Search results for: linearized Euler equation
2057 Magnetic Survey for the Delineation of Concrete Pillars in Geotechnical Investigation for Site Characterization
Authors: Nuraddeen Usman, Khiruddin Abdullah, Mohd Nawawi, Amin Khalil Ismail
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A magnetic survey is carried out in order to locate the remains of construction items, specifically concrete pillars. The conventional Euler deconvolution technique can perform the task but it requires the use of fixed structural index (SI) and the construction items are made of materials with different shapes which require different SI (unknown). A Euler deconvolution technique that estimate background, horizontal coordinate (xo and yo), depth and structural index (SI) simultaneously is prepared and used for this task. The synthetic model study carried indicated the new methodology can give a good estimate of location and does not depend on magnetic latitude. For field data, both the total magnetic field and gradiometer reading had been collected simultaneously. The computed vertical derivatives and gradiometer readings are compared and they have shown good correlation signifying the effectiveness of the method. The filtering is carried out using automated procedure, analytic signal and other traditional techniques. The clustered depth solutions coincided with the high amplitude/values of analytic signal and these are the possible target positions of the concrete pillars being sought. The targets under investigation are interpreted to be located at the depth between 2.8 to 9.4 meters. More follow up survey is recommended as this mark the preliminary stage of the work.Keywords: concrete pillar, magnetic survey, geotechnical investigation, Euler Deconvolution
Procedia PDF Downloads 2532056 A Numerical Model Simulation for an Updraft Gasifier Using High-Temperature Steam
Authors: T. M. Ismail, M. A. El-Salam
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A mathematical model study was carried out to investigate gasification of biomass fuels using high-temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promising way in its capability and sensitivity for the parameter effects that influence the gasification process.Keywords: computational fluid dynamics, gasification, biomass fuel, fixed bed gasifier
Procedia PDF Downloads 3922055 Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation
Authors: Sachin Kumar
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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method
Procedia PDF Downloads 1922054 Optimal Hybrid Linear and Nonlinear Control for a Quadcopter Drone
Authors: Xinhuang Wu, Yousef Sardahi
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A hybrid and optimal multi-loop control structure combining linear and nonlinear control algorithms are introduced in this paper to regulate the position of a quadcopter unmanned aerial vehicle (UAV) driven by four brushless DC motors. To this end, a nonlinear mathematical model of the UAV is derived and then linearized around one of its operating points. Using the nonlinear version of the model, a sliding mode control is used to derive the control laws of the motor thrust forces required to drive the UAV to a certain position. The linear model is used to design two controllers, XG-controller and YG-controller, responsible for calculating the required roll and pitch to maneuver the vehicle to the desired X and Y position. Three attitude controllers are designed to calculate the desired angular rates of rotors, assuming that the Euler angles are minimal. After that, a many-objective optimization problem involving 20 design parameters and ten objective functions is formulated and solved by HypE (Hypervolume estimation algorithm), one of the widely used many-objective optimization algorithms approaches. Both stability and performance constraints are imposed on the optimization problem. The optimization results in terms of Pareto sets and fronts are obtained and show that some of the design objectives are competing. That is, when one objective goes down, the other goes up. Also, Numerical simulations conducted on the nonlinear UAV model show that the proposed optimization method is quite effective.Keywords: optimal control, many-objective optimization, sliding mode control, linear control, cascade controllers, UAV, drones
Procedia PDF Downloads 662053 Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method
Authors: Emad K. Jaradat, Ala’a Al-Faqih
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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation
Procedia PDF Downloads 1802052 Relativistic Energy Analysis for Some q Deformed Shape Invariant Potentials in D Dimensions Using SUSYQM Approach
Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi
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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function
Procedia PDF Downloads 3392051 A Mathematical Equation to Calculate Stock Price of Different Growth Model
Authors: Weiping Liu
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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.Keywords: stock price, multistage model, different growth model, discounted cash flow method
Procedia PDF Downloads 3982050 Free Vibration Analysis of Symmetric Sandwich Beams
Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun
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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model
Procedia PDF Downloads 4682049 Energy Conservation and H-Theorem for the Enskog-Vlasov Equation
Authors: Eugene Benilov, Mikhail Benilov
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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition
Procedia PDF Downloads 1472048 Numerical Solution of Manning's Equation in Rectangular Channels
Authors: Abdulrahman Abdulrahman
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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow
Procedia PDF Downloads 2092047 Geometrically Linear Symmetric Free Vibration Analysis of Sandwich Beam
Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun
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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model
Procedia PDF Downloads 4662046 Exactly Fractional Solutions of Nonlinear Lattice Equation via Some Fractional Transformations
Authors: A. Zerarka, W. Djoudi
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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation
Procedia PDF Downloads 6512045 Analysis of Transverse Vibrations in Uniform Beams Subject to Different End Restraints
Authors: Falek Kamel
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Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory
Procedia PDF Downloads 782044 Local Radial Basis Functions for Helmholtz Equation in Seismic Inversion
Authors: Hebert Montegranario, Mauricio Londoño
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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion
Procedia PDF Downloads 5412043 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation
Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha
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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law
Procedia PDF Downloads 4902042 Analysis of a Generalized Sharma-Tasso-Olver Equation with Variable Coefficients
Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará
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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media
Procedia PDF Downloads 5082041 Kernel Parallelization Equation for Identifying Structures under Unknown and Periodic Loads
Authors: Seyed Sadegh Naseralavi
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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation
Procedia PDF Downloads 2752040 Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions
Authors: Gholamreza Koochaki
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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam
Procedia PDF Downloads 3872039 A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation
Authors: Johnson Oladele Fatokun, I. P. Akpan
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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator
Procedia PDF Downloads 4112038 State Estimation Based on Unscented Kalman Filter for Burgers’ Equation
Authors: Takashi Shimizu, Tomoaki Hashimoto
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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation
Procedia PDF Downloads 1462037 Study on the Central Differencing Scheme with the Staggered Version (STG) for Solving the Hyperbolic Partial Differential Equations
Authors: Narumol Chintaganun
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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.Keywords: central differencing scheme, STG, advection equation, burgers equation
Procedia PDF Downloads 5522036 Numerical Simulation of Wishart Diffusion Processes
Authors: Raphael Naryongo, Philip Ngare, Anthony Waititu
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This paper deals with numerical simulation of Wishart processes for a single asset risky pricing model whose volatility is described by Wishart affine diffusion processes. The multi-factor specification of volatility will make the model more flexible enough to fit the stock market data for short or long maturities for better returns. The Wishart process is a stochastic process which is a positive semi-definite matrix-valued generalization of the square root process. The aim of the study is to model the log asset stock returns under the double Wishart stochastic volatility model. The solution of the log-asset return dynamics for Bi-Wishart processes will be obtained through Euler-Maruyama discretization schemes. The numerical results on the asset returns are compared to the existing models returns such as Heston stochastic volatility model and double Heston stochastic volatility modelKeywords: euler schemes, log-asset return, infinitesimal generator, wishart diffusion affine processes
Procedia PDF Downloads 3712035 A Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers
Authors: H. Ozbasaran
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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.Keywords: cantilever, IPN, IPE, lateral torsional buckling
Procedia PDF Downloads 5352034 Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects
Authors: H. Triki, Y. Hamaizi, A. El-Akrmi
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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution
Procedia PDF Downloads 6282033 Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity
Authors: Mishu Gupta, Rama Gupta
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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation
Procedia PDF Downloads 1482032 A Dynamic Equation for Downscaling Surface Air Temperature
Authors: Ch. Surawut, D. Sukawat
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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.Keywords: dynamic equation, downscaling, inverse distance, weight interpolation
Procedia PDF Downloads 2982031 Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian
Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma
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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental
Procedia PDF Downloads 2032030 Modeling of Physico-Chemical Characteristics of Concrete for Filling Trenches in Radioactive Waste Management
Authors: Ilija Plecas, Dalibor Arbutina
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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste
Procedia PDF Downloads 3152029 Periodicity of Solutions of a Nonlinear Impulsive Differential Equation with Piecewise Constant Arguments
Authors: Mehtap Lafcı
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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments
Procedia PDF Downloads 5062028 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation
Authors: Aziz Sezgin
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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems
Procedia PDF Downloads 396