Search results for: finite difference formula

Authors: Thomas Jin-Chee Liu

Abstract:

In this paper, the thermo-electro-structural coupled-field in a cracked metal plate is studied using the finite element analysis. From the computational results, the compressive stresses reveal near the crack tip. This conclusion agrees with the past reference. Furthermore, the compressive condition can retard and stop the crack growth during the Joule heating process.

Keywords: compressive stress, crack tip, Joule heating, finite element

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Authors: Tzu-Hsuan Lei, Shu-Chien Wu, Kuang-Che Lo, Shu-Chi Liu, Yu-Cheng Liu

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The focus of this study was on the effects of air propagation associated with vented holes on acoustic resistance properties. A cylindrical hole with diameter and depth of 0.7 mm and 1.0 mm, respectively, was the research target. By constructing a finite element analytical model of its sound field properties, the acoustic-specific airflow resistance relationships were obtained for the differences in sound pressure and flow velocity at the two ends of this vented hole. In addition, the acoustic properties of this vented hole were included in the in-ear earphone simulation model to complete the sound pressure curve simulation analysis of the in-ear earphone system with a vented hole of corresponding size. Then, the simulation results were compared with actual measurements obtained from the standard system. Based on the results, when the in-ear earphone vented hole simulation model considered the simulated specific airflow resistance values of this cylindrical hole, the overall simulated sound pressure performance was highly consistent with that of measured values. The difference in the first peak values of sound pressure at mid-to-low frequencies was reduced from 5.64% when the simulation model did not consider the specific airflow resistance of the cylindrical hole to 1.18%, and the accuracy of the overall simulation was around 70%. This indicates the importance of the acoustic resistance properties of vented holes. Moreover, as specific airflow resistance values were able to be further quantified, the accuracy of the entire in-ear earphone simulation was ultimately and effectively elevated.

Keywords: specific airflow resistance, vented holes, in-ear earphone, finite element method

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Authors: Sh. Minapoor, S. Ajeli, M. Javadi Toghchi

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Non-crimp 3D orthogonal fabric composite is one of the textile-based composite materials that are rapidly developing light-weight engineering materials. The present paper focuses on geometric and micro mechanical modeling of non-crimp 3D orthogonal carbon fabric and composites reinforced with it for aerospace applications. In this research meso-finite element (FE) modeling employs for stress analysis in different load conditions. Since mechanical testing of expensive textile carbon composites with specific application isn't affordable, simulation composite in a virtual environment is a helpful way to investigate its mechanical properties in different conditions.

Keywords: woven composite, aerospace applications, finite element method, mechanical properties

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Authors: Zhi-Jun Lu, Qi Lu, Meng Wu, Qian Xiang, Jun Gu

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The analysis of perforated steel members is a 3D problem in nature, therefore the traditional analytical expressions for the ultimate load of thin-walled steel sections cannot be used for the perforated steel member design. In this study, finite element method (FEM) and artificial neural network (ANN) were used to simulate the process of stub column tests based on specific codes. Results show that compared with those of the FEM model, the ultimate load predictions obtained from ANN technique were much closer to those obtained from the physical experiments. The ANN model for the solving the hard problem of complex steel perforated sections is very promising.

Keywords: artificial neural network (ANN), finite element method (FEM), perforated sections, thin-walled Steel, ultimate load

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Authors: Wenbo Duan, Hossein Habibi, Vassilios Kappatos, Cem Selcuk, Tat-Hean Gan

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Ultrasonic guided waves are often used to remove ice or fouling in different structures, such as ship hulls, wind turbine blades and so on. To achieve maximum sound power output, it is important that multiple transducers are arranged in a particular way so that a desired mode can be excited. The objective of this paper is thus to provide a theoretical basis for generating a particular mode in a finite width rectangular plate which can be used for removing potential ice or fouling on the plate. The number of transducers and their locations with respect to a particular mode will be investigated, and the link between dispersion curves and practical applications will be explored. To achieve this, a semi-analytical finite element (SAFE) method is used to study the dispersion characteristics of all the modes in the ultrasonic frequency range. The detailed modal shapes will be revealed, and from the modal analysis, the particular mode with the strongest yet continuous transverse and axial displacements on the surfaces of the plate will be chosen for the purpose of removing potential ice or fouling on the plate. The modal analysis is followed by providing information on the number, location and amplitude of transducers needed to excite this particular mode. Modal excitation is then implemented in a standard finite element commercial package, namely COMSOL Multiphysics. Wave motion is visualized in COMSOL, and the mode shapes generated in SAFE is found to be consistent with the mode shapes generated in COMSOL.

Keywords: dispersion analysis, finite width plate, guided wave, modal excitation

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Authors: Pawan S. Nagda, Purnank S. Bhatt, Mit K. Shah

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Earing defect in drawing process is highly undesirable not only because it adds on an additional trimming operation but also because the uneven material flow demands extra care. The objective of this work is to study the earing problem in the Deep Drawing of circular cup and to optimize the blank shape to reduce the earing. A finite element model is developed for 3-D numerical simulation of cup forming process in ABAQUS. Extra-deep-drawing (EDD) steel sheet has been used for simulation. Properties and tool design parameters were used as input for simulation. Earing was observed in the simulated cup and it was measured at various angles with respect to rolling direction. To reduce the earing defect initial blank shape was modified with the help of anisotropy coefficient. Modified blanks showed notable reduction in earing.

Keywords: anisotropy, deep drawing, earing, finite element simulation

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Authors: Mahesh Koti

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In this paper, we present a quantum transport study of a quantum dot in steady state in the presence of static gate potential. We consider a quantum dot coupled to the two metallic leads. The quantum dot under study is modeled through Anderson Impurity Model (AIM) with hopping parameter modulated through voltage drop between leads and the central dot region. Based on the Landauer's formula derived from Nonequilibrium Green's Function and Single Electron Theory, the essential ingredients of transport properties are revealed. We show that the results out of two approaches closely agree with each other. We demonstrate that Landauer current response derived from single electron approach converges with non-zero interaction through gate potential whereas Landauer current response derived from Nonequilibrium Green's Function (NEGF) hits a pole.

Keywords: Anderson impurity model (AIM), nonequilibrium Green's function (NEGF), Landauer's formula, single electron analysis

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: axisymmetric problem, compressible Navier-Stokes equations, continuous finite elements, swirling flow

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

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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: finite element, temperature dependency, wave dispersion characteristics, wave finite element, wave scattering properties

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Authors: Jingjing Ye, Cijun Fan, Yan Dong

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The development of financial sector plays an important role in shaping industrial structure. However, evidence on the micro-level channels through which this relation manifest remains relatively sparse, particularly for developing countries. In this paper, we compile an industry-by-city dataset based on manufacturing firms and registered banks in 287 Chinese cities from 1998 to 2008. Based on a difference-in-difference approach, we find the highly concentrated banking sector decreases the competitiveness of firms in each manufacturing industry. There are two main reasons: i) bank accessibility successfully fosters firm expansion within each industry, however, only for sufficiently large enterprises; ii) state-owned enterprises are favored by the banking industry in China. The results are robust after considering alternative concentration and external finance dependence measures.

Keywords: bank concentration, China, difference-in-difference, industry structure

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Authors: Aderet M. Pantierer, Shmuel Pantierer, Raphael Cordina, Yougashwar Budhoo

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Stress concentration occurs when there is an abrupt change in geometry, a mechanical part under loading. These changes in geometry can include holes, notches, or cracks within the component. The modifications create larger stress within the part. This maximum stress is difficult to determine, as it is directly at the point of the minimum area. Strain gauges have yet to be developed to analyze stresses at such minute areas. Therefore, a stress concentration factor must be utilized. The stress concentration factor is a dimensionless parameter calculated solely on the geometry of a part. The factor is multiplied by the nominal, or average, stress of the component, which can be found analytically or experimentally. Stress concentration graphs exist for common loading conditions and geometrical configurations to aid in the determination of the maximum stress a part can withstand. These graphs were developed from historical data yielded from experimentation. This project seeks to verify a stress concentration graph for combined loading conditions. The aforementioned graph was developed using CATIA Finite Element Analysis software. The results of this analysis will be validated through further testing. The 3D modeled parts will be subjected to further finite element analysis using Patran-Nastran software. The finite element models will then be verified by testing physical specimen using a tensile testing machine. Once the data is validated, the unique stress concentration graph will be submitted for publication so it can aid engineers in future projects.

Keywords: stress concentration, finite element analysis, finite element models, combined loading

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Authors: Wentao He, Jingxi Liu, De Xie

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It is necessary to manage the fatigue crack growth (FCG) once those cracks are detected during in-service inspections. In this paper, a simulation program (FCG-System) is developed utilizing the commercial software ABAQUS with its object-oriented programming interface to simulate the fatigue crack path and to compute the corresponding fatigue life. In order to apply FCG-System in large-scale marine structures, the substructure modeling technique is integrated in the system under the consideration of structural details and load shedding during crack growth. Based on the nodal forces and nodal displacements obtained from finite element analysis, a formula for shell elements to compute stress intensity factors is proposed in the view of virtual crack closure technique. The cracks initiating from the intersection of flange and the end of the web-stiffener are investigated for fatigue crack paths and growth lives under water pressure loading and axial force loading, separately. It is found that the FCG-System developed by authors could be an efficient tool to perform fatigue crack growth analysis on marine structures.

Keywords: crack path, fatigue crack, fatigue live, FCG-system, virtual crack closure technique

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Li Yin, Xiaoqin Wang

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Background and purpose: Cancer diagnosis is part of a complex stochastic process, in which patients' personal and social characteristics influence the choice of diagnosing methods, diagnosing methods, in turn, influence the initial assessment of cancer stage, the initial assessment, in turn, influences the choice of treating methods, and treating methods in turn influence cancer outcomes such as cancer survival. To evaluate diagnosing methods, one needs to estimate and test the causal effect of a regime of cancer diagnosis and treatments. Recently, Wang and Yin (Annals of statistics, 2020) derived a new general formula, which expresses these causal effects in terms of the point effects of treatments in single-point causal inference. As a result, it is possible to estimate and test these causal effects via point effects. The purpose of the work is to estimate and test causal effects under various regimes of cancer diagnosis and treatments via point effects. Challenges and solutions: The cancer stage has influences from earlier diagnosis as well as on subsequent treatments. As a consequence, it is highly difficult to estimate and test the causal effects via standard parameters, that is, the conditional survival given all stationary covariates, diagnosing methods, cancer stage and prognosis factors, treating methods. Instead of standard parameters, we use the point effects of cancer diagnosis and treatments to estimate and test causal effects under various regimes of cancer diagnosis and treatments. We are able to use familiar methods in the framework of single-point causal inference to accomplish the task. Achievements: we have applied this method to stomach cancer survival from a clinical study in Sweden. We have studied causal effects under various regimes, including the optimal regime of diagnosis and treatments and the effect moderation of the causal effect by age and gender.

Keywords: cancer diagnosis, causal effect, point effect, G-formula, sequential causal effect

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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: Emmanuel Kamal Aziz Saba

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Aim of the work: This study proposed to assess the role of the median versus ulnar medial thenar motor (MTM) recording in supporting the diagnosis of carpal tunnel syndrome (CTS). Patients and methods: The present study included 130 hands (70 CTS and 60 controls). Clinical examination was done for all patients. The following tests were done (using surface electrodes recording) for patients and control: (1) sensory nerve conduction studies: median nerve, ulnar nerve and median versus ulnar digit four sensory study; (2) motor nerve conduction studies: median nerve, ulnar nerve, median (second lumbrical) versus ulnar (interosseous) (2-LINT) motor study and median versus ulnar (MTM) study. Results: The tests with higher sensitivity in diagnosing CTS were median versus ulnar (2-LINT) motor latency difference (87.1%), median versus ulnar (MTM) motor latency difference (80%) and median versus ulnar digit four sensory latency differences (91.4%). There was no statistically significant difference between median versus ulnar (MTM) motor latency difference with both median versus ulnar (2-LINT) motor latency difference and median versus ulnar digit four sensory latency difference (P > 0.05) as regards the confirmation of CTS. Conclusions: Median versus ulnar (MTM) motor latency difference has high sensitivity and specificity for the diagnosis of CTS as for both median versus ulnar (2-LINT) motor latency difference and median versus ulnar digit four sensory latency differences. It can be considered a useful neurophysiological test to be used in combination with another median versus ulnar comparative tests for confirming the diagnosis of CTS beside other well-known electrophysiological tests.

Keywords: carpal tunnel syndrome, medial thenar motor, median nerve, ulnar nerve

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Authors: Abu Afree Andalib, Rafiur Rahman, Md Mezbah Uddin

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The main objective of this work is to anatomize on the various parameters of AGM 88 missile anatomized using FSI module in Ansys. Computational fluid dynamics is used for the study of fluid flow pattern and fluidic phenomenon such as drag, pressure force, energy dissipation and shockwave distribution in water. Using finite element analysis module of Ansys, structural parameters such as stress and stress density, localization point, deflection, force propagation is determined. Separate analysis on structural parameters is done on Abacus. State of the art coupling module is used for FSI analysis. Fine mesh is considered in every case for better result during simulation according to computational machine power. The result of the above-mentioned parameters is analyzed and compared for two phases using graphical representation. The result of Ansys and Abaqus are also showed. Computational Fluid Dynamics and Finite Element analyses and subsequently the Fluid-Structure Interaction (FSI) technique is being considered. Finite volume method and finite element method are being considered for modelling fluid flow and structural parameters analysis. Feasible boundary conditions are also utilized in the research. Significant change in the interaction and interference pattern while the impact was found. Theoretically as well as according to simulation angled condition was found with higher impact.

Keywords: FSI (Fluid Surface Interaction), impact, missile, high viscous fluid, CFD (Computational Fluid Dynamics), FEM (Finite Element Analysis), FVM (Finite Volume Method), fluid flow, fluid pattern, structural analysis, AGM-88, Ansys, Abaqus, meshing, k-omega, turbulence model

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Authors: Si Abdallah Mayouf

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In this work, the effects of the wavy surface on free convection heat transfer boundary layer flow between two parallel wavy plates have been studied numerically. The two plates are considered at a constant temperature. The equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm. The important parameters in this problem are the amplitude of the wavy surfaces and the distance between the two wavy plates. Results are presented as velocity profiles, temperature profiles and local Nusselt number according to the important parameters.

Keywords: free convection, wavy surface, parallel plates, fluid dynamics

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Authors: Mohamed Gaith, Zaid Haddadin, Abdulah Wahbe, Mahmoud Hamam, Mahmoud Qunees, Mohammad Al Khatib, Mohammad Bsaileh, Abd Al-Aziz Jaber, Ahmad Aqra’a

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The crack is one of the most common types of failure in pipelines that convey fluid, and early detection of the crack may assist to avoid the piping system from experiencing catastrophic damage, which would otherwise be fatal. The influence of flow velocity and the presence of a crack on the performance of a tapered simply supported pipe containing moving fluid is explored using the finite element approach in this study. ANSYS software is used to simulate the pipe as Bernoulli's beam theory. In this paper, the fluctuation of natural frequencies and matching mode shapes for various scenarios owing to changes in fluid speed and the presence of damage is discussed in detail.

Keywords: damage detection, finite element, tapered pipe, vibration characteristics

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Authors: Pragyan Paramita Das, Vishwas N. Khatri

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By using the lower- and upper- bound finite elements to limit analysis in conjunction with second-order conic programming (SOCP), the effect of seismic forces on the bearing capacity of surface strip footing resting on dense sand underlain by loose sand deposit is explored. The soil is assumed to obey the Mohr-Coulomb’s yield criterion and an associated flow rule. The angle of internal friction (ϕ) of the top and the bottom layer is varied from 42° to 44° and 32° to 34° respectively. The coefficient of seismic acceleration is varied from 0 to 0.3. The variation of bearing capacity with different thickness of top layer for various seismic acceleration coefficients is generated. A comparison will be made with the available solutions from literature wherever applicable.

Keywords: bearing capacity, conic programming, finite elements, seismic forces

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Authors: Sergei P. Efimov

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The anomalous magnetic moment of the electron is calculated by introducing the effective mass of the virtual part of the electron structure. In this case, the anomalous moment is inversely proportional to the effective mass Meff, which is shown to be a linear combination of the neutron, proton, and electrostatic electron field masses. The spin of a rotating structure is assumed to be equal to 3/2, while the spin of a 'bare' electron is equal to unity, the resultant spin being 1/2. A simple analysis gives the coefficients for a linear combination of proton and electron masses, the approximation precision giving here nine significant digits after the decimal point. The summand proportional to α² adds four more digits. Thus, the conception of the effective mass Meff leads to the formula for the total magnetic moment of the electron, which is accurate to fourteen digits. Association with the virtual beta-decay reaction and possible reasons for simplicity of the derived formula are discussed.

Keywords: anomalous magnetic moment of electron, comparison with quantum electrodynamics. effective mass, fifteen significant figures, proton and neutron masses

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Authors: Farrukh Javed, Krzysztof Podgórski

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We propose a new model that accounts for the asymmetric response of volatility to positive ('good news') and negative ('bad news') shocks in economic time series the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of 'bad' and 'good' news processes given the past the property that is important for the statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

Keywords: heavy tails, volatility clustering, generalized asymmetric laplace distribution, leverage effect, conditional heteroskedasticity, asymmetric power volatility, GARCH models

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Authors: Erik Vassøy Olsen, Hirpa G. Lemu

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Inspired by the Formula-1 competition, IMechE (Institute of Mechanical Engineers) and Formula SAE (Society of Mechanical Engineers) organize annual competitions for University and College students worldwide to compete with a single-seat race car they have designed and built. The design of the chassis or the frame is a key component of the competition because the weight and stiffness properties are directly related with the performance of the car and the safety of the driver. In addition, a reduced weight of the chassis has a direct influence on the design of other components in the car. Among others, it improves the power to weight ratio and the aerodynamic performance. As the power output of the engine or the battery installed in the car is limited to 80 kW, increasing the power to weight ratio demands reduction of the weight of the chassis, which represents the major part of the weight of the car. In order to reduce the weight of the car, ION Racing team from the University of Stavanger, Norway, opted for a monocoque design. To ensure fulfilment of the above-mentioned requirements of the chassis, the monocoque design should provide sufficient torsional stiffness and absorb the impact energy in case of a possible collision. The study reported in this article is based on the requirements for Formula Student competition. As part of this study, diverse mechanical tests were conducted to determine the mechanical properties and performances of the monocoque design. Upon a comprehensive theoretical study of the mechanical properties of sandwich composite materials and the requirements of monocoque design in the competition rules, diverse tests were conducted including 3-point bending test, perimeter shear test and test for absorbed energy. The test panels were homemade and prepared with an equivalent size of the side impact zone of the monocoque, i.e. 275 mm x 500 mm so that the obtained results from the tests can be representative. Different layups of the test panels with identical core material and the same number of layers of carbon fibre were tested and compared. Influence of the core material thickness was also studied. Furthermore, analytical calculations and numerical analysis were conducted to check compliance to the stated rules for Structural Equivalency with steel grade SAE/AISI 1010. The test results were also compared with calculated results with respect to bending and torsional stiffness, energy absorption, buckling, etc. The obtained results demonstrate that the material composition and strength of the composite material selected for the monocoque design has equivalent structural properties as a welded frame and thus comply with the competition requirements. The developed analytical calculation algorithms and relations will be useful for future monocoque designs with different lay-ups and compositions.

Keywords: composite material, Formula student, ION racing, monocoque design, structural equivalence

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Hamadi Djamal, Labiodh Bachir, Ounis Abdelhafid, Chaalane Mourad

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The objective of this work is setting numerically operational finite element CAXI_L for the axisymmetric and nonaxisymmetric shells. This element is based on the Reissner-Mindlin theory and mixed model formulation. The MATLAB language is used for the programming. In order to test the elaborated program, some applications are carried out.

Keywords: axisymmetric shells, nonaxisymmetric behaviour, finite element, MATLAB programming

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Authors: Meysam Lak, Mohammad Fatehi Marji, Alireza Yarahamdi Bafghi, Abolfazl Abdollahipour

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A wellbore is a hole that is drilled to aid in the exploration and recovery of natural resources including oil and gas. Occasionally, in order to increase productivity index and porosity of the wellbore and reservoir, the well stimulation methods have been used. Hydraulic fracturing is one of these methods. Moreover, several explosions at the end of the well can stimulate the reservoir and create fractures around it. In this study, crack initiation in rock around the wellbore has been numerically modeled due to explosion. One, two, three, and four pairs of explosion have been set at the end of the wellbore on its wall. After each stage of the explosion, results have been presented and discussed. Results show that this method can initiate and probably propagate several fractures around the wellbore.

Keywords: crack initiation, explosion, finite difference modelling, well productivity

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Authors: T. J. Stepien, L. T. Stepien

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This abstract concerns an extremely fundamental issue. Namely, the fundamental problem of science is the issue of consistency. In this abstract, we present the theorem saying that the classical calculus of quantifiers is inconsistent in the traditional sense. At the beginning, we introduce a notation, and later we remind the definition of the consistency in the traditional sense. S1 is the set of all well-formed formulas in the calculus of quantifiers. RS1 denotes the set of all rules over the set S1. Cn(R, X) is the set of all formulas standardly provable from X by rules R, where R is a subset of RS1, and X is a subset of S1. The couple < R,X > is called a system, whenever R is a subset of RS1, and X is a subset of S1. Definition: The system < R,X > is consistent in the traditional sense if there does not exist any formula from the set S1, such that this formula and its negation are provable from X, by using rules from R. Finally, < R0+, L2 > denotes the classical calculus of quantifiers, where R0+ consists of Modus Ponens and the generalization rule. L2 is the set of all formulas valid in the classical calculus of quantifiers. The Main Result: The system < R0+, L2 > is inconsistent in the traditional sense.

Keywords: classical calculus of quantifiers, classical predicate calculus, generalization rule, consistency in the traditional sense, Modus Ponens

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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