Search results for: Taylor's Law

Authors: A. Esmael, A. El Shrif

Abstract:

In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

Keywords: Hydrodynamic Instability, Modified Taylor-Couette Flow, Turbulence, Taylor vortices.

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: Chaos theory, GMM estimator, Lyapunov Exponent, Monetary System, Taylor Rule.

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Authors: S. Damodaran, T. V. S.Sekhar

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The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.

Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

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One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: U. C. Amadi, N. A. Udoh

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One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.

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Authors: Gen Sakoda, Hideki Takayasu, Misako Takayasu

Abstract:

Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant  of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual  value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.

Keywords: Food waste reduction, particle filter, point of sales, sustainable development goals, Taylor's Law, time series analysis.

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

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In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Ahmed M. Mansour, Ali M. El-Sawy, Ahmed T Sayed

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Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving insights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

Keywords: Logarithms, log2, floor, iterative, CORDIC, Taylor series.

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Authors: Md. Kamruzzaman, L. Djenidi, R. A. Antonia

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This paper reports an experimental investigation of the energy spectrum of turbulent velocity fields at low Reynolds numbers in grid turbulence. Hot wire measurements are carried out in grid turbulence with subjected to a 1.36:1 contraction of the wind tunnel. Three different grids are used: (i) large square perforated grid (mesh size 43.75mm), (ii) small square perforated grid (mesh size 14. and (iii) woven mesh grid (mesh size 5mm). The results indicate that the energy spectrum at small Reynolds numbers does not follow Kolmogorov’s universal scaling. It is further found that the critical Reynolds number, below which the scaling breaks down, is around 25.

Keywords: Decay exponent, Energy spectrum, Taylor microscale Reynolds number, Taylor microscale, Turbulent kinetic energy.

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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Authors: Changhong Guo, Shaomei Fang, Yong He

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In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.

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Authors: R. Tandlich, S. Hoossein, K. A. Tagwira, M. M. Marais, T. A. Ludwig, R. P. Chidziva, M. N. Munodawafa, W. M. Wrench

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Response to the public health-related emergencies is analysed here for a rural university in South Africa. The structure of the designated emergency plan covers all the phases of the disaster management cycle. The plan contains elements of the vulnerability model and the technocratic model of emergency management. The response structures are vertically and horizontally integrated, while the planning contains elements of scenario-based and functional planning. The available number of medical professionals at the Rhodes University, along with the medical insurance rates, makes the staff and students potentially more medically vulnerable than the South African population. The main improvements of the emergency management are required in the tornado response and the information dissemination during health emergencies. The latter should involve the increased use of social media and e-mails, following the Taylor model of communication. Infrastructure must be improved in the telecommunication sector in the face of unpredictable electricity outages.

Keywords: Public health, Rural university, Taylor model of communication.

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Authors: Jaime Muñoz, José Arcos, Oscar Bautista Federico Méndez

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The influence of a pulsatile electroosmotic flow (PEOF) at the rate of spread, or dispersivity, for a non-reactive solute released in a microcapillary with slippage at the boundary wall (modeled by the Navier-slip condition) is theoretically analyzed. Based on the flow velocity field developed under such conditions, the present study implements an analytical scheme of scaling known as the Theory of Homogenization, in order to obtain a mathematical expression for the dispersivity, valid at a large time scale where the initial transients have vanished and the solute spreads under the Taylor dispersion influence. Our results show the dispersivity is a function of a slip coefficient, the amplitude of the imposed electric field, the Debye length and the angular Reynolds number, highlighting the importance of the latter as an enhancement/detrimental factor on the dispersivity, which allows to promote the PEOF as a strong candidate for chemical species separation at lab-on-a-chip devices.

Keywords: Dispersivity, microcapillary, Navier-slip condition, pulsatile electroosmotic flow, Taylor dispersion, Theory of Homogenization.

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Authors: Sameena Tarannum, S. Pranesh

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A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.

Keywords: Couple stress liquid, Ginzburg-Landau model, rotation, triple diffusive convection.

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Authors: Chai Mingming, Li Lei, Lu Xiaoxia

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In this paper, the mechanism of stratified liquids’ mixing in a cylinder is investigated. It is focused on the effects of Rayleigh-Taylor Instability (RTI) and rotation of the cylinder on liquid interface mixing. For miscible liquids, Planar Laser Induced Fluorescence (PLIF) technique is applied to record the concentration field for one liquid. Intensity of Segregation (IOS) is used to describe the mixing status. For immiscible liquids, High Speed Camera is adopted to record the development of the interface. The experiment of RTI indicates that it plays a great role in the mixing process, and meanwhile the large-scale mixing is triggered, and subsequently the span of the stripes decreases, showing that the mesoscale mixing is coming into being. The rotation experiments show that the spin-down process has a great role in liquid mixing, during which the upper liquid falls down rapidly along the wall and crashes into the lower liquid. During this process, a lot of interface instabilities are excited. Liquids mix rapidly in the spin-down process. It can be concluded that no matter what ways have been adopted to speed up liquid mixing, the fundamental reason is the interface instabilities which increase the area of the interface between liquids and increase the relative velocity of the two liquids.

Keywords: Interface instability, liquid mixing, Rayleigh-Taylor Instability, spin-down process, spin-up process.

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Authors: P. G. Siddheshwar, T. N. Sakshath

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In the paper we make linear and non-linear stability analyses of Rayleigh-Bénard convection of a Newtonian nanoliquid in a rotating medium (called as Rayleigh-Bénard-Taylor convection). Rigid-rigid isothermal boundaries are considered for investigation. Khanafer-Vafai-Lightstone single phase model is used for studying instabilities in nanoliquids. Various thermophysical properties of nanoliquid are obtained using phenomenological laws and mixture theory. The eigen boundary value problem is solved for the Rayleigh number using an analytical method by considering trigonometric eigen functions. We observe that the critical nanoliquid Rayleigh number is less than that of the base liquid. Thus the onset of convection is advanced due to the addition of nanoparticles. So, increase in volume fraction leads to advanced onset and thereby increase in heat transport. The amplitudes of convective modes required for estimating the heat transport are determined analytically. The tri-modal standard Lorenz model is derived for the steady state assuming small scale convective motions. The effect of rotation on the onset of convection and on heat transport is investigated and depicted graphically. It is observed that the onset of convection is delayed due to rotation and hence leads to decrease in heat transport. Hence, rotation has a stabilizing effect on the system. This is due to the fact that the energy of the system is used to create the component V. We observe that the amount of heat transport is less in the case of rigid-rigid isothermal boundaries compared to free-free isothermal boundaries.

Keywords: Nanoliquid, rigid-rigid, rotation, single-phase.

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Authors: Kholod M. Abualnaja

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This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

Keywords: Matrix Splines, Cubic Splines, Quartic Splines.

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Authors: Mohammed A. Abutheraa, David Lester

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We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: Rahul Bansal, Sudipta Majumdar

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This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: K. Boumediene, S. E. Belhenniche

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This article presents a numerical analysis of a turbulent flow past DTMB 4119 marine propeller by the means of RANS approach; the propeller designed at David Taylor Model Basin in USA. The purpose of this study is to predict the hydrodynamic performance of the marine propeller, it aims also to compare the results obtained with the experiment carried out in open water tests; a periodical computational domain was created to reduce the unstructured mesh size generated. The standard kw turbulence model for the simulation is selected; the results were in a good agreement. Therefore, the errors were estimated respectively to 1.3% and 5.9% for KT and KQ.

Keywords: propeller flow, CFD simulation, hydrodynamic performance, RANS

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

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Authors: Brent McKenzie, Victoria Taylor

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The use of QR (Quick Response Codes) codes for customer scanning with mobile phones is a rapidly growing trend. The QR code can provide the consumer with product information, user guides, product use, competitive pricing, etc. One sector for QR use has been in retail, through the use of Electronic Shelf Labeling (henceforth, ESL). In Europe, the use of ESL for pricing has been in practice for a number of years but continues to lag in acceptance in North America. Stated concerns include costs as a key constraint, but there is also evidence that consumer acceptance represents a limitation as well. The purpose of this study is to present the findings of a consumer based study to gage the impact on their use in the retail food sector.

Keywords: Electronic shelf labels (ESL), consumer insights, retail food sector.

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Authors: Shaneil Taylor

Abstract:

Gender-based violence is a reflection of the inequalities that are associated within a society between the men and women that affects the health, dignity, security and autonomy of its victims. There are various determinants that contribute to the health risk of young women who have experienced sexual violence, in countries that have a high prevalence rate for HIV. For instance, in South Africa, where the highest prevalence rate for HIV is among young women, their susceptibility to the virus has been increased by sexual violence and cultural inequalities. Therefore, this study is a review of literature that explores how gender-based violence increases the possibility for HIV/AIDS among young women in South Africa.

Keywords: Gender based violence, HIV/AIDS transmission, young women, Risky sexual behavior.

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Authors: Seong-Ho Song, Ki-Seob Kim, Seop-Hyeong Park, Seon-Woo Lee

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In this paper, the data correction algorithm is suggested when the environmental air temperature varies. To correct the infrared data in this paper, the initial temperature or the initial infrared image data is used so that a target source system may not be necessary. The temperature data obtained from infrared detector show nonlinear property depending on the surface temperature. In order to handle this nonlinear property, Taylor series approach is adopted. It is shown that the proposed algorithm can reduce the influence of environmental temperature on the components in the board. The main advantage of this algorithm is to use only the initial temperature of the components on the board rather than using other reference device such as black body sources in order to get reference temperatures.

Keywords: Infrared camera, Temperature Data compensation, Environmental Ambient Temperature, Electric Component

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Authors: Timothy Hinchman, Carrie Taylor

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This quantitative quasi-experimental research investigated disparities in mean and median performance among millennial soccer players. According to research, the fear of failure causes millennials to struggle with difficult jobs. The application of specified limitations has been found to increase individual productivity. The study utilized the constraint-based model of novelty (C-BMN) framework and the game performance assessment instrument (GPAI) to assess data concerning constraint-type and its impact on the productivity of 18 soccer players. Individual components cooperation and trapping had statistical significance throughout the intervention, while positioning, passing, and dribbling did not. The GPAI was statistically significant between the control and both restriction types. A two-way mixed ANOVA revealed no significant interaction between limitations and temperaments, however only 72% of individuals completed the temperament exam.

Keywords: Constraints, temperament, physical performance, GPAI.

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Authors: B. Zare-Farsani, M. Valieghbal, M. Tarkashvand, A. H. Farahbod

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To provide the conditions for nuclear fusion by high energy and powerful laser beams, it is required to have a high degree of symmetry and surface uniformity of the spherical capsules to reduce the Rayleigh-Taylor hydrodynamic instabilities. In this paper, we have used the digital microscopic holography based on Mach-Zehnder interferometer to study the quality of targets for inertial fusion. The interferometric pattern of the target has been registered by a CCD camera and analyzed by Holovision software. The uniformity of the surface and shell thickness are investigated and measured in reconstructed image. We measured shell thickness in different zone where obtained non uniformity 22.82 percent.  

Keywords: Inertial confinement fusion, Mach-Zehnder interferometer, Digital holographic microscopy.

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Authors: K. Horáková, K. Fraňa, V. Honzejk

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This part of study deals with description of unsteady isothermal melt flow in the container with cuboid shape. This melt flow is driven by rotating magnetic field. Input data (instantaneous velocities, grid coordinates and Lorentz forces) were obtained from in-house CFD code (called NS-FEM3D) which uses DDES method of computing. Description of the flow was performed by contours of Lorentz forces and caused velocity field. Taylor magnetic numbers of the flow were used 1.10^6, 5.10^6 and 1.10^7, flow was in 3D turbulent flow regime.

Keywords: In-house computing code, Lorentz forces, magnetohydrodynamics, rotating magnetic field.

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Authors: J. M. Breed, E. Taylor

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In this paper challenges associated with a new generation of Computer Science students are examined. The mode of education in tertiary institutes has progressed slowly while the needs of students have changed rapidly in an increasingly technological world. The major learning paradigms and learning theories within these paradigms are studied to find a suitable strategy for educating modern students. These paradigms include Behaviourism, Constructivism, Humanism and Cogntivism. Social Learning theory and Elaboration theory are two theories that are further examined and a survey is done to determine how these strategies will be received by students. The results and findings are evaluated and indicate that students are fairly receptive to a method that incorporates both Social Learning theory and Elaboration theory, but that some aspects of all paradigms need to be implemented to create a balanced and effective strategy with technology as foundation.

Keywords: Computer Science, Education, Elaboration Theory, Learning Paradigms, Social Learning Theory.

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: Axisymmetric problem, compressible Navier- Stokes equations, continuous finite elements, swirling flow.

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