Search results for: finite difference methods

Authors: Clarinda V. Nhangumbe, Ercília Sousa

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Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.

Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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In the current paper, a residual generation filter with finite memory structure is proposed for fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite observations and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noise-free systems. Finally, to illustrate the capability of the proposed residual generation filter, numerical examples are performed for the discretized DC motor system having the multiple sensor faults.

Keywords: residual generation filter, finite memory structure, kalman filter, fast detection

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Mahmoudi Noureddine, Bouregba Rachid

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In this paper the stress intensity factors of a slant-cracked plate of AISI 304 stainless steel, have been calculated using extended finite element method and finite element method (FEM) in ABAQUS software, the results were compared with theoretical values.

Keywords: stress intensity factors, extended finite element method, stainless steel, abaqus

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Mohammad Reza Akhavan Khaleghi

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This paper shows changes done to the Reduced Finite Element Method (RFEM) that its result will be the most powerful numerical method that has been proposed so far (some forms of this method are so powerful that they can approximate the most complex equations simply Laplace equation!). Finite Element Method (FEM) is a powerful numerical method that has been used successfully for the solution of the existing problems in various scientific and engineering fields such as its application in CFD. Many algorithms have been expressed based on FEM, but none have been used in popular CFD software. In this section, full monopoly is according to Finite Volume Method (FVM) due to better efficiency and adaptability with the physics of problems in comparison with FEM. It doesn't seem that FEM could compete with FVM unless it was fundamentally changed. This paper shows those changes and its result will be a powerful method that has much better performance in all subjects in comparison with FVM and another computational method. This method is not to compete with the finite volume method but to replace it.

Keywords: reduced finite element method, new computational package, new finite element formulation, new higher-order form, new isogeometric analysis

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Authors: Sultan Al Shafian, Mozaher Ul Kabir, Khondoker Istiak Ahmad, Masnun Abrar, Mahfuza Khanum, Hossain M. Shahin

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For structural evaluation of shallow foundation, the modulus of subgrade reaction is one of the most widely used and accepted parameter for its ease of calculations. To determine this parameter, one of the most common field method is Plate Load test method. In this field test method, the subgrade modulus is considered for a specific location and according to its application, it is assumed that the displacement occurred in one place does not affect other adjacent locations. For this kind of assumptions, the modulus of subgrade reaction sometimes forced the engineers to overdesign the underground structure, which eventually results in increasing the cost of the construction and sometimes failure of the structure. In the present study, the settlement of a shallow foundation has been analyzed using both conventional and numerical analysis. Around 25 plate load tests were conducted on a sand fill site in Bangladesh to determine the Modulus of Subgrade reaction of ground which is later used to design a shallow foundation considering different depth. After the collection of the field data, the field condition was appropriately simulated in a finite element software. Finally results obtained from both the conventional and numerical approach has been compared. A significant difference has been observed in the case of settlement while comparing the results. A proper correlation has also been proposed at the end of this research work between the two methods of in order to provide the most efficient way to calculate the subgrade modulus of the ground for designing the shallow foundation.

Keywords: modulus of subgrade reaction, shallow foundation, finite element analysis, settlement, plate load test

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

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Authors: Abdur Rosyid, Mohamed El-Madany, Mohanad Alata

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Due to simplicity and low cost, rotordynamic system is often modeled by using lumped parameters. Recently, finite elements have been used to model rotordynamic system as it offers higher accuracy. However, it involves high degrees of freedom. In some applications such as control design, this requires higher cost. For this reason, various model reduction methods have been proposed. This work demonstrates the quality of model reduction of rotor-bearing-support system through substructuring. The quality of the model reduction is evaluated by comparing some first natural frequencies, modal damping ratio, critical speeds and response of both the full system and the reduced system. The simulation shows that the substructuring is proven adequate to reduce finite element rotor model in the frequency range of interest as long as the numbers and the locations of master nodes are determined appropriately. However, the reduction is less accurate in an unstable or nearly-unstable system.

Keywords: rotordynamic, finite element model, timoshenko beam, 3D solid elements, Guyan reduction method

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Authors: Rong-Yang Lai, Jia-Yu Wu, Chih-Han Chang, Yung-Chung Chen

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The dental bridge is one of the clinical methods of the treatment for missing teeth. The dental bridge is generally designed for two layers, containing the inner layer of the framework(zirconia) and the outer layer of the porcelain-fused to framework restorations. The design of a conventional bridge is generally based on the antagonist tooth profile so that the framework evenly indented by an equal thickness from outer contour. All-ceramic dental bridge made of zirconia have well demonstrated remarkable potential to withstand a higher physiological occlusal load in posterior region, but it was found that there is still the risk of all-ceramic bridge failure in five years. Thus, how to reduce the incidence of failure is still a problem to be solved. Therefore, the objective of this study is to develop mechanical designs for all-ceramic dental bridges framework by reducing the stress and enhancing fracture resistance under given loading conditions by finite element method. In this study, dental design software is used to design dental bridge based on tooth CT images. After building model, Bi-directional Evolutionary Structural Optimization (BESO) Method algorithm implemented in finite element software was employed to analyze results of finite element software and determine the distribution of the materials in dental bridge; BESO searches the optimum distribution of two different materials, namely porcelain and zirconia. According to the previous calculation of the stress value of each element, when the element stress value is higher than the threshold value, the element would be replaced by the framework material; besides, the difference of maximum stress peak value is less than 0.1%, calculation is complete. After completing the design of dental bridge, the stress distribution of the whole structure is changed. BESO reduces the peak values of principle stress of 10% in outer-layer porcelain and avoids producing tensile stress failure.

Keywords: dental bridge, finite element analysis, framework, automatic program

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Authors: Kelemewerk Destalem, Joongjae Cho, Jaeseong Lee, Ju H. Park, Joonhyuk Yoo

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Background subtraction and temporal difference are often used for moving object detection in video. Both approaches are computationally simple and easy to be deployed in real-time image processing. However, while the background subtraction is highly sensitive to dynamic background and illumination changes, the temporal difference approach is poor at extracting relevant pixels of the moving object and at detecting the stopped or slowly moving objects in the scene. In this paper, we propose a moving object detection scheme based on adaptive background subtraction and temporal difference exploiting dynamic background updates. The proposed technique consists of a histogram equalization, a linear combination of background and temporal difference, followed by the novel frame-based and pixel-based background updating techniques. Finally, morphological operations are applied to the output images. Experimental results show that the proposed algorithm can solve the drawbacks of both background subtraction and temporal difference methods and can provide better performance than that of each method.

Keywords: background subtraction, background updating, real time, light weight algorithm, temporal difference

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Authors: Yasser El-Henawy, M. Abd El-Kader, Gamal H. Moustafa

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A theoretical study of a humidification dehumidification solar desalination unit has been carried out to increase understanding the effect of weather conditions on the unit productivity. A humidification-dehumidification (HD) solar desalination unit has been designed to provide fresh water for population in remote arid areas. It consists of solar water collector and air collector; to provide the hot water and air to the desalination chamber. The desalination chamber is divided into humidification and dehumidification towers. The circulation of air between the two towers is maintained by the forced convection. A mathematical model has been formulated, in which the thermodynamic relations were used to study the flow, heat and mass transfer inside the humidifier and dehumidifier. The present technique is performed in order to increase the unit performance. Heat and mass balance has been done and a set of governing equations has been solved using the finite difference technique. The unit productivity has been calculated along the working day during the summer and winter sessions and has compared with the available experimental results. The average accumulative productivity of the system in winter has been ranged between 2.5 to 4 kg/m2.day, while the average summer productivity has been found between 8 to 12 kg/m2 day.

Keywords: solar desalination, solar collector, humidification and dehumidification, simulation, finite difference, water productivity

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Authors: Momoh Omeiza Sheidu

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Finite element method as a method of providing solutions to problems in computational bio mechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical forces. In this paper, we present an integrative finite element strategy for solution to problems in tissue bio mechanics as a case study.

Keywords: finite element, biomechanics, modeling, computational biomechanics

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Authors: Nguyen Van Loi, Le Thanh Son, Tran Trung Kien

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The paper deals with the problem of the formation of range profiles (RPs) for an X-band coastal surveillance radar. Two popular methods, the difference operator method, and the window-based method, are reviewed and analyzed via two tests with different datasets. The test results show that although the original window-based method achieves a better performance than the difference operator method, it has three main drawbacks that are the use of 3 or 4 peaks of an RP for creating the windows, the extension of the window size using the power sum of three adjacent cells in the left and the right sides of the windows and the same threshold applied for all types of vessels to finish the formation process of RPs. These drawbacks lead to inaccurate RPs due to the low signal-to-clutter ratio. Therefore, some suggestions are proposed to improve the original window-based method.

Keywords: range profile, difference operator method, window-based method, automatic target recognition

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Authors: Najibullah M, Soumendra Nath Kuiry

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Dams and reservoirs are perceived for their estimable alms to irrigation, water supply, flood control, electricity generation, etc. which civilize the prosperity and wealth of society across the world. Meantime the dam breach could cause devastating flood that can threat to the human lives and properties. Failures of large dams remain fortunately very seldom events. Nevertheless, a number of occurrences have been recorded in the world, corresponding in an average to one to two failures worldwide every year. Some of those accidents have caused catastrophic consequences. So it is decisive to predict the dam break flow for emergency planning and preparedness, as it poses high risk to life and property. To mitigate the adverse impact of dam break, modeling is necessary to gain a good understanding of the temporal and spatial evolution of the dam-break floods. This study will mainly deal with one-dimensional (1D) dam break modeling. Less commonly used in the hydraulic research community, another possible option for modeling the rapidly varied dam-break flows is the extended Boussinesq equations (BEs), which can describe the dynamics of short waves with a reasonable accuracy. Unlike the Shallow Water Equations (SWEs), the BEs taken into account the wave dispersion and non-hydrostatic pressure distribution. To capture the dam-break oscillations accurately it is very much needed of at least fourth-order accurate numerical scheme to discretize the third-order dispersion terms present in the extended BEs. The scope of this work is therefore to develop an 1D fourth-order accurate in both space and time Boussinesq model for dam-break flow analysis by using finite-volume / finite difference scheme. The spatial discretization of the flux and dispersion terms achieved through a combination of finite-volume and finite difference approximations. The flux term, was solved using a finite-volume discretization whereas the bed source and dispersion term, were discretized using centered finite-difference scheme. Time integration achieved in two stages, namely the third-order Adams Basforth predictor stage and the fourth-order Adams Moulton corrector stage. Implementation of the 1D Boussinesq model done using PYTHON 2.7.5. Evaluation of the performance of the developed model predicted as compared with the volume of fluid (VOF) based commercial model ANSYS-CFX. The developed model is used to analyze the risk of cascading dam failures similar to the Panshet dam failure in 1961 that took place in Pune, India. Nevertheless, this model can be used to predict wave overtopping accurately compared to shallow water models for designing coastal protection structures.

Keywords: Boussinesq equation, Coastal protection, Dam-break flow, One-dimensional model

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: K. Djellabi, M. E. H. Latreche

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Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper deals with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries. For the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.

Keywords: numerical methods, induction furnaces, induction heating, finite element method, Comsol multiphysics software

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Authors: Bang-Fuh Chen, Chih-Chun Chu

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The flow induced cylinder vibration or earthquake-induced cylinder motion are moving in an arbitrary direction with time. The phenomenon of flow across cylinder is highly nonlinear and a linear-superposition of flow pattern across separated oscillating direction of cylinder motion is not valid to obtain the flow pattern across a cylinder oscillating in multiple directions. A novel finite difference scheme is developed to simulate the viscous flow across an arbitrary moving circular cylinder and we call this a complete 2D (two-dimensional) flow-cylinder interaction. That is, the cylinder is simultaneously oscillating in x- and y- directions. The time-dependent domain and meshes associated with the moving cylinder are mapped to a fixed computational domain and meshes, which are time independent. The numerical results are validated by several bench mark studies. Several examples are introduced including flow across steam-wise, transverse oscillating cylinder and flow across rotating cylinder and flow across arbitrary moving cylinder. The Morison’s formula can not describe the complex interaction phenomenon between cross flow and oscillating circular cylinder. And the completed 2D computational fluid dynamic analysis should be made to obtain the correct hydrodynamic force acting on the cylinder.

Keywords: 2D cylinder, finite-difference method, flow-cylinder interaction, flow induced vibration

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Mohamed Mohamed, Philip Bonello, Peter Russhard

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Blade Tip Timing (BTT) is a technology concerned with the estimation of both frequency and amplitude of rotating blades. A BTT system comprises two main parts: (a) the arrival time measurement system, and (b) the analysis algorithms. Simulators play an important role in the development of the analysis algorithms since they generate blade tip displacement data from the simulated blade vibration under controlled conditions. This enables an assessment of the performance of the different algorithms with respect to their ability to accurately reproduce the original simulated vibration. Such an assessment is usually not possible with real engine data since there is no practical alternative to BTT for blade vibration measurement. Most simulators used in the literature are based on a simple spring-mass-damper model to determine the vibration. In this work, a more realistic experimentally validated simulator based on the Finite Element (FE) model of a bladed disc (blisk) is first presented. It is then used to generate the necessary data for the assessment of different BTT algorithms. The FE modelling is validated using both a hammer test and two firewire cameras for the mode shapes. A number of autoregressive methods, fitting methods and state-of-the-art inverse methods (i.e. Russhard) are compared. All methods are compared with respect to both synchronous and asynchronous excitations with both single and simultaneous frequencies. The study assesses the applicability of each method for different conditions of vibration, amount of sampling data, and testing facilities, according to its performance and efficiency under these conditions.

Keywords: blade tip timing, blisk, finite element, vibration measurement

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Authors: Swati Sharma, R. P. Sharma

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We intend to study the nonlinear evolution of the parallel propagating finite frequency Alfvén wave (also called Dispersive Alfvén wave/Hall MHD wave) propagating in the solar wind regime of the solar region when a perpendicularly propagating magnetosonic wave is present in the background. The finite frequency Alfvén wave behaves differently from the usual non-dispersive behavior of the Alfvén wave. To study the nonlinear processes (such as filamentation) taking place in the solar regions such as solar wind, the dynamical equation of both the waves are derived. Numerical simulation involving finite difference method for the time domain and pseudo spectral method for the spatial domain is then performed to analyze the transient evolution of these waves. The power spectra of the Dispersive Alfvén wave is also investigated. The power spectra shows the distribution of the magnetic field intensity of the Dispersive Alfvén wave over different wave numbers. For DAW the spectra shows a steepening for scales larger than the proton inertial length. This means that the wave energy gets transferred to the solar wind particles as the wave reaches higher wave numbers. This steepening of the power spectra can be explained on account of the finite frequency of the Alfvén wave. The obtained results are consistent with the observations made by CLUSTER spacecraft.

Keywords: solar wind, turbulence, dispersive alfven wave

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Authors: Alisawi Alaa T., Collins P. E. F.

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The analysis and evaluation of slope stability and landslide hazards are landslide hazards are critically important in civil engineering projects and broader considerations of safety. The level of slope stability risk should be identified due to its significant and direct financial and safety effects. Slope stability hazard analysis is performed considering static and/or dynamic loading circumstances. To reduce and/or prevent the failure hazard caused by landslides, a sophisticated and practical hazard analysis method using advanced constitutive modeling should be developed and linked to an effective solution that corresponds to the specific type of slope stability and landslides failure risk. Previous studies on slope stability analysis methods identify the failure mechanism and its corresponding solution. The commonly used approaches include used approaches include limit equilibrium methods, empirical approaches for rock slopes (e.g., slope mass rating and Q-slope), finite element or finite difference methods, and district element codes. This study presents an overview and evaluation of these analysis techniques. Contemporary source materials are used to examine these various methods on the basis of hypotheses, the factor of safety estimation, soil types, load conditions, and analysis conditions and limitations. Limit equilibrium methods play a key role in assessing the level of slope stability hazard. The slope stability safety level can be defined by identifying the equilibrium of the shear stress and shear strength. The slope is considered stable when the movement resistance forces are greater than those that drive the movement with a factor of safety (ratio of the resistance of the resistance of the driving forces) that is greater than 1.00. However, popular and practical methods, including limit equilibrium approaches, are not effective when the slope experiences complex failure mechanisms, such as progressive failure, liquefaction, internal deformation, or creep. The present study represents the first episode of an ongoing project that involves the identification of the types of landslides hazards, assessment of the level of slope stability hazard, development of a sophisticated and practical hazard analysis method, linkage of the failure type of specific landslides conditions to the appropriate solution and application of an advanced computational method for mapping the slope stability properties in the United Kingdom, and elsewhere through geographical information system (GIS) and inverse distance weighted spatial interpolation(IDW) technique. This study investigates and assesses the different assesses the different analysis and solution techniques to enhance the knowledge on the mechanism of slope stability and landslides hazard analysis and determine the available solutions for each potential landslide failure risk.

Keywords: slope stability, finite element analysis, hazard analysis, landslides hazard

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Authors: H. S. Kang

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Coupled electrical and optical model for conversion of electrical energy into coherent optical energy for transmitter-receiver link by solid state device is presented. Probability distribution for travelling laser beam switching time intervals and the number of switchings in the time interval is obtained. Selector function mapping is employed to regulate optical data transmission speed. It is established that regulated laser transmission from PhotoActive Laser transmitter follows principal of invariance. This considerably simplifies design of PhotoActive Laser Transmission networks.

Keywords: computational mathematics, finite difference Markov chain methods, sequence spaces, singularly perturbed differential equations

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: A. Mohamed, A. El-Hamalawi, M. Frost, A. Connell

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Often design standards do not provide guidance or formulae for the calculation of stresses on buried pipelines caused by external loads. Frequently engineers rely on other methods and published sources of information to calculate such imposed stresses and a variety of methods can be used. This paper reviews three current approaches to soil pipeline interaction modelling to predict stresses on buried pipelines subjected to soil overburden and traffic loading. The traditional approach to use empirical stress formulas to calculate circumferential bending stresses on pipelines. The alternative approaches considered are the use of a finite element package to compute an estimate of circumferential bending stress and a proprietary stress analysis system (SURFLOAD) to estimate the circumferential bending stress. The results from analysis using the methods are presented and compared to experimental results in terms of predicted and measured circumferential stresses. This study shows that the approach used to assess externally generated stress is important and can lead to an over-conservative analysis. Using FE analysis either through SURFLOAD or a general FE package to predict circumferential stress is the most accurate way to undertake stress analysis due to traffic and soil loads. Although conservative, classical empirical methods will continue to be applied to the analysis of buried pipelines, an opportunity exists, therefore, in many circumstances, to use applied numerical techniques, made possible by advances in finite element analysis.

Keywords: buried pipelines, circumferential bending stress, finite element analysis, soil overburden, soil pipeline interaction analysis (SPIA), traffic loadings

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: Abdulmajid Mukhtar Afat

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This paper aims at introducing nondeterministic finite automata with ε value which is used to perform some operations on languages. a program is created to implement the algorithm that converts nondeterministic finite automata with ε value (ε-NFA) to deterministic finite automata (DFA).The program is written in c++ programming language. The program inputs are FA 5-tuples from text file and then classifies it into either DFA/NFA or ε -NFA. For DFA, the program will get the string w and decide whether it is accepted or rejected. The tracking path for an accepted string is saved by the program. In case of NFA or ε-NFA automation, the program changes the automation to DFA to enable tracking and to decide if the string w exists in the regular language or not.

Keywords: DFA, NFA, ε-NFA, eclose, finite automata, operations on languages

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Authors: Arefeh Arabaninezhad, Ali Fakher

Abstract:

Since the deterministic analysis methods fail to take system uncertainties into account, probabilistic and non-probabilistic methods are suggested. Geotechnical analyses are used to determine the stress and deformation caused by construction; accordingly, many input variables which depend on ground behavior are required for geotechnical analyses. The Random Set approach is an applicable reliability analysis method when comprehensive sources of information are not available. Using Random Set method, with relatively small number of simulations compared to fully probabilistic methods, smooth extremes on system responses are obtained. Therefore random set approach has been proposed for reliability analysis in geotechnical problems. In the present study, the application of random set method in reliability analysis of deep excavations is investigated through three deep excavation projects which were monitored during the excavating process. A finite element code is utilized for numerical modeling. Two expected ranges, from different sources of information, are established for each input variable, and a specific probability assignment is defined for each range. To determine the most influential input variables and subsequently reducing the number of required finite element calculations, sensitivity analysis is carried out. Input data for finite element model are obtained by combining the upper and lower bounds of the input variables. The relevant probability share of each finite element calculation is determined considering the probability assigned to input variables present in these combinations. Horizontal displacement of the top point of excavation is considered as the main response of the system. The result of reliability analysis for each intended deep excavation is presented by constructing the Belief and Plausibility distribution function (i.e. lower and upper bounds) of system response obtained from deterministic finite element calculations. To evaluate the quality of input variables as well as applied reliability analysis method, the range of displacements extracted from models has been compared to the in situ measurements and good agreement is observed. The comparison also showed that Random Set Finite Element Method applies to estimate the horizontal displacement of the top point of deep excavation. Finally, the probability of failure or unsatisfactory performance of the system is evaluated by comparing the threshold displacement with reliability analysis results.

Keywords: deep excavation, random set finite element method, reliability analysis, uncertainty

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Authors: A. Khernane, N. Khelil, L. Djerou

Abstract:

The aim of this work is to study the numerical implementation of the Hilbert uniqueness method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control, and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: boundary control, exact controllability, finite difference methods, functional optimization

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