Search results for: State Dependent Riccati Equation (SDRE)

Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Virendra J. Majarikar, Harikrishnan N. Unni

Abstract:

This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m³ and 0 mol/m³, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process.

Keywords: COMSOL, electrokinetic, electroosmotic, microfluidics, zeta potential.

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Authors: Mohammad Faisal

Abstract:

This paper investigates the relationship between state and business in the context of structural and institutional transformations in Indonesia following the collapse of the New Order regime in 1998. Since 1998, Indonesia has embarked on a shift from an authoritarian to democratic polity and from a centralised to a decentralised system of governance, transforming the country into the third largest democracy and one of the most decentralised states in the world. This paper examines whether the transformation of the Indonesian state has altered the pattern of state and business relations with focus on clientism and corruption as the key dependent variable, and probes how/to what extent this has changed as a result of the transformation and the ensuring shifts in business and state relations. Based on interviews with key government and business actors as well as prominent scholars in Indonesia, it is found that since the demise of the New Order, business associations in Indonesia have become more independent of state control and more influential in public decision-making whereas the government has become more responsive of business concerns and more committed to combat corruption and clientism. However, these changes have not necessarily rendered business people completely leave individualclientelistic relationship with the government, and simply pursue wider sectoral and business-wide collectivism as an alternative way of channelling their aspirations, which is expected to help reduce corruption and clientism in Indonesia. This paper concludes that democratisation and a more open politics may have helped reduce corruption and clientism in Indonesia through changes in government. However, it is still difficult to imply that such political transformation has fostered business collective action and a broader, more encompassing pattern of business lobbying and activism, which is expected to help reduce corruption and clientism.

Keywords: Business activism, business power, democratisation, clientism, corruption.

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Authors: Afaq Ahmad

Abstract:

Using state space technique and GF(2) theory, a simulation model for external exclusive NOR type LFSR structures is developed. Through this tool a systematic procedure is devised for computing pseudo-random binary sequences from such structures.

Keywords: LFSR, external exclusive NOR type, recursivebinary sequence, initial state - next state, state transition matrix.

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Authors: Chuanyun Gu, Shouming Zhong

Abstract:

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator

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Authors: M. Chitsazi, B. Maraghechi, M. H. Rouhani

Abstract:

Three-dimensional simulation of harmonic up generation in free electron laser amplifier operating simultaneously with a cold and relativistic electron beam is presented in steady-state regime where the slippage of the electromagnetic wave with respect to the electron beam is ignored. By using slowly varying envelope approximation and applying the source-dependent expansion to wave equations, electromagnetic fields are represented in terms of the Hermit Gaussian modes which are well suited for the planar wiggler configuration. The electron dynamics is described by the fully threedimensional Lorentz force equation in presence of the realistic planar magnetostatic wiggler and electromagnetic fields. A set of coupled nonlinear first-order differential equations is derived and solved numerically. The fundamental and third harmonic radiation of the beam is considered. In addition to uniform beam, prebunched electron beam has also been studied. For this effect of sinusoidal distribution of entry times for the electron beam on the evolution of radiation is compared with uniform distribution. It is shown that prebunching reduces the saturation length substantially. For efficiency enhancement the wiggler is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point of tapering and the slope of radiation in the amplitude of wiggler are found by successive run of the code.

Keywords: Free electron laser, Prebunching, Undulator, Wiggler.

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Authors: Amir Badkoubeh, Guchuan Zhu

Abstract:

This paper addresses the problem of asymptotic tracking control of a linear parabolic partial differential equation with indomain point actuation. As the considered model is a non-standard partial differential equation, we firstly developed a map that allows transforming this problem into a standard boundary control problem to which existing infinite-dimensional system control methods can be applied. Then, a combination of energy multiplier and differential flatness methods is used to design an asymptotic tracking controller. This control scheme consists of stabilizing state-feedback derived from the energy multiplier method and feed-forward control based on the flatness property of the system. This approach represents a systematic procedure to design tracking control laws for a class of partial differential equations with in-domain point actuation. The applicability and system performance are assessed by simulation studies.

Keywords: Tracking Control, In-domain point actuation, PartialDifferential Equations.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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Authors: D. Benasciutti, M. Gallina, M. Gh. Munteanu, F. Flumian

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This paper presents a numerical approach for the static and dynamic analysis of hydrodynamic radial journal bearings. In the first part, the effect of shaft and housing deformability on pressure distribution within oil film is investigated. An iterative algorithm that couples Reynolds equation with a plane finite elements (FE) structural model is solved. Viscosity-to-pressure dependency (Vogel- Barus equation) is also included. The deformed lubrication gap and the overall stress state are obtained. Numerical results are presented with reference to a typical journal bearing configuration at two different inlet oil temperatures. Obtained results show the great influence of bearing components structural deformation on oil pressure distribution, compared with results for ideally rigid components. In the second part, a numerical approach based on perturbation method is used to compute stiffness and damping matrices, which characterize the journal bearing dynamic behavior.

Keywords: Journal bearing, finite elements, deformation, dynamic analysis

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Authors: V. V. Lyahov, V. M. Neshchadim

Abstract:

We offer a new technique for research of stability of current sheaths in space plasma taking into account the effect of polarization. At the beginning, the found perturbation of the distribution function is used for calculation of the dielectric permeability tensor, which simulates inhomogeneous medium of a current sheath. Further, we in the usual manner solve the system of Maxwell's equations closed with the material equation. The amplitudes of Fourier perturbations are considered to be exponentially decaying through the current sheath thickness. The dispersion equation follows from the nontrivial solution requirement for perturbations of the electromagnetic field. The resulting dispersion equation allows one to study the temporal and spatial characteristics of instability modes of the current sheath (within the limits of the proposed model) over a wide frequency range, including low frequencies.

Keywords: Current sheath, distribution function, effect of polarization, instability modes, low frequencies, perturbation of electromagnetic field dispersion equation, space plasma, tensor of dielectric permeability.

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Authors: Mohammad Najafi, Ali Jamshidi

Abstract:

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.

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Authors: Nizami Mustafa, C. Ardil

Abstract:

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

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

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

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Authors: K. Diwakar, K. Aanandha Saravanan, C. Senthilpari

Abstract:

Higher order ΔΣ Modulator (DSM) is basically an unstable system. The approximate conditions for stability cannot be used for the design of a DSM for industrial applications where risk is involved. The existing second order, single stage, single bit, unity feedback gain , discrete DSM cannot be used for the normalized full range (-1 to +1) of an input signal since the DSM becomes unstable when the input signal is above ±0.55. The stability is also not guaranteed for input signals of amplitude less than ±0.55. In the present paper, the above mentioned second order DSM is modified with input signal dependent forward path gain. The proposed DSM is suitable for industrial applications where one needs the digital representation of the analog input signal, during each sampling period. The proposed DSM can operate almost for the full range of input signals (-0.95 to +0.95) without causing instability, assuming that the second integrator output should not exceed the circuit supply voltage, ±15 Volts.

Keywords: DSM, stability, SNR, state variables.

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

Abstract:

There exist a wide range of failure modes in composite structures due to the increased usage of the structures especially in aerospace industry. Moreover, temperature dependent wave response of composite and layered structures have been continuously studied, though still limited, in the last decade mainly due to the broad operating temperature range of aerospace structures. A wave finite element (WFE) and finite element (FE) based computational method is presented by which the temperature dependent wave dispersion characteristics and interaction phenomenon in composite structures can be predicted. Initially, the temperature dependent mechanical properties of the panel in the range of -100 ◦C to 150 ◦C are measured experimentally using the Thermal Mechanical Analysis (TMA). Temperature dependent wave dispersion characteristics of each waveguide of the structural system, which is discretized as a system of a number of waveguides coupled by a coupling element, is calculated using the WFE approach. The wave scattering properties, as a function of temperature, is determined by coupling the WFE wave characteristics models of the waveguides with the full FE modelling of the coupling element on which defect is included. Numerical case studies are exhibited for two waveguides coupled through a coupling element.

Keywords: Temperature dependent mechanical characteristics, wave propagation properties, damage detection, wave finite element, composite structure.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

Abstract:

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: Nik Mohd Asri Nik Long, Koo Lee Feng, Zainidin K. Eshkuvatov, A. A. Khaldjigitov

Abstract:

This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.

Keywords: Elliptical crack, stress intensity factors, hyper singular integral equation, shear loading, conformal mapping.

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Authors: M. Duran Toksarı, B. Uçarkuş

Abstract:

In this paper, we propose two algorithms to optimally solve makespan and total completion time scheduling problems with learning effect and job dependent delivery times in a single machine environment. The delivery time is the extra time to eliminate adverse effect between the main processing and delivery to the customer. In this paper, we introduce the job dependent delivery times for some single machine scheduling problems with position dependent learning effect, which are makespan are total completion. The results with respect to two algorithms proposed for solving of the each problem are compared with LINGO solutions for 50-jobs, 100-jobs and 150- jobs problems. The proposed algorithms can find the same results in shorter time.

Keywords: Delivery times, learning effect, makespan, scheduling, total completion time.

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Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

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Authors: Henok Hailemariam, Frank Wuttke

Abstract:

Collapsible soils are weak soils that appear to be stable in their natural state, normally dry condition, but rapidly deform under saturation (wetting), thus generating large and unexpected settlements which often yield disastrous consequences for structures unwittingly built on such deposits. In this study, a prediction model for the relative subsidence of stressed collapsible soils based on dielectric permittivity measurement is presented. Unlike most existing methods for soil subsidence prediction, this model does not require moisture content as an input parameter, thus providing the opportunity to obtain accurate estimation of the relative subsidence of collapsible soils using dielectric measurement only. The prediction model is developed based on an existing relative subsidence prediction model (which is dependent on soil moisture condition) and an advanced theoretical frequency and temperature-dependent electromagnetic mixing equation (which effectively removes the moisture content dependence of the original relative subsidence prediction model). For large scale sub-surface soil exploration purposes, the spatial sub-surface soil dielectric data over wide areas and high depths of weak (collapsible) soil deposits can be obtained using non-destructive high frequency electromagnetic (HF-EM) measurement techniques such as ground penetrating radar (GPR). For laboratory or small scale in-situ measurements, techniques such as an open-ended coaxial line with widely applicable time domain reflectometry (TDR) or vector network analysers (VNAs) are usually employed to obtain the soil dielectric data. By using soil dielectric data obtained from small or large scale non-destructive HF-EM investigations, the new model can effectively predict the relative subsidence of weak soils without the need to extract samples for moisture content measurement. Some of the resulting benefits are the preservation of the undisturbed nature of the soil as well as a reduction in the investigation costs and analysis time in the identification of weak (problematic) soils. The accuracy of prediction of the presented model is assessed by conducting relative subsidence tests on a collapsible soil at various initial soil conditions and a good match between the model prediction and experimental results is obtained.

Keywords: Collapsible soil, relative subsidence, dielectric permittivity, moisture content.

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Authors: D. Bala Bhaskar

Abstract:

An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.

Keywords: Multi variable systems, order reduction, stability equation method, SRAM, time domain characteristics, ISE.

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Authors: P. Srinivas, P. V. N. Prasad

Abstract:

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 analyzed by two methods. In one method, 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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Authors: Yasuo Obikane

Abstract:

This work is to study a roll of the fluctuating density gradient in the compressible flows for the computational fluid dynamics (CFD). A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups: group proportional to the mean velocity, and that proportional to the mean strain rate, and that proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vorticity in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.

Keywords: Turbulence Modeling , Density Gradient Correlation, Compressible

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Authors: Sarun Phibanchon, Michael A. Allen

Abstract:

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.

Keywords: Soliton, instability, variational method, spectral method.

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Authors: Seung-Jun Yu, Yong-Jun Kim, Jung-In Baik, Hyoung-Kyu Song

Abstract:

In this paper, a dual-hop relay based on channel state is studied. In the conventional relay scheme, a relay uses the same modulation method without reference to channel state. But, a relay uses an adaptive modulation method with reference to channel state. If the channel state is poor, a relay eliminates latter 2 bits and uses Quadrature Phase Shift Keying (QPSK) modulation. If channel state is good, a relay modulates the received symbols with 16-QAM symbols by using 4 bits. The performance of the proposed scheme for Symbol Error Rate (SER) and throughput is analyzed.

Keywords: Adaptive transmission, channel state, dual-hop, hierarchical modulation, relay.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee

Abstract:

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.

Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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