Search results for: perturbation of electromagnetic field dispersion equation

Authors: Suchi Barua, Narottam Das, Sven Nordholm, Mohammad Razaghi

Abstract:

This paper presents nonlinear pulse propagation characteristics for different input optical pulse shapes with various input pulse energy levels in semiconductor optical amplifiers. For simulation of nonlinear pulse propagation, finite-difference beam propagation method is used to solve the nonlinear Schrödinger equation. In this equation, gain spectrum dynamics, gain saturation are taken into account which depends on carrier depletion, carrier heating, spectral-hole burning, group velocity dispersion, self-phase modulation and two photon absorption. From this analysis, we obtained the output waveforms and spectra for different input pulse shapes as well as for different input energies. It shows clearly that the peak position of the output waveforms are shifted toward the leading edge which due to the gain saturation of the SOA for higher input pulse energies. We also analyzed and compared the normalized difference of full-width at half maximum for different input pulse shapes in the SOA.

Keywords: Finite-difference beam propagation method, pulse shape, pulse propagation, semiconductor optical amplifier.

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Authors: Nebojsa B. Raicevic, Slavoljub R. Aleksic, Sasa S. Ilic

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A power cable is widely used for power supply in power distributing networks and power transmission lines. Due to limitations in the production, delivery and setting up power cables, they are produced and delivered in several separate lengths. Cable itself, consists of two cable terminations and arbitrary number of cable joints, depending on the cable route length. Electrical stress control is needed to prevent a dielectric breakdown at the end of the insulation shield in both the air and cable insulation. Reliability of cable joint depends on its materials, design, installation and operating environment. The paper describes design and performance results for new modeled cable joints. Design concepts, based on numerical calculations, must be correct. An Equivalent Electrodes Method/Boundary Elements Method-hybrid approach that allows electromagnetic field calculations in multilayer dielectric media, including inhomogeneous regions, is presented.

Keywords: Cable joints, deflector's cones, equivalent electrodemethod, electric field distribution

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Authors: Kannanut Chamsri

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Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

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Authors: K. L. Verma

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Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

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Authors: Ming-Chu Yin, Ping-An Du

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The shielding ability of a shielding cavity with an aperture will be greatly degraded at resonance frequencies, and the resonance modes and frequencies are affected by aperture resonances and aperture-cavity coupling, which are closely related with aperture sizes. The equivalent circuit method and numerical method of Transmission Line Matrix (TLM) are used to analyze the effects of aperture resonances and aperture-cavity coupling on the electromagnetic resonances of a cavity with an aperture in this paper. Both analytical and numerical results show that the resonance modes of a shielding cavity with an aperture consist of cavity resonance modes and aperture resonance modes, and the resonance frequencies will shift with the change of the aperture sizes because of the aperture resonances and aperture-cavity coupling. Variation rules of electromagnetic resonances with aperture sizes for a cavity with an aperture are given, which will be useful for design of shielding cavities.

Keywords: Aperture-cavity coupling, equivalent circuit method, resonances, shielding equipment.

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Authors: Reza Abazari, Rasool Abazari

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In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: Rekik Rima, Aouachria Mekki

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We study the movement of a two-level atom in interaction with time dependent nonuniform magnetic filed using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus the Rabi formula of the system are deduced.

Keywords: Path integral, Formalism, Propagator, Transition probability.

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Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

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The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail

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An existing RC building in Madinah is seismically evaluated with and without infill wall. Four model systems have been considered i.e. model I (no infill), model IIA (strut infill-update from field test), model IIB (strut infill- ASCE/SEI 41) and model IIC (strut infill-Soft storey- ASCE/SEI 41). Three dimensional pushover analyses have been carried out using SAP2000 software incorporating inelastic material behavior for concrete, steel and infill walls. Infill wall has been modeled as equivalent strut according to suggested equation matching field test measurements and to the ASCE/SEI 41 equation. The effect of building modeling on the performance point as well as capacity and demand spectra due to EQ design spectrum function in Madinah area has been investigated. The response modification factor (R) for the 5 story RC building is evaluated from capacity and demand spectra (ATC-40) for the studied models. The results are summarized and discussed.

Keywords: Infill wall, Pushover Analysis, Response Modification Factor, Seismic Assessment.

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Authors: Ahmet Tekcan

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Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: H. Loumi-Fergane, A. Belaidi

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The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qⁱ, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: Field theories, relativistic mechanics, Lagrangian formalism, multisymplectic geometry, symmetries, Noether theorem, conservation laws.

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Authors: Swetha Priya Darshini Thammadi, Sateesh Kumar Pisini, Sanjay Kumar Shukla

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Source apportionment using Dispersion model depends primarily on the quality of Emission Inventory. In the present study, a CMB receptor model has been used to identify the sources of PM_2.5, while the AERMOD dispersion model has been used to account for missing sources of PM_2.5 in the Emission Inventory. A statistical approach has been developed to quantify the missing sources not considered in the Emission Inventory. The inventory of each grid was improved by adjusting emissions based on road lengths and deficit in measured and modelled concentrations. The results showed that in CMB analyses, fugitive sources - soil and road dust - contribute significantly to ambient PM_2.5 pollution. As a result, AERMOD significantly underestimated the ambient air concentration at most locations. The revised Emission Inventory showed a significant improvement in AERMOD performance which is evident through statistical tests.

Keywords: CMB, GIS, AERMOD, PM2.5, fugitive, emission inventory.

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Authors: N. Outili, A-H. Meniai

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Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

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By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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Authors: İnci M. Erhan

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A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: Pham Ngoc Thang, Le Thai Hung, Nguyen Quang Bau

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The influence of confined acoustic phonons on the Shubnikov – de Haas magnetoresistance oscillations in a doped semiconductor superlattice (DSSL), subjected in a magnetic field, DC electric field, and a laser radiation, has been theoretically studied based on quantum kinetic equation method. The analytical expression for the magnetoresistance in a DSSL has been obtained as a function of external fields, DSSL parameters, and especially the quantum number m characterizing the effect of confined acoustic phonons. When m goes to zero, the results for bulk phonons in a DSSL could be achieved. Numerical calculations are also achieved for the GaAs:Si/GaAs:Be DSSL and compared with other studies. Results show that the Shubnikov – de Haas magnetoresistance oscillations amplitude decrease as the increasing of phonon confinement effect.

Keywords: Shubnikov–de Haas magnetoresistance oscillations, quantum kinetic equation, confined acoustic phonons, laser radiation, doped semiconductor superlattices.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Masoud Abedini, Azrul A. Mutalib, Shahrizan Baharom, Hong Hao

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This study was conducted published to investigate there liability of the equation pressure-impulse (PI) reinforced concrete column inprevious studies. Equation involves three different levels of damage criteria known as D =0. 2, D =0. 5 and D =0. 8.The damage criteria known as a minor when 0-0.2, 0.2-0.5is known as moderate damage, high damage known as 0.5-0.8, and 0.8-1 of the structure is considered a failure. In this study, two types of reliability analyzes conducted. First, using pressure-impulse equation with different parameters. The parameters involved are the concrete strength, depth, width, and height column, the ratio of longitudinal reinforcement and transverse reinforcement ratio. In the first analysis of the reliability of this new equation is derived to improve the previous equations. The second reliability analysis involves three types of columns used to derive the PI curve diagram using the derived equation to compare with the equation derived from other researchers and graph minimum standoff versus weapon yield Federal Emergency Management Agency (FEMA). The results showed that the derived equation is more accurate with FEMA standards than previous researchers.

Keywords: Blast load, RC column, P-I curve, Analytical formulae, Standard FEMA.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

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The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Ehsan Mahdavi

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In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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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

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Authors: Zdravka Aljinović, Snježana Pivac, Boško Šego

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According to the interaction of inflation and unemployment, expectation of the rate of inflation in Croatia is estimated. The interaction between inflation and unemployment is shown by model based on three first-order differential i.e. difference equations: Phillips relation, adaptive expectations equation and monetary-policy equation. The resulting equation is second order differential i.e. difference equation which describes the time path of inflation. The data of the rate of inflation and the rate of unemployment are used for parameters estimation. On the basis of the estimated time paths, the stability and convergence analysis is done for the rate of inflation.

Keywords: Differencing, inflation, time path, unemployment.

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Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

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In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

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This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: Tao Shun, Xiao Xiangning, HadjSaid, N.

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In a liberalized electricity market, it is not surprising that different customers require different power quality (PQ) levels at different price. Power quality related to several power disturbances is described by many parameters, so how to define a comprehensive hierarchy evaluation system of power quality (PQCHES) has become a concerned issue. In this paper, based on four electromagnetic compatibility (EMC) levels, the numerical range of each power disturbance is divided into five grades (Grade I –Grade V), and the “barrel principle" of power quality is used for the assessment of overall PQ performance with only one grade indicator. A case study based on actual monitored data of PQ shows that the site PQ grade indicates the electromagnetic environment level and also expresses the characteristics of loads served by the site. The shortest plank principle of PQ barrel is an incentive mechanism, which can combine with the rewards/penalty mechanism (RPM) of consumed energy “on quality demand", to stimulate utilities to improve the overall PQ level and also stimulate end-user more “smart" under the infrastructure of future SmartGrid..

Keywords: Power quality, electromagnetic compatibility, SmartGrid, comprehensive evaluation, barrel principle, electricitymarket

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle.

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Authors: Shabbir Chowdhury, Japatosh Mondal

Abstract:

Photonic Crystal Fiber (PCF) uses are no longer limited to telecommunication only rather it is now used for many sensors-based fiber optics application, medical science, space application and so on. In this paper, the authors have proposed a microstructure PCF that is designed by using Finite Element Method (FEM) based software. Besides designing, authors have discussed the necessity of the characteristics that it poses for some specified applications because it is not possible to have all good characteristics from a single PCF. Proposed PCF shows the property of ultra-high birefringence (0.0262 at 1550 nm) which is more useful for sensor based on fiber optics. The non-linearity of this fiber is 50.86 w^-1km^-1 at 1550 nm wavelength which is very high to guide the light through the core tightly. For Perfectly Matched Boundary Layer (PML), 0.6 μm diameter is taken. This design will offer the characteristics of Nonzero-Dispersion-Shifted Fiber (NZ-DSF) for 450 nm waveband. Since it is a software-based design and no practical evaluation has made, 2% tolerance is checked and the authors have found very small variation of the characteristics.

Keywords: Chromatic dispersion, birefringence, NZ-DSF, FEM, non-linear coefficient, DCF, waveband.

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Authors: Jian Huang, Weixin Qian, Haitao Zhang, Weiyong Ying

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Cobalt-gadolinium catalyst for Fischer-Tropsch synthesis was prepared by impregnation method with commercial silica gel, and its texture properties were characterized by BET, XRD, and TPR. The catalytic performance of the catalyst was tested in a fixed bed reactor. The results showed that the addition of gadolinium to the cobalt catalyst might decrease the size of cobalt particles, and increased the dispersion of catalytic active cobalt phases. The carbon number distributions for the catalysts was calculated by ASF equation.

Keywords: Fischer-Tropsch synthesis, cobalt-based catalysts, gadolinium, carbon number distributions.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

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In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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