Search results for: linear fractional differential equations

Authors: Nima Farshidfar, Navid Daryasafar

Abstract:

In this paper, the seismic stability of reinforced soil slopes is studied using pseudo-dynamic analysis. Equilibrium equations that are applicable to the every kind of failure surface are written using Horizontal Slices Method. In written equations, the balance of the vertical and horizontal forces and moment equilibrium is fully satisfied. Failure surface is assumed to be log-spiral, and non-linear equilibrium equations obtained for the system are solved using Newton-Raphson Method. Earthquake effects are applied as horizontal and vertical pseudo-static coefficients to the problem. To solve this problem, a code was developed in MATLAB, and the critical failure surface is calculated using genetic algorithm. At the end, comparing the results obtained in this paper, effects of various parameters and the effect of using pseudo - dynamic analysis in seismic forces modeling is presented.

Keywords: soil slopes, pseudo-dynamic, genetic algorithm, optimization, limit equilibrium method, log-spiral failure surface

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Authors: Panwasn Mahalawalert

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The purposes of this research were analyzed differential item functioning and differential test functioning of SWUSAT aptitude test classification by sex variable. The data used in this research is the secondary data from Srinakharinwirot University Scholastic Aptitude Test 2013 (SWUSAT). SWUSAT test consists of four subjects. There are verbal ability test, number ability test, reasoning ability test and spatial ability test. The data analysis was analyzed in 2 steps. The first step was analyzing descriptive statistics. In the second step were analyzed differential item functioning (DIF) and differential test functioning (DTF) by using the DIFAS program. The research results were as follows: The results of DIF and DTF analysis for all 10 tests in year 2013. Gender was the characteristic that found DIF all 10 tests. The percentage of item number that found DIF is between 6.67% - 60%. There are 5 tests that most of items favors female group and 2 tests that most of items favors male group. There are 3 tests that the number of items favors female group equal favors male group. For Differential test functioning (DTF), there are 8 tests that have small level.

Keywords: aptitude test, differential item functioning, differential test functioning, educational measurement

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Authors: Madhu Aneja, Sapna Sharma

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Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

Procedia PDF Downloads 126

Authors: Ruangdech Sirikit

Abstract:

The purposes of this study were analyzed differential item functioning and differential test functioning of SWUSAT aptitude test classification by sex variable. The data used in this research is the secondary data from Srinakharinwirot University Scholastic Aptitude Test 2011 (SWUSAT 2011) SWUSAT test consists of four subjects. There are verbal ability test, number ability test, reasoning ability test and spatial ability test. The data analysis was carried out in 2 steps. The first step was analyzing descriptive statistics. In the second step were analyzed differential item functioning (DIF) and differential test functioning (DTF) by using the DIFAS program. The research results were as follows: The results of data analysis for all 10 tests in year 2011. Sex was the characteristic that found DIF all 10 tests. The percentage of item number that found DIF was between 10% - 46.67%. There are 4 tests that most of items favors female group. There are 3 tests that most of items favors male group and there are 3 tests that the number of items favors female group equal favors male group. For Differential test functioning (DTF), there are 8 tests that have small DIF effect variance.

Keywords: differential item functioning, differential test functioning, SWUSAT, aptitude test

Procedia PDF Downloads 586

Authors: Michael Fundator

Abstract:

Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

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The edges of low contrast images are not clearly distinguishable to the human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: low contrast image, fractional order differentiator, Laplacian of Gaussian (LoG) method, chebyshev polynomial

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Authors: K. Godazandeh, K. Sadeghy

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In the present study, the effect of magnetic field on the hydrodynamic instability of Taylor-Couette flow between two concentric rotating cylinders has been numerically investigated. At the beginning the basic flow has been solved using continuity, Cauchy equations (with regards to Lorentz force) and the constitutive equations of a viscoelastic model called "Giesekus" model. Small perturbations, considered to be normal mode, have been superimposed to the basic flow and the unsteady perturbation equations have been derived consequently. Neglecting non-linear terms, the general eigenvalue problem obtained has been solved using pseudo spectral method (combination of Chebyshev polynomials). The objective of the calculations is to study the effect of magnetic fields on the onset of first mode of instability (axisymmetric mode) for different dimensionless parameters of the flow. The results show that the stability picture is highly influenced by the magnetic field. When magnetic field increases, it first has a destabilization effect which changes to stabilization effect due to more increase of magnetic fields. Therefor there is a critical magnetic number (Hartmann number) for instability of Taylor-Couette flow. Also, the effect of magnetic field is more dominant in large gaps. Also based on the results obtained, magnetic field shows a more considerable effect on the stability at higher Weissenberg numbers (at higher elasticity), while the "mobility factor" changes show no dominant role on the intense of suction and injection effect on the flow's instability.

Keywords: magnetic field, Taylor-Couette flow, Giesekus model, pseudo spectral method, Chebyshev polynomials, Hartmann number, Weissenberg number, mobility factor

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Authors: N. R. Badurally Adam, S. R. Monebhurrun, M. Z. Dauhoo, A. Khoodaruth

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Transport energy demand is vital for the economic growth of any country. Globalisation and better standard of living plays an important role in transport energy demand. Recently, transport energy demand in Mauritius has increased significantly, thus leading to an abuse of natural resources and thereby contributing to global warming. Forecasting the transport energy demand is therefore important for controlling and managing the demand. In this paper, we develop a model to predict the transport energy demand. The model developed is based on a system of five stochastic differential equations (SDEs) consisting of five endogenous variables: fuel price, population, gross domestic product (GDP), number of vehicles and transport energy demand and three exogenous parameters: crude birth rate, crude death rate and labour force. An interval of seven years is used to avoid any falsification of result since Mauritius is a developing country. Data available for Mauritius from year 2003 up to 2009 are used to obtain the values of design variables by applying genetic algorithm. The model is verified and validated for 2010 to 2012 by substituting the values of coefficients obtained by GA in the model and using particle swarm optimisation (PSO) to predict the values of the exogenous parameters. This model will help to control the transport energy demand in Mauritius which will in turn foster Mauritius towards a pollution-free country and decrease our dependence on fossil fuels.

Keywords: genetic algorithm, modeling, particle swarm optimization, stochastic differential equations, transport energy demand

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Authors: Babak Safaei, A. M. Fattahi

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In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ)

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

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Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Iyai Davies, Olivier L. C. Haas

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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability

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Authors: Romaric Desbrousses, Lan Lin

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The objective of this study is to determine how Canadian seismic design provisions affect the column axial load resistance of moment-resisting frame reinforced concrete buildings subjected to the differential settlement of their foundation. To do so, two four-storey buildings are designed in accordance with the seismic design provisions of the Canadian Concrete Design Standards. One building is located in Toronto, which is situated in a moderate seismic hazard zone in Canada, and the other in Vancouver, which is in Canada’s highest seismic hazard zone. A finite element model of each building is developed using SAP 2000. A 100 mm settlement is assigned to the base of the building’s center column. The axial load resistance of the column is represented by the demand capacity ratio. The analysis results show that settlement-induced tensile axial forces have a particularly detrimental effect on the conventional settling columns of the Toronto buildings which fail at a much smaller settlement that those in the Vancouver buildings. The results also demonstrate that particular care should be taken in the design of columns in short-span buildings.

Keywords: Columns, Demand, Foundation differential settlement, Seismic design, Non-linear analysis

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: J. Liu, Z. P. Yu, L. Xiong, Y. Feng, J. He

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According to the independence, accuracy and controllability of the driving/braking torque of the distributed drive electric vehicle, a control strategy of differential drive assisted steering was designed. Firstly, the assisted curve under different speed and steering wheel torque was developed and the differential torques were distributed to the right and left front wheels. Then the steering return ability assisted control algorithm was designed. At last, the joint simulation was conducted by CarSim/Simulink. The result indicated: the differential drive assisted steering algorithm could provide enough steering drive-assisted under low speed and improve the steering portability. Along with the increase of the speed, the provided steering drive-assisted decreased. With the control algorithm, the steering stiffness of the steering system increased along with the increase of the speed, which ensures the driver’s road feeling. The control algorithm of differential drive assisted steering could avoid the understeer under low speed effectively.

Keywords: differential assisted steering, control strategy, distributed drive electric vehicle, driving/braking torque

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Authors: D. S. Gomes, A. T. Silva

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Analysis of the uncertainty quantification related to nuclear safety margins applied to the nuclear reactor is an important concept to prevent future radioactive accidents. The nuclear fuel performance code may involve the tolerance level determined by traditional deterministic models producing acceptable results at burn cycles under 62 GWd/MTU. The behavior of nuclear fuel can simulate applying a series of material properties under irradiation and physics models to calculate the safety limits. In this study, theoretical predictions of nuclear fuel failure under transient conditions investigate extended radiation cycles at 75 GWd/MTU, considering the behavior of fuel rods in light-water reactors under reactivity accident conditions. The fuel pellet can melt due to the quick increase of reactivity during a transient. Large power excursions in the reactor are the subject of interest bringing to a treatment that is known as the Fuchs-Hansen model. The point kinetic neutron equations show similar characteristics of non-linear differential equations. In this investigation, the multivariate logistic regression is employed to a probabilistic forecast of fuel failure. A comparison of computational simulation and experimental results was acceptable. The experiments carried out use the pre-irradiated fuels rods subjected to a rapid energy pulse which exhibits the same behavior during a nuclear accident. The propagation of uncertainty utilizes the Wilk's formulation. The variables chosen as essential to failure prediction were the fuel burnup, the applied peak power, the pulse width, the oxidation layer thickness, and the cladding type.

Keywords: logistic regression, reactivity-initiated accident, safety margins, uncertainty propagation

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding

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Authors: Mandy W. M. Chan, Samantha Y. N. Shek, Chi K. Yeung, Taro Kono, Henry H. L. Chan

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Fractional radiofrequency devices have shown to improve skin texture such as smoothness, rhytides, brightness as well as atrophic acne scars by increasing dermal thickness, dermal collagen content and dermal fibrillin content. The objective of the study is to assess the efficacy and adverse effects of this device on Asian patients with skin textural changes. In this study, 20 Chinese patients (ranging from 21-60 years old) with irregularities of skin texture, rhytides and acne scars were recruited. Patients received six treatments at 2-4 week intervals. Treatment was initiated with maximum energy tolerated and was adjustable during treatment if patients felt excessive discomfort. A total of two passes were delivered at each session. Physician assessment and standardized photographs were taken at baseline, all treatment visits and at one, two, and six month after final treatment. As a result, 17 patients were recruited and completed the study according to the study protocol. One patient withdrew after the first treatment due to reaction to local anesthesia and two patients were lost to follow-up. At six months follow-up, 71% of the patients were satisfied and 24% were very satisfied, while treatment physician reported various degrees of improvement based on the global assessment scale in 60% of the subjects. Anticipated side effects including erythema, edema, pinpoint bleeding, scabs formation and flare of acne were recorded, but there were no serious adverse effects noted. Conclude up, the use of fractional radiofrequency improves skin texture and appears to be safe in Asian patients. No long-term serious adverse effect was noted.

Keywords: Asian, fractional radiogrequency, skin, texture

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Authors: Parisa Khoshvaght, Mehdi Hosseinzadeh

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During the past few years, the Residue Number System (RNS) has been receiving considerable interest due to its parallel and fault-tolerant properties. This system is a useful tool for Digital Signal Processing (DSP) since it can support parallel, carry-free, high-speed and low power arithmetic. One of the drawbacks of Residue Number System is the fractional numbers, that is, the corresponding circuit is very hard to realize in conventional CMOS technology. In this paper, we propose a method in which the numbers of transistors are significantly reduced. The related delay is extremely diminished, in the first glance we use this method to solve concerning problem of one decimal functional number some how this proposition can be extended to generalize the idea. Another advantage of this method is the independency on the kind of moduli.

Keywords: computer arithmetic, residue number system, number system, one-Hot, VLSI

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Authors: L. Belounar, K. Gerraiche, C. Rebiai, S. Benmebarek

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This paper presents the development of a new three dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending behavior. The developed element has the three essential external degrees of freedom (U, V and W) at each of the eight corner nodes. The displacements field of the developed element is based on assumed functions for the various strains satisfying the compatibility and the equilibrium equations. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element.

Keywords: brick element, strain approach, plate bending, civil engineering

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Authors: Pavlo Selyshchev

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A theoretical approach to describe kinetic of heat transfer between an irradiated sample and environment is developed via formalism of the Complex systems and kinetic equations. The irradiated material is a metastable system with non-linear feedbacks, which can give rise to different regimes of buildup and annealing of radiation-induced defects, heating and heat transfer with environment. Irradiation with energetic particles heats the sample and produces defects of the crystal lattice of the sample. The crystal with defects accumulates extra (non-thermal) energy, which is transformed into heat during the defect annealing. Any increase of temperature leads to acceleration of defect annealing, to additional transformation of non-thermal energy into heat and to further growth of the temperature. Thus a non-linear feedback is formed. It is shown that at certain conditions of irradiation this non-linear feedback leads to self-oscillations of the defect density, the temperature of the irradiated sample and the heat transfer between the sample and environment. Simulation and analysis of these phenomena is performed. The frequency of the self-oscillations is obtained. It is determined that the period of the self-oscillations is varied from minutes to several hours depending on conditions of irradiation and properties of the sample. Obtaining results are compared with experimental ones.

Keywords: irradiation, heat transfer, non-linear feed-back, self-oscillations

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Authors: Puneet Kumar, Jonnalagadda Srinivas

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The authors report here vibration and buckling analysis of functionally graded carbon nanotube-polymer composite (FG-CNTPC) beams under hygro-thermo-mechanical environments using higher order shear deformation theory. The material properties of CNT and polymer matrix are often affected by temperature and moisture content. A micromechanical model with agglomeration effect is employed to compute the elastic, thermal and moisture properties of the composite beam. The governing differential equation of FG-CNTRPC beam is developed using higher-order shear deformation theory to account shear deformation effects. The elastic, thermal and hygroscopic strain terms are derived from variational principles. Moreover, thermal and hygroscopic loads are determined by considering uniform, linear and sinusoidal variation of temperature and moisture content through the thickness. Differential equations of motion are formulated as an eigenvalue problem using appropriate displacement fields and solved by using finite element modeling. The obtained results of natural frequencies and critical buckling loads show a good agreement with published data. The numerical illustrations elaborate the dynamic as well as buckling behavior under uniaxial load for different environmental conditions, boundary conditions and volume fraction distribution profile, beam slenderness ratio. Further, comparisons are shown at different boundary conditions, temperatures, degree of moisture content, volume fraction as well as agglomeration of CNTs, slenderness ratio of beam for different shear deformation theories.

Keywords: hygrothermal effect, free vibration, buckling load, agglomeration

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: Arin Ghazarian, Cyril Rakovski

Abstract:

Differential privacy has become the leading technique to protect the privacy of individuals in a database while allowing useful analysis to be done and the results to be shared. It puts a guarantee on the amount of privacy loss in the worst-case scenario. Differential privacy is not a toggle between full privacy and zero privacy. It controls the tradeoff between the accuracy of the results and the privacy loss using a single key parameter called

Keywords: arrhythmia, cardiology, differential privacy, ECG, epsilon, medi-cal data, privacy preserving analytics, statistical databases

Procedia PDF Downloads 127

Authors: Minas Balyan

Abstract:

In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Elsayed M. A. Elbashbeshy, T. G. Emam, M. S. El-Azab, K. M. Abdelgaber

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The effect of thermal radiation on flow, heat and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder embedded in a porous medium with suction/injection is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.

Keywords: laminar flow, boundary layer, stretching horizontal cylinder, thermal radiation, suction/injection, nanofluid

Procedia PDF Downloads 362