Search results for: richardson extrapolation

Authors: Jiahau Guo, Yihe Zhang

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This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations.

Keywords: daily price limit, discrete dividend, early exercise, fast Fourier transform, multi-day density function, Richardson extrapolation

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Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

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Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Fernanda M. Bastos, Teógenes A. da Silva

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Extrapolation chambers were designed to be used as primary standard dosimeter for measuring absorbed dose in a medium in beta radiation and low energy x-rays. The International Organization for Standardization established series of reference x-radiation for calibrating and determining the energy dependence of dosimeters that are to be reproduced in metrology laboratories. Standardization of the low energy x-ray beams with tube potential lower than 30 kV may be affected by the instrument used for dosimetry. In this work, parameters of a 23392 model PTW extrapolation chamber were determined aiming its use in low energy x-ray beams as a reference instrument.

Keywords: extrapolation chamber, low energy x-rays, x-ray dosimetry, X-ray metrology

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Authors: Olukunle C. Olawole, Dilip Kumar De

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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: Daniel C. Bonzo

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Practical considerations lead to the use of unit of analysis within subjects, e.g., bleeding episodes or treatment-related adverse events, in rare disease settings. This is coupled with data augmentation techniques such as extrapolation to enlarge the subject base. In general, one can think about extrapolation of data as extending information and conclusions from one estimand to another estimand. This approach induces hierarchichal clustered data with varying cluster sizes. Extrapolation of clinical trial data is being accepted increasingly by regulatory agencies as a means of generating data in diverse situations during drug development process. Under certain circumstances, data can be extrapolated to a different population, a different but related indication, and different but similar product. We consider here the problem of estimation (point and interval) using a mixed-models approach under an extrapolation. It is proposed that estimators (point and interval) be constructed using weighting schemes for the clusters, e.g., equally weighted and with weights proportional to cluster size. Simulated data generated under varying scenarios are then used to evaluate the performance of this approach. In conclusion, the evaluation result showed that the approach is a useful means for improving statistical inference in rare disease settings and thus aids not only signal detection but risk-benefit evaluation as well.

Keywords: clustered data, estimand, extrapolation, mixed model

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Authors: K. Al-Heuseen, M. R. Hashim

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The current-voltage (I-V) characteristics of Pd/n-GaN Schottky barrier were studied at temperatures over room temperature (300-470K). The values of ideality factor (n), zero-bias barrier height (φB0), flat barrier height (φBF) and series resistance (Rs) obtained from I-V-T measurements were found to be strongly temperature dependent while (φBo) increase, (n), (φBF) and (Rs) decrease with increasing temperature. The apparent Richardson constant was found to be 2.1x10-9 Acm-2K-2 and mean barrier height of 0.19 eV. After barrier height inhomogeneities correction, by assuming a Gaussian distribution (GD) of the barrier heights, the Richardson constant and the mean barrier height were obtained as 23 Acm-2K-2 and 1.78eV, respectively. The corrected Richardson constant was very closer to theoretical value of 26 Acm-2K-2.

Keywords: electrical properties, Gaussian distribution, Pd-GaN Schottky diodes, thermionic emission

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Authors: A. B. Bolkhir, A. Elshafie, T. K. Yousif

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This paper highlights the methods of error estimation in finite element analysis (FEA) results. It indicates that the modeling error could be eliminated by performing finite element analysis with successively finer meshes or by extrapolating response predictions from an orderly sequence of relatively low degree of freedom analysis results. In addition, the paper eliminates the round-off error by running the code at a higher precision. The paper provides application in finite element analysis results. It draws a conclusion based on results of application of methods of error estimation.

Keywords: finite element analysis (FEA), discretization error, round-off error, mesh refinement, richardson extrapolation, monotonic convergence

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

Procedia PDF Downloads 329

Authors: M. Saiful Islam, M. Mohandes, S. Rehman, S. Badran

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Increasing necessity of wind power is directing us to have precise knowledge on wind resources. Methodical investigation of potential locations is required for wind power deployment. High penetration of wind energy to the grid is leading multi megawatt installations with huge investment cost. This fact appeals to determine appropriate places for wind farm operation. For accurate assessment, detailed examination of wind speed profile, relative humidity, temperature and other geological or atmospheric parameters are required. Among all of these uncertainty factors influencing wind power estimation, vertical extrapolation of wind speed is perhaps the most difficult and critical one. Different approaches have been used for the extrapolation of wind speed to hub height which are mainly based on Log law, Power law and various modifications of the two. This paper proposes a Artificial Neural Network (ANN) and Genetic Algorithm (GA) based hybrid model, namely GA-NN for vertical extrapolation of wind speed. This model is very simple in a sense that it does not require any parametric estimations like wind shear coefficient, roughness length or atmospheric stability and also reliable compared to other methods. This model uses available measured wind speeds at 10m, 20m and 30m heights to estimate wind speeds up to 100m. A good comparison is found between measured and estimated wind speeds at 30m and 40m with approximately 3% mean absolute percentage error. Comparisons with ANN and power law, further prove the feasibility of the proposed method.

Keywords: wind profile, vertical extrapolation of wind, genetic algorithm, artificial neural network, hybrid machine learning

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

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In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: Belmiloud Mohamed Amine, Sad Chemloul Nord-Eddine

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In this study we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity and the varying of the Richardson number on the variation of the average Nusselt number. The vertical walls of the cavity are differentially heated, the left wall is maintained at a uniform temperature higher than the right wall, and the two horizontal walls are adiabatic. The finite volume method is used for solving the dimensionless governing equations. Emissivity values used in this study are ranged between 0 and 1, the Richardson number in the range 0.1 to10. The Rayleigh number is fixed to Ra = 10000 and the Prandtl number is maintained constant Pr = 0.71. Streamlines, isothermal lines and the average Nusselt number are presented according to the surface emissivity. The results of this study show that the Richardson number and emissivity affect the average Nusselt number.

Keywords: mixed convection, square cavity, wall emissivity, lid-driven, numerical study

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Authors: Sari Elkahina, Zergoug Mourad, Benachenhou Kamel

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The main purpose of this paper is to perform a computations comparison of stress intensity factor 'SIF' evaluation in case of cracked thin plate with Aluminum alloy 7075-T6 and 2024-T3 used in aeronautics structure under uniaxial loading. This evaluation is based on finite element method with a virtual power principle through two techniques: the extrapolation and G−θ. The first one consists to extrapolate the nodal displacements near the cracked tip using a refined triangular mesh with T3 and T6 special elements, while the second, consists of determining the energy release rate G through G−θ method by potential energy derivation which corresponds numerically to the elastic solution post-processing of a cracked solid by a contour integration computation via Gauss points. The SIF obtained results from extrapolation and G−θ methods will be compared to an analytical solution in a particular case. To illustrate the influence of the meshing kind and the size of integration contour position simulations are presented and analyzed.

Keywords: crack tip, SIF, finite element method, concentration technique, displacement extrapolation, aluminum alloy 7075-T6 and 2024-T3, energy release rate G, G-θ method, Gauss point numerical integration

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Ajith Kumar S., Sankaran Namboothiri, Sankrish J., SarathKumar S., S. Anil Lal

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A numerical analysis of flow over a heated circular cylinder is done in this paper. The governing equations, Navier-Stokes, and energy equation within the Boussinesq approximation along with continuity equation are solved using hybrid FEM-FVM technique. The density gradient created due to the heating of the cylinder will induce buoyancy force, opposite to the direction of action of acceleration due to gravity, g. In the present work, the flow direction and the direction of buoyancy force are taken as same (vertical flow configuration), so that the buoyancy force accelerates the mean flow past the cylinder. The relative dominance of the buoyancy force over the inertia force is characterized by the Richardson number (Ri), which is one of the parameter that governs the flow dynamics and heat transfer in this analysis. It is well known that above a certain value of Reynolds number, Re (ratio of inertia force over the viscous forces), the unsteady Von Karman vortices can be seen shedding behind the cylinder. The shedding wake patterns could be seriously altered by heating/cooling the cylinder. The non-dimensional shedding frequency called the Strouhal number is found to be increasing as Ri increases. The aerodynamic force coefficients CL and CD are observed to change its value. In the present vertical configuration of flow over the cylinder, as Ri increases, shedding frequency gets increased and suddenly drops down to zero at a critical value of Richardson number. The unsteady vortices turn to steady standing recirculation bubbles behind the cylinder after this critical Richardson number. This phenomenon is well known in literature as "Breakdown of the Karman Vortex Street". It is interesting to see the flow structures on further increase in the Richardson number. On further heating of the cylinder surface, the size of the recirculation bubble decreases without loosing its symmetry about the horizontal axis passing through the center of the cylinder. The separation angle is found to be decreasing with Ri. Finally, we observed a second critical Richardson number, after which the the flow will be attached to the cylinder surface without any wake behind it. The flow structures will be symmetrical not only about the horizontal axis, but also with the vertical axis passing through the center of the cylinder. At this stage, there will be a "single plume" emanating from the rear stagnation point of the cylinder. We also observed the transition of the plume is a strong function of the Richardson number.

Keywords: drag reduction, flow over circular cylinder, flow control, mixed convection flow, vortex shedding, vortex breakdown

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Authors: Farhat Imtiaz, Umar Farooq

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In this work, we developed a computational model to predict ply level failure in impacted composite laminates. Data obtained from physical testing from flat and round nose impacts of 8-, 16-, 24-ply laminates were considered. Routine inspections of the tested laminates were carried out to approximate ply by ply inflicted damage incurred. Plots consisting of load–time, load–deflection, and energy–time history were drawn to approximate the inflicted damages. Impact test generated unwanted data logged due to restrictions on testing and logging systems were also filtered. Conventional filters (built-in, statistical, and numerical) reliably predicted load thresholds for relatively thin laminates such as eight and sixteen ply panels. However, for relatively thick laminates such as twenty-four ply laminates impacted by flat nose impact generated clipped data which can just be de-noised using oscillatory algorithms. The literature search reveals that modern oscillatory data filtering and extrapolation algorithms have scarcely been utilized. This investigation reports applications of filtering and extrapolation of the clipped data utilising fast Fourier Convolution algorithm to predict load thresholds. Some of the results were related to the impact-induced damage areas identified with Ultrasonic C-scans and found to be in acceptable agreement. Based on consistent findings, utilizing of modern data filtering and extrapolation algorithms to data logged by the existing machines has efficiently enhanced data interpretations without resorting to extra resources. The algorithms could be useful for impact-induced damage approximations of similar cases.

Keywords: fibre reinforced laminates, fast Fourier algorithms, mechanical testing, data filtering and extrapolation

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Authors: A. P. Joshi, H. V. Warrior, J. P. Panda

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This paper is a continuation of the work carried out by various turbulence modelers in Oceanography on the topic of oceanic turbulent mixing. It evaluates the evolution of ocean water temperature and salinity by the appropriate modeling of turbulent mixing utilizing proper prescription of eddy viscosity. Many modelers in past have suggested including terms like shear, buoyancy and vorticity to be the parameters that decide the slow pressure strain correlation. We add to it the fact that dissipation anisotropy also modifies the correlation through eddy viscosity parameterization. This recalibrates the established correlation constants slightly and gives improved results. This anisotropization of dissipation implies that the critical Richardson’s number increases much beyond unity (to 1.66) to accommodate enhanced mixing, as is seen in reality. The model is run for a couple of test cases in the General Ocean Turbulence Model (GOTM) and the results are presented here.

Keywords: Anisotropy, GOTM, pressure-strain correlation, Richardson critical number

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Authors: Olukunle C. Olawole, Dilip K. De, Moses Emetere, Omoje Maxwell

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Graphene can stand very high temperature up to 4500 K in vacuum and has potential for application in thermionic energy converter. In this paper, we discuss the application of energy dynamics principles and the modified Richardson-Dushman Equation, to estimate the efficiency of solar power conversion to electrical power by a solar thermionic energy converter (STEC) containing emitter made of graphene. We present detailed simulation of power output for different solar insolation, diameter of parabolic concentrator, area of the graphene emitter (same as that of the collector), temperature of the collector, physical dimensions of the emitter-collector etc. After discussing possible methods of reduction or elimination of space charge problem using magnetic field and gate, we finally discuss relative advantages of using emitters made of graphene, carbon nanotube and metals respectively in a STEC.

Keywords: graphene, high temperature, modified Richardson-Dushman equation, solar thermionic energy converter

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Authors: Farhad Hekmatipour, M. A. Akhavan-Behabadi, Farzad Hekmatipour

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In this paper, experiments were conducted to investigate the heat transfer of Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid laminar flow in vertical smooth and microfin tubes as the surface temperature is constant. The effect of adding the nanoparticle to base fluid and Richardson number on the heat transfer enhancement is investigated as Richardson number increases from 0.1 to 0.7. The experimental results demonstrate that the combined forced-natural convection heat transfer rate may be improved significantly with an increment of mass nanoparticle concentration from 0% to 1.5%. In this experiment, a correlation is also proposed to predict the mixed convection heat transfer rate of CuO-HTO nanofluid flow. The maximum deviation of both correlations is less than 14%. Moreover, a correlation is presented to estimate the Nusselt number inside vertical smooth and microfin tubes as Rayleigh number is between 2´105 and 6.8´106 with the maximum deviation of 12%.

Keywords: mixed convection, heat transfer, nanofluid, vertical tube, microfin tube

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Authors: S. Boorboor, S. A. H. Feghhi, H. Jafari

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The ionizing radiations cause different kinds of damages in electronic components. MOSFETs, most common transistors in today’s digital and analog circuits, are severely sensitive to TID damage. In this work, the threshold voltage shift of CD4007 device, which is an integrated circuit including P-channel and N-channel MOS transistors, was investigated for low dose gamma irradiation under different gate bias voltages. We used linear extrapolation method to extract threshold voltage from I_D-V_G characteristic curve. The results showed that the threshold voltage shift was approximately 27.5 mV/Gy for N-channel and 3.5 mV/Gy for P-channel transistors at the gate bias of |9 V| after irradiation by Co-60 gamma ray source. Although the sensitivity of the devices under test were strongly dependent to biasing condition and transistor type, the threshold voltage shifted linearly versus accumulated dose in all cases. The overall results show that the application of CD4007 as an electronic buffer in a radiation therapy system is limited by TID damage. However, this integrated circuit can be used as a cheap and sensitive radiation dosimeter for accumulated dose measurement in radiation therapy systems.

Keywords: threshold voltage shift, MOS transistor, linear extrapolation, gamma irradiation

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Authors: Wei Yongxiang, Zhu Haoyue, Tang Heng, Yuan Qunwei

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In order to study the preparation method of gear fatigue load spectrum for loaders, the load signal of four typical working conditions of loader is collected. The signal that reflects the law of load change is obtained by preprocessing the original signal. The torque of the drive axle is calculated by using the rain flow counting method. According to the operating time ratio of each working condition, the two-dimensional load spectrum based on the real working conditions of the drive axle of loader is established by the cycle extrapolation and synthesis method. The two-dimensional load spectrum is converted into one-dimensional load spectrum by means of the mean of torque equal damage method. Torque amplification includes the maximum load torque of the main reduction gear. Based on the theory of equal damage, the accelerated cycles are calculated. In this way, the load spectrum of the loading condition of the drive axle is prepared to reflect loading condition of the loader. The load spectrum can provide reference for fatigue life test and life prediction of loader drive axle.

Keywords: load spectrum, axle, torque, rain-flow counting method, extrapolation

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Authors: Sanjib Kr Pal, S. Bhattacharyya

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Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: conjugate heat transfer, mixed convection, nano fluid, wall waviness

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Authors: Benseghir Omar, Bahmed Mohamed

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In this work, we presented a numerical study of the phenomenon of heat transfer through the laminar, incompressible and steady mixed convection in a closed square cavity with the left vertical wall of the cavity is subjected to a warm temperature, while the right wall is considered to be cold. The horizontal walls are assumed adiabatic. The governing equations were discretized by finite volume method on a staggered mesh and the SIMPLER algorithm was used for the treatment of velocity-pressure coupling. The numerical simulations were performed for a wide range of Reynolds numbers 1, 10, 100, and 1000 numbers are equal to 0.01,0.1 Richardson, 0.5,1 and 10.The analysis of the results shows a flow bicellular (two cells), one is created by the speed of the fan placed in the inner cavity, one on the left is due to the difference between the temperatures right wall and the left wall. Knowledge of the intensity of each of these cells allowed us to get an original result. And the values obtained from each of Nuselt convection which allow to know the rate of heat transfer in the cavity.Finally we find that there is a significant influence on the position of the fan on the heat transfer (Nusselt evolution) for values of Reynolds studied and for low values of Richardson handed this influence is negligible for high values of the latter.

Keywords: thermal transfer, mixed convection, square cavity, finite volume method

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Authors: F. Hekmatipour, M. A. Akhavan-Behabadi, B. Sajadi

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In this paper, the combined free and forced convection heat transfer of the Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid flow in horizontal and inclined microfin tubes is studied experimentally. The flow regime is laminar, and pipe surface temperature is constant. The effect of nanoparticle and microfin tube on the heat transfer rate is investigated with the Richardson number which is between 0.1 and 0.7. The results show an increasing nanoparticle concentration between 0% and 1.5% leads to enhance the combined free and forced convection heat transfer rate. According to the results, five correlations are proposed to provide estimating the free and forced heat transfer rate as the increasing Richardson number from 0.1 to 0.7. The maximum deviation of both correlations is less than 16%. Moreover, four correlations are suggested to assess the Nusselt number based on the Rayleigh number in inclined tubes from 1800000 to 7000000. The maximum deviation of the correlation is almost 16%. The Darcy friction factor of the nanofluid flow has been investigated. Furthermore, CuO-HTO nanofluid flows in inclined microfin tubes.

Keywords: nanofluid, heat transfer oil, mixed convection, inclined tube, laminar flow

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Authors: Jannes Quer, Amir Niknejad, Marcus Weber

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Computational Drug Design is often based on Molecular Dynamics simulations of molecular systems. Molecular Dynamics can be used to simulate, e.g., the binding and unbinding event of a small drug-like molecule with regard to the active site of an enzyme or a receptor. However, the time-scale of the overall binding event is many orders of magnitude longer than the time-scale of simulation. Thus, there is a need to speed-up molecular simulations. In order to speed up simulations, the molecular dynamics trajectories have to be ”steared” out of local minimizers of the potential energy surface – the so-called metastabilities – of the molecular system. Increasing the kinetic energy (temperature) is one possibility to accelerate simulated processes. However, with temperature the entropy of the molecular system increases, too. But this kind ”stearing” is not directed enough to stear the molecule out of the minimum toward the saddle point. In this article, we give a new mathematical idea, how a potential energy surface can be changed in such a way, that entropy is kept under control while the trajectories are still steared out of the metastabilities. In order to compute the unsteared transition behaviour based on a steared simulation, we propose to use extrapolation methods. In the end we mathematically show, that our method accelerates the simulations along the direction, in which the curvature of the potential energy surface changes the most, i.e., from local minimizers towards saddle points.

Keywords: extrapolation, Eyring-Kramers, metastability, multilevel sampling

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Authors: Y.J. Wang, C. Q. Ru

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A key issue of cohesive zone models is how to determine the cohesive zone model parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model (CZM): The maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is modeled by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

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Authors: Y. J. Wang, C. Q. Ru

Abstract:

A key issue of cohesive zone models is how to determine the cohesive zone model (CZM) parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model: the maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is simulated by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

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Authors: B. Elshafei, X. Mao

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The demand for renewable energy is significantly increasing, major investments are being supplied to the wind power generation industry as a leading source of clean energy. The wind energy sector is entirely dependable and driven by the prediction of wind speed, which by the nature of wind is very stochastic and widely random. This s0tudy employs deep multi-fidelity Gaussian process regression, used to predict wind speeds for medium term time horizons. Data of the RUNE experiment in the west coast of Denmark were provided by the Technical University of Denmark, which represent the wind speed across the study area from the period between December 2015 and March 2016. The study aims to investigate the effect of pre-processing the data by denoising the signal using empirical wavelet transform (EWT) and engaging the vector components of wind speed to increase the number of input data layers for data fusion using deep multi-fidelity Gaussian process regression (GPR). The outcomes were compared using root mean square error (RMSE) and the results demonstrated a significant increase in the accuracy of predictions which demonstrated that using vector components of the wind speed as additional predictors exhibits more accurate predictions than strategies that ignore them, reflecting the importance of the inclusion of all sub data and pre-processing signals for wind speed forecasting models.

Keywords: data fusion, Gaussian process regression, signal denoise, temporal extrapolation

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: M. Mamor

Abstract:

GaN-based compounds have attracted much interest in the fabrication of high-power, high speed and high-frequency electronic devices. Other examples of GaN-based applications are blue and ultraviolet (UV) light-emitting diodes (LEDs). All these devices require high-quality ohmic and Schottky contacts. Gaining an understanding of the electrical characteristics of metal/GaN contacts is of fundamental and technological importance for developing GaN-based devices. In this work, the barrier characteristics of Pt and Pd Schottky contacts on n-type GaN were studied using temperature-dependent forward current-voltage (I-V) measurements over a wide temperature range 80–400 K. Our results show that the barrier height and ideality factor, extracted from the forward I-V characteristics based on thermionic emission (TE) model, exhibit an abnormal dependence with temperature; i.e., by increasing temperature, the barrier height increases whereas the ideality factor decreases. This abnormal behavior has been explained based on the TE model by considering the presence of double Gaussian distribution (GD) of nonhomogeneous barrier height at the metal/GaN interface. However, in the high-temperature range (160-400 K), the extracted value for the effective Richardson constant A* based on the barrier inhomogeneity (BHi) model is found in fair agreement with the theoretically predicted value of about 26.9 A.cm-2 K-2 for n-type GaN. This result indicates that in this temperature range, the conduction current transport is dominated by the thermionic emission mode. On the other hand, in the lower temperature range (80-160 K), the corresponding effective Richardson constant value according to the BHi model is lower than the theoretical value, suggesting the presence of other current transport, such as tunneling-assisted mode at lower temperatures.

Keywords: Schottky diodes, inhomogeneous barrier height, GaN semiconductors, Schottky barrier heights

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Authors: Morteza Khashehchi, Kamel Hooman

Abstract:

Thermal effects on the dynamics and stability of the flow past a circular cylinder operating in the mixed convection regime is studied experimentally for Reynolds number (ReD) between 1000 and 4000, and different cylinder wall temperatures (Tw) between 25 and 75°C by means of Particle Image Velocimetry (PIV). The experiments were conducted in a horizontal wind tunnel with the heated cylinder placed horizontally. With such assumptions, the direction of the thermally induced buoyancy force acting on the fluid surrounding the heated cylinder would be perpendicular to the flow direction. In each experiment, to acquire 3000 PIV image pairs, the temperature and Reynolds number of the approach flow were held constant. By adjusting different temperatures in different Reynolds numbers, the corresponding Richardson number (RiD = Gr/Re^2) was varied between 0:0 (unheated) and 10, resulting in a change in the heat transfer process from forced convection to mixed convection. With increasing temperature of the wall cylinder, significant modifications of the wake flow pattern and wake vortex shedding process were clearly revealed. For cylinder at low wall temperature, the size of the wake and the vortex shedding process are found to be quite similar to those of an unheated cylinder. With high wall temperature, however, the high temperature gradient in the wake shear layer creates a type of vorticity with opposite sign to that of the shear layer vorticity. This temperature gradient vorticity weakens the strength of the shear layer vorticity, causing delay in reaching the recreation point. In addition to the wake characteristics, the shedding frequency for the heated cylinder is determined for all aforementioned cases. It is found that, as the cylinder wall is heated, the organization of the vortex shedding is altered and the relative position of the first detached vortices with respect to the second one is changed. This movement of the first detached vortex toward the second one increases the frequency of the shedding process. It is also found that the wake closure length decreases with increasing the Richardson number.

Keywords: heated cylinder, PIV, wake, Reynolds number

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