Search results for: semidiscrete approximations

Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Marian Sagat, Mariana Remesikova

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In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros.

Keywords: geodesic, geodesic curvature flow, mesh, Rhinoceros software

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Authors: Navdeep Goel, Salvador Gabarda

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Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.

Keywords: chirp signals, image multiplexing, image transformation, linear canonical transform, polynomial approximation

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Authors: Joonas Pääkkönen

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In sports, individuals and teams are typically interested in final rankings. Final results, such as times or distances, dictate these rankings, also known as places. Places can be further associated with ordered random variables, commonly referred to as order statistics. In this work, we introduce a simple, yet accurate order statistical ordinal regression function that predicts relay race places with changeover-times. We call this function the Fenton-Wilkinson Order Statistics model. This model is built on the following educated assumption: individual leg-times follow log-normal distributions. Moreover, our key idea is to utilize Fenton-Wilkinson approximations of changeover-times alongside an estimator for the total number of teams as in the notorious German tank problem. This original place regression function is sigmoidal and thus correctly predicts the existence of a small number of elite teams that significantly outperform the rest of the teams. Our model also describes how place increases linearly with changeover-time at the inflection point of the log-normal distribution function. With real-world data from Jukola 2019, a massive orienteering relay race, the model is shown to be highly accurate even when the size of the training set is only 5% of the whole data set. Numerical results also show that our model exhibits smaller place prediction root-mean-square-errors than linear regression, mord regression and Gaussian process regression.

Keywords: Fenton-Wilkinson approximation, German tank problem, log-normal distribution, order statistics, ordinal regression, orienteering, sports analytics, sports modeling

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Authors: Duvert A. Puentes T., Javier A. Maldonado E., Ivan Quintero., Diego F. Villegas

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Mechanical Computation is a great tool to study the performance of complex models. An example of it is the study of the human body structure. This paper took advantage of different types of software to make a 3D model of the glenohumeral joint and apply a finite element analysis. The main objective was to study the change in the biomechanical properties of the joint when it presents an injury. Specifically, a BANKART lesion, which consists in the detachment of the anteroinferior labrum from the glenoid. Stress and strain distribution of the soft tissues were the focus of this study. First, a 3D model was made of a joint without any pathology, as a control sample, using segmentation software for the bones with the support of medical imagery and a cadaveric model to represent the soft tissue. The joint was built to simulate a compression and external rotation test using CAD to prepare the model in the adequate position. When the healthy model was finished, it was submitted to a finite element analysis and the results were validated with experimental model data. With the validated model, it was sensitized to obtain the best mesh measurement. Finally, the geometry of the 3D model was changed to imitate a BANKART lesion. Then, the contact zone of the glenoid with the labrum was slightly separated simulating a tissue detachment. With this new geometry, the finite element analysis was applied again, and the results were compared with the control sample created initially. With the data gathered, this study can be used to improve understanding of the labrum tears. Nevertheless, it is important to remember that the computational analysis are approximations and the initial data was taken from an in vitro assay.

Keywords: biomechanics, computational model, finite elements, glenohumeral joint, bankart lesion, labrum

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Authors: H. Duggal, G. Singh, G. Singh, A. Bhalla, S. Kumar, J. S. Shahi, D. Mehta

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The total differential cross section for scattering of the 5.895 keV photons by various polymers has been measured at scattering angle of 135o. The experimental measurements were carried out using the energy dispersive setup involving annular source of the 55Fe radioisotope and a low energy germanium (LEGe) detector. The cross section values are measured for 20 polymer targets namely, Paraffin Wax, Polytetrafluoro ethylene (PTFE), Cellulose, Silicone oil, Polyvinyl alcohol (PVA), Polyvinyl purrolidone (PVP), Polymethyl methacrylate (PMMA), Kapton, Mylar, Chitosan, Polyvinyl chloride (PVC), Bakelite, Carbopol, Chlorobutyl rubber (CBR), Polyetylene glycol (PEG), Polysorbate-20, Nylon-6, Cetyl alcohol, Carboxyl methyl sodium cellulose and Sodium starch glucolate. The measurements were performed in vacuum so as to avoid scattering contribution due to air and strong absorption of low energy photons in the air column. In the present investigations, the geometrical factor and efficiency of the detector were determined by measuring the K x-rays emitted from the 22Ti and 23V targets excited by the Mn K x-rays in the same experimental set up. The measured scattering cross sections have been compared with the sum of theoretically calculated elastic and inelastic scattering cross sections. The theoretical elastic (Rayleigh) scattering cross sections based on the various form factor approximations, namely, non-relativistic form factor (NF), relativistic form factor (RF), modified form factor (MF), and MF with anomalous scattering factor (ASF) as well as the second order S-matrix formalisms, and the inelastic scattering differential cross sections based on the Klein-Nishina formula after including the inelastic scattering function (KN+ISF) have been calculated. The experimental results show fairly good agreement with theoretical cross sections.

Keywords: photon, polymers, elastic and inelastic, scattering cross sections

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Adamu S. Salawu, Ibrahim O. Isah

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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: Musa Akdere, Gunnar Seide, Thomas Gries

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Carbon fibres are fibrous materials with a carbon atom amount of more than 90%. They combine excellent mechanicals properties with a very low density. Thus carbon fibre reinforced plastics (CFRP) are very often used in lightweight design and construction. The precursor material is usually polyacrylonitrile (PAN) based and wet-spun. During the production of carbon fibre, the precursor has to be stabilized thermally to withstand the high temperatures of up to 1500 °C which occur during carbonization. Even though carbon fibre has been used since the late 1970s in aerospace application, there is still no general method available to find the optimal production parameters and the trial-and-error approach is most often the only resolution. To have a much better insight into the process the chemical reactions during stabilization have to be analyzed particularly. Therefore, a model of the chemical reactions (cyclization, dehydration, and oxidation) based on the research of Dunham and Edie has been developed. With the presented model, it is possible to perform a complete simulation of the fibre undergoing all zones of stabilization. The fiber bundle is modeled as several circular fibers with a layer of air in-between. Two thermal mechanisms are considered to be the most important: the exothermic reactions inside the fiber and the convective heat transfer between the fiber and the air. The exothermic reactions inside the fibers are modeled as a heat source. Differential scanning calorimetry measurements have been performed to estimate the amount of heat of the reactions. To shorten the required time of a simulation, the number of fibers is decreased by similitude theory. Experiments were conducted to validate the simulation results of the fibre temperature during stabilization. The experiments for the validation were conducted on a pilot scale stabilization oven. To measure the fibre bundle temperature, a new measuring method is developed. The comparison of the results shows that the developed simulation model gives good approximations for the temperature profile of the fibre bundle during the stabilization process.

Keywords: carbon fibre, coupled simulation, exothermic reactions, fibre-air-interface

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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: Gholba Niranjan Dilip, Anil Kumar

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Conduct of accurate reliable mapping of oil palm plantations and census of individual palm trees is a huge challenge. This study addresses this challenge and developed an optimized solution implemented deep learning techniques on remote sensing data. The oil palm is a very important tropical crop. To improve its productivity and land management, it is imperative to have accurate census over large areas. Since, manual census is costly and prone to approximations, a methodology for automated census using panchromatic images from Cartosat-2, SkySat and World View-3 satellites is demonstrated. It is selected two different study sites in Indonesia. The customized set of training data and ground-truth data are created for this study from Cartosat-2 images. The pre-trained model of Single Shot MultiBox Detector (SSD) Lite MobileNet V2 Convolutional Neural Network (CNN) from the TensorFlow Object Detection API is subjected to transfer learning on this customized dataset. The SSD model is able to generate the bounding boxes for each oil palm and also do the counting of palms with good accuracy on the panchromatic images. The detection yielded an F-Score of 83.16 % on seven different images. The detections are buffered and dissolved to generate polygons demarcating the boundaries of the oil palm plantations. This provided the area under the plantations and also gave maps of their location, thereby completing the automated census, with a fairly high accuracy (≈100%). The trained CNN was found competent enough to detect oil palm crowns from images obtained from multiple satellite sensors and of varying temporal vintage. It helped to estimate the increase in oil palm plantations from 2014 to 2021 in the study area. The study proved that high-resolution panchromatic satellite image can successfully be used to undertake census of oil palm plantations using CNNs.

Keywords: object detection, oil palm tree census, panchromatic images, single shot multibox detector

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Authors: Aurélia Jandot

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With the oil and economic crises which began in the 1970’s, it has progressively appeared necessary to convince the French “general public“ that a use of new energy sources was essential. In this field, nuclear energy represented the future and concentrated lots of hopes. However, the discourse about nuclear energy has progressively seen negative arguments growing in the French media. The gradual changes in the perception of nuclear energy will be studied here through the arguments given in the main French weekly newsmagazines, which had a great impact on the readers, thus on the “general public“, from the 1970’s to the end of the 1980’s. Indeed, to understand better these changes will be taken into account the major international events, the reorientations of the French domestic policy, and the evolutions of the nuclear technology. As this represents a considerable amount of copies and thus of information, will be selected here the main articles which emphasize the “mental images“ aiming to direct the thought of the readers, and which have led the public awareness and acceptance to evolve. From the 1970’s to the end of the 1980’s, two dichotomous trends are in confrontation : one is promoting the perception of the nuclear energy, the other is discrediting it. Moreover, these two trends are organized in two axes. The first axis is about the engineerings evolutions, such as the main French media represent them, with its approximations, its exaggerations, its fictions sometimes. Is added the will to make accessible to the “general public“ some concepts which are quite difficult to understand for the largest number. The second axis rests on the way the major accidents of the period are approached, including those of Three Mile Island and Chernobyl. Thanks to these accidents and because of the international relations evolutions, the ecologist movements and their impacts have progressively grown, with evident consequences on the public perception of nuclear energy and on the way the successive governments can implement new power plants in France. Then, in both cases, over the period considered, the language has changed, as the perceptible objectives of the communication, allowing to discern the deepest intentions of the newsmagazines editing. This is all these changes that will be emphasized, over a period where the nuclear energy technology, to there a field for specialists, bearing mystery and secret, has become a social issue seemingly open to all.

Keywords: social issues, public acceptance, mediatization, discourse changes

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Authors: Verena M. Moock, Darien E. Arce Chávez, Mariana M. Espejel González, Leopoldo Ruíz-Huerta, Crescencio García-Segundo

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Uncertainty analysis in industrial computed tomography is commonly related to metrological trace tools, which offer precision measurements of external part features. Unfortunately, there is no such reference tool for internal measurements to profit from the unique imaging potential of X-rays. Uncertainty approximations for computed tomography are still based on general aspects of the industrial machine and do not adapt to acquisition parameters or part characteristics. The present study investigates the impact of the acquisition time on the dimensional uncertainty measuring a stainless steel cylinder with a circular tomography scan. The authors develop the figure difference method for X-ray radiography to evaluate the volumetric differences introduced within the projected absorption maps of the metal workpiece. The dimensional uncertainty is dominantly influenced by photon energy dissipated as heat causing the thermal expansion of the metal, as monitored by an infrared camera within the industrial tomograph. With the proposed methodology, we are able to show evolving temperature differences throughout the tomography acquisition. This is an early study showing that the number of projections in computer tomography induces dimensional error due to energy absorption. The error magnitude would depend on the thermal properties of the sample and the acquisition parameters by placing apparent non-uniform unwanted volumetric expansion. We introduce infrared imaging for the experimental display of metrological uncertainty in a particular metal part of symmetric geometry. We assess that the current results are of fundamental value to reach the balance between the number of projections and uncertainty tolerance when performing analysis with X-ray dimensional exploration in precision measurements with industrial tomography.

Keywords: computed tomography, digital metrology, infrared imaging, thermal expansion

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Authors: Ramzi Suleiman

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Recently, the author proposed an observationally-based relativity theory termed information relativity theory (IRT). The theory is simple and is based only on basic principles, with no prior axioms and no free parameters. For the case of a body of mass in uniform rectilinear motion relative to an observer, the theory transformations uncovered a matter-dark matter duality, which prescribes that the sum of the densities of the body's baryonic matter and dark matter, as measured by the observer, is equal to the body's matter density at rest. It was shown that the theory transformations were successful in predicting several important phenomena in small particle physics, quantum physics, and cosmology. This paper extends the theory transformations to the cases of rotating disks and spheres. The resulting transformations for a rotating disk are utilized to derive predictions of the radial distributions of matter and dark matter densities in rotationally supported galaxies based solely on their observed rotation curves. It is also shown that for galaxies with flattening curves, good approximations of the radial distributions of matter and dark matter and of the dark matter fraction could be obtained from one measurable scale radius. Test of the model on five galaxies, chosen randomly from the SPARC database, yielded impressive predictions. The rotation curves of all the investigated galaxies emerged as accurate traces of the predicted radial density distributions of their dark matter. This striking result raises an intriguing physical explanation of gravity in galaxies, according to which it is the proximal drag of the stars and gas in the galaxy by its rotating dark matter web. We conclude by alluding briefly to the application of the proposed model to stellar systems and black holes. This study also hints at the potential of the discovered matter-dark matter duality in fixing the standard model of elementary particles in a natural manner without the need for hypothesizing about supersymmetric particles.

Keywords: dark matter, galaxies rotation curves, SPARC, rotating disk

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Authors: Manish Chand, Subhrojit Bagchi, R. Kumar

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A new dry tube (DT) has been installed in the tank of KAMINI research reactor, Kalpakkam India. This tube will be used for neutron activation analysis of small to large samples and testing of neutron detectors. DT tube is 375 cm height and 7.5 cm in diameter, located 35 cm away from the core centre. The experimental thermal flux at various axial positions inside the tube has been measured by irradiating the flux monitor (¹⁹⁷Au) at 20kW reactor power. The measured activity of ¹⁹⁸Au and the thermal cross section of ¹⁹⁷Au (n,γ) ¹⁹⁸Au reaction were used for experimental thermal flux measurement. The flux inside the tube varies from 10⁹ to 10¹⁰ and maximum flux was (1.02 ± 0.023) x10¹⁰ n cm⁻²s⁻¹ at 36 cm from the bottom of the tube. The Au and Zr foils without and with cadmium cover of 1-mm thickness were irradiated at the maximum flux position in the DT to find out the irradiation specific input parameters like sub-cadmium to epithermal neutron flux ratio (f) and the epithermal neutron flux shape factor (α). The f value was 143 ± 5, indicates about 99.3% thermal neutron component and α value was -0.2886 ± 0.0125, indicates hard epithermal neutron spectrum due to insufficient moderation. The measured flux profile has been validated using theoretical model of KAMINI reactor through Monte Carlo N-Particle Code (MCNP). In MCNP, the complex geometry of the entire reactor is modelled in 3D, ensuring minimum approximations for all the components. Continuous energy cross-section data from ENDF-B/VII.1 as well as S (α, β) thermal neutron scattering functions are considered. The neutron flux has been estimated at the corresponding axial locations of the DT using mesh tally. The thermal flux obtained from the experiment shows good agreement with the theoretically predicted values by MCNP, it was within ± 10%. It can be concluded that this MCNP model can be utilized for calculating other important parameters like neutron spectra, dose rate, etc. and multi elemental analysis can be carried out by irradiating the sample at maximum flux position using measured f and α parameters by k₀-NAA standardization.

Keywords: neutron flux, neutron activation analysis, neutron flux shape factor, MCNP, Monte Carlo N-Particle Code

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Authors: Murilo G. Mendes

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This text presents part of the results presented in the Ph.D. thesis that has used John Baily's theory and method as well as its ethnographic application in the context of the fife flutes of the Banda Cabaçal dos Irmãos Aniceto in the state of Ceará, northeast of Brazil. John Baily is a British ethnomusicologist dedicated to studying the relationships between music, musical gesture, and embodied cognition. His methodology became a useful tool to highlight historical-social aspects present in the group's instrumental music. Remaining indigenous and illiterate, these musicians played and transmitted their music from generation to generation, for almost two hundred years, without any nomenclature or systematization of the fingering performed on the flute. In other words, his music, free from any theorization, is learned, felt, perceived, and processed directly through hearing and through the relationship between the instrument's motor skills and its sound result. For this reason, Baily's assumptions became fundamental in the analysis processes. As the author's methodology recommends, classes were held with the natives and provided technical musical learning and some important concepts. Then, transcriptions and analyses of musical aspects were made from patterns of movement on the instrument incorporated by repetitions and/or by the intrinsic facility of the instrument. As a result, it was discovered how the group reconciled its indigenous origins with the demand requested by the public power and the interests of the local financial elite from the mid-twentieth century. The article is structured from the cultural context of the group, where local historical and social aspects influence the social and musical practices of the group. Then, will be present the methodological conceptions of John Baily and, finally, their application in the music of the Irmãos Aniceto. The conclusion points to the good results of identifying, through this methodology and analysis, approximations between discourse, historical-social factors, and musical text. Still, questions are raised about its application in other contexts.

Keywords: Banda Cabaçal dos Irmãos Aniceto, John Baily, pífano, spatial-motor thinking

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Authors: Maria Miranda-Medina, Sara Salopek, Andras Vernes, Martin Jech

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Sliding lubricated surfaces induce the formation of tribofilms that reduce friction, wear and prevent large-scale damage of contact parts. Engine oils and lubricants use antiwear and antioxidant additives such as zinc dialkyldithiophosphate (ZDDP) from where protective tribofilms are formed by degradation. The ZDDP tribofilms are described as a two-layer structure composed of inorganic polymer material. On the top surface, the long chain polyphosphate is a zinc phosphate and in the bulk, the short chain polyphosphate is a mixed Fe/Zn phosphate with a gradient concentration. The polyphosphate chains are partially adherent to steel surface through a sulfide and work as anti-wear pads. In this contribution, ZDDP tribofilms formed on gray cast iron surfaces are studied. The tribofilms were generated in a reciprocating sliding tribometer with a piston ring-cylinder liner configuration. Fully formulated oil of SAE grade 5W-30 was used as lubricant during two tests at 40Hz and 50Hz. For the estimation of the tribofilm thicknesses, spectroscopic ellipsometry was used due to its high accuracy and non-destructive nature. Ellipsometry works under an optical principle where the change in polarisation of light reflected by the surface, is associated with the refractive index of the surface material or to the thickness of the layer deposited on top. Ellipsometrical responses derived from tribofilms are modelled by effective medium approximation (EMA), which includes the refractive index of involved materials, homogeneity of the film and thickness. The materials composition was obtained from x-ray photoelectron spectroscopic studies, where the presence of ZDDP, O and C was confirmed. From EMA models it was concluded that tribofilms formed at 40 Hz are thicker and more homogeneous than the ones formed at 50 Hz. In addition, the refractive index of each material is mixed to derive an effective refractive index that describes the optical composition of the tribofilm and exhibits a maximum response in the UV range, being a characteristic of glassy semitransparent films.

Keywords: effective medium approximation, reciprocating sliding tribometer, spectroscopic ellipsometry, zinc dialkyldithiophosphate

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Authors: Joshua Buli, David Pietrowski, Samuel Britton

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Processing SAR data usually requires constraints in extent in the Fourier domain as well as approximations and interpolations onto a planar surface to form an exploitable image. This results in a potential loss of data requires several interpolative techniques, and restricts visualization to two-dimensional plane imagery. The data can be interpolated into a ground plane projection, with or without terrain as a component, all to better view SAR data in an image domain comparable to what a human would view, to ease interpretation. An alternate but computationally heavy method to make use of more of the data is the basis of this research. Pre-processing of the SAR data is completed first (matched-filtering, motion compensation, etc.), the data is then range compressed, and lastly, the contribution from each pulse is determined for each specific point in space by searching the time history data for the reflectivity values for each pulse summed over the entire collection. This results in a per-3D-point reflectivity using the entire collection domain. New advances in GPU processing have finally allowed this rapid projection of acquired SAR data onto any desired reference surface (called backprojection). Mathematically, the computations are fast and easy to implement, despite limitations in SAR phase history data size and 3D-point cloud size. Backprojection processing algorithms are embarrassingly parallel since each 3D point in the scene has the same reflectivity calculation applied for all pulses, independent of all other 3D points and pulse data under consideration. Therefore, given the simplicity of the single backprojection calculation, the work can be spread across thousands of GPU threads allowing for accurate reflectivity representation of a scene. Furthermore, because reflectivity values are associated with individual three-dimensional points, a plane is no longer the sole permissible mapping base; a digital elevation model or even a cloud of points (collected from any sensor capable of measuring ground topography) can be used as a basis for the backprojection technique. This technique minimizes any interpolations and modifications of the raw data, maintaining maximum data integrity. This innovative processing will allow for SAR data to be rapidly brought into a common reference frame for immediate exploitation and data fusion with other three-dimensional data and representations.

Keywords: backprojection, data fusion, exploitation, three-dimensional, visualization

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Authors: Andreea Halunga, Chris D. Orme, Takashi Yamagata

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This paper proposes a heteroskedasticity-robust Breusch-Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel-data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: (i) either N is fixed as T→∞; or, (ii) N²/T→0, as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would provide an adequate guide to finite sample performance when T/N is "small". Because of this, we also propose and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap "version" of the original Breusch-Pagan test our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch-Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries.

Keywords: cross-section correlation, time-series heteroskedasticity, dynamic panel data, heteroskedasticity robust Breusch-Pagan test

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Authors: Mostafa Shahriari, Theophile Chaumont-Frelet, David Pardo

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Resistivity measurements are used to characterize the Earth’s subsurface. They are categorized into two different groups: (a) those acquired on the Earth’s surface, for instance, controlled source electromagnetic (CSEM) and Magnetotellurics (MT), and (b) those recorded with borehole logging instruments such as Logging-While-Drilling (LWD) devices. LWD instruments are mostly used for geo-steering purposes, i.e., to adjust dip and azimuthal angles of a well trajectory to drill along a particular geological target. Modern LWD tools measure all nine components of the magnetic field corresponding to three orthogonal transmitter and receiver orientations. In order to map the Earth’s subsurface and perform geo-steering, we invert measurements using a gradient-based method that utilizes the derivatives of the recorded measurements with respect to the inversion variables. For resistivity measurements, these inversion variables are usually the constant resistivity value of each layer and the bed boundary positions. It is well-known how to compute derivatives with respect to the constant resistivity value of each layer using semi-analytic or numerical methods. However, similar formulas for computing the derivatives with respect to bed boundary positions are unavailable. The main contribution of this work is to provide an adjoint-based formulation for computing derivatives with respect to the bed boundary positions. The key idea to obtain the aforementioned adjoint state formulations for the derivatives is to separate the tangential and normal components of the field and treat them differently. This formulation allows us to compute the derivatives faster and more accurately than with traditional finite differences approximations. In the presentation, we shall first derive a formula for computing the derivatives with respect to the bed boundary positions for the potential equation. Then, we shall extend our formulation to 3D Maxwell’s equations. Finally, by considering a 1D domain and reducing the dimensionality of the problem, which is a common practice in the inversion of resistivity measurements, we shall derive a formulation to compute the derivatives of the measurements with respect to the bed boundary positions using a 1.5D variational formulation. Then, we shall illustrate the accuracy and convergence properties of our formulations by comparing numerical results with the analytical derivatives for the potential equation. For the 1.5D Maxwell’s system, we shall compare our numerical results based on the proposed adjoint-based formulation vs those obtained with a traditional finite difference approach. Numerical results shall show that our proposed adjoint-based technique produces enhanced accuracy solutions while its cost is negligible, as opposed to the finite difference approach that requires the solution of one additional problem per derivative.

Keywords: inverse problem, bed boundary positions, electromagnetism, potential equation

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Authors: Gamaliel Salazar, Adriana Chazaro, Oscar Madrigal

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The evolution of Unmanned Aerial Systems (UAS) has made it possible to develop new vehicles capable to perform microgravity experiments which due its cost and complexity were beyond the reach for many institutions. In this study, the aerodynamic behavior of an UAS is studied through its deceleration stage after an initial free fall phase (where the microgravity effect is generated) using Computational Fluid Dynamics (CFD). Due to the fact that the payload would be analyzed under a microgravity environment and the nature of the payload itself, the speed of the UAS must be reduced in a smoothly way. Moreover, the terminal speed of the vehicle should be low enough to preserve the integrity of the payload and vehicle during the landing stage. The UAS model is made by a study pod, control surfaces with fixed and mobile sections, landing gear and two semicircular wing sections. The speed of the vehicle is decreased by increasing the angle of attack (AoA) of each wing section from 2° (where the airfoil S1091 has its greatest aerodynamic efficiency) to 80°, creating a circular wing geometry. Drag coefficients (Cd) and forces (Fd) are obtained employing CFD analysis. A simplified 3D model of the vehicle is analyzed using Ansys Workbench 16. The distance between the object of study and the walls of the control volume is eight times the length of the vehicle. The domain is discretized using an unstructured mesh based on tetrahedral elements. The refinement of the mesh is made by defining an element size of 0.004 m in the wing and control surfaces in order to figure out the fluid behavior in the most important zones, as well as accurate approximations of the Cd. The turbulent model k-epsilon is selected to solve the governing equations of the fluids while a couple of monitors are placed in both wing and all-body vehicle to visualize the variation of the coefficients along the simulation process. Employing a statistical approximation response surface methodology the case of study is parametrized considering the AoA of the wing as the input parameter and Cd and Fd as output parameters. Based on a Central Composite Design (CCD), the Design Points (DP) are generated so the Cd and Fd for each DP could be estimated. Applying a 2nd degree polynomial approximation the drag coefficients for every AoA were determined. Using this values, the terminal speed at each position is calculated considering a specific Cd. Additionally, the distance required to reach the terminal velocity at each AoA is calculated, so the minimum distance for the entire deceleration stage without comprising the payload could be determine. The Cd max of the vehicle is 1.18, so its maximum drag will be almost like the drag generated by a parachute. This guarantees that aerodynamically the vehicle can be braked, so it could be utilized for several missions allowing repeatability of microgravity experiments.

Keywords: microgravity effect, response surface, terminal speed, unmanned system

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Authors: M. Qamarul Islam, Ergun Dogan, Mehmet Yazici

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There is a growing body of evidence that non-normal data is more prevalent in nature than the normal one. Examples can be quoted from, but not restricted to, the areas of Economics, Finance and Actuarial Science. The non-normality considered here is expressed in terms of fat-tailedness and asymmetry of the relevant distribution. In this study a skew t distribution that can be used to model a data that exhibit inherent non-normal behavior is considered. This distribution has tails fatter than a normal distribution and it also exhibits skewness. Although maximum likelihood estimates can be obtained by solving iteratively the likelihood equations that are non-linear in form, this can be problematic in terms of convergence and in many other respects as well. Therefore, it is preferred to use the method of modified maximum likelihood in which the likelihood estimates are derived by expressing the intractable non-linear likelihood equations in terms of standardized ordered variates and replacing the intractable terms by their linear approximations obtained from the first two terms of a Taylor series expansion about the quantiles of the distribution. These estimates, called modified maximum likelihood estimates, are obtained in closed form. Hence, they are easy to compute and to manipulate analytically. In fact the modified maximum likelihood estimates are equivalent to maximum likelihood estimates, asymptotically. Even in small samples the modified maximum likelihood estimates are found to be approximately the same as maximum likelihood estimates that are obtained iteratively. It is shown in this study that the modified maximum likelihood estimates are not only unbiased but substantially more efficient than the commonly used moment estimates or the least square estimates that are known to be biased and inefficient in such cases. Furthermore, in conventional regression analysis, it is assumed that the error terms are distributed normally and, hence, the well-known least square method is considered to be a suitable and preferred method for making the relevant statistical inferences. However, a number of empirical researches have shown that non-normal errors are more prevalent. Even transforming and/or filtering techniques may not produce normally distributed residuals. Here, a study is done for multiple linear regression models with random error having non-normal pattern. Through an extensive simulation it is shown that the modified maximum likelihood estimates of regression parameters are plausibly robust to the distributional assumptions and to various data anomalies as compared to the widely used least square estimates. Relevant tests of hypothesis are developed and are explored for desirable properties in terms of their size and power. The tests based upon modified maximum likelihood estimates are found to be substantially more powerful than the tests based upon least square estimates. Several examples are provided from the areas of Economics and Finance where such distributions are interpretable in terms of efficient market hypothesis with respect to asset pricing, portfolio selection, risk measurement and capital allocation, etc.

Keywords: least square estimates, linear regression, maximum likelihood estimates, modified maximum likelihood method, non-normality, robustness

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Authors: Mustapha Rilwan Adewale, Salau Ayobami Muhammed

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This study focuses on the heat transfer analysis of magneto-hydrodynamics (MHD) squeezing flow between parallel disks, considering a viscous incompressible fluid. The upper disk exhibits both upward and downward motion, while the lower disk remains stationary but permeable. By employing similarity transformations, a system of nonlinear ordinary differential equations is derived to describe the flow behavior. To solve this system, a numerical approach, namely the Chebyshev collocation method, is utilized. The study investigates the influence of flow parameters and compares the obtained results with existing literature. The significance of this research lies in understanding the heat transfer characteristics of MHD squeezing flow, which has practical implications in various engineering and industrial applications. By employing the similarity transformations, the complex governing equations are simplified into a system of nonlinear ordinary differential equations, facilitating the analysis of the flow behavior. To obtain numerical solutions for the system, the Chebyshev collocation method is implemented. This approach provides accurate approximations for the nonlinear equations, enabling efficient computations of the heat transfer properties. The obtained results are compared with existing literature, establishing the validity and consistency of the numerical approach. The study's major findings shed light on the influence of flow parameters on the heat transfer characteristics of the squeezing flow. The analysis reveals the impact of parameters such as magnetic field strength, disk motion amplitude, fluid viscosity on the heat transfer rate between the disks, the squeeze number(S), suction/injection parameter(A), Hartman number(M), Prandtl number(Pr), modified Eckert number(Ec), and the dimensionless length(δ). These findings contribute to a comprehensive understanding of the system's behavior and provide insights for optimizing heat transfer processes in similar configurations. In conclusion, this study presents a thorough heat transfer analysis of magneto-hydrodynamics squeezing flow between parallel disks. The numerical solutions obtained through the Chebyshev collocation method demonstrate the feasibility and accuracy of the approach. The investigation of flow parameters highlights their influence on heat transfer, contributing to the existing knowledge in this field. The agreement of the results with previous literature further strengthens the reliability of the findings. These outcomes have practical implications for engineering applications and pave the way for further research in related areas.

Keywords: squeezing flow, magneto-hydro-dynamics (MHD), chebyshev collocation method(CCA), parallel manifolds, finite difference method (FDM)

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Authors: Isabella Bianco, Gian Andrea Blengini

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The environmental impact related to ornamental stones (such as marbles and granites) is largely debated. Starting from the industrial revolution, continuous improvements of machineries led to a higher exploitation of this natural resource and to a more international interaction between markets. As a consequence, the environmental impact of the extraction and processing of stones has increased. Nevertheless, if compared with other building materials, ornamental stones are generally more durable, natural, and recyclable. From the scientific point of view, studies on stone life cycle sustainability have been carried out, but these are often partial or not very significant because of the high percentage of approximations and assumptions in calculations. This is due to the lack, in life cycle databases (e.g. Ecoinvent, Thinkstep, and ELCD), of datasets about the specific technologies employed in the stone production chain. For example, databases do not contain information about diamond wires, chains or explosives, materials commonly used in quarries and transformation plants. The project presented in this paper aims to populate the life cycle databases with specific data of specific stone processes. To this goal, the methodology follows the standardized approach of Life Cycle Assessment (LCA), according to the requirements of UNI 14040-14044 and to the International Reference Life Cycle Data System (ILCD) Handbook guidelines of the European Commission. The study analyses the processes of the entire production chain (from-cradle-to-gate system boundaries), including the extraction of benches, the cutting of blocks into slabs/tiles and the surface finishing. Primary data have been collected in Italian quarries and transformation plants which use technologies representative of the current state-of-the-art. Since the technologies vary according to the hardness of the stone, the case studies comprehend both soft stones (marbles) and hard stones (gneiss). In particular, data about energy, materials and emissions were collected in marble basins of Carrara and in Beola and Serizzo basins located in the province of Verbano Cusio Ossola. Data were then elaborated through an appropriate software to build a life cycle model. The model was realized setting free parameters that allow an easy adaptation to specific productions. Through this model, the study aims to boost the direct participation of stone companies and encourage the use of LCA tool to assess and improve the stone sector environmental sustainability. At the same time, the realization of accurate Life Cycle Inventory data aims at making available, to researchers and stone experts, ILCD compliant datasets of the most significant processes and technologies related to the ornamental stone sector.

Keywords: life cycle assessment, LCA datasets, ornamental stone, stone environmental impact

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Authors: Najibullah M, Soumendra Nath Kuiry

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Dams and reservoirs are perceived for their estimable alms to irrigation, water supply, flood control, electricity generation, etc. which civilize the prosperity and wealth of society across the world. Meantime the dam breach could cause devastating flood that can threat to the human lives and properties. Failures of large dams remain fortunately very seldom events. Nevertheless, a number of occurrences have been recorded in the world, corresponding in an average to one to two failures worldwide every year. Some of those accidents have caused catastrophic consequences. So it is decisive to predict the dam break flow for emergency planning and preparedness, as it poses high risk to life and property. To mitigate the adverse impact of dam break, modeling is necessary to gain a good understanding of the temporal and spatial evolution of the dam-break floods. This study will mainly deal with one-dimensional (1D) dam break modeling. Less commonly used in the hydraulic research community, another possible option for modeling the rapidly varied dam-break flows is the extended Boussinesq equations (BEs), which can describe the dynamics of short waves with a reasonable accuracy. Unlike the Shallow Water Equations (SWEs), the BEs taken into account the wave dispersion and non-hydrostatic pressure distribution. To capture the dam-break oscillations accurately it is very much needed of at least fourth-order accurate numerical scheme to discretize the third-order dispersion terms present in the extended BEs. The scope of this work is therefore to develop an 1D fourth-order accurate in both space and time Boussinesq model for dam-break flow analysis by using finite-volume / finite difference scheme. The spatial discretization of the flux and dispersion terms achieved through a combination of finite-volume and finite difference approximations. The flux term, was solved using a finite-volume discretization whereas the bed source and dispersion term, were discretized using centered finite-difference scheme. Time integration achieved in two stages, namely the third-order Adams Basforth predictor stage and the fourth-order Adams Moulton corrector stage. Implementation of the 1D Boussinesq model done using PYTHON 2.7.5. Evaluation of the performance of the developed model predicted as compared with the volume of fluid (VOF) based commercial model ANSYS-CFX. The developed model is used to analyze the risk of cascading dam failures similar to the Panshet dam failure in 1961 that took place in Pune, India. Nevertheless, this model can be used to predict wave overtopping accurately compared to shallow water models for designing coastal protection structures.

Keywords: Boussinesq equation, Coastal protection, Dam-break flow, One-dimensional model

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Authors: Qaisar Ali, Waqar A. Khan, Shafiq R. Qureshi

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Heat transfer in Power Law Fluids across cylindrical surfaces has copious engineering applications. These applications comprises of areas such as underwater pollution, bio medical engineering, filtration systems, chemical, petroleum, polymer, food processing, recovery of geothermal energy, crude oil extraction, pharmaceutical and thermal energy storage. The quantum of research work with diversified conditions to study the effects of combined heat transfer and fluid flow across porous media has increased considerably over last few decades. The most non-Newtonian fluids of practical interest are highly viscous and therefore are often processed in the laminar flow regime. Several studies have been performed to investigate the effects of free and mixed convection in Newtonian fluids along vertical and horizontal cylinder embedded in a saturated porous medium, whereas very few analysis have been performed on Power law fluids along wedge. In this study, boundary layer analysis under the effects of radiation-mixed convection in power law fluids along vertical wedge in porous medium have been investigated using an implicit finite difference method (Keller box method). Steady, 2-D laminar flow has been considered under prescribed surface heat flux condition. Darcy, Boussinesq and Roseland approximations are assumed to be valid. Neglecting viscous dissipation effects and the radiate heat flux in the flow direction, the boundary layer equations governing mixed convection flow over a vertical wedge are transformed into dimensionless form. The single mathematical model represents the case for vertical wedge, cone and plate by introducing the geometry parameter. Both similar and Non- similar solutions have been obtained and results for Non similar case have been presented/ plotted. Effects of radiation parameter, variable heat flux parameter, wedge angle parameter ‘m’ and mixed convection parameter have been studied for both Newtonian and Non-Newtonian fluids. The results are also compared with the available data for the analysis of heat transfer in the prescribed range of parameters and found in good agreement. Results for the details of dimensionless local Nusselt number, temperature and velocity fields have also been presented for both Newtonian and Non-Newtonian fluids. Analysis of data revealed that as the radiation parameter or wedge angle is increased, the Nusselt number decreases whereas it increases with increase in the value of heat flux parameter at a given value of mixed convection parameter. Also, it is observed that as viscosity increases, the skin friction co-efficient increases which tends to reduce the velocity. Moreover, pseudo plastic fluids are more heat conductive than Newtonian and dilatant fluids respectively. All fluids behave identically in pure forced convection domain.

Keywords: porous medium, power law fluids, surface heat flux, vertical wedge

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Authors: M. Pienaar, J. W. Odendaal, J. C. Smit, J. Joubert

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Simulations are commonly used to predict the bistatic radar cross section (RCS) of military targets since characterization measurements can be expensive and time consuming. It is thus important to accurately predict the bistatic RCS of targets. Computational electromagnetic (CEM) methods can be used for bistatic RCS prediction. CEM methods are divided into full-wave and asymptotic methods. Full-wave methods are numerical approximations to the exact solution of Maxwell’s equations. These methods are very accurate but are computationally very intensive and time consuming. Asymptotic techniques make simplifying assumptions in solving Maxwell's equations and are thus less accurate but require less computational resources and time. Asymptotic techniques can thus be very valuable for the prediction of bistatic RCS of electrically large targets, due to the decreased computational requirements. This study extends previous work by validating the accuracy of asymptotic techniques to predict bistatic RCS through comparison with full-wave simulations as well as measurements. Validation is done with canonical structures as well as complex realistic aircraft models instead of only looking at a complex slicy structure. The slicy structure is a combination of canonical structures, including cylinders, corner reflectors and cubes. Validation is done over large bistatic angles and at different polarizations. Bistatic RCS measurements were conducted in a compact range, at the University of Pretoria, South Africa. The measurements were performed at different polarizations from 2 GHz to 6 GHz. Fixed bistatic angles of β = 30.8°, 45° and 90° were used. The measurements were calibrated with an active calibration target. The EM simulation tool FEKO was used to generate simulated results. The full-wave multi-level fast multipole method (MLFMM) simulated results together with the measured data were used as reference for validation. The accuracy of physical optics (PO) and geometrical optics (GO) was investigated. Differences relating to amplitude, lobing structure and null positions were observed between the asymptotic, full-wave and measured data. PO and GO were more accurate at angles close to the specular scattering directions and the accuracy seemed to decrease as the bistatic angle increased. At large bistatic angles PO did not perform well due to the shadow regions not being treated appropriately. PO also did not perform well for canonical structures where multi-bounce was the main scattering mechanism. PO and GO do not account for diffraction but these inaccuracies tended to decrease as the electrical size of objects increased. It was evident that both asymptotic techniques do not properly account for bistatic structural shadowing. Specular scattering was calculated accurately even if targets did not meet the electrically large criteria. It was evident that the bistatic RCS prediction performance of PO and GO depends on incident angle, frequency, target shape and observation angle. The improved computational efficiency of the asymptotic solvers yields a major advantage over full-wave solvers and measurements; however, there is still much room for improvement of the accuracy of these asymptotic techniques.

Keywords: asymptotic techniques, bistatic RCS, geometrical optics, physical optics

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Authors: S. Pradhan, V. Kumaran

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Centrifugal gas separation processes effect separation by utilizing the difference in the mole fraction in a high speed rotating cylinder caused by the difference in molecular mass, and consequently the centrifugal force density. These have been widely used in isotope separation because chemical separation methods cannot be used to separate isotopes of the same chemical species. More recently, centrifugal separation has also been explored for the separation of gases such as carbon dioxide and methane. The efficiency of separation is critically dependent on the secondary flow generated due to temperature gradients at the cylinder wall or due to inserts, and it is important to formulate accurate models for this secondary flow. The widely used Onsager model for secondary flow is restricted to very long cylinders where the length is large compared to the diameter, the limit of high stratification parameter, where the gas is restricted to a thin layer near the wall of the cylinder, and it assumes that there is no mass difference in the two species while calculating the secondary flow. There are two objectives of the present analysis of the rarefied gas flow in a rotating cylinder. The first is to remove the restriction of high stratification parameter, and to generalize the solutions to low rotation speeds where the stratification parameter may be O (1), and to apply for dissimilar gases considering the difference in molecular mass of the two species. Secondly, we would like to compare the predictions with molecular simulations based on the direct simulation Monte Carlo (DSMC) method for rarefied gas flows, in order to quantify the errors resulting from the approximations at different aspect ratios, Reynolds number and stratification parameter. In this study, we have obtained analytical and numerical solutions for the secondary flows generated at the cylinder curved surface and at the end-caps due to linear wall temperature gradient and external gas inflow/outflow at the axis of the cylinder. The effect of sources of mass, momentum and energy within the flow domain are also analyzed. The results of the analytical solutions are compared with the results of DSMC simulations for three types of forcing, a wall temperature gradient, inflow/outflow of gas along the axis, and mass/momentum input due to inserts within the flow. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used diffuse reflection boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a temperature slip (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity.

Keywords: rotating flows, generalized onsager and carrier-Maslen model, DSMC simulations, rarefied gas flow

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Authors: Dorian Audot, Isobel Margaret Thompson, Dominic Hudson, Joseph Banks, Martin Warner

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In competitive swimming, after dives and turns, athletes perform underwater undulatory swimming (UUS), copying marine mammals’ method of locomotion. The body, performing this wave-like motion, accelerates the fluid downstream in its vicinity, generating propulsion with minimal resistance. Through this technique, swimmers can maintain greater speeds than surface swimming and take advantage of the overspeed granted by the dive (or push-off). Almost all previous work has considered UUS when performed at maximum effort. Critical parameters to maximize UUS speed are frequently discussed; however, this does not apply to most races. In only 3 out of the 16 individual competitive swimming events are athletes likely to attempt to perform UUS with the greatest speed, without thinking of the cost of locomotion. In the other cases, athletes will want to control the speed of their underwater swimming, attempting to maximise speed whilst considering energy expenditure appropriate to the duration of the event. Hence, there is a need to understand how swimmers adapt their underwater strategies to optimize the speed within the allocated energetic cost. This paper develops a consistent methodology that enables different sets of UUS kinematics to be investigated. These may have different propulsive efficiencies and force generation mechanisms (e.g.: force distribution along with the body and force magnitude). The developed methodology, therefore, needs to: (i) provide an understanding of the UUS propulsive mechanisms at different speeds, (ii) investigate the key performance parameters when UUS is not performed solely for maximizing speed; (iii) consistently determine the propulsive efficiency of a UUS technique. The methodology is separated into two distinct parts: kinematic data acquisition and computational fluid dynamics (CFD) analysis. For the kinematic acquisition, the position of several joints along the body and their sequencing were either obtained by video digitization or by underwater motion capture (Qualisys system). During data acquisition, the swimmers were asked to perform UUS at a constant depth in a prone position (facing the bottom of the pool) at different speeds: maximum effort, 100m pace, 200m pace and 400m pace. The kinematic data were input to a CFD algorithm employing a two-dimensional Large Eddy Simulation (LES). The algorithm adopted was specifically developed in order to perform quick unsteady simulations of deforming bodies and is therefore suitable for swimmers performing UUS. Despite its approximations, the algorithm is applied such that simulations are performed with the inflow velocity updated at every time step. It also enables calculations of the resistive forces (total and applied to each segment) and the power input of the modeled swimmer. Validation of the methodology is achieved by comparing the data obtained from the computations with the original data (e.g.: sustained swimming speed). This method is applied to the different kinematic datasets and provides data on swimmers’ natural responses to pacing instructions. The results show how kinematics affect force generation mechanisms and hence how the propulsive efficiency of UUS varies for different race strategies.

Keywords: CFD, efficiency, human swimming, hydrodynamics, underwater undulatory swimming

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Authors: Ye Xue, Zhenhua Deng

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Objectives: Facial soft tissue thickness (FSTT) data could be obtained from CT scans by measuring the face-to-skull distances at sparsely distributed anatomical landmarks by manually located on face and skull. However, automated measurement using 3D facial and skull models by dense points using open-source software has become a viable option due to the development of computed assisted imaging technologies. By utilizing dense FSTT information, it becomes feasible to generate plausible automated facial approximations. Therefore, establishing a comprehensive and detailed, densely calculated FSTT database is crucial in enhancing the accuracy of facial approximation. Materials and methods: This study utilized head CT scans from 250 Chinese adults of Han ethnicity, with 170 participants originally born and residing in northern China and 80 participants in southern China. The age of the participants ranged from 14 to 82 years, and all samples were divided into five non-overlapping age groups. Additionally, samples were also divided into three categories based on BMI information. The 3D Slicer software was utilized to segment bone and soft tissue based on different Hounsfield Unit (HU) thresholds, and surface models of the face and skull were reconstructed for all samples from CT data. Following procedures were performed unsing MeshLab, including converting the face models into hollowed cropped surface models amd automatically measuring the Hausdorff Distance (referred to as FSTT) between the skull and face models. Hausdorff point clouds were colorized based on depth value and exported as PLY files. A histogram of the depth distributions could be view and subdivided into smaller increments. All PLY files were visualized of Hausdorff distance value of each vertex. Basic descriptive statistics (i.e., mean, maximum, minimum and standard deviation etc.) and distribution of FSTT were analysis considering the sex, age, BMI and birthplace. Statistical methods employed included Multiple Regression Analysis, ANOVA, principal component analysis (PCA). Results: The distribution of FSTT is mainly influenced by BMI and sex, as further supported by the results of the PCA analysis. Additionally, FSTT values exceeding 30mm were found to be more sensitive to sex. Birthplace-related differences were observed in regions such as the forehead, orbital, mandibular, and zygoma. Specifically, there are distribution variances in the depth range of 20-30mm, particularly in the mandibular region. Northern males exhibit thinner FSTT in the frontal region of the forehead compared to southern males, while females shows fewer distribution differences between the northern and southern, except for the zygoma region. The observed distribution variance in the orbital region could be attributed to differences in orbital size and shape. Discussion: This study provides a database of Chinese individuals distribution of FSTT and suggested opening source tool shows fine function for FSTT measurement. By incorporating birthplace as an influential factor in the distribution of FSTT, a greater level of detail can be achieved in facial approximation.

Keywords: forensic anthropology, forensic imaging, cranial facial reconstruction, facial soft tissue thickness, CT, open-source tool

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