Search results for: integral equation approach
15292 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories
Authors: Ranajay Bhowmick
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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion
Procedia PDF Downloads 11215291 Complex Fuzzy Evolution Equation with Nonlocal Conditions
Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli
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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups
Procedia PDF Downloads 24715290 Differential Transform Method: Some Important Examples
Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen
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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions
Procedia PDF Downloads 51315289 Rogue Waves Arising on the Standing Periodic Wave in the High-Order Ablowitz-Ladik Equation
Authors: Yanpei Zhen
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The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables
Procedia PDF Downloads 15515288 Concrete Cracking Simulation Using Vector Form Intrinsic Finite Element Method
Authors: R. Z. Wang, B. C. Lin, C. H. Huang
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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.Keywords: VFIFE, crack propagation, fictitious crack model, crack critical
Procedia PDF Downloads 31415287 Nanofocusing of Surface Plasmon Polaritons by Partially Metal- Coated Dielectric Conical Probe: Optimal Asymmetric Distance
Authors: Ngo Thi Thu, Kazuo Tanaka, Masahiro Tanaka, Dao Ngoc Chien
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Nanometric superfocusing of optical intensity near the tip of partially metal- coated dielectric conical probe of the convergent surface plasmon polariton wave is investigated by the volume integral equation method. It is possible to perform nanofocusing using this probe by using both linearly and radially polarized Gaussian beams as the incident waves. Strongly localized and enhanced optical near-fields can be created on the tip of this probe for the cases of both incident Gaussian beams. However the intensity distribution near the probe tip was found to be very sensitive to the shape of the probe tip.Keywords: waveguide, surface plasmons, electromagnetic theory
Procedia PDF Downloads 45515286 The Soliton Solution of the Quadratic-Cubic Nonlinear Schrodinger Equation
Authors: Sarun Phibanchon, Yuttakarn Rattanachai
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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.Keywords: soliton, ion-acoustic waves, plasma, spectral method
Procedia PDF Downloads 38815285 A Fundamental Functional Equation for Lie Algebras
Authors: Ih-Ching Hsu
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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions
Procedia PDF Downloads 19815284 Modeling Thermionic Emission from Carbon Nanotubes with Modified Richardson-Dushman Equation
Authors: Olukunle C. Olawole, Dilip Kumar De
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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density
Procedia PDF Downloads 35215283 On the Mathematical Modelling of Aggregative Stability of Disperse Systems
Authors: Arnold M. Brener, Lesbek Tashimov, Ablakim S. Muratov
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The paper deals with the special model for coagulation kernels which represents new control parameters in the Smoluchowski equation for binary aggregation. On the base of the model the new approach to evaluating aggregative stability of disperse systems has been submitted. With the help of this approach the simple estimates for aggregative stability of various types of hydrophilic nano-suspensions have been obtained.Keywords: aggregative stability, coagulation kernels, disperse systems, mathematical model
Procedia PDF Downloads 28815282 Towards a Rigorous Analysis for a Supercritical Particulate Process
Authors: Yousef Bakhbakhi
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Crystallization with supercritical fluids (SCFs), as a developed technology to produce particles of micron and sub-micron size with narrow size distribution, has found appreciable importance as an environmentally friendly technology. Particle synthesis using SCFs can be achieved employing a number of special processes involving solvent and antisolvent mechanisms. In this study, the compressed antisolvent (PCA) process is utilized as a model to analyze the theoretical complexity of crystallization with supercritical fluids. The population balance approach has proven to be an effectual technique to simulate and predict the particle size and size distribution. The nucleation and growth mechanisms of the particles formation in the PCA process is investigated using the population balance equation, which describes the evolution of the particle through coalescence and breakup levels with time. The employed mathematical population balance model contains a set of the partial differential equation with algebraic constraints, which demands a rigorous numerical approach. The combined Collocation and Galerkin finite element method are proposed as a high-resolution technique to solve the dynamics of the PCA process.Keywords: particle formation, particle size and size distribution, PCA, supercritical carbon dioxide
Procedia PDF Downloads 17415281 Prediction of Thermodynamic Properties of N-Heptane in the Critical Region
Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci
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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.Keywords: crossover model, critical region, fundamental equation, n-heptane
Procedia PDF Downloads 44615280 A Survey on Routh-Hurwitz Stability Criterion
Authors: Mojtaba Hakimi-Moghaddam
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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots
Procedia PDF Downloads 29115279 New High Order Group Iterative Schemes in the Solution of Poisson Equation
Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali
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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation
Procedia PDF Downloads 40715278 Bubble Point Pressures of CO2+Ethyl Palmitate by a Cubic Equation of State and the Wong-Sandler Mixing Rule
Authors: M. A. Sedghamiz, S. Raeissi
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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate
Procedia PDF Downloads 44015277 Second Harmonic Generation of Higher-Order Gaussian Laser Beam in Density Rippled Plasma
Authors: Jyoti Wadhwa, Arvinder Singh
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This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.
Procedia PDF Downloads 14815276 Comparison of Selected Pier-Scour Equations for Wide Piers Using Field Data
Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif
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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.Keywords: field data, local scour, scour equation, wide piers
Procedia PDF Downloads 37915275 Collocation Method Using Quartic B-Splines for Solving the Modified RLW Equation
Authors: A. A. Soliman
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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.Keywords: collocation method, MRLW equation, Quartic B-splines, solitons
Procedia PDF Downloads 28015274 Calculate Consumer Surplus and Producer Surplus Using Integration
Authors: Bojan Radisic, Katarina Stavlic
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The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.Keywords: consumer surplus, producer surplus, definite integral, integration
Procedia PDF Downloads 54515273 Study of Composite Beam under the Effect of Shear Deformation
Authors: Hamid Hamli Benzahar
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The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.Keywords: composite beam, shear deformation, moments, finites elements
Procedia PDF Downloads 4815272 Symbolic Partial Differential Equations Analysis Using Mathematica
Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan
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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica
Procedia PDF Downloads 13415271 A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions
Authors: Khaled Moaddy
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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions
Procedia PDF Downloads 10915270 The Dynamics of Unsteady Squeezing Flow between Parallel Plates (Two-Dimensional)
Authors: Jiya Mohammed, Ibrahim Ismail Giwa
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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow
Procedia PDF Downloads 44615269 Membrane Distillation Process Modeling: Dynamical Approach
Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati
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This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated.Keywords: membrane distillation, dynamical modeling, advection-diffusion equation, thermal equilibrium, heat equation
Procedia PDF Downloads 24715268 Performances Analysis of the Pressure and Production of an Oil Zone by Simulation of the Flow of a Fluid through the Porous Media
Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled
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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility
Procedia PDF Downloads 18515267 On the Grid Technique by Approximating the Derivatives of the Solution of the Dirichlet Problems for (1+1) Dimensional Linear Schrodinger Equation
Authors: Lawrence A. Farinola
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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error
Procedia PDF Downloads 10215266 Mapping Methods to Solve a Modified Korteweg de Vries Type Equation
Authors: E. V. Krishnan
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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation
Procedia PDF Downloads 30415265 Sharp Estimates of Oscillatory Singular Integrals with Rough Kernels
Authors: H. Al-Qassem, L. Cheng, Y. Pan
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In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness
Procedia PDF Downloads 43515264 Chaotic Motion of Single-Walled Carbon Nanotube Subject to Damping Effect
Authors: Tai-Ping Chang
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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube
Procedia PDF Downloads 29415263 Comparative Analysis of DTC Based Switched Reluctance Motor Drive Using Torque Equation and FEA Models
Authors: P. Srinivas, P. V. N. Prasad
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Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. The DTC of SRM is analysed by two methods. In one of the methods, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.Keywords: direct toque control, simplified torque equation, finite element analysis, torque ripple
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