGs.

Keywords: Sustainable public procurement, sustainable development goals, SDG targets, Zambia.

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Authors: Himanshu Dehra

Abstract:

This paper presents a paradigm for characterization and checking of human noise behavior. The definitions of ‘Noise’ and ‘Noise Behavior’ are devised. The concept of characterization and examining of Noise Behavior is obtained from the proposed paradigm of Psychoacoustics. The measurement of human noise behavior is discussed through definitions of noise sources and noise measurements. The noise sources, noise measurement equations and noise filters are further illustrated through examples. The theory and significance of solar energy acoustics is presented for life and its activities. Human comfort and health are correlated with human brain through physiological responses and noise protection. Examples of heat stress, intense heat, sweating and evaporation are also enumerated.

Keywords: Human brain, noise behavior, noise characterization, noise filters, physiological responses, psychoacoustics.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: E. Jomehzadeh, A.R. Saidi

Abstract:

In the present article, nonlinear vibration analysis of single layer graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton's principle, the three coupled nonlinear equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of Free nonlinear vibration, based on a one term mode shape, are found for both simply supported and clamped graphene sheets. A complete analysis of graphene sheets with movable as well as immovable in-plane conditions is also carried out. The results obtained herein are compared with those available in the literature for classical isotropic rectangular plates and excellent agreement is seen. Also, the nonlinear effects are presented as functions of geometric properties and small scale parameter.

Keywords: Small scale, Nonlinear vibration, Graphene sheet, Nonlocal continuum

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Authors: Sachin Kumar, Michael Pecht

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A study was conducted to formally characterize notebook computer performance under various environmental and usage conditions. Software was developed to collect data from the operating system of the computer. An experiment was conducted to evaluate the performance parameters- variations, trends, and correlations, as well as the extreme value they can attain in various usage and environmental conditions. An automated software script was written to simulate user activity. The variability of each performance parameter was addressed by establishing the empirical relationship between performance parameters. These equations were presented as baseline estimates for performance parameters, which can be used to detect system deviations from normal operation and for prognostic assessment. The effect of environmental factors, including different power sources, ambient temperatures, humidity, and usage, on performance parameters of notebooks was studied.

Keywords: Health monitoring, Electronic prognostics, Reliability, Usage monitoring, Notebook computer.

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Authors: Amir Hossein Daei Sorkhabi, Farid Vakili Tahami

Abstract:

In this paper, creep constitutive equations of base (Parent) and weld materials of the weldment for cold-drawn 304L stainless steel have been obtained experimentally. For this purpose, test samples have been generated from cold drawn bars and weld material according to the ASTM standard. The creep behavior and properties have been examined for these materials by conducting uniaxial creep tests. Constant temperatures and constant load uni-axial creep tests have been carried out at two high temperatures, 680 and 720 oC, subjected to constant loads, which produce initial stresses ranging from 240 to 360 MPa. The experimental data have been used to obtain the creep constitutive parameters using numerical optimization techniques.

Keywords: Creep, Constitutive equation, Cold-drawn 304L stainless steel, Weld, Base material

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Authors: Abouzar Moshfegh, Mehrzad Shams, Goodarz Ahmadi, Reza Ebrahimi

Abstract:

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier-Stokes equations were solved and the velocity jump at the gas-particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The Simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed.

Keywords: CFD, Cunningham correction, Slip correction factor, Spherical aerosol.

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Authors: V. K. Rattan, Baljinder K. Gill, Seema Kapoor

Abstract:

Isobaric vapor-liquid equilibrium measurements are reported for binary mixture of 2-Methyltetrahydrofuran and Cumene at 97.3 kPa. The data were obtained using a vapor recirculating type (modified Othmer's) equilibrium still. The mixture shows slight negative deviation from ideality. The system does not form an azeotrope. The experimental data obtained in this study are thermodynamically consistent according to the Herington test. The activity coefficients have been satisfactorily correlated by means of the Margules, and NRTL equations. Excess Gibbs free energy has been calculated from the experimental data. The values of activity coefficients have also been obtained by the UNIFAC group contribution method.

Keywords: Binary mixture, 2-Methyltetrahydrofuran, Cumene, Vapor-liquid equilibrium, UNIFAC, Excess Gibbs free energy.

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Authors: E. G. Bautista, J. M. Reyes, O. Bautista, J. C. Arcos

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In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law distribution. We show that the spatial distribution of the waves in the varying cross-section is a function of a kinematic parameter,κ , and two geometrical parameters εh and w ε . The above spatial behavior of the surface elevation is modeled by an ordinary differential equation. The use of single formulas to model the varying cross sections or transitions considered in this work can be a useful approximation to natural or artificial geometrical configurations.

Keywords: Surface waves, Asymptotic solution, Power law function, Non-dispersive waves.

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